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LIBRARY Michigan State University This is to certify that the dissertation entitled Rapid-Scanning Stopped-Flow Studies of Tryptophanase Activation/Deactivation by Sudden Addition/Removal of Potassium Ions presented by Iraj Behbahani-Nejad has been accepted towards fulfillment of the requirements for Ph . D . degree in Chemistry éZé駣?ZLL,- ames L. Dye Major professor Date October 20, 1987 MS U is an Affirmative Action/Equal Opportunity Institution 0-12771 lv1531_} RETURNING MATERIALS: ' Place in book drop to LJBRARJES remove this checkout from —;-——. your record. FINES will .- — r be charged if book is 4 returned after the date stamped below. RAPID-SCANNING STOPPED-FLOW STUDIES OF TRYPTOPHANASE ACTIVATION/DEACTIVATION BY SUDDEN ADDITION/REMOVAL OF POTASSIUM IONS By Iraj Behbahani—Nejad AN ABSTRACT OF A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1986 To My Wife, Lili for her Everlasting Love 11 ACKNOWLEDGMENTS I would like to express my deepest appreciation to Professor James L. Dye for his encouragement, guidance, patience and invalu- able assistance throughout my stay at Michigan State University. I appreciate his stimulating discussions and his many helpful sug- gestions in the preparation of this dissertation. I am most grateful to Professor Clarence H. Suelter for his guidance, ideas and suggestions throughout the course of this work. I am also grateful to the other members of my committee, Professor Gerald T. Babcock for acting as second reader, and Professor C. K. Chang for serving on my Guidance Committee on such short notice. I would like to express my sincere appreciation to Dr. Tom V. Atkinson for his help with the computer work that appears throughout this dissertation, and for assisting me with the computer graphics. Thanks are also extended to Mr. Martin Rabb, Electronic Designer, for his constant help in keeping the stopped-flow interface "alive". I wish to thank the Ministry of Science and Higher Education of Iran, National Science Foundation, Nyandotte Corporation, and the Department of Chemistry for their financial support as scholar- ship, research, and teaching assistantships. My stay here at Michigan State University has been more pleasant for me with the companionship of my colleagues and friends, especi- ally those in both past and present Dye groups from whom I have learned much. I would like to thank my family for the constant love and sup- port they have given me in my life. I would also like to thank my wife's family for their kindness and generosity, but especially I thank them for their daughter. Finally, no words can express my feelings and love for my wife, Lili, who stood by me constantly, enabling me to complete this work. She never lost faith, and without her I could never have completed this work. To her and to the memory of my father, I dedicate this thesis. iv ABSTRACT RAPID-SCANNING STOPPED-FLOW STUDIES OF TRYPTOPHANASE ACTIVATION “ACTIVATION BY SUDDEN ADDITION/REMOVAL OF POTASSIUM IONS By Iraj Behbahani-Nejad Rapid scanning and fixed-wavelength stopped-flow spectrophotom- etry were used to study the activation/deactivation of tryptophanase by sudden addition/removal of potassium ions with the aid of a crown- ether or cryptand. Tryptophanase catalyzes a,8—elimination reactions of amino acid substrates, and requires activating monovalent cations, such as K+, for catalytic activity. An additional requirement is a prosthetic group, pyridoxal-S'-phosphate (PLP) with which it covalently forms a Schiff's base. The active holoenzyme has absorption maxima at 337 nm and 420 nm, whose relative amplitudes depend on both pH and the monovalent cation activator used. A 420 nm absorption band also dominates the spectrum of the K+-free (inactive) enzyme. An amino acid substrate or inhibitor, added to the active enzyme, forms a quinonoid by a-elimination, with an intense absorption maximum at mSOO nm. For true substrates, B-elimination finally yields pyruvate and ammonia. With inhibitors, however, the reaction stops at the quinonoid. Iraj Behbahani-Nejad Two well known complexants of potassium ion, l8-crown-6 and cryptand [2.2.2], were used to suddenly reduce the concentration of free K+ in an enzyme solution. In deactivation by l8-crown-6 at pH 8.70, a single exponential fit most of the absorbance change with a rate constant proportional to the square of the lB-crown-G concen- tration. This strongly suggests that two Ki ions per subunit are required for activation. In activation experiments at the same pH, even at saturating K+ concentrations, only about 50% of the original absorbance at 337 nm was recovered although enzymatic activity was completely restored. This suggests that substrate or inhibitor, in addition to K+, are required to completely reverse the deactivation brought about by depletion of potassium. The activation kinetics data showed that the growth of absorbance at 337 nm is triphasic at saturat- ing K+ concentrations, and quantitatively matches the decay at 420 nm after a small fast growth at this wavelength. The results suggest "kinetic anticooperativity" in the enzyme protomers upon binding potassium. Tryptophanase activation and deactivation were also studied in the presence of L-ethionine, a competitive inhibitor of the enzyme. The decay of absorbance at 508 nm and growth at 420 nm upon deactiva-. tion were monophasic (95% of the change) and the lst-order rate constant was inversely proportional to the square of the free K+ concentration. This dependence again suggests that two Ki ions per subunit are re- quired for activation. The reverse process, however, was found to be triphasic at saturating KI concentrations. The data were again ex- plained on the basis of kinetic anticooperativity in the binding of potassium ion to the enzyme. Iraj Behbahani-Nejad The method of weighted principal component analysis (PCA) was used to resolve the 3-dimensional data surface obtained by the scanning stopped-flow method. In the deactivation in the absence of ethionine (Chapter III), the absorbance-wavelength-time data surface was re— solved into the spectral shapes and time courses of the independent components. Spectral shapes obtained by PCA for the 337 and 420 nm absorbers agree well with the reported assignments for the components of the enzyme. PCA analysis was also performed for the activation experiments (Chapters IV and V); however, only partial resolution was obtained due to an insufficient number of target absorbers. Chapter LIST OF TABLE OF CONTENTS TABLES .................. LIST OF FIGURES ........................ CHAPTER A. B. CHAPTER A. B. I. INTRODUCTION ............. Brief Review of Catalysis by Pyridoxal-p and Pyridoxal-p Enzymes .......... Tryptophanase ............... B.l. Enzyme Source ............ 8.2. Structural Properties ........ B.2.l. Subunit Structure ...... B.2.2. PLP Binding ......... B.2.3. Monovalent Cation Specificity ...... Spectral Properties ......... Catalytic Properties ........ Mechanism of Tryptophanase Catalysis B. 6. Kinetic Studies ........... Scanning Stopped-Flow Technique for the Study of Enzyme Reactions ......... Macrocyclic Complexing Agents for the Study of Tryptophanase Activation/ Deactivation Monovalent Cations ...... D.l. Structures and Properties ...... D.2. Complexation ............ II. EXPERIMENTAL METHODS ......... Materials ................. Methods ....... WWW 01.9w B. l. Preparation of the l, 7- -diaminoheptane Sepharose Column. B. 2. Purification of Tryptophanase. : : I . O . . . 3. Activity Assays of Tryptophanase ........ B. B. 4. Purification of the Complexing Agents The Stopped-Flow Method .......... C. l. A Historical Background ....... C. 2. Stopped-Flow System ......... C.2.l. Scanning Mode ........ . Fixed Wavelength Mode. . . . Flow Velocity ........ Dead Time .......... Stopping Time ........ Mixing Efficiency ...... 0000C) NNNNN 0101-wa 28 28 3] 33 33 34 34 35 36 37 43 43 44 45 46 Chapter CHAPTER OW) D. CHAPTER A. C. D. CHAPTER A. B. C. Data Collection, Calibration and Computer Graphics ....................... Analysis of Scanning Stopped—Flow Data ........ E.l. Rate Equations - Program KINFIT4 ........ E.2. Weighted Principle Component Analysis ...... III. TRYPTOPHANASE INACTIVATION BY SUDDEN REMOVAL OF K+ WITH THE AID OF A CROWN- ETHER OR CRYPTAND ................ Introduction ..................... Experimental Section ................. Studies and Results .................. C.l. Equilibrium Studies ............... C.2. Kinetic Studies ................. C.2.l. Deactivation as a Function of the Enzyme Concentration ....... C.2.2. Deactivation as a Function of 18-C5 Concentration ......... C.2.3. Results ................. C.3. Kinetics of Deactivation by Cryptand[2.2.2]. . . Discussion and Conclusions .............. IV. TRYPTOPHANASE ACTIVATION BY CONTROL OF FREE K+-C0NCENTRATIOE\*aK+ JUMP .......... Studies in the Presence of (CH3)4NC1 ......... A.l. Methods ..................... A.2. Stability Studies ................ A.3. Spectral Studies ................ Stopped-Flow Studies of Tryptophanase Activation by K+ ................... 8.1. Experimental Methods .............. 8.2. Results ..................... B.2.l. Absorbance Change at 337 nm ....... B.2.2. Absorbance Change at 420 nm ....... Discussion ...................... Conclusions ...................... V. TRYPTOPHANASE ACTIVATION BY K+ IN THE PRESENCE OF ETHIONINE-QUINONOID FORMATION ..... Introduction ..................... Experimental Section ................. Activation of Inactive-Tryptophanase by a KT-Ethionine Mixture-(a-Enz) vs (K+-Eth) ....... C.l. Spectral Shape Analysis ............. C.2. Kinetics .................... C.2.l. Absorbance change at 508 nm ....... C.2.2. Absorbance Change at 420 nm ....... Activation of Inactive-Tryptophanase-Ethionine Complex by KT-(q-Eth) vs. (KT) ............ 0.]. Spectral Shape Analysis ............. D.2. Kinetics .................... vi 47 48 57 64 64 79 89 98 100 108 108 108 111 118 122 127 129 129 130 131 133 135 135 139 139 Chapter E. F. CHAPTER A. B. C D E. F. CHAPTER A. B. F. CHAPTER D.2.l. Absorbance Change at 508 nm ....... D.2.2. Absorbance Change at 420 nm ....... Discussion ...................... Conclusions ...................... VI. REACTION OF THE TRYPTOPHANASE-ETHIONINE COMPLEX WITH lB-CROWN-6 - "QUINONOID-DROP". . . . Introduction ..................... Experimental Section ................. Spectral Shape Analysis ................ Kinetics of the Quinonoid Disappearance After Mixing Tryptophanase-Ethionine-K+ Complex with lB-Crown-6 ...................... 0.1. Absorbance Change at 508 nm ........... 0.2. Absorbance Change at 420 nm ........... Discussion ...................... Conclusions ...................... VII. PRINCIPAL COMPONENT ANALYSIS OF TRYPTOPHANASE ACTIVATION/DEACTIVATION PROCESSES ........ Introduction ..................... The Method of Principal Component Analysis (PCA) . . . 8.1. Application of PCA to Errorless Data ... . . . . B.l.l. M Analysis ............... B.l.2. S Analysis ............... 8.2. Effect of Random Measurement Errors, Actual Case ................... B.2.l. Inclusion of Error in Absorbance Model .................. B.2.2. Weighted Principal Component Analysis ................ B.3. PCA Determination of Real Components ...... Principal Component Analysis of Tryptophanase Deactivation by lB-C5 ................. C.l. Number of Absorbers ............... C.2. Concentration Profiles of Individual Absorbers .................... C.3. Spectra of Individual Absorbers ......... PCA Analysis of the Reactivation of Deactivated Enzyme with K+ .................... 0.1. Number of Absorbers ............... D.2. Individual Absorbers .............. PCA on the Reaction of Deactivated Enzyme with a K+-Ethionine Mixture .............. E.l. Number of Absorbers ............... E.2. Individual Absorbers .............. Conclusions ...................... VIII. SUGGESTIONS FOR FUTURE WORK .......... REFERENCES .......................... vii Page 141 145 146 156 157 157 157 158 163 163 167 170 177 178 178 179 182 182 183 184 184 187 190 196 197 203 206 206 206 215 215 219 227 229 231 Table 111.1 111.2 III.3 111.4 111.5 111.6 111.7 111.8 IV.1 IV.2 LIST OF TABLES Concentration of Various Species After Mixing in the K+-Drop (Deactivation) Experiment ........... Analysis of the Burst Region of the De- activation Process by lB-crown-G in Bicine Buffer at pH 8.75 at 24il°C ........................ Variation of the "Slope" of Linear Region of the Deactivation Process as a Function of the Enzyme Concentration at Fixed Crown Concentra- tion of 148 mM ..................................... Variation of the "Slope of Linear Region of the Deactivation Process as a Function of lB-Crown-6 at Fixed Enzyme Concentration of 2.0 mg.ml-1 (36 pM) ................................ Kinetic Parameters for the Exponential Region of the Deactivation Process as a Function of the Enzyme Concentration at Fixed Crown Con- centration of 148 mM ............................... Kinetic Parameters for the Exponential Region of the Deactivation Process as a Function of l8C6 Concentration at Fixed En Enzyme Concentration of 2.0 mg.ml-1 (36 uM) ........ Summary of the Results of the "KT-Drop" Experiments Described in the Text .................. Kinetic Parameters at 337 and 420 nm for the Deactivation of Tryptophanase by Cryptand [2.2.2]. The Data were fit to Equation III.3. in the Text ..................... Concentration of VariousSpecies After Mixing in the Stopped-Flow Studies of Tryptophanase Reactivation by K+ (K+ JUMP). E0 = 2.0 mg.ml'1 ................................... Kinetic Parameters for the Reactivation of Tryptophanase by K+ at Saturating Con- centrations of the Cation .......................... viii Page 60 72 73 74 77 78 81 86 109 116 Table IV.3 IV.4 V.1 V.2 V.3 V.4 V1.1 V1.3 Kinetic Parameters for the Reactivation of Tryptophanase by K+ at Concentrations of the Cation Below Saturation ..................... Kinetic Parameters Obtained from the Fit of the Early Growth (600 mSec) at 420 nm by a Single Exponential Equation in Trypto- phanase Activation by K+ at pH 8.70 (K+-Jump) ...... Apparent Rate Constants at 508 and 420 nm for the Activation of Tryptophanase by a Mixture of Ethionine and K+ in Bicine Buffer at pH 8.70 (a-Enz vs. K+—Eth) ...................... The Amplitude and Percentage of the Absorbance Changes at 508 and 420 nm for the Activation of Tryptophanase by a Mixture of K+ and Ethionine (a-Enz vs. KT-Eth) ................................. Apparent Rate Constants at 508 and 420 nm for the Activation of "Ki-Depleted-Trypto- phanase-Ethionine" Complex by K+ in Bicine Buffer at pH 8.70. (a-Eth. vs. KT) ................ The Amplitude and Percentage of the Absor- bance Changes at 508 and 420 nm for the Activation of "K+-Dep1eted-Tryptophanase- Ethionine" Complex by KT in Bicine Buffer at pH 8.70 (a-Eth. vs. K+) ......................... Concentrations of K+ and lB-Crown-6 After Mixing in the Stopped-flow Studies of the Tryptophanase«Ethionine Complex Disappearance by 18C6. £0 = 1.0 mg.m1-l (18 uM), L- Ethionine = 8.0 mM for all Pushes (After Mixing) ............................................ Analysis of the Fast Phase of the Quinonoid Disappearance by 18C6 in Bicine Buffer at pH 8.70 ............................................ Analysis of the Slow Phase of the Quinonoid Disappearance by 18C6 in Bicine Buffer at pH 8.70 ............................................ ix Page 117 121 137 138 142 144 159 164 169 Figure 1.1 1.2 1.3 1.4 1.5 1.6 1.7 111.1 111.2 111.3 LIST OF FIGURES Reaction Sequence of PLP-catalyzed a,8- elimination and B-replacement reactions ........... Comparative Effects of Monovalent Cations on the Spectrum of Holotryptophanase .............. Structures of 420 nm and 337 nm Forms of Tryptophanase Suggested by Metzler ................ Interconversion of Tryptophanase Spectral Forms ............................................. Mechanism for tryptophanase catalyzed reactions ......................................... Mechanism for the formation of quinonoid (EQ and EQH+) from the competitive inhibitor, L-ethionine ....................................... Cryptand and lB-crown-6 structural formulas .......................................... Molecular distillation apparatus for puri- fication of Crown ................................. Block Diagram of the computer interfaced scanning stopped-flow system ...................... Initial and final spectra collected during deactivation of 3.0 mg.ml-'1 (55 uM) Tryptophanase by 148 mM lB-Crown-6 in 15 mM Bicine buffer at pH 8.75 ....................... Absorbance-time-wavelength surface in the 300-500 nm region for the deactivation of tryptophanase by l8-crown-6. Conditions are the same as in Figure III.1 ................... Selected difference spectra constructed from Figure 111.2 by subtracting the first spectrum from subsequent spectra .................. Page 15 16 18 21 26 30 38 42 59 61 62 Figure Page 111.4 Time dependence of absorbance at 337 and 420 nm taken from the spectra shown in Figure 111.2. ....................................... 63 111.5 Effect of various concentrations of 18C6 on the rate of deactivation at 337 nm............... 65 111.6 Time dependence of absorbance change at 420 nm during the reaction of holotrypto- phanase in K -Bicine buffer at pH 8.75 with lB-crown-6 .......................................... 67 111.7 Fit of the burst and linear phases for the deactivation of tryptophanase by 18C6 by Equation 111.1 in the text.................. 71 111.8 Fit of the exponential region of the deactivation process by Equation 111.2 in the text.- ....................................... 76 111.9 Slow exponential changes occurring at the completion of the deactivation process (region 5).. ........................................ 80 111.10 Selected difference spectra collected during the reaction of tryptophanase with Cryptand [2.2.2] in 15 mM. TMA-Bicine buffer at pH 8.75. Concentrations are [Enz] = 3.0 mg.ml‘1 (55 uM), [C222] = 15.8 mM before mixing ................................... 84 111.11 Fit of the overall absorbance change at 420 nm (subtracting the tail) for the de- activation of tryptophanase by C222 by the double exponential Equation III.3 .................. 85 111.12 Slow exponential changes occurring at the end of the reaction between tryptophanase and cryptand [2.2.2] ............................... 88 111.13 Dependence of the apparent lst-order rate constant for the exponential region of the deactivation process (x) and the slope of linear region (Q, of the process on the square of 1806 concentration ....................... 90 1V.1 Dependence of the absorbance growth at 420 nm upon titration of apotryptophanase with pyri- doxal-p in (CH3)4NC1-buffer at pH 8.0, 2.0 mM DTT. Concentrat1on of the enzyme was 50 pM.. ...... 102 xi Figure IV.2 ' IV.3 IV.4 1V.5 1V.6 1V.7 1V.8 IV.9 V.1 V.2 Difference spectrum obtained during titration of a 50 pM solution of apotryptophanase with excess pyridoxal-p in TMA-EPPS buffer at pH 8.0 (0). Spectrum of 50 uM PLP in the same buffer NI) ........................................ Spectral changes obtained during titration of 50 MM pyridoxal-p with dithiothreitol (DTT) in CH3)4NC1-EPPS buffer at pH 8.0 ........... A suggested scheme for the reaction between pyridoxal-phosphate (PLP) and dithiothreitol (DTT) ............................................. Absorbance-wavelength-time surface for activa- tion of tryptophanase (freshly deactivated by 18C6) by K+ in Bicine buffer at pH 8.70. Concentrations are: [Enz] = 2.0 mg.m1'1 and [KT] = 33.0 mM .................................... Selected difference spectra at three dif- ferent times presenting changes in absorbance observed during the “K+ drop" experiment (---) and ”K+ Jump" experiment (———) .................... Fit of the data at 337 nm for tryptophanase activation by K+ (K+ Jump) by Equation IV.2. X's are the data and the solid line is the calculated curve. Concentrations of the Enzyme and K+ were: 2.0 mg.m1'1 (36 uM) and 18.7 mM, respectively ............................. Difference spectrum at completion of the fast growth at 430 nm in tryptOphanase activa- tion by K+ (K+ Jump). Concentrations were: Enz., 2.0 mg.m1'1; KT, 19.2 mM, respectively ...... Fit of the fast growth at 420 nm (600 mSec) in “K+-Jump" by a single exponential .............. Absorbance-wavelength-time surface for re- activation of tryptophanase by a K+-Ethionine mixture (a vs. K+-Eth). Concentrations after mixing were: Enz., 1.25 mg.m1'1; Ethionine, 8.0 mM; KT, 16.0 mM ............................... Selected difference spectra constructed from Figure V.1 by subtracting the spectrum of the inactive enzyme (first spectrum). All conditions were the same as in Figure V.1 ......... xii Page 103 106 107 110 113 115 119 120 132 134 Figure Page V.3 Fit of the data at 508 nm in "a-Enz. vs. K+-Eth" experiment by a three "first-order" exponential equation. (K+)f was 12.0 mM. Other conditions were the same as Figure V.1 ........ 136 v.4 Two-exponential fit to the first 50 seconds of the absorbance-time data at 420 nm in "a-enzyme vs. KT—ethionine" experiment at 25.0 mM free K+. Other conditions are the same as Figure V.1 .................................. 140 V.5 Three-exponential fit of the data at 508 nm in "a-Ethionine vs K+“ experiment at 16.0 mM free KT. Other conditions were: Enz, 1.25 mg.m1‘1 (23 M); L-ethionine, 8.0 mM (after mixing); pH = 8.70 .......................... 143 V.6 Dependence of the amplitude of the absorbance change of the fast phase in experiment 1 (a-Enz vs. KT-Eth), A] in Table V.2, on the square of the free K+ concentration ................. 148 V1.1 Absorbance-time-wavelength surface for the quinonoid disappearance by 18-crown-6. Concentrations after mixing were: trypto- phanase, 1.0 mg.m1'1; crown, 190 mM, respec- tively .............................................. 160 V1.2 Selected difference spectra constructed from Figure V11.1 during the reaction of the holoenzyme-ethionine complex (quinonoid) with 18-crown-6 (---). Conditions are the same as in Figure V1.1 .............................. 162 V1.3 Fit of the fast decay at 506 nm by a single exponential during the reaction of the quinonoid complex with 18C6. Conditions are the same as in Figure V1.1 ...................... 165 V1.4. Effect of various concentrations of 1806 on the rate of quinonoid disappearance at 508 nm .............................................. 166 V1.5 Dependence of pseudo first-order rate constant of the slow phase, kg in Table V1.3, on the inverse square of the free K+ concentration ......... 168 V11.l Block diagram for main steps in Principal Component Analysis .................................. 180 xiii Figure V11. V11 V11. V11 V11 V11. V11. V11. V11 V11 V11 V11. V11. 2 .3A 38 .4A .4B .8A .8B .8C 10A Experimental absorbance-wavelength-time surface forthe deactivation of 3.0 mg.m1’1 tryptophanase by 150 mM 18C6 ............... Principal Component Analysis (PCA) re- constructed surface of the data in Figure V11.2 using three eigenvectors in M- analysis ................................... Reconstructed surface of the data in Figure V11.2 using only one eigenvector in M- analysis ................................... Residual (A43)-A) of the data presented in Figure V 1.2 ............................ Residuals (A7 )-A) of the data presented in Figure V11.2 ............................ M-analysis fit of the 337 and 420 nm con- centration profiles from the data in Figure V11.2. Three eigenvectors were used in the fit .................................... Estimated static spectra of the three ab- sorbers in Figure V11.2 .................... Experimental absorbance-wavelength-time surface for the reactivation of 2.0 mg.m1'1 tryptophanase by 33.0 mM free K+ at pH 8.70 Residuals (Aégg-A) of the data presented in Figure V1 . ............................ Residuals (3‘3g-A) of the data presented in Figure VI . ............................ S-analysis residuals of the data presented in Figure V11.7 using two eigenvectors ..... S-analysis fit of the Iprop = (£337-f420) in tryptophanase reactivation by K+ using two eigenvectors ........................... Experimental absorbance-wavelength-time surface for the reaction of 2.0 mg.m1'1 de- activated tryptophanase by a Kt-Ethionine mixture containing 16.0 mM free K+ and 8 mM L-Ethionine at pH 8.75 .............................. xiv Page 198 199 200 201 202 205 208 210 211 212 213 216 217 Figure V11 V11. V11. V11 V11. V11. V11 V11. .10B 11A 11B .12A 12B 13A .13B PCA reconstructed surface of the data presented in Figure VII.10A using three eigenvectors in M-analysis ....................... Residuals( )-A) of the data presented in Figure V11. (1 A) ................................... Residuals (A63)-) -A) of the data presented in Figure V11 1 Experimental difference surface of the data represented in Figure VII.10A .................... PCA reconstructed difference surface of the data represented in Figure VII.10A using three eigenvectors in S-analysis ........... Two eigenvectors S-analysis residuals of the data represented in Figure VII.10A .......................................... Three eigenvectors S-analysis residuals of the data represented in Figure VII.10A. ......................................... (A) M-analysis fit of the quinonoid spectrum from the data presented in Figure VII.10A. Three eigenvectors were used. (8) Estimated spectrum ............... XV A ................................... Page 218 220 221 222 223 224 225 226 CHAPTER 1 INTRODUCTION A. A Brief Review on Catalysis by Pyridoxal-P and Pyridoxal-P (Enzymes A11 living organisms use pyridoxal-phosphate (PLP vit. B6)’ the biochemically functional form of vitamin-86, to synthesize, degrade, and interconvert amino acids. Although this versatile coenzyme en- ables proteins to perform a class of different reactions such as race- mization, transamination, decarboxylation, and a,B elimination reac- tions (1,2), most of these processes depend on a common structural and mechanistic principle. In addition, pyridoxal and pyridoxal-p alone catalyze similar reactions in the complete absence of the enzymes requiring this cofactor (3). The reaction of pyridoxal-p with amino acids is generally believed to occur through formation of a Schiff base intermediate between the carbonyl group of pyridoxal-p and the a-amino group of amino acid substrates (4,5,6,7) according to reaction (1.1): The SPECIFIC role of pyridoxal-p in the reaction is then to promote electron withdrawal from the a-carbon of the bound amino acid leading to the cleavage of the bonds, Ca-H(a-elimination), ca-coo' (decarboxylation), cB-v (s- elimination and B-replacement) of this intermediate. In general, 1 H I - R-CH-C-COO (B) 111‘") /+\H 1 V / ° +R-CH-c-c00‘—+ \ I (1.1) NH; N HT reactions occurring in the amino acid moieties of these Schiff bases are influenced by two major factors: (1) The electron-withdrawing effect of the pyridine ring, which may be further amplified by protona— tion of pyridinium nitrogen in acidic solution; (2) The electron-with- drawing effect of the azomethine nitrogen that contains a covalently bound proton. This covalent bonding which is somewhat strengthened by hydrogen-bonding to the adjacent carboxylate and phenolic oxygen, exerts a strong electron-withdrawal effect on the carbon atoms adjacent to the azomethine nitrogen, a factor which is believed to be respon— sible for a large fraction of the catalytic effect observed in the aldimine-type structure. Also because of the proximity of this (N-H) covalent bonding to the a-carbon of the imino acid, the effect of this electron-withdrawing group may be greater than that of the pyridine ring. The mode of binding of pyridoxal-p and its derivatives to proteins has been investigated by a number of physiochemical techniques (8,9, 10). Although large differences in behavior exist among the various 86-dependent enzymes, in every FHJLdependent enzyme examined so far, the e-amino group ofaalysine residue at the active site binds the co- factor as a Schiff base (11.12.13). Treatment of a number of PLP enzymes with sodium borhydride followed by enzymatic digestion has led to the isolation of pyridoxal-lysine compound which strongly supports this postulate (14,15,16,17,18). Very little, however is known about the nature of the bonds formed between the other groups of the coenzyme and the app-enzymes. Mechanism of Catalysis: A general mechanism for pyridoxal-p cata- lyzed reactions was proposed independently by Snell (19) and Braunstein (20) and was later supported by other studies (21,22). This mechanism emphasizes the function of pyridoxal-p in weakening the sigma bonds around the a-carbon of the bound amino acid because the conjugated pyri- dine system acts as an electron-sink especially if the ring nitrogen is protonated. Scheme 1 (Figure 1.1) shows the probable reaction se- quence for the diprotonated form of the Schiff base in the case of labilization of the a—hydrogen for the a,8-elimination and B-replace- ment reactions. The first step in each case is formation of an aldamine Schiff base (Structure 1, Scheme 1) between a substrate amino acid and pyridoxal-D by transaldiminization reaction (1.1)(12). The next step in the reac- tion sequence involves dissociation of the a-proton to give the inter- mediate indicated by Structure 11. The driving force for this reaction is explained by the gain of delocalization energy upon formation of the intermediate 11 due to the contribution of a quinonoid structure resonance form which characteristically absorbs at around 500 nm (23). Following the labilization step, the quinonoid Structure 11 can then eliminate the B substituent to form a bound a-amino-acrylate Complex .m:o_pummc pcmsmomFchtm use cowumcwew_m1m.a emePmum61aba eo mucmzcmm cowpummm .F.H mczmwu .TH Bani +ch + mououfum AH mezum. 0...... .2535155 an. 3.2: , :8 on on _ / + DOUIWINIUIK N -o \ c To «:29 ..., \ ..., \ on...» o moubfiwé GEES—yam. 1 Q ..o V>H 5:05.56 1 Q 2: V AH. I _ +IH @I Y Z T 2(V _.\_ 9:058:96 _ N N .b _ -o \ r a F m 97 why. a. -xwi p066 51¢ 86% 3-x > A» I > III. The resulting unsaturated imine (111) can either add a different nucleophile than the one eliminated (B-replacement), or it can be con- verted to an a—imino acid (Structure 1V, Scheme 1). Since such imino acids are unstable in aqueous solutions, they subsequently undergo non- enzymatic hydrolysis to produce an a-keto acid and ammonia. It should be emphasized that the establishment of cationic character at substrate carbon 8 to nitrogen in intermediate III (resonance form of 111 in Scheme 1) further facilitates a,B-e1imination and B-replacement reac- tions. What then is the function of the protein in catalysis? A "clas- sical" answer to this question is that the enzymes provide a rate en- hancement and specificity which is certainly unattainable in their absence in model system reactions. Their major functions perhaps in- clude increased acid—base catalysis (a single base on the active site of aminotransferases facilitates the a-proton abstraction) (24,25), anchoring of the phosphate group of the coenzyme (26,27,28,29), and recognition of the correct reaction partners. Dunathan postulated that PLP enzymes orient the bond to be broken in the Schiff base complex orthogonal to the plane of the conjugated system, since this conformation of the breaking 0 bond achieves maximal orbital overlap with the w system of the SB complex (30,31). The principle that bonds parallel to the w-plane are more labile than those not so aligned, has also been used by other workers (32). Later studies by Floss et al. (33,34) with model systems showed the non enzymatic rate of a- hydrogen exchange in pyridoxal Schiff bases is detenmined by the pro- portion of conformer having the Ca-H bond orthogonal to the fl-system. Therefore, it follows that the PLP-dependent enzymes control the reac- tion specificity by controlling the conformation about the N-Ca bond of the Schiff's base intermediate. Several reviews of other aspects of this subject are available. Examples are the following: Metzler et a1. (35.36.37) and Morozav et al. (38.39) on optical and luminescence properties and band shape analysis of vitamin-B6 derivatives; Martel (4). Fasella (11) and Davis (40) on PLP reaction pathways; Perault et a1. (23) on the electronic aspect of the PLP reactions; Dunathan (30,31) and Floss et al. (33.34) on the stereochemistry of PLP-catalyzed enzyme reactions. 8. Tryptophanase The production of indole during protein decomposition has been known since the work of Nenki (41) and Kuhne (42) in 1875. The source of this compound, however. was unknown until Hopkins and Cole (43) showed in 1903 that it was produced by bacterial decomposition of the newly isolated (44) amino acid. tryptophan. In 1935. Happold and Hoyle (45) identified tryptophanase as the enzyme responsible for the production of indole in bacterial cells. Subsequent studies by Happold, Struyvenberg (46) and Wada (47) demonstrated that trypto- phanase requires NH+. K+ or Rb+ for enzymatic activity. and was in— hibited by Na+ or Li+. In 1947, Wood, Gunsalus and Umbreit (48) dis- covered that tryptophanase also requires the coenzyme pyridoxal-phos- phate and that indole, pyruvate and ammonia are formed in stoichio— metric amount from L-tryptOphan. Summarizing the data available by 1954 allows one to formulate the reaction catalyzed by crude. cellvfree preparations of tryptophanase as: Tryptophanase L-Tryptophan + H 0 t: Indole + Pyruvate + NH 2 + 3 PLP. NH4 (1.2) Early studies of this topic are reviewed by Happold (49) and Wada (50) while a review by Snell (51) covers the studies up to 1975. 8.1. Enzyme Source Tryptophanase is believed to play a catabolic role in metabolism. perhaps by regulating the intracellular concentration of tryptophan (51). Tryptophanase is present in very small amount in cells grown without tryptOphan, but it can be induced to comprise as much as 10% of the soluble cell protein (51,52). In order to produce pure tryptophanase. free from tryptophan syn- thetase, Newton and Snell (53) developed a constitutive strain of Escherichia Coli called B/lt7A. This mutant lacks the genes for tryptophan synthetase (54) and hence tryptophan for protein (trypto- phanase) synthesis must be obtained by reversal of reaction 1.2. This strain produces large amounts of tryptophanase (up to 10% of the soluble protein) under proper cultural conditions (55.57) and it was first used by Newton and Snell (56) to obtain homogeneous crystal- line tryptophanase. 8.2. Structural Properties B.2.l. Subunit Structure - Tryptophanase (Mx = 220,000) from E-Coli Blt7/A is a tetrameric enzyme composed of four identical sub- units (58,59). The four subunit model of tryptophanase obtained from hydrodynamic studies is also confirmed by electron micrographs of the enzyme which show four subunits arranged in a square planar rather than a tetrahedral configuration (59). From thermodynamic studies on the dissociation of tryptophanase into its apoprotomers. Morino and Snell (59,60) conclude that both hydrophobic and ionic forces are important in maintaining the quaternary structure of apotryptophanase. Dissociation of the enzyme into its subunits and the reverse process are highly dependent on temperature. ionic environment. concentration. [Uh andthe presence or absence of the coenzyme pyridoxal-P (59.60). Snell and Goldberg showed that each subunit contains a single peptide chain (61). 8.2.2. PLP Binding - Apotryptophanase is catalytically inactive in the absence of added pyridoxal-phosphate (62). In the presence of PLP. however. the apoenzyme binds one coenzyme moiety per subunit in an azomethine linkage to an e-amino group of a lysine residue at the active site; that is. 4 pyridoxal-p are bound per molecule of native tetrameric enzyme (58.63.64). The four binding sites appear to be equivalent since only one major peptide containing the pyridoxal group was found upon reduction of holotryptophanase (65.66). Similar to other PLP dependent enzymes. the coenzyme can be resolved from the 10 holoenzyme by addition of penicillamine (59), cysteine (67) or high concentrations of ammonium salts (68). all of which form thiazolidine derivatives with pyridoxal-p. Extensive ultracentrifugation studies on both holo- and apoenzymes by Snell and coworkers (59.69) showed that a large conformational change accompanies the binding of PLP by apotryptophanase. This con-, formational change results in a more compact structure such that the coenzyme becomes "locked" in the holoenzyme and increases its stability to denaturation by sodium dodecyl sulfate (59). heat (69.70) and changes in pH. Goldberg et al. (71,72) showed that fixation of the first two pyridoxal-p molecules to the apoprotomers results in a decrease in binding rate of the two remaining apoprotomers but each protomer. once saturated with the coenzyme. exhibits the same catalytic proper- ties independent of the state of saturation of the surrounding protomers, 8.2.3. Monovalent Cation Specificity - The requirement of certain monovalent cations by some enzymes to express their optimum catalytic activity was reported over 40 years ago by Boyer and coworkers (73). Since that time. more than 60 different enzymes including tryptophanase have been found to require these ions (74,75). In some cases partial activity is observed while in other cases no activity is expressed in the absence of these cations. Extensive studies by Snell (56). Happold (49), and Wada (50) revealed that tryptophanase requires NH: or K+ while Na+ and Li+ have essentially no activating effect. Tl+ can also replace K+ and has a greater affinity and Rb+ also activates the enzyme but less effectively than K+ (46). 11 Reviewing a number of studies of the activation of tryptophanase by monovalent cations. Snell (51) finds that both K+ and Na+ are . equally effective in permitting the dissociation of tetrameric to dimeric apotryptophanase at low temperatures. This effect thus seems unlikely to serve as a basis for their markedly different catalytic effects. Toraya et a1. (76) carried out gel filtration studies on the effect of various monovalent cations on the binding of the coenzyme and their relation to catalytic activity. They found that NHZ, K+ and Rb+, which are good activators, enhanced the binding constant for the coenzyme while enzyme in presence of the poor activators Na+. Li+ and 05+ showed a lower affinity for pyridoxal-p. The dissociation constant was >31 pM and 1.8 uM in the presence of Na+ and K+. respec- tively. They hence concluded that activating monovalent cations play an essential role in formation and maintenance of the firm binding of PLP to apoenzyme. This conclusion is also supported by the work of Happold (46) who showed that removal of K+ ions from the holo-enzyme causes dissociation of the complex and that the coenzyme can then be removed by dialysis. Suelter et al. (77) have shown that the activating constants for the various cations vary from 0.2 mM for NH: (most effective) to 54 mM for Li+ (least effective). They suggested that lack of activity in previous studies in the presence of poor activators may be par— tially attributed to low cation concentrations rather than to intrin- sic differences in pyridoxal-p binding. Their data show that 0.5 M Na+ brings about nearly 50% of the activity observed with 0.1 M K+. Both Suelter (77) and Toraya et al. (76) point to the size of 12 monovalent cations as an interesting feature in catalysis. They found that cations with ionic radii smaller than 1.3 A or larger than 1.5 A (K+ crystal ionic radius is about 1.35 A) are poor acti- vators. In light of this. they suggest that any monovalent cation having an ionic radius near that of K+ might bind to the appropriate positions of the protein and bring about the alignment of the peptide. backbone into an optimum configuration so that proper orientation of the reacting groups needed for efficient catalysis is achieved. These studies. plus the fact that distinct spectral differences are observed in the presence of K+ vs. Na+. demonstrate a general differ- ence in the structure of tryptophanase and in the mode of binding of pyridoxal—p in the two environments. A more compact structure and tighter binding of pyridoxal-p in the K+ environment is consis- tent with these observations. Since the 3-dimensional structure of a monovalent cation binding site of any enzyme has not been described to date. however, this difference does not elucidate the molecular basis for those dissimilarities. In spite of the above discussion. the essential role played by these cations in catalysis, that is whether they are directly in- volved in catalysis, and/or they are simply required to affect the 3-dimensional configuration of the enzyme molecule in solution is not yet known. Two separate studies by Suelter et a1. (77.78). however. point to the former case. Nuclear magnetic resonance studies of pyruvate kinase, a monovalent cation dependent enzyme that catalyzes phosphoryl transfer reactions, showed that thallium (Tl+) binds within 4-8 A of the divalent cation activator at the catalytic site (78). 13 indicating that it may participate in the catalytic process. A stoichiometry of 2 T1+ bound per subunit of tryptophanase. obtained by incorporation of radioactive thallium into the enzyme through di— alysis (77), also supports a specific role for the cation rather than a non-specific conformational effect. In addition. the fact that most pyridoxal-p dependent enzymes that catalyze a.B-elimination reactions. require monovalent cations for maximum activity whereas those catalyz- ing transamination do not. also supports the view that these cations are directly or indirectly involved in the catalytic process (74). B.3. Spectral Properties In the absence of pyridoxal-p. apotryptophanase has the spectrum of a simple protein with a maximum centered at 278 nm. Upon addi- tion of PLP, two new absorption maxima centered at 420 nm and 337 nm appear. the relative amplitudes of which depend upon pH and the nature of the monovalent cation (59,65). Morino and Snell (65) demonstrated that at low pH values the 420 nm form of the enzyme predominated and as the pH was raised. absorbance at 337 nm increased at the expense of 420 nm absorbance. They described this change with pH by a single proton process titration curve. Morino and Snell also showed that in the presence of non-activat- ing monovalent cations such as Na+ and imidazole (and in the absence of K+ or NHZ). the enzyme (inactive) was entirely in a form also absorbing at 420 nm and that the spectrum did not change significantly between pH 7.0 and 9.0 (59). When K+ replaced Na+ as the cation. however, a dramatic change in the spectrum was observed in which 14 the 337 nm form became the dominant species at pH 8.0 (Figure 1.2). They attributed the 337 nm absorption to the active form of the enzyme because this form predominated at pH values above 8.0 where the en- zyme displays its maximum catalytic activity. The observation that activating monovalent cations such as K+ promoted the formation of the 337 nm form. was also consistent with this interpretation. Model studies have shown that pyridoxal-p aldamines absorb in the wavelength range of 440 nm - 430 nm (36.79.80). 0n the basis of these model studies, Metzler et al. (37,40) suggested the structure in Scheme 11 (Figure 1.3) for the 337 nm and 420 nm forms. Since proton action of Schiff's bases on the ring nitrogen has a minor effect on both absorbance change and positions of absorption maxima, the state of protonation at the pyridinium nitrogen for either structure I or 11 in Figure 1.3 is unclear. Recent studies on tryptophanase spectral forms by June et al. (81.82.83) demonstrated that interconversion of the 420 nm and 337 nm forms following a change in pH or monovalent cation over the range of enzyme stability occurs in a complex fashion on the stopped flow time scale. The authors performed the following three experiments: (a) An incremental drop in pH from 8.5 to 6.7; (pH DROP) (b) An incremental jump in pH from 7.4 to 9.3; (pH JUMP) (c) A sudden change in K+ concentration from 0.1 MNa+ to equal .05 MNa+ and K+ at pH 8.0; (K+ JUMP). The major features of the pH-DROP and pH-JUMP experiments were interpreted by June et al. in terms of 3 distinct time-dependent phases: 15 ABSORBANCE be I H 300 350 400 450 WAVELENGTH (mu) Figure 1.2. Comparative effects of monovalent cations on the spec- _ trum of holotryptophanase. [Taken from Reference (59).] 16 goimmv .E um cm—Npmz >3 emummmmsm mmmcm;80paxcu to mELow E: Nmm vcm E: owe mo mmcsuuacum .m.H mczmwu :H ~52.me Eco“. In. :9... Eco... Id 33 as: SD u E: 0st H .33 .m3 .33 17 (1) An abrupt_phase, which was complete in less than m6.5 msec (instrument dead time). The systematic changes observed at 295 nm were interpreted as fast protonation-deprotonation steps at the pyridinium nitrogen within the B and Y ”manifolds". (Figure 1.4) (2) A fast lst order conformational interconversion of 420 nm and 337 nm absorbances. (3) A slow first order process involving growth at 355 nm coupled to two decays at 325- and 430-nm in the incremental PH JUMP, and decay at 355 nm with accompanying growth at 430 nm in the incre- mental pH DROP experiments. Their K+ JUMP experiment also showed slow conversion of the 420 nm peak to 337 nm absorption but the kinetics were not clean. The results from these experiments led them to propose Scheme 111 (Figure 1.4) involving enzyme forms Ea, Ed’ EB’ EBH+’ EY and EYH+' The Ea form (not shown) is predominant in the absence of activating monovalent cations and absorbs at 420 nm. EB and EBH+ in the B manifold also absorb at 420 nm while those in the y manifold. EY and EYH+’ absorb at 337 nm. The form E6 absorbs at 355 nm. The structures giving rise to various absorptions shown in Scheme III were assigned by the authors on the basis of both model studies and studies on another pyridoxal-p dependent enzyme. namely asparate aminotransferase (28.37.84). Computed equilibrium distributions in- dicated that among the four species of the B and y manifolds, EBH+ and EY predominate at low and high pH, respectively. Further details of their work appears in the references (81.82.83). CON FORMATION [OW 9" HIGH pH (Scheme 111) Figure 1.4. Interconversion of tryptophanase spectral forms. 19 8.4. Catalytic Properties Tryptophanase is one of a group of pyridoxal-p dependent enzymes which catalyzes a variety of a.8-elimination and B-replacement reac- tions (56.85.86). Following purification of the enzyme, Newton and Snell (56) were able to establish that not only tryptophan and trypto- phan analogs but a variety of other B—substituted amino acids undergo a, B -e1imination according to reaction 1.3. RCH '+H TPase ’+R + 2CHNH2COO 20-—-—--.-CH3C0C00 H NH3 (1.3) In addition, amino acids that serve as a substrate in reaction 1.3, can also undergo a B-replacement reaction in the presence of indole to yield tryptophan according to reaction 1.4. TPaSQ Indole + RCHZCHNH2c00'——>Tryptophan + RH (1.4) In fact, it is a reaction similar to (1.4) that permits an E—Coli B/lt7-A culture which lacks enzymes for tryptophan synthesis (such as tryptophan synthetase), but which contains a constitutive trypto- phanase, to grow when supplied with indole. 8.5. Mechanism of Tryptophanase Catalysis A mechanism for tryptophanase action consistent with all observa- tions reported up to 1975 was outlined by Snell (51). In this mechan- ism (Scheme IV, Figure 1.5) the exact ionic forms of both coenzyme 20 Figure 1.5. Mechanism for tryptophanase catalyzed reactions. Taken from Reference (83). 21 1H1 11 U A RCHZCHCOO’ NH.z NH2 H 1 RCHZCECOO' :H" N t +— j ‘7 1 <7“ m A :RH 11 II+CH ccooQNH; .. s NH, CH2=C-COO' I /N / 1 N Figure 1.5. 22 and substrate, as well as the catalytic groups of the apoenzyme which may contribute to the process are unknown. The first step in this mechanism involves the conversion of the inactive form of the enzyme absorbing at 420 nm (Structure 1. Figure 1.5) to an active form 11 which absorbs at 337 nm. As described earlier, since the pH optimum of tryptophanase is near 8.5. it was assumed that the deprotonated form of the coenzyme (Amax = 337 nm) is that which exhibits activity. The second and third steps involve formation of the enzyme-substrate complex (Structure 111. Figure 1.5) via a transaldimination reaction, and the subsequent labilization of the a—hydrogen from the bound amino acid to form the quinonoid intermediate 1V which has an intense absorption at m500 nm (65). The reaction with dead-end inhibitors (substrates which lack a labilizable B-substituent such as L-alanine and L-ethionine) stops here. but with trace substrates this absorption band disappears as substrate is depleted. Studies by Morino and Snell (65) on L-alanine and true substrates in the presence of 020 and 3 H20 indicated that the a-proton is labilized during quinonoid formation,and that for true substrates this labilization proceeds at a faster rate than elimination of the B-substituent. They thus con- cluded that elimination of the B-substituent of the substrate is the rate-limiting step. Later Suelter and Snell using s—orthonitrophenyl- L-cysteine (SOPC)as:substrate in 3H20, demonstrated that no tritium is incorporated into the unreacted SOPC. Based on this observation and the fact that no 500 nm absorbing species could be detected by a scanning stopped-flow study of the reaction with SOPC (87). they 23 concluded that loss of the a-proton was rate-limiting for the reace tion with this substrate. The fourth and fifth steps in Figure 1.5 represent the elimination of the B-substituent of the substrate with formation of the enzyme- bound o-aminoacrylate complex (Structure V). and subsequent decomposi- tion of this complex to yield pyruvate and ammonia along with regen- eration of the active enzyme. Hillebrand et a1. (88) also using SOPC as substrate, suggested that either a-iminopropionate or the carbinolamine of pyruvate are the immediate products of the SOPC degredation by tryptOphanase. The intermediate then undergoes a non- enzymatic hydrolysis to yield pyruvate and ammonia. In an effort to gain more information on the role played by mono- valent cationsirithe mechanism. Suelter and Snell (77) studied the reaction of tryptophanase with the competitive inhibitor L-ethionine. They demonstrated that the absorption spectrum of holoenzyme in the absence of monovalent cations,p1usor minus ethionine are nearly identical. However, the circular dichroic spectra of the same solu- tions were very different and are consistent with complex formation between the holoenzyme and ethionine. Upon addition of activating monovalent cations to the holoenzyme-ethionine complex. they observed a marked increase in absorption at 508 nm resulting from labilization of the a-proton that leads to formation of a quinonoid structure. They therefore concluded that ethionine interacts with the holoenzyme in the absence of monovalent cation, but does so in such a way that the 508 nm absorbing species is not formed. This observation clearly indicates that the cation exerts its effect by interacting directly 24 at or near the catalytic center rather than at some site on the pro- tein surface which is distant from the active site. However. as dis- cussed earlier. whether it participates directly in the catalytic process is still uncertain. 8.6. Kinetic Studies To study the transient kinetics of quinonoid formation and cor- relate the rate of change of the enzyme to that of the product in tryptophanase reactions. June et al. (83,89) performed stopped-flow studies of tryptophanase catalysis with the inhibitors L-alanine and L-ethionine under various experimental conditions. Their results. in contrast to the conclusions of Morino and Snell (65). showed that the 420 — not the 337—nm form of the enzyme is the active form. They support this assignment by the following observations: (1) The rate constant for disappearance of the 420 nm absorbance (l8.0:2.2 Sec-1) was the same as that of the fast phase of the bi— phasic growth of the quinonoid at 508 nm (15.0:1.2 Sec"); (2) The rate constant for disappearance of the 337 nm absorbance (0.56:0.08 Sec-1) was the same as that of the slow phase of the quin— onoid formation (0.63i.06 Sec'1) and was essentially unaffected by the inhibitor concentration or the nature of the inhibitor, alanine or ethionine; (3) The average rate constant for the slow phase obtained with ethionine (0.51:0.14 Sec") and alanine (0.47:0.15 Sec“) agrees 1 closely with the rate constant, 0.42 Sec" . for conversion of the 25 337 nm absorbance (y form) to the 420 nm absorbance (8 form) follow— ing a rapid decrease in pH (82). These results led them to conclude that the 337 nm form apparently does not form quinonoid directly but is first converted to the 420 nm form by a conformational change before the a-proton of the amino acid inhibitor is removed to form quinonoid (89). In addition, they ' found that with deuterium at the a-position of alanine, the fast phase of quinonoid growth slowed down while the slow phase remained virtually unchanged. This was interpreted by the authors as indicat- ing that the abstraction of the a-proton is the rate limiting step of quinonoid formation while the slower phase reflects an enzyme conformation change. Based on these results and those from the incremental pH—JUMP and pH-DROP studies (82,83), June et al. proposed Scheme V (Figure 1.6) as a mechanism for quinonoid formation. They also presented the following additional factors as evidence supporting their proposed mechanism: (a) The effect of pH on quinonoid formation revealed that as the pH was increased, the rate constant for the fast phase of the biphasic quinonoid growth also increased while the relative amplitude of the fast phase diminished. This supports their previous suggestion that conformation B (420 nm form) is the one poised for reattion. i.e., the active form of the enzyme. (b) The rate constant for the fast phase of the quinonoid growth exhibited a hyperbolic dependence on ethionine concentration. 26 (Scheme V) Figure 1.6. Mechanism for the formation of quinonoid (E0 and EQH+) from the competitive inhibitor, L-Ethionine (SH). 27 indicative of formation of the Michaelis complex SH; (c) The rate constant for the slow phase of quinonoid growth appeared to be essentially constant over the range of ethionine concentrations used and comparable to that obtained with alanine. This again presents further support to the authors' previous proposal that k2 reflects an enzyme confonnational change. Recent rate studies with the true amino acid substrate. S-benzyl- L—cysteine (SBC) are also in agreement with Scheme IV (90). C. Scanning_Stopped-Flow Technique for the Study of Enzyme Reactions Stopped-flow kinetics has been extensively used in the study of non-steady-state enzyme reactions at high enzyme concentrations. In a typical stopped-flow experiment, absorbance is monitored as a function of time at a certain wavelength. Recent advances in computer-controlled data acquisition have made "scanning stopped-flow" practical for many enzymatic reactions (81.89 91-95). In Rapid Scanning Spectroscopy (RSS), a selected region of the electromagnetic spectrum is rapidly and repeatedly scanned while a spectrophotometric response such as absorbance or fluorescence is measured at a fixed number of wavelength "channels" across the spec- trum during each scan (96.97). If the time duration of each scan is short compared to the half-life of the reaction studied. the data can be regarded as a matrix A composed of N consecutive instantaneous spectra measured at P wavelength channels (98). The element Aij of this matrix is then the spectrophotometric response measured at 28 wavelength channel i at the time of scan j. The advantage of collecting this “time-wavelength-absorbance" sur- face for a spectral region rather than a fixed-wavelength experiment. is that the reacting enzyme, enzyme bound intermediates, substrates, and products may all be spectrophotometrically detectable in the sgmg_ experiment. This obviously minimizes problems resulting from lack of. reproducibility from one experiment to another and eliminates somewhat the problem of long time baseline drift. In our laboratory a computer-interfaced rapid scanning stopped flow system has been successfully used for the studies on Cytochrome g_oxidase (95,99), AMP-aminohydrolase (90) and tryptophanase (82.89. 100). Further details about the system including a historical background handling and performance of the system. and treatment of scanning stopped-flow data will appear in Chapter II. D. Macrocyclic Complexing Agents for the Study_of Tryptoohanase Activation/Deactivation by Monovalent Cations 0.1. Structure and Properties A large variety of naturally occurring macrocyclic antibiotics such as porphyrin, nonactin, and valinomycin and their unique ion binding and ion transport properties have been known for over fifty years. In 1964. Moore and Pressman (101) reported that valinomycin induces the transport of potassium ion through mitochondrial membrane by complexation. The biological activity of these compounds is be- lieved to be related to their macrocyclic structure which consists 29 of a lipophilic exterior and a hydrophilic central cavity ringed with electronegative donor atoms (102). The macrocyclic nature of these compounds allows Charged cations to bind in the central cavity, hence making the cation soluble in the lipid region of the membrane. During the past two decades. a large number of synthetic macro- cyclic compounds that contain multiple donor atoms capable of binding~ cations have been prepared and investigated. Many of these organic macrocyclic ligands possess very interesting and unusual ion binding properties. These chemicals are classified under two general classes: (1) "Macrocyclic Crown-ethers", which were first synthesized by Pederson in 1967 (103,104) are cyclic polyethers whose trivial names indicate both the total number of atoms and the number of oxygen atoms in the ring. For example, lB-crown-6 or simply 18C6 contains a ring of 18 atoms. 6 of which are oxygen. (2) "Cryptands", which were first synthesized by Lehn and cowork- ers in 1969 (105,106)are bicyclic diamines which have a 3-dimensional cavity for complexation of metal cations. The trivial name of this class denotes the number of oxygens in each of the polyether chains which bridge the two nitrogens. For example, Cryptand 222 or simply C222.Contains 2 oxygen in each strand. The structural formulas of cryptands and 18C6, a member of the first class. are shown in Figure 1.7. One of the most interesting features of these cyclic compounds is their ability to "selectively" bind various cations to form very strong complexes. Particularly interesting is the strong "affinity" and "selectivity“ shown by the polyethers for alkali metal cations. "1:05 “:1 (C211) m: I; ":0 (C221) m: n=| (C222) m. 1, 11:2 (0322) |/\O/\| o 0 Figure 1.7. Cryptand and 18-Crown-6 structural formulas. 31 Since the alkali metal ions are generally regarded as poor complex- ing cations. the cyclic polyethers appear to be the only neutral com- pounds (with the exception of macrocyclic antibiotics)ix1complex ap- preciably with these metals. This has resulted in their use as com- plexing agents to increase the solubility of alkali metals in amines and other solvents (108,109). and as models for carrier molecules in the study of ion transport phenomena in biological systems (110. 111.112). 0.2. Complexation The cyclic polyethers form strong one to one (1:1) polyether: metal complexes with a large array of metal ions (110,113). Complexa- tion constants at least as high as 108 M.1 for complexes formed between cryptands and alkali metal cations are known (114,115). These com- plexes are generally assumed to consist of the metal ion bound in the cavity of the polyether ring (116). This "metal in the hole" picture has been substantiated by x-ray crystallographic studies of several of these complexes (117,118,119). The stable bonds in these systems have been attributed to ion-dipole interactions between the positively charged cation and the dipole created by the inwardly oriented oxygen atoms (113). The following factors are believed to influence the formation. stability. and selectivity of the macrocyclic ligand complexation: (a) Relative size of cation and ligand cavity; (b) arrangement of ligand binding sites; 32 (c) type and charge of cation; (d) number and type of donor atoms. Both lB-Crown-6 and 0222 are selective for K+ ion and form strong 1:1 complexes with this ion. Hence both of these compounds were used during the course of this study. CHAPTER II EXPERIMENTAL METHODS A. Materials E-Coli B/1t7-A was grown in the Biochemistry Department at Michigan State University under conditions described elsewhere (2). Pyridoxal- Slphosphate (PLP), N-2-hydroxyethy1piperazine propane sulfonic acid (EPPS),N-N-bis(2-hydroxyethyl)glycine (Bicine). DL-dithiothreitol (DTT),ethylenediamine tetracetic acid (EDTA), and Sepharose 48 were obtained from Sigma Chemical 00. Potassium Epps (KEPPS). DEDTA. and K-Bicine were prepared by titrating the reagents with KOH. Ammonium Sulfate was Schwarz/Mann enzyme grade. lB-Crown-6- and Cryptand 222 were purchased from PCR. Inc.. and were further purified before use (see 8.4 in this Chapter). Tetramethyl ammonium chloride. (CH3)4N01, obtained from Aldrich Chemical Company was recrystallized from n- propanol prior to use. (CH3)4N0H was freshly prepared by passage of recrystallized (CH3)4N01 through a Dowex-l-OH column. Cyanogen bro- mide, CNBr.and 1.7-diaminoheptane were obtained from Aldrich Chemical 00. Water used for the preparation of all solutions was double dis- tilled. All other reagents were of analytical grade and were used without further purification. 33 34 8. Methods 8.1. Preparation of the 1.7-diaminoheptane Sepharose Column The ligand 1.7-diaminoheptane was coupled to sepharose 48 after cyanogen bromide activation in a procedure adapted from that of Shal- tiel and Er-el (120). Sepharose 4B is activated at pH 10.5-11.0 and 22° by the addition of l g of CNBr to 10 g (wet weight) of sepharose (121). In the process. 24 grams of CNBr dissolved in 24 ml dioxane dis- tilled over Na metal was added rapidly to 240 g of sepharose suspended in about 200 ml water as it was being stirred under the fume hood. The reaction was allowed to proceed for 8 minutes and the pH was maintain- ed between 10.5-1l.0 by addition of 5N NaOH. The pH tends to stabi- lize as the reaction proceeds. Activation was terminated by addi- tion of crushed ice to the mixture. The activated gel was then filtered quickly and washed by m2 L.ice-cold deionized water and re- suspended in about twice the settled volume of the gel (“500 m1 cold 0.1 MNaHCO3 (pH 9.0). To this sepharose suspension. an equal volume of H20 containing N120 g of 1.7-diaminoheptane at pH 9-9.5 was im- mediately added and the pH of the solution was readjusted to 9-9.5 with 6N H01 if necessary (in general, one needs 4 moles of ligand per mole of CNBr used for activation). The coupling reaction was allowed to proceed overnight at room temperature while the solution was gently swirled. Finally the gel was filtered and washed with water. 0.1 A_NaHCO 0.05 A_NaOH, water. 0.1 M_0H3COOH. then water 39 again. The alkyl-sepharose was stored at 4°C in aqueous suspension 35 in the presence of 0.02% sodium azide, Na3N. to prevent growth of bacteria. The sepharose column described above can be stored for months at 4°C and can be used repeatedly. It is regenerated with washes of 0.2 N KOH. H20, 0.2 N KOH. H20. 0.2 N H01. H20, followed by adjust- ing the pH to 7.0 in water and finally washing with the column-equil-_ ibration buffer. The column has a high binding capacity and high flow rate (1-3 ml/min). The retention power of the column is assumed to involve hydrophic interactions between the hydrocarbon "arms" of the ligand and accessible hydrophobic pockets or regions of the en- zyme and hence the method is referred to as "hydrophobic chromato- graphy". 8.2. Preparation of Tryptophanase Tryptophanase from E-Coli B/lt7-A was prepared as described by Watanabe and Snell (122) including the modification of Suelter et al. (123). Frozen wet cells of E-Coli (usually N30 9) suspended in 0.1 A_potassium phosphate buffer at pH 7.0 were either sonicated with a Branson Sonic Oscillator or treated with a French Press to break the cells. During the preparation, all precipitation steps were carried out at 2-5°C by using an ice-bath. Whenever ammonium sul- fate was added during the purification. the drop in pH from 7.0 was compensated for by addition of 10% ammonium hydroxide. With the exception of the dialysis buffer. all other buffers were made 0.1 mM in pyridoxal-p for enzyme stability. The dialysis buffer contained 36 20 uM pyridoxal-p. When apotryptophanase was desired, the holoenzyme was made 10 mM in DL-penicillamine and dialyzed at 4°C against a 90% ammonium sulfate saturated phosphate buffer at pH 7.0. During the preparation, the protein concentration was monitored by the Lowrey procedure (124). The enzyme prepared in this way is 90-95% homogeneous and is stored in the apoenzyme form as a suspension under nitrogen in 90% saturated (NH4)ZSO4 buffer containing 10 mM DTT to preserve activity. Loss of activity upon long time storage was observed in some cases; however, retreatment of the apoenzyme with 10 mM DTT in a phosphate buffer at 50°C followed by precipitation restored the activity. A detailed description of the preparation procedure is given elsewhere (123). 8.3. Activity Assay of Tryptophanase The activity of tryptophanase was measured spectrophotometrically by using the chromogenic substrate S-o-nitrophenyl-L-cysteine (SOPC ). This compound was prepared according to the published method (125). Suelter et al. (123) have shown that SOPC absorbs maximally at 370 nm and undergoes a,B-eliminationir1the presence of tryptophanase accord- ing to Equation 11.1: TPase 0-N0206H4SCH20HNH2000 + H20 ——-0-N02c6H4s + CH300000 + NH4 (11.1) The reaction was monitored as a decrease in absorbance at 370 nm with A6 = 1860 £.mol'].cm']. The assays were carried out in 50 mM 37 potassium phosphate buffer containing 50 mM K01, 0.6 mM SOPC. pH 8.0 at 30°C. The activity, which is the number of moles of product formed per ml per minute. is calculated from the Equation 11.2: (40.0.)370 x Enz. Dilution Factor Activity = (11.2) 1.86 The specific activity is calculated by dividing the activity by the protein concentration in mg/ml. The protein concentration was de- termined spectrophotometrically using 6278 = 0.795 m1.mg'].cm'1 (65). Specific activity greater than 40 pmole.min'].mg'1 is indicative of pure protein. Specific activity as high as 50-55 bmoi.min".mg" is reported for the enzyme (82.83.present work). 8.4. Purification of the Complexing Agents 18-Crown-6 (or 1UPAC: l,4.7.10.13.16-hexaoxacyc1ooctadecane) was first recrystallized from warm acetonitrile as the crown-acetonitrile complex (126). The weakly bound acetonitrile was then removed from the crown by placing the crystals in a vacuum oven for several hours. The crown obtained by vacuum decomposition of the complex was then high vacuum sublimed with the apparatus shown in Figure (11.1). The impure crown was placed in the apparatus below the cup and was heated with an oil bath to 60-70°C while the cold inner tube was maintained at m-60°C with chilled N2 gas. After completion of the sublimation. the purified crown was scraped from the walls of the inner tube as a white powder (M.P. 39-40°C) and was stored in the dark in a closed 38 To Vacuum Manifold Cold N2 Gas \ Trap to protect Vacuum Manifold lmpure Crown Figure 11.1. Molecular distillation apparatus for purification of C Y‘OWTl . 39 reservoir (extremely hygroscopic and light sensitive). Cryptand 222 (or 1UPAC: 4,7,13,16,21,24-hexaoxa-l.10-diazabicyclo[8.8.8]hexa- cosane) was high-vacuum sublimed at 110°C by Dr. Long Dinh Le. C. The Stopped-Flow Method 0.1. A Historical Background A history of flow methods begins with the classical studies of continuous-flow by Roughton and co-workers (127) in 1923. They studied rates of chemical reactions by allowing the reactants to flow from large reservoirs into a mixer and then into a long tube. Con- centration-time profiles were obtained by observation of the absor- bance of the solution at various points along the tube. Some 17 years later, Chance (128) was the first to apply the continuous-flow method in the development of stopped-flow methods of analysis. Further modifications were later made by different workers including Crouch et al. (129), Malmstadt (130). Dye and Feldman (131). Dye et a1. (92,96)'h10rder to tailor the system for their particular needs. Essentially. the stopped-flow technique involves rapid and efficient mixing of the two reactants (milliseconds). stopping the flow. and monitoring the spectrophotometric response as the reaction proceeds. Modern stopped-flow systems are usually computer-interfaced for fast data acquisition. 40 0.2. The Rapid Scanning Stopped-Flow System A thermostated, computer-interfaced. double beam rapid scanning stopped-flow system built by G. H. H0 (132) was used in this research. A block diagram of the system is shown in Figure 11.2. The system utilizes a 1000 watt xenon arc lamp as the light source. The entire flow system is made up of inert material and is housed inside a water- tight bath capable of circulating water. thus allowing for the tem- perature-controlled experiments. Both the sample and reference cells are provided with two path-length options (1.86 cm and 0.20 cm). To assure complete mixing of reagents prior to observation, a quartz double four-jet mixing chamber is used. In absorbance measurements, the light dispersed from the scanning monochromotor is transmitted through a beam splitting fiber optic to the observation and reference cells. Light from the cells is then brought to a pair of matched photomultiplier tubes by the use of similar fibers. The reference and sample photocurrents are next con- verted to absorbance and amplified by using an operational amplifier and the absorbance signal is stored on floppy disk in a PDP/81 com- puter. A detailed description of the system is given in the Ph.D. dissertations of G. H. Ho (construction of the flow system). N. Papa- dakis (133) and R. B. Coolen (134) (interface and software, synchron- ization of scans. and signal averaging scheme). C.2.l. Scanning Mode - The system utilizes a Perkin-Elmer Model 108 scanning monochromotor which is capable of repeatedly scanning 41 .Emumxm Zoreiumaaoum mcwcchm umomecmpcw cmuaaeou asp to Emcmmwu xoo_m .N.HH mczmwm 42 _ 2.52....— .N.HH mczmwa 3...... EniHa o». > an :3. .0: a 5 a . L 1:50 ..a _ 1.03.. 10: a R 33E ( mM.—“I EL OWCCOaw. U o < own—E om Ed ~ 1.3.4358. ...: 35...... mzu>_zo .-n _ .0::OU - to. .009; _ ...o.:...oc.o.o;& \‘I’( mauZBUR 10235 021.0 )‘I\)I 43 from 3 to 150 complete spectra per second. By using appropriate photo- multiplier tubes (PMT). a range of about 250 to 1200 nanometer (nm) of the electromagnetic spectrum can be scanned. As described earlier. the scanning mode is advantageous in the sense that it eliminates the need for several fixed-wavelength mode experiments which mini- mizes reproducibility problems and problems associated with long- time baseline drift. C.2.2. Fixed-wavelength Mode - The scanning mode has two main disadvantages associated with it; (a) some noise is introduced by the nutating mirror of the monochromator, (b) reactions with half- lives of less than 50 mS (limited by the scan speed) are not suitable for kinetic studies in this mode (only 4 forward spectra can be col- lected in 50 mS at the 150 scan Speed). These problems. however. are eliminated in the fixed wavelength mode. In this mode. the pro- gress of a reaction can be followed at any selected wavelength by manually setting the monochromotor to that particular wavelength. In this case reactions with half-lives in the order of the "dead-time" of the instrument (few msec) are possible to study (see 0.2.4). In addition. the absence of noise introduced by the nutating mirror contributes to the enhancement of the signal-to-noise ratio (S/N). C.2.3. Flow Velocity - In stopped-flow experiments, the flow of solutions should be fast enough to cause turbulence necessary for efficient mixing. The "flow velocity" is obtained by measur- ing the distance between the start and stop flags and the flow 44 time, whichis the time required for the stopping syringe to travel this distance. A measure of turbulent flow is given by Reynolds' Number R (135): R = dV p/n (11.3) where d is the diameter of the tube in (cm). V is the flow velocity in (cm.sec']). p and n are the dynamic density and viscosity in (gcm'3) and poise (9.cm'].sec’]), respectively. For practical pur- poses. the range of Reynolds' number for efficient turbulent flow might be from 2000 to 2500, but it can be as low as 10 for jet-type mixers (135). The critical velocity required to get turbulent flow for aqueous solution at 20°C is found to be V = 200/d. where d is in mm. Since 2 mm diameter tubes were used for construction of mixing and observa- tion cells. the critical velocity is thus about 100 cm/sec. From the velocity profile of an aqueous solution as function of time, a flow velocity of about 550 cm/sec was calculated at N40 psi pushing pres- sure for our system (90). This value (corresponding to R m 110) is well above the critical velocity of 100 cm/sec and thus assures us of turbulent flow. 0.2.4. Dead Time - The time required to transfer the solutions from the mixing chamber to the observation point and bring them to a complete stop is defined as the "dead time". It thus depends upon the mixing efficiency, stopping time. and the flow velocity for a 45 particular experiment. 1f the stopping time is very small and the mixing very efficient. then the dead time can be estimated from Equation (11.4): t = V/U (11.4) where V, the "dead volume" is the volume from the point of mixing to the end of observation window. and U is the average flow velocity in ml/sec. For our mixing and observation cells. the dead volume was calculated from physical measurements to be 0.048 and 0.121 ml for the short and long path lengths respectively (132). With our typical flow velocity of about 550 cm/sec (~18 ml/sec), a dead time of 2.7 mSec for the short path length, and 6.7 mSec for the long path length can be computed. 0.2.5. Stopping Time — The ”stopping time" is the time required for the mixed solutions to come to complete rest after the flow has been stopped. It was measured by N. Papadakis (133) by studying the fast reaction; Fe+3 (0.01m) + SCN' (0.01 D) + FeSCN2+ (11.5) and monitoring the absorbance change at 455 nm. He found the stopping time to be reproducible and ~0.5 mSec under the experimental pushing pressure. - ,, , w- . , ,- _ - 1.. -, -.. _. , w __ ,, _ . ._ ..— 46 0.2.6. Mixipg Efficiency.- The mixing efficiency of the stopped- flow sytem was tested by G. H. H0 (132) and N. Papadakis (133) with the aid of a specific reaction. They mixed equal volumes of 0.2 mM p-nitrophenolate and 0.1 mM hydrochloric acid and followed the ab- sorbance change at 400 nm where the paranitrophenol absorbs. They found the resultant absorbance to be a flat straight line. This in- dicates the reaction which is diffusion-controlled (136). is over by the time the mixed solutions reach the observation point (i.e., the instrument dead time, m7 msec). Such a result could not have been obtained if complete mixing (100%) had not occurred prior to observation. The same results were also obtained by F. Halaka (99) and S. Elias (90) using different acid-base indicator reactions. 0. Data Collection, Calibration and Computer Graphics The stopped-flow system is interfaced to a PDP 8/1 computer for data acquisition. The raw data are stored on floppy disks for later calibration and analysis. The stored data can also be retrieved and displayed on a Tektronix Model 610 storage-display scope connected to a Tektronix Model 4601 hard-copy unit. This unit was used for visual inspection, preliminary examination of the results. and production of photocopies. This capability in the system allows the experimenter to examine the results from an experiment during the performance or anytime thereafter. The calibration procedure for the system involves collection of a set of neutral density filter spectra in order to calibrate the absorbance values. The spectra of holmium oxide and didymium oxide 47 glass filters are also collected in order to calibrate the wavelength in intervals. Data stored on floppy disks, including the calibration data. BFEIMIC on magnetic tapes and then transferred to the Michigan State University 000750 computer where kinetic and principal component analysis are performed. Calibration of raw data was performed as described in Appendix E of the Ph.D. Dissertation of R. Cochran (98).. Two dimensional graphics of this work were obtained by using program MULPLT written by Dr. T. V. Atkinson at Michigan State Uni- versity for the Chemistry Department PDP/ll computer. Computer pro- grams to transfer calibrated stopped-flow data from the 000 750 computer to the PDP/ll to be used in MULPLT. were written by Dr. F. Halaka and Dr. T. H. Pierce. Three dimensional plots were construct- ed by using program GEOSYS. available on the Michigan State University HAL routines. E. Analysis of Scanning Stopped-Flow Data Scanning stopped-flow experiments produce massive amounts of data. A general procedure for analyzing these data is as follows: E.l. Rate Equations - Program K1NFIT4 Finding the rate law(s) that fit the time course of a reaction progress curve is the first step in studying the kinetics of that reaction. K1NFIT4. an existing general non-linear curvefitting com- puter program was used for this purpose. This program is a modified 48 version of the program KINFIT originally written by Dye and Nicely in 1971 (137). Individual or simultaneous multiple data sets can be fitted to integrated or differential equation(s) in order to find the "best" parameters that fit the experimental results. The program also computes the estimates of the marginal standard deviations. which include the effect of coupling among the adjustable parameters. A detailed description of the program is given elsewhere (137). E.2. Weighted Principal Component Analysis (PCA) An essential step in data analysis is to determine how many de- tectable species occur in a reaction. This information. coupled with the rate law results obtained from the first step. can lead one to propose and explain a plausible mechanism that accounts for the ex- perimental facts about a particular reaction. The statistical method of Principal Component Analysis (PCA) is ideally suited for detennin- ing the number of light-absorbing species in a chemical reaction in rapid scanning wavelength kinetics experiments. The method of PCA was developed by Cochran and Horne (138.139. 140) and is discussed in detail in Cochran's Ph.D. dissertation (98). The method was successfully used by Dr. F. Halaka in resolving the reduction of cytochrome g oxidase by MPH (99). Neither mechanistic assumptions nor any assumptions about the spectral shapes of light absorbing species are needed to apply PCA. The applicability of PCA requires only that the response at each wavelength channel be a linear function of the concentration of each detectable species (Beer's law). 49 Two kinds of principal component analysis are useful for kinetic experiments. Each requires only the matrix A (with proper weights), and each gives a lower bound estimate of g; the number of independent detectable chromophores in the reaction. The first method, "Second moment matrix principal component analysis" or (M analysis). gives for q a lower bound estimate that is sensitive to the linear dependence of the concentrations of the detectable species. The second method. "sample covariance matrix principal component analysis" or (S analysis). gives for g_an estimate that is sensitive to the linear dependence of the time-rates of the concentrations. The two estimates of g_are not necessarily the same.and application of both methods enables one to discriminate between alternate mechanisms. The following example illustrates the application of M and S analyses, suppose: 1--.~‘\“‘. where A].A2, and A3 are three different absorbers. Application of M analysis to this mechanism would give qM = 3. since there are three absorbers in the reaction and all three change concentration with time (n0tice that a linear relation between the concentrations does not exist). However, mechanism (11.6) has the constraint: d[A3] . _ (d[A1] + d[A23) dt dt dt (11.7) 50 which says that the rate of one absorber depends upon the rates of the other two. Thus, for this example, application of S analysis would give gS = 2, since there are only two absorbers whose concentrations change independently of one another during the reaction. The PCA procedure along with its application to this work will be discussed in more detail later in Chapter VII. CHAPTER 111 "TRYPTOPHANASE INACTIVATION BY SUDDEN REMOVAL" OF K+ WITH THE AID OF A CROWN-ETHER OR CRYPTAND A. Introduction Inorganic monovalent cations such as K+. Na+, or NH; play an important role in biological processes. For example, they act as cofactors in transport. charge carriers in nerve impulses. and ac- tivators of enzymes. The latter is the basis of our interest in these cations. Monovalent cation activated enzymes fall into two main classes; those that catalyze phosphoryl transfer reactions. and those that catalyze elimination reactions. The latter group includes a subgroup of pyridoxal phosphate-dependent enzymes that catalyze 0,8-elimination reactions of o-amino acids. Tryptophanase from Escherichia Coli B/1t7-A is a member of such a group which also re- quires certain monovalent cations for catalysis (51). The spectrum of active tryptophanase above 280-nm contains ab- sorption maxima centered at 337 and 420 nm; their relative ampli- tudes are sensitive to the nature and concentration of monovalent cations andixipH (46.82). An absorption band at 420 nm dominates the spectrum of the inactive K+-free enzyme. A variety of experimental approaches are used to investigate the specific role of monovalent cations in maintaining the tryptophanase 51 52 structure as well as their mode of action in the catalytic processes. For example. on the basis of spectroscopic and ultracentrifugal experi- ments, Mornio and Snell reported differences between K+- and Na+- tryptophanase in the sedimentation rate of the holoenzyme. in the af- finity of the apoenzyme for pyridoxal-phosphate, in the spectrum of the holoenzyme, and in the rate of recombination of the apoenzyme with pyridoxal-phosphate (59,65). Suelter and Snell studied the effect of different monovalent cations on the kinetic parameters. Km and Vmax’ when using SOPC as substrate. They showed that each cation activates the enzyme, Li+ being the least effective and am- monium the best (77). Toraya et a1. established that K+ is absolutely required for conversion of the apoenzyme-pyridoxal-phosphate complex into the functional form (76). This was later supported by the work of Suelter and Snell who showed that with ethionine as substrate. the extent of formation of the quinonoid intermediate is linearly related to the maximum velocity observed with each cation (77). Despite these and a number of other studies on the subject, however. a de- tailed study of the kinetics of activation and/or deactivation of trypt0phanase has not been reported to date. Studying the monovalent cation activation of tryptophanase is made difficult by the following observations: (1) it is difficult to replace K+ with a less effective cation such as Na+ within a reasonable experimental time and simul- taneously observe the changes because tryptophanase shows a greater affinity for K+ than for Na+; (2) a suitable K+-free medium in which holotryptophanase remains stable for a period long enough to be ac- tivated has not been investigated or reported. 53 In order to gain some insight into the mechanism of monovalent cation activation/deactivation of tryptophanase. we used the stopped flow system1x1change immediately the concentration of monovalent cation (K+ in our case) and simultaneously follow the kinetics of the processes. For this purpose we took advantage of the selective ion binding properties of the two classes of macrocyclic compounds known as crown ethers and cryptands described in Chapter 1. l.4,7.10,l3,16-hexaoxacyc1ooctadecane. referred to as lB-crown-6. 18-06 or simply crown in the text. and 4,7,13,16,21.24-hexaoxe-l.10- diazobicyclo[8.8.8]hexacosane. referred to as cryptand[2.2.2] or 0222 (See Figure 1.7 for structural formulas) are both well-known complexants for K+ and were hence used in this study. This study made use of scanning and fixed-wavelength stopped-flow spectrophotom- etry. In a scanning experiment. digitized data are stored for the entire wavelength region spanned as a function of time. These data describe the kinetics of absorbance changes for every wavelength chan- nels at essentially the same time. The deactivation process was fol- lowed spectrophotometrically by noting the changes in absorbance at 420 and 337 nm as a function of time. results of which are reported in this chapter. 8. Experimental Section Trypt0phanase from Escherichia Coli B/1t7-A was prepared as des- cribed previously (123). Holoenzyme was prepared from stock apo- enzyme by incubation in 25 mM K+-Epps. pH 8.0, 1 mM EDTA. 0.2 M KCl, 54 20 mM dithiothreitol (DTT), and sufficient pyridoxal-p for 15 min at 50°C as suggested by Hfigberg-Raibaud et a1. (63). Protein concentra- tion was determined spectrophotometrically using €278 = 0.795 ml-- mg'l-cm-l (65). The enzyme had a specific activity of 50-55 °mole° min'A-mg'1 when assayed with 0.6 mM S-orthanitrophenyl-L-cysteine (SOPC) in 50 mM potassium phosphate. pH 8.0. 50 mM K01, at 30°C (123). The activated enzyme was then extensively dialyzed while cold against three changes of 15 mM bicine buffer at pH 8.75. 3 mM K01. 1 mM EDTA. 5 mM DTT. 5 pM PLP, with a total K+ concentration of about 17 mM. When cryptand[2.2.2] was used. the buffer contained tetramethyl-am- monium ion (TMA) rather than K+ for maintenance of ionic strength, and the initial pH was adjusted so that the pH after mixing with the enzyme solution would be 8.70. This pH was chosen in order to see a large change in absorbance upon activation/deactivation. The macro- cyclic crown ether. lB-crown-6, was recrystallized from acetonitrile as the crown-acetonitrile complex (126), vacuum dried. and sublimed under high vacuum for maximum purity. Cryptand[2.2.2] was also vacuum sublimed before use. A computerized double-beam rapid scanning absorbance stopped- flow spectrophotometer (91.92.96) was used either in the scanning mode to collect up to 150 spectra/second in the region 300-500 nm or in the fixed wavelength mOde to collect absorbance-time data at any desired wavelength. In either case. the stopped-flow system measures and stores data in progressive pairs of time points and their corresponding voltages. Through existing software programs 55 described elsewhere (98). each data pair was then converted to a calibrated absorbance and a corrected time. These constitute the final data used by KINFIT and PCA for all data fitting and analysis. Un- less otherwise indicated. all stopped-flow concentrations are the final values after mixing. All experiments were carried out at the ambient temperature of 24:1°C. 0. Studies and Results C.l. Equilibrium Studies In order to carry out the deactivation experiment with either 18-06 or 0222 properly. it was necessary to determine the effects of these reagents (if any) on the activity under assay condition as well as on the spectrum of tryptophanase. For this purpose. assay experiments were carried out under the same conditions at pH 8.0 with 18-06 or 0222 present at various concentrations in the assay mixture. The results showed that the activity is not affected by addition of 18-06 as long as K+ is present in excess. Cary 17 experiments also showed no significant effect due to presence of 18-06 on the spectrum of the enzyme under the same conditions. However. in con- trast to the absence of an effect of lB-Crown-G on the enzyme ac- tivity when K+ is present in excess. cryptand[2.2.2] decreased the activity by about one-third. This might be expected considering that cryptand[2.2.2] is a diamine and it is possible for it to inter- act with an ionizable group(s) on the protein near the active site and thus affect the activity. For this reason the effects of 56 different enzyme and cryptand[2.2.2] concentrations were not deter- mined by the stopped-flow. Nevertheless. a single stopped-flow experiment that used 0222 was done in order to qualitatively compare the results with those obtained with lB-crown-G. C.2. Kinetic Studies The deactivation process was studied as a function of the enzyme concentration at a fixed concentration of 18-06 and as a function ofla-crown-6 concentration at a fixed concentration of the enzyme. In all cases, the active enzyme at pH 8.70 was rapidly mixed in a st0pped-flow apparatus with a solution of lB-crown-6 which suddenly reduced the concentration of free K+ and thus caused the enzyme to deactivate. Both scanning and fixed-wavelength experiments were per- formed; however. kinetic analyses were usually done on data collected in a fixed-wavelength mode. This is due to the fact that. in a fixed- wavelength experiment. it is possible to collect more data points for a particular wavelength under study than is possible in the scann- ing mode because of computer memory limitations and the finite scan speed. The major overall process involves a decay of the 337 nm band of the active enzyme and growth of the 420 nm band of the inactive enzyme as expected from previous studies (81.82.89). These studies showed that the agtjyg_enzyme also has an absorption band at 420 nm whose intensity relative to the 337 nm band is pH dependent. The rate of interconversion of these two bands following pH jump and drop experiments and their role in catalysis were also described. 57 Figure 111.1 shows the overall changes in terms of initial and final spectra in a typical deactivation experiment. C.2.l. Deactivation Process as a Function of the Enzyme Concen- tratipn- This experiment was carried out at the four enzyme concen- trations indicated in Table 1. In all cases the enzyme solution was pushed against a solution of the same buffer that contained 18- crown-6 with a final concentration of 148 mM (after mixing). This crown concentration is large enough to reduce the free K+ concentra- tion from about 17 mM originally present to a final value of 1.06 mM. The final value of K+ free constant of 115 M"1 reported for complexation of K+ with lB-crown-6 was calculated from an equilibrium in aqueous solutions (119). neglecting the amount of K+ bound to the enzyme (KD = 1.44 mM). Figure 111.2 displays a 3-dimensional plot of the overall spectral changes from 300 to 500 nm that occur when a solution of 3.0 mg/ml tryptophanase is mixed with 148 mM 18-crown-6 (values after mixing). This wavelength region was chosen to insure simultaneous observation of the 337 nm y form and the resulting 420 nm 0 form (inactive). The principal changes in absorbance shown in Figure 111.2 are the decay of the active enzyme with maximal absor— bance at 337 nm. and growth of the inactive band at 420 nm as expected. Figure111.3cfisplays. in two dimensions, selected difference spectra from Figure 111.2 as a function of time, and Figure 111.4 shows the overall time courses at the two maximal wavelengths. 58 .Essuumam Fm:_e u As. .5236me 70.5.2. u ADV .5 34 u £982qu :8 .5508 22.05.85 asp c_ umnwcummc Empmxm zopeiumaooum any xn umuumFFou mam: mcaomam .m~.m In .cmewsn mcwown :5 mp cw Amcwxwa cmuwmv micZocoiw_ 25 me. »n mmmcmcaouaacu A2: mmv _E\me o m mo cowum>wpummu mcwczu coyom__ou espomam Facet use meuwcH ...... ecsm.. 59 ..... ecsm.. AEcv 59.2963 0N¢ 00a — 1.0N.0 I 00.0 0°00 P p P p p — p L p — F p — p . b . 36.. . .. I I - IIIIII P II 0 Ill-ll .1 I I O Illi- °*o°l. I I I 0 III! 1 I I I O 000‘. 1 36.. .o. 1.00.0 nun..u 1 . . . . . . a . _ . 00.0 eouquosqv 60 Table 111.1. Concentration of Various Species After Mixing in the K+- Drop (deactivation) experiment. Deactivation as f(E) Ca: 148 mM Deactivation as f(Co) Kfree o(iina1)= 1.06 mM E: = 2 mg/ml (36 uM) [ENZ], mg/ml [00], mM K;ree (final). mM 1. 0 (18 pM) 60.0 2.70 1.5 (2 0M) 61.0 2.67 2.0 (3 0M) 76.0 2.13 3.0 (55 0M) 112.2 1.42 148 1.06 ‘fi aCo is the total concentration of 18-crown-6. bE0 is the total concentration of the enzyme. 61 T: the 300-500 nm 6 C d't by lB-crown- . length surface in in Figure 111.1. (Cell path length - 1.85 cm. activation of tryptophanase Figure 111.2. Absorbance-time-wave 62 .omm omp .mm mumm mm .mv momm N.N_ .mm muom m .mm mumm e .om um.m mmswp .m.uomgm ucmaommaam soc. 5:.uowam um._m as» mcwpom.un:m x2 N.HHH c.3mw. 50.. umpoz.um:ou m.uumam mo:m.mewwc umuuumm .m.HHH m.:mw. «ES 59.0.2.2: 000 00¢ 0NQ 00» 0*” 00» 0‘00' » p . _ p _ . — - p . — p — p p p b b 0*IOII I IIIIII III. I a ONI°| i 00. 0.00 0.00.03 II on o- m II II 0 III. III. It, i 0000000 IIIIIIIouHL ... D IIII IOIIIIIOIIIu v Mn... . 36 a. occlindmoo . oaoumufiuoi N m u I I I I I Ion I I I I I I H I I I 1 m. I I I I I I I I I I a I D I I O I 0 Inn. 0 O I O u o I I I I I I I o a on o 1 . . .8. . . i on o a 0 Inn. 0 2.... . . . H . _ . . . a 4 . . . . _ . _ . 36 63 .N.HHu mgzmwm cw :zozm mguumam mg» 50;; :mxmg A v E: omq ucm on “mm um mucmngomnm mo mucmvcmamu mE_H .v.HHH mgzmwn «003 IE: on. cup no on on o r . — b — h — h — b — NPIO 1 «a... I I I O o O o 0 III w 00 I I. NnIo s 00 O O O r J o I q no mu I 00 l N‘Io a O. O O . . . . . . . . . .. 13.0 x I «0.0 64 C.2.2. Deactivation as a Function of l8eC£ Concentration - This experiment was carried out with an enzyme concentration of 2.0 mg/ml (36 HM) and five concentrations of l8-crown—6 (see Table 111.1 for the concentrations used) in order to determine the effect of free K+ on the rate of deactivation. In each case a solution of the enzyme in Bicine buffer at pH 8.70 was pushed against the same buffer to which had been added an amount of lB-crown-G to give the final con- centrations indicated in Table III.l. The overall changes of absor- bance were the same as those shown in Figure 111.2. Reducing the l8-crown-6 concentration, and hence increasing the free K+ concentra- tion, slowed down the effective rate of deactivation. For example, the process which is complete in less than two minutes in the presence of T48 mM l8-crown-6 is not completely over after about 3.5 minutes at the lowest crown concentration indicated in Table T. Figure III.5 shows the effect of different lB-crown-6 concentrations on the kin- etic profile at 337 nm. C.2.3. Results - Detailed examination of the deactivation process showed five distinct temporal regions as indicated in Figure 111.6 l. An "abrupt“ change in absorbance occurred which was too fast to follow by the stopped-flow method. These changes occurred during the 7 mSec dead-time of the instrument (l.85 cm pathlength cell). The changes in spectra during this time were obtained by subtracting the enzyme spectrum at t = 0 obtained by mixing enzyme with buffer in the absence of lB-crown-6, from the first spectrum collected after mixing (m7-l3 mSec). The changes in absorbance consisted of a 65 .czocu 25 oo Any .czocu :2 cu on .czocu 25 N__ Any .czogu :5 map Amy .F.HHH wczmwd cw mm mamm mg» mew mcowpwucoo .52 um um cowpm>wuummv we mum; wgu co m-czocunw_ Io mcowumgpcmucoo mzowcm> Io pummmm .m.HHH mczmwd «003 IE: 0‘... our 00.. on on 0“ ON 0 F . . . p . c . _ . . . _ . _ 2.0 u u u . . . . i and V I I I I q . . . . . .D I w . . . . . 1 3.0 W . . .3 I r W I I I I II o I I I I I I I onIo a I I I I \l/ I I U II II an m . . . . .. .. .. and I. I I? II II II j u . . ....I w . 5.2. ,. 3.0 Ix ... n¢.O 66 .P.HHH mczmwm c_ mm msmm an» mcm mcowp Imgucmucou .ouczogu-m— saw; m~.m :q we cmvmsn mcwuwm-+x cw mmmcmcaougzgp IoFo; Io cowpummg mg» mcwczu E: omq pm mocmcu mucmncomam Io mucmucmamu mewh .w.HHH mesmwd 67 eouquosqv 9.0 O N O m.HHH azsmwa one 8.: ON 0._ 0.0 _ 4 1 0v.0 9&0 mN.0 OS aouquosqv 68 generalized decrease in absorbance in the range of m325-360 nm with a possible peak at m340 nm, and an increase in the range m300-3l5 nm with a possible peak at m3l0 nm. The amplitude of this abrupt change was proportional to the enzyme concentration (AA20.025 per mg enzyme at 3l0 nm) and was constant at all concentrations of l8-crown-6 in- dicated in Table l. . 2. Following the abrupt changes a fast exponential change (burst) was observed which consisted of a decay at 337 nm (2.5:0.4% of the total change) and a growth at 420 nm (3.9:0.3% of the total change). The burst occurred at all enzyme concentrations indicated in Table 1, however, it was not detectable at low concentrations of l8—crown-6. The apparent first-order rate constant for the changes in this region at 337 and 420 nm were obtained by fitting the first three seconds of the absorbance vs time data at each wavelength to equation (III.l) by using the non-linear curve-fitting program KINFIT4 des- cribed elsewhere (l37). 420 nm} 337 nm (111°1) Aobs = A(o)ilAAexp (-két) i ct { g This equation combines the exponential change observed in this region and the changes of the following region which were found to be linear. The 3rd-term in equation (III.l) accounts for the contri- bution of the latter phase to the kinetic profiles at the two wave- lengths. The adjustable parameters were A(o), the absorbance change of the linear region extrapolated to time zero, IAAI, the absolute value of the change in absorbance between A0 (absorbance at t = 0) 69 and A(o), C, the slope of the linear region, and ké the apparent first-order rate constant for the burst. Relatively small and random residuals were obtained for the computer fit of the data to equation (III.l) at both wavelengths. This fit indicates that the equation used adequately describes the data. Figure 111.7 shows a computer fit of such data at 337 nm along with the residual plot for concen- trations of 3.0 mg/ml and l48 mM of the enzyme and l8-crown-6, respec- tively. The rate constants thus obtained are tabulated in Table 111.2. As the results indicate, the apparent lst-order rate constant is essentially independent of wavelength and enzyme concentration. Since the burst disappears at the lower crown concentrations, the dependence of ké (if any) on the concentration of lB—crown—G could not be determined. 3. The third temporal region of the deactivation process con- sisted of a linear decay at 337 nm or growth at 420 nm. This change occurred at all concentrations of both the enzyme and l8-crown-6. Inspection of the time courses at both wavelengths showed that this region lasts about 7 to l0 seconds in time, and so the data in this region were fitted to a linear function with K1NFIT4 in order to determine the effect of the enzyme and l8-crown-6 on the rate (slope) A of this change. Again, small and random residuals (A ) were calc obtained for the fit, indicating that the proper equation was used. obs" Tables 111.3 and 111.4 summarize the results of the analysis of this phase. 4. Most of the change in absorbance after Z_seconds (67:4% of the total change after the abrupt phase) occurs as a single exponential Figure 111.7. 70 (A) Fit of the burst and linear phases for the deactivation of tryptophanase by 18—C5 by Equa- tion III.l. X's are the experimental data points and the solid line is the calculated curve. Data collected in a fixed-wavelength mode. (8) Residuals of the fit shown in (A). Residuals are defined as A(calc)-A(obs). Conditions are again the same as in Figure III.l. Absorbance Residuals (x 103) 71 cam- (L59- ' com-- 050- osc- oss- 0'5‘ I l l T I I o 1 2 3 260 Tune (sec) . "‘ X Lao-a i‘ ‘ X 1.00 - "x x 52‘ ’°‘ " ‘ .x xx X x 0.20-- xxx)“, x x ._ ”K:§%q§ xxx): Xi x -o.eo - i "x x _‘ 1* X x 1X Xx -1.40 a ’5: -2I20 [x l T I 1 T o 1 2 3 Thne (sec) Figure 111.7 72 Table 111.2. Analysis of the Burst Region of the Deactivation Process by l8-Crown-6 in Bicine Buffer, pH = 8.70, at 24il°C. ki is the Observed lst-order Rate Constant for the Process. kéioa s‘1 kétoa 5“ [E0], mg/ml (A=337 nm) (A=420 nm) 3.0 (55 uM) 2.57: .60 2.14:.18 2.0 (36 uM) 2.80: .75 1.94:.23 1.5 (27 uM) 1.79: .50 1.85:.38 1.0 (18 0M) 2.80:].05 1.77:.23 AVE = 2.2:.5 Sec- l aMarginal Standard deviation. Each measurement is the average of two separate pushes. 73 Table III.3. Variation of the "Slope" of Linear Region of the Deactiva- tion Process as a Function of the Enzyme Concentration at Fixed Crown Concentration of l48 mM. Conditions of the Experiment are Described in the Experimental Section. Slope (337 nm) Slope (420 nm) [50], mg/ml x 102 s“ x 102 s" 3.0 1.42:.01 1.71:.01 1.40:.01a 1.751.01a 2.0 .97:.Ol 1.22:.0l .96i.0la 1.21:.01a 1.5 .73:.01 .92:.01 .7li.0la .91:.01a 1.0 .47¢.o1 .61:.01 .44i.Ola .59:.01a aSeparate pushes. 74 Table 111.4. Variation of the "Slope" of Linear Region of the Deactiva- tion Process as a Function of l8-Crown-6 Concentration at Fixed Enzyme Concentration of 2.0 mg/ml (36 uM). Condi- tions of the Experiment are Described in the Experimental Section. Slope (337 nm) Slope (420 nm) [co], mM x 102 s"1 x 102 s“ l48. .96 1.01 l.2l2:.006 .97 :01a l.2l6i.007a 112.2 .583:.004 .773:.003 .550:.006a .778:.003a 76.0 .255:.005 .354:.003 .278:.005a .356i.OOZa 61.0 .154:.005 .225:.003 .147:.005a .222:.003a 60.0 .l65:.003 .212:.003 .140:.004a .219:.004a aSeparate pushes. 75 decay (337 nm) or growth (420 nm). This phase was analyzed by simply choosing data points collected after'w7 seconds and eliminating data points that occur in the very last slow process. Data for this phase were fit by a single exponential equation (111.2): At = A00 1 AAexp (-kAt) (111.2) where Am, the absorbance at infinite time, AA, the total change in absorbance in this phase and k', the apparent lst-order rate constant, were the three adjustable parameters. Figure 111.8 represents a typical fit for this region at 337 nm, and Tables 111.5 and 111.6 list the values obtained for the rate constant, k', for this region. As indicated in Table 111.5, the rate constants for this phase are practically independent of the wavelength and the enzyme concentra— tion (except for a m20% decrease at the lowest enzyme concentration). It is important to note that the 420 nm band shows a slight but re— producible shift to shorter wavelengths during this time period. This shift was also reflected in the computer fit of the data at 420 nm as small but systematic deviations in the residuals at this wave- length. When the concentration of l8-crown—6 was varied, the resid— uals became smaller and more randomized at lower concentrations. This shift may imply that the 420 nm absorbing species produced at the end of the exponential stage is not the resting form of the in- active enzyme but that the final product has its peak at a shorter wavelength possibly around 382 nm. 5. Finally, a very slow exponential process following the 76 (DJZS - (3426 - a, 0.24- A g. u OI22 "‘ IQ 3 g, (DJZO - IQ " 0.18d (3516 - 0.14 1 f , , , 1 , 1 1 O 20 4O 60 80 Time (sec) 1.00 '- x I. x B '3‘ 0.60- x X c x '—' l x x x x x x X x x x x x >< 0.20 -‘ x X x X X X x X to J X {XX x X X X X X X “ x x x g -o.2o ~ x551} x x xx x 1: f ”a! " x 0. d x x «a x S; ao.60- x x ‘ x ‘1-00 1 r f 1 ' 1 ' 1* O 20 4O 60 80 Figure 111.8. Time (sec) Fit of the exponential region of the deactivation pro- cess by Equation 111.2. Conditions are the same as in Figure III.l. Again X's are the experimental data points and the solid line is the calculated curve. (B) Residuals of the fit shown in (A). 77 Table 111.5. Kinetic Parameters for the Exponential Region of the De- activation Process as a Function of the Enzyme Concentra- tion at Fixed Crown Concentration of l48 mM. t=24il°C. [E0], mg/ml k; (337)xl02 3'1 k4 (420)xl02 S'la 3.0 6.67:.02 7.51:.04 6.77:.02b 7.71:.04b 2.0 6.61:.02 7.64:.04 6.65:.02b 7.64:.04b 1.5 6.37:.03 7.44:.04 6.l0:.06b 7.45:.04b 6.33:.06c 7.03:.06C 1.0 5.06:.03. 6.15:.03 5.33:.03b 6.00:.03b 4.90:.03C 5.82:.08c aFit shows systematic deviations at this wavelength bDuplicate pushes. cScanning file. 78 Table 111.6. Kinetic Parameters for the Exponential Region of the De- activation Process as a Function of l8-Crown-6 Concentra- tion at a Fixed Enzyme Concentration of 2.0 mg/ml (36 uM). See the text for conditions of the experiment. Results are from duplicate pushes. 2 -1 2 4“” [C0], mM ki(337)xlO S kA(420)xl0 S l48 6.65:.02 7.64:.04 6.61:.02 7.64:.04 ll2.2 3.69:.0l 4.26:.02 3.69:.0l 4.27:.02 76.0 l.632:.004 l.96i.Ol l.657i.006 l.97i.01 61.0 .928:.005 l.l66:.005 .923:.003 1.183:.004 60.0 .920:.004 l.ll2i.004 .904:.003 l.l15:.003 aAgain fit shows systematic and non-random residuals at this A especially at higher Crown concentrations. 79 lst-order exponential phase occurred at all enzyme concentrations (Table III.l). Changes in the spectra during this stage involve decays centered at m443 nm and m330 nm and a simultaneous growth centered at N382 nm as indicated in the difference soectra of Figure 111.9 collected during this phase. The changes in absorbance were very small (m2.5% of the total change at 330 nm, (AA) 2 0.0l0 0.0.. 382 at the highest enzyme concentration), essentially about 3 times the signal/noise ratio in a scanning experiment at N400 nm. When the data in this phase were fitted to a single exponential equation by KINFIT, the same values were obtained for the rate constant at each 2 -l wavelength. The values thus obtained were l.4:0.3 x 10' Sec at 382 nm (growth), 0.8t0.4 x l0"2 Sec'1 at 443 nm (decay) and l.6i0.9 x 10'2 See" at 330 nm (decay). These values were calculated for data obtained at llZ and l48 mM l8-crown-6; the changes in absorbance at lower concentrations of l8—crown-6 were too small to permit a reasonable evaluation of the effect of concentration on the rate. The rate constants for regions 2 to 5 are summarized in Table 111.7. C.3. Kinetics of Deactivation by CryptandL2.2.2] The experiment with Cryptand[2.2.2]. or simply C222, was carried out in order to compare the results with those of l8-crown-6. Since K+ forms a much stronger complex with C222 than with lB-crown-6 (bind- ing equilibrium constant with K+ is 8.70 x l05 M'] for C222 compared to ll5 M7] for l8-C6), a substantially lower concentration of C222 was required for this experiment. An enzyme concentration of 3.0 mg/ml 80 .mgpumam ucmzcmmnzm Eogm AI :opmmgv omega copum>Fuummc _mpu:mcoaxm mg» we new asp um Ezcuuwam wzu m=_uomgun=m xn N. HHH mgzmwm :_ mmozu sop; vmuozgpmcou mgmz mguomam mg» .Am covmmgv mmmuoca cowam>wuummu on» 0o co_uw—asou asp an mcwggzuuo mmmcmzu meucmcoaxm 30pm «ES 23:20:: com oov out can cvn can b — b I — b b p — h p — h b b b J I I I I I II II ...I I I I I III II I k . . . . . . .u......n.... I......I. . L H I I I I I I I "IIIIIII IIIIHIIIIwu‘I ..l 1 I I I I I I I I I I III I memuI III I I I I "I IIIIIII OI I O .00 I C II III :1 I I II I. . . ... . O O I I I 1 T I. O . I IIIII O O O I II C O O C O O O 1 II .m.HHH mgamwu o_o.o1 wood: 0 a H wood... 0 V a. S wood 0 J a. w mood O a oped Bl .3825 :5 no 1:0 I... .I 85.1021 v5 . IE: “I 92.3321 ... 038.5% 2 E008 035 I 32... .-.: x a... n e: I ... 5: .-.: x ...... a 98 I ... a 8.9: as: .12 x a... A 1: I ... is... I .2331 3.8860 c.=onx:v :3 72 a... H I.» I ... .Gxisiu I .333“. 1:883. 83 ...: 8.: H 84 I ... a Set. 2.3 .1: 8.: H 93 I I .3033: I .3718» .32.: awaonwzv 8% + 88 3 H 3 I 4 33:7. I 3.??? E3 1255.5 A55 $680. .03 8:538 83— 3a— 23— 888.— 05 go ...—BIZ .pxah 6;“ :. umnwgummo mucwswgmaxm :aoco +¥= any we mppsmmm mzp $0 Accessm .N.HHH mpamk 82 (55 pM) and a C222 concentration of'vl6 mM (both before mixing) were used for this experiment. This concentration of cryptand was cal- culated to be large enough to reduce the concentration of free K7 tol.()mM after mixing, so that the data could be compared with those obtained with l8-crown-6 at the same enzyme concentration. As men- tioned earlier, since C222 reduced the activity of the enzyme (even at concentrations much below l6 mM), the effects of enzyme and cryp- tand concentrations were not studied. The general behavior with C222 was very similar to that obtained with l8-C6 except that no linear region was detected at this concen- tration of C222. Similarly, the 420 nm band shifted slightly toward shorter wavelength as indicated in the difference spectra of Figure III.lD collected for this experiment. A generalized double-exponential equation (111.3) was used to fit the data at 337 and 420 nm; At = A0° i AA]exp (-k{t) i AAZexp (-k't) (III.3) where Am, the absorbance at infinite time, AA1 and 0A2, the changes in absorbance due to the two exponential phases, and k; and ké, the observed first order rate constants for the two phases respectively, were the adjustable parameters. The equation seemed to describe the data relatively well. Figure III.ll represents the fit of the data at 420 nm to equation (111.3) along with the residual plot obtained for the fit, and Table 111.8 shows the values obtained for the rate constants. Comparison of the results with those of l8-crown-6 at the same 83 .uo_H¢N n H .Eu mw.P u space, sung Fpmu .umm No— .ec m0mm Pm .ov "0mm m.~m .wm "umm m.m~ .om muwm “.mp .em mumm N.NF .Nm mumm m.m .om mumm 0 .mm ”mcm mmewh .Amcwst mgommnv zs x.m_ u HNNNUH .Az mmv _E\me o.m u mszH ”mew mcowamgpcmucou .mN.w In as mewsn mzHuHm1<2H :5 m_ cw HN.N.NHu:mpaxgu zuwz mmmcmca0pa>gp mo :owuomwg asp mcwgzn uIHUIFFOU mguumam mocmgmwywu vmuom_mm .oF.HHH 6.3600 84 cow _ SJ: 953... «ES 59.2962 owv can b _ con 1 8.9.. 1 3.? IAXYO I.AYo IMXYO 1.Nfd II I I b I I IIII L I II I. I IIII I J I I I IIIIIIIIII II I IHIIIIIII IIHIIIJI .I I] IIIHIIIIIIIIIIIII//” III I IIIIH . 60.....07 , I I II-mHIIIII IIIIIIII” O n O I I I I I u q.” - I H H I I I IQNI I I I n n u u I. ~ . O O I C I .l u H I I I I IOWI I I I I H I II. N I I I I INHI I I I I I I I I I I I I I H I I I ItnI I I 1 I I I I I I I I. I I IDOI I I I I I L I I IQWI I I I I I IO¢I I II. C O Iva I - I — I - I — I «for aouquosqv onea 85 Figure III.ll. 0.22-1 .D '0.18 '1 ‘3 ‘3 61. A <> . «a 9) a -I ‘<: ‘0.10 -' 0.06,.T.,.r.l,j O 20 4O 60 80 100 Time (sec) 1.00- x x ,3" moo-g: B 2 - x . O.2£l-* 15* x x)! x x >< 1“ IIX \Ip -‘ k W X x XX x x x X ‘5 )(x x "x x 2 -O.20- x! x "‘ e .1 x =’ x :2 --O.60-"x 3 “g °‘ -1.oo- '- x -‘I‘o I I T I I I ' I r T 1 0 20 4O 60 80 100 Time (sec) (A) Fit of the overall absorbance change at 420 nm (subtracting the tail) for the deactivation of trypto- phanase by C222 by the double exponential Equation III.3. Conditions of the experiment are the same as 2n)Figure III.lO. (B) Residuals of the fit shown in A . 86 Table 111.8. Kinetic Parameters at 337 and 420 nm for the Deactiva- tion of Tryptophanase by Cryptand [2.2.2]. The data were fit to Equation 111.3 in the text. ---Wavelength--- ---Two Exponentials--- I. 337 nm ki(S']) ké(S"1) 2.44:0.28 (2.96:0.01)x10’2 2.64:0.29 (2.90:0.01)x10'2 11. 420 nm _2 1.72:0.07 (3.70:0.01)x10 2.09:0.07 (3.78:0.01)x10’2 AVE = 2.2:0.4 87 enzyme concentration (Tables 111.2 for k; and 111.5 for ké) shows that k{, the rate constant for the burst, is the same for both complex- ing agents, however, ké values are smaller in magnitude when C222 is used. This difference could be due to a buffer effect (Since TMA+ is present in the C222 buffer) and/or an inhibiting effect of C222 on the enzyme similar to that observed in the assay measure- ments. Similar to the crown experiments, a very slow process also followed the second exponential phase with absorbance changes at the same wavelengths, i.e., decays centered at m440 and 330 nm, and a growth at 382 nm. Figure III.lZ displays the spectral changes col- lected during this phase when C222 is used. Since at this cryptand concentration the changes were small and there were not sufficient data points to allow a reasonable computer evaluation of this phase, another experiment with a cryptand concentration of 30 mM (before mixing) was performed in order to analyze these changes. When the data were fit to an exponential equation with the KINFIT program, the same values were obtained again for the rate constant at each wavelength [0.9:0.4 x 10‘2 Sec“ at 382 nm (growth), 0.7:0.1 x 10'2 '1 at 335 nm (decay). and 1.03:0.03 x 10'2 '1 Sec Sec at 443 nm (decay)]. The values are practically the same as those obtained with lB-crown-6 and again seem to suggest that the 420 nm form produced is not the final product of the deactivation process. It should be mentioned here that cryptand [2.2.2] at the latter concentration completely deplets free K+ and thus strictly speaking, the data here cannot be compared to a similar case for l8-crown—6. .umm: mI onczoLUIw. can: mmmcmzu mEmm asp mcwzozm m.IHI mgzmwu :IIz umcmaeou mg on m_ mesme mwch .m~.~.mgvcmuaxgu new mmmcmca -ougxep :mmzpmn cowuummg mg» me new mnp In mcwggzuuo mmmcmgu Imwpcmcoaxm zoIm .N—.IHH mgzmwm «E5 59:20.63 con 00% ONI can ctn can I - p p I — I L I — I P L — I — I P I J—l NPOIOII .l I I IIIIIII I fl 4 I I I I I IIIIIIIIIII a I ”00.0- I I III. 4 I I I I I I I H II IIIIII II‘I'II x m 8 I I I I I I “I I IIIIII‘I II *OCICI “ 8 I I I I I I I I I II IIIII II It! D [I u I u I I I I I III I III I r mm.“ ..I .. [89° W . . I." 4 .0; I9 I I I I I n J . . . . . . . .. r .85 a. I I I D .I. I I I I fly u I I I I I o I I I I I I I II ”00.0 8 I4 I I I I I ... ... I I I I II NFOIO . _ I _ . I 14 _ . I . _ . I . I . I . 89 0. Discussion and Conclusions The kinetic studies of tryptophanase deactivation with the aid of l8-crown-6 or cryptand [2.2.2] provide some insights into the interconversion of the active to inactive enzyme. Inspection of the results presented in Tables 111.3 and 111.5 shows that the rate of deactivation is proportional to the total enzyme concentration and to' the square of the lB-crown-6 concentration (see also Figure III.l3) during the linear region of the process. If E0 and C0 are the initial concentrations of the total enzyme and l8-crown-6 respectively, then the rate of this process can be represented as d(E t' ) 2 a§t1ve = -k3(Eo)(Co) . (111.4) To find k3 from the data presented in Tables 111.3 and 111.4, we can rewrite equation (111.4) in terms of absorbance such that d(E [ active) = 1 d(M337 _ (510p9)337 = k (E )(c )2 (III.5) Solved for k3 equation (111.5) becomes (k3)337 = (slope)337/e337-b-(E0)(CO)2 (111.6) Similarly at 420 nm we have 90 .cowumgpcmucoo o-:zogo-mp Io wgmscm mcu co mmmuoga mg» Io A V cowmmg Immcwp Io mao_w wnp use Axv mmmuoca cowaw>wpummu mzp Io cowamg meucmcoqu mg» go» Icmumcou mum; ImugouumI ucmgmagm mcu Io mucmucmamo .m_.III mgamwm «3:5 . n13 x was—30» cJN Qua ch od— 96— 0.: o.N— 06— o.» 0.0 04 o.~ cIo IIII—IIIb—IIILPFII—IIIIpbIIIPIIIIbIIII—PIIIpIIIbbrbIb °I° I 1 n.o «.0.4 1 10.— 5 ..OJ InIF x mu 1 , 1.c.« .v Au . n1 I was Ina I X I . X c.c.4 I o n l 1 linIn m nu 7v c.I.J I ogv 79 In: Ind S 1 106 . TI: 1nd 1 10.0 c.—1 1 1nd cI— ...:.1....«......1......_ ... ......._ ... .... ... ... ......._ ...4 9.5 91 (k3)420 = (slope)420/e420-b'(EO)(CO)2 (111.7) -l. —l -l, -l Values of 3500 M Cm for £337 and 4600 M Cm for 8420 obtained from previous studies (82) and a cell path length of l.86 Cm (b) were used. The rate constant k3 was found to be l.85:0.08 '2 Sec" at 337 nm and 1.91:0.09 11'2 Sec" at 420 nm. We assumed M that the extinction coefficient at 420 nm of the inactive species formed in the reaction is the same as that of the 420 nm active species. The fact that the same value of k3 is obtained at 420 nm and 337 nm when using this assumption, might suggest that the coenzyme form which gives rise to the inactive 420 nm absorption is in fact similar in structure to the active 420 nm forms (EB,EBH+ in Figure 1.4) but is bound in such a way as to prevent direct interaction with groups necessary for catalysis at the active site. The data obtained in the exponential region show that while the observed rate constant for this region is essentially independent of the enzyme concentration (Table 111.5), it depends again on the square of the l8-crown-6 concentration (Table 111.6, also Figure 111.13). Similar dependence was also observed qualitatively when cryptand[2.2.2] was used. Thus, the rate equation for this region can be written as 91%%§1 = -k4(Abs)(Co)2 (111.8) To find k4, we used only data obtained at 337 nm (Table 111.6) since the computer fit of the data at 420 nm during this time period showed small (l0.4 to l0'3) but systematic deviations due to a slight shift 92 of the 420 nm band to shorter wavelengths as indicated earlier. The results (excluding the lowest enzyme concentration) give a value of 2.8:0.2 M“?- Sec"I for k4. The systematic deviation at 420 nm may indicate that the change of absorbance at this wavelength is perhaps not due to a single process involving growth of the inactive 420 nm form but other slow processes involving species absorbing at or close. to this wavelength may also be occurring during this time period. The fact that the residuals of the fit at this wavelength are greater in magnitude and are more systematic at higher concentrations of l8- crown—6 where the final slow changes (decay at 443 nm, growth at 382 nm) are observed, indicate that the latter process may be going on during this time region. In addition, one would expect that the 420 nm form of the active enzyme which is present to an extent of l5 to 20 percent at this pH (83), also converts into the inactive form(s) absorbing at the same wavelength and thus addsixathe complexity of the analysis at this wavelength. The mechanism of deactivation of tryptophanase by control of free K+ concentration is complex and the results described indicate that multiple enzyme forms are probably involved. Since l8—crown-6 reacts with free K+ very rapidly (Kf = 4.3 x l08 M'l-Sec'l) (l48) we expect essentially instantaneous reduction in the free K+ concentration in a K+-drop experiment. The abrupt changes observed during the dead- time of the instrument are perhaps due to the immediate perturbation of the enzyme spectrum caused by sudden removal of potassium ions. Qualitatively similar changes have been observed earlier during the pH-drop experiments (83) which may indicate that sudden removal of 93 K+ by crown or cryptand causes deprotonation of an amino group at or close to the enzyme active site resulting in an immediate "local" pH drop, thus perturbing the enzyme spectrum. The changes observed in the exponential burst region (region 2) seem to suggest a perturbation in the equilibrium distribution of the 337 and 420 nm active species in favor of the 420 nm species before deactivation takes place. The apparent rate constant obtained for this region in both crown and cryptand cases, k = 2.2:0.5 Sec'], is similar to the observed fast first—order rate constant for the inter- conversion of the 337 and 420 nm forms, 1.41 Sec" , obtained by 0. June (83) at a similar pH. In addition, the ratio of the magnitude of the absorbance change at 420 nm to 337 nm (AA420/AA337) compares favorably in both cases; being l.32 in the pH change experiments and l.47 in the deactivation experiments. Zero-order kinetics are typically observed in surface catalysis where the concentration of the catalyst is very small. The zero- order decay observed here after the burst phase and before the onset of the first-order kinetics thus suggested catalysis by a minor species whose concentration is proportional to the total enzyme concentration. In the buffer system uSed for the experiment, the only species which may be available at very low concentration relative to the enzyme is pyridoxal-p. We expect a substantial change in the rate of deactiva- tion as the concentration of PLP in solution is changed if it is in- volved as a catalyst for the conversion process. To check this, a similar experiment was performed at a substantially different PLP concentration (25 mM PLP). There was no effect on the rate of the 94 reaction, thus, eliminating the possibility of catalysis by PLP. The zero-order process, however, may be explained qualitatively if one considers that the deactivation occurs simultaneously with a redistribution process involving the 337 and 420 nm forms. Recall that the relative concentrations of these two forms had been altered during the burst phase. The redistribution process may occur during this time region (region 3) if one assumes that the potassium-crown complex is released slowly from the enzyme. The release of the (K+C) complex would allow diffusion of the buffer into the enzyme active site, thus, causing the described redistribution process. This explanation is drawn from the fact that the magnitude of the experimental absorbance change during the linear region is always less than that calculated by using the exponential deactivation param- eters (region 4) by a magnitude equal to that of the burst absorbance change (region 2) at all concentrations in which a burst was detected. However, the data could not be quantitatively accounted for by this hypothesis in the absence of information about diffusion rates. The second order dependence of the rate of deactivation on the concentration of l8-crown-6 strongly suggests that two potassium ions per subunit are required for activation, consistent with the binding of two thallium(1) ions per subunit as reported earlier (77). The slow exponential changes at the completion of the deactivation pro- cess (region 5) observed with both l8-crown-6 and cryptand suggest that the 420 nm species formed is not the final form of the inactive enzyme. However, partial dissociation of pyridoxal-p from the enzyme may also be occurring during this time region. Principal component 95 analysis (PCA) indicates the existence of at least three independent absorbers in the system. This and other PCA results will be discussed in Chapter VII. CHAPTER IV TRYPTOPHANASE ACTIVATION BY CONTROL OF FREE k+ CONCENTRATION - K+ JUMP As described in the previous chapter, there are two forms of holotryptophanase, a form that absorbs at 420 nm and one which ab- sorbs at 337 nm. The latter form is observed only in the presence of activating monovalent cations such as K+ and NH: and at sufficiently high pH values, while the former is dominant at low pH values. An absorption band at 420 nm also dominates the absorption spectrum of the K+-free (inactive) enzyme. Thus, in order to study the kinetics of interconversion of the inactive enzyme conformer(s) into active conformer(s), one needs to prepare the enzyme in a medium that is free of activating monovalent cations, and keep it "stable" long enough to be reactivated by mixing with an activating cation. For this purpose, we first attempted to prepare the enzyme in the presence of tetramethylammonium chloride, (CH3)4NCl, and then mix it with a solution of K+ ion to reactivate it. The following section describes the en- zyme stability and spectral studies in the presence of (CH3)4NCl done in search of finding a suitable medium for such an experiment. 96 97 A. Studies in the Presence of (CH314WC1_ A.l. Methods, Tryptophanase from E-Coli Blt7/A was prepared as previously des- cribed (l23). An “ll x 2" cm Sephadex G-25 medium grade column was used to prepare the enzyme in the presence of tetramethylammonium ion. The column was packed and equilibrated with a (CH3)4NCl buffer containing 25 mM Epps, 50 mM (CH3)4NCl, 2 mM EDTA and 2 mM dithio- threitol (DTT) titrated to pH 8.0 with tetramethylammonium hydroxide, TMA-OH. The TMA-OH for the titration was prepared by passing 50 ml of a 1 molar solution of recrystallized TMACl over a Dowex-l-OH column. To prepare tryptophanase in the TMA-buffer, an aliquot of the apo- enzyme precipitate in 9 % saturated ammonium sulfate buffer at pH 7.0 was centrifuged, decanted,auuithe precipitate was dissolved in 0.l-0.l5 ml of the activation buffer. The latter buffer contained 25 mM K+-Epps, pH 8.0, 1 mM EDTA, 0.2 M KCl, and 20 mM DTT but no pyridoxal-phosphate. The enzyme typically had a concentration of N30 mg-ml'] at this stage, measured spectrophotometrically at 278 nm with 8278 = 0.795 ml°mg"]ocm"1 (65). This solution was then loaded into a Sephadex column that had been preequilibrated with the TMA- Epps buffer and was subsequently eluted with the same buffer. Frac- tions which contained the enzyme were pooled for the experiments. The apoenzyme had a typical concentration of 2 mg-ml"1 at this stage. 98 A.2. Stability Studies The stability of tryptophanase in the presence of tetramethyl— ammonium ion was checked at different concentrations of pyridoxal-p and dithiothreitol (DTT) to find a suitable medium for the enzyme. Since pyridoxal-p absorbs in the same spectral region as the enzyme (maxima centered at 390 and 330 nm corresponding to the aldehyde and hydrated forms of pyridoxal-p, respectively), an "ideal" medium would be one in which no excess pyridoxal-p is present to interfer with the spectral forms of the enzyme. For this reason, the enzyme collected from the Sephadex column in the TMA-buffer was made equimolar in pyridoxal-p and then activated. The specific activity of the solu- tion was then sampled at different times as a measure of the enzyme stability. The results showed that tryptophanase in the TMA-buffer with the same PLP concentration as the enzyme and a DTT concentration of 2 mM is unstable and gradually looses activity; up to 65 percent in a period of 2 hours. To see whether the activity loss is due to dis- sociation of PLP from the enzyme, a two-fold excess of pyridoxal-p was added to the above solution which was then heated at 50°C to be reactivated. The resultant solution showed no gain of activity which suggests that PLP is not dissociated from the enzyme. However, when the same solution (no excess pyridoxal-p) which had lost 65 percent of its activity was made 20 mM in DTT (the reducing agent), the en- zyme regained about 45 percent of its activity but again lost it with time. When the same partially deactivated enzyme solution was 99 reactivated in the presence of excess pyridoxal-p and DTT, the enzyme regained most of its activity and retained it for about five hours. Gradual loss of activity occurs at longer times. Thus, it seems that the activity loss of the enzyme in this system is at least partially due to oxidation of the -SH groups on the enzyme, essential for enzymatic activity, rather than dissociation of the coenzyme, pyri- doxal-p. When the enzyme activity loss in the original solution was allowed to proceed for longer than 2-3 hours, the activity could not be recovered by addition of excess PLP and DTT. The results, there- fore, showed that the (CH3)4NCl-buffer, containing 2 mM DTT and equi- normal pyridoxal-p and enzyme, is not a suitable medium for keeping tryptophanase stable in the absence of activating monovalent cations. Next,the stability of tryptophanase in the same buffer solution but in the presence of either excess pyridoxal-p (100 uM) or DTT (20 mM) was investigated. A 2.0 mg-ml'1 solution of the apoenzyme in the TMA buffer prepared as before was divided into three portions. The first solution was made equinormal in PLP (40 pM) but excess in DTT, the second solution excess in pyridoxal-p but low in DTT (2 mM) and the final portion was made with excess pyridoxal-p and DTT to be used as a control solution. All solutions were activated by heating in a 50°C water bath and their activities were subsequently monitored. The two former enzyme solutions gradually lost their activities; up to 80 percent in a period of five hours, while the control solution was stable during this time period. When excess pyridoxal-p was added to the first solution after the activity loss, the regain of activity was found to be consistently higher than that of the second solution 100 after addition of excess DTT. In neither case could the activity be fully recovered. (Specific activity under assay conditions was used to monitor the activity recovery.) The results suggest again, that loss of the enzyme activity in the absence of activating monovalent cations is at least partially due to oxidation of the -SH groups on the enzyme. Finally, the stability of tryptophanase in the presence of TMA ion was investigated by preparing the holoenzyme first, followed by passing the solution through the Sephadex column. The enzyme was eluted with a similar TMA-buffer solution which contained 20 mM DTT. The results were similar. The enzyme lost 40 percent of its activity by passing through the column and an additional 20 percent activity loss occurred in a period of six hours. When such a solution (de- activated for less than 2 hours) was reactivated by addition of potassium ions, the enzyme regained and retained its activity. How- ever, if the activity loss proceeded for longer than six hours, full activity could not be restored upon addition of K+ ions. A.3. Spectral Studies The stability of tryptophanase in the presence of tetramethyl- ammonium ion was also studied spectrophotometrically with a Cary l7 spectrophotometer. A 50 0M solution of apotryptophanase in a TMA- Epps buffer at pH 8.0 (2 mM DTT) was titrated with pyridoxal-p up to the stoichiometric point by successive additions of 5 pt increments of a 2 mM PLP solution. Formation of the holoenzyme complex was followed by growth of the absorption band at 420 nm. The magnitude 101 of the absorbance change was found to be directly proportional to the concentration of pyridoxal-p in the solution as shown in Figure IV.l, which indicates a tight binding of pyridoxal-p to the enzyme in this system. No other changes occurred during the titration in the wave- length region scanned, 320-500 nm. Monitoring the holoenzyme spectrum after saturation with pyridoxal—p (50 pM) showed no significant de— crease in absorbance at 420 nm which would be expected if pyridoxal- p slowly dissociated from the holoenzyme. This confirms the stability studies which showed that addition of excess PLP to the enzyme in this buffer cannot restore the lost activity. A similar solution of apotryptophanase in the same TMA-Epps buffer was further titrated with pyridoxal-p to see whether the excess pyri- doxal-p, which is required to restore the enzyme activity in the presence of excess DTT, remains free in solution. The titration was carried to l00 pM pyridoxal-p (two fold excess). The results were indicative of two binding sites for pyridoxal-p on the enzyme; a bind- ing site which gives rise to an absorption band at 420 nm as indicated earlier (Figure 1V.l) and a second site that yields an absorption band centered at 355 nm after completion of the first process. A difference Spectrum, obtained by subtracting the spectrum at saturation of the first binding site (50 pM PLP) from the final spectrum (l00 uM PLP), is shown in Figure IV.2. The spectrum of 50 pM pyridoxal-p in the same buffer is also shown for comparison. If the excess pyridoxal-p had remained free in the solution, the two spectra would be super- imposable. The fact that they are different suggests the existence of a second set of binding sites on the enzyme for PLP, as 102 .coIImIIII ocoowm a EOLI cwcmmuno mew Aaupmxocnga z owuoov cowumgzumm Imumm mpcwoq .2: om mm: mechm esp Io eOIIesIeeoeeu .IIo :5 o.~ .o.m :6 om IIIIze-_uzeAmzuv eI e-_exoeILI6 eIIz mmmcmcaowaxguoam Io cowumguwp con: 5: omc um spzogm mucengomnm one we wucmvcwamo «25 0126x6230 0.00 0.00 0.0x. 0.00 0.0m 0.0+ 0.0m 0.0a 0.0— 0.0 Hi I I — I r I _ — .F.>H szme 86 wv 36 a. S o J q . 0 So u 3 a . ) «S .7 7o nu 2.0 u mm /l\ 0N0 103 .mewzn mEmm Isa :I :4: z: om Io Ezguumgm 20v .o.w I: am :mIIsn maau1<2I :w HAQJQ z: omv mechwIA64: 2: copy mE>~:mH .ai_mxocw:aa mmmuxm :Iwz mmmcmcaouax:u loam mo :owuzpom z: om m we :owpmgpwu mcwgsu umcwwuno Ezguumam mucmngmIo on «E5 50:266.: 00.0 «0.0 I;0.0 00.0 00.0 0—.0 Nw.nv I.P.0 0.3.0 00¢. one 0¢¢ 0N¢ _ nxuv P own. b 000 I 0¢n. .N.>I eezmwd own III T r T r 00.0 «0.0 #0.0 00.0 00.0 0P.0 NF.0 ¢P.0 0—.0 eouquosqv 104 evidenced by the growth at 355 nm. The stability and spectral studies clearly show that pyridoxal-p does not dissociate from the enzyme in the presence of tetramethyl- ammonium ion and 2 mM DTT. However, tryptOphanase gradually loses activity probably due to partial oxidation of the -SH groups on the enzyme. The stability studies show that a (CH3)4NCl-buffer with both_ pyridoxal-p and DTT present in excess can be used to keep tryptophan- ase relatively stable in the absence of activating monovalent cations and, thus, might be employed in the reactivation kinetic studies. Further studies revealed, however, the following problems associated with such a buffer system: l. Activation of tryptophanase in this buffer by addition of saturating amounts of potassium ions gives only small absorbance changes, 00.0. = 0.0l2 per mg of the enzyme at 420 and at 337 nm. The change is even smaller for lower K+ concentrations which makes the study of the K+ dependence of activation nearly impractical. 2. The deactivation process, to exchange K+ ion for the (CH3)4- lt+ ion on the enzyme, is not feasible because tryptophanase has a higher affinity for potassium ion than for tetramethylammonium ion. 3. Activation experiments should be completed in less than five hours, otherwise, the enzyme irreversibly loses activity. Scanning stoppped-flow experiments, however, require an: least a full day of experimentation. 4. The amount of pyridoxal-p which may remain free in the solu- tion cannot be measured and, thus, a proper baseline cannot be de- termined. 105 5. Pyridoxal-p reacts with dithiothreitol (DTT), another component of the buffer solution as indicated by changes in absorbance at 390 and 325 nm. To measure the extent of this reaction, a 50 MM solution of pyri- doxal-p in the TMA-Epps buffer at pH 8.0 was titrated with a 0.2 molar solution of dithiothreitol as indicated in Figure IV.3. An equilibrium constant of 15.1:l.0 mM"1 was calculated for reaction 1V.1 by KINFIT. A possible scheme for this reaction is presented in Figure IV.4. Since the spectral changes associated with this reaction occur in the same wavelength region as those of the enzyme (see Figure IV.3), use of such a buffer system adds complexities to the enzyme spectral changes in the activation experiments. Because of these problems associated with the TMA—buffer (excess pyridoxal-p, excess DTT), we decided not to use such a system in the stopped-flow reactivation studies. To carryCNHlthe activation experiments, we finally decided to use 18-crown-6. To circumvent the loss of stability of the enzyme in the absence of monovalent cations, the activation process was studied by mixing a solution of the enzyme, freshly deactivated by addition of complexant l8«crown-6 with an excess of K+. This technique proved to be a useful new tool for the study of enzyme activation by mono- valent cations. The remainder of this chapter explains time results obtained from such stopped-flow activation studies. Cryptand[Z-Z-Z] was not used in this study because of its effect on the enz)’me ac- tivity as discussed in Chapter III. 106 .IoacIIm Ibo comm Io :owuwvum :wIIm mapscIs xpcmzp .Imumsopocaoguumam up xgmu m :IIz Imugoum: mgmz mgaomam och .o.w I: II LIIIsn mgamnpuzcfimzuv :I AIIQV Fouwmgcp Iowsumu saw: aupmonIan 2: cm 00 :owpmguwp mcwgzu umcwmuao mmmcmzu PIIIUIQm .m.>H mgzmwm Ea: 00m 8m owe 8v 8m .kph_<€:.0N .._L.0 SE 0. 0::uezc_mg .hIhueanm ....5 EE 6. LI:u_2:Im“ 0120.24 ¢9IIODD aouquosqv 107 .Appov Fouwmgguowcuwu ucm A64av wpmgamoca-ImxouI:xa :mmzpmn :owuumm: 6:0 Low memgom umummmmzm < .¢.>H mgzmwm 2H 65669 mmm .onx 08 .652 2285 CR: :33 II II III.ll «IoinfoxoTNIo + _ ..o \ -o \ m m \ wk 6 IO OI 108 B. Stopped-Flow Studies of Tryptophanase Activation_by K+ 8.1. Experimental Procedure A solution of holotryptophanase in K+-bicine buffer at pH 8.70 with a total K7 concentration of 17 mM was prepared as previously described(123,(fimpter 111). The enzyme had a specific activity of 50 p-mOl-min’1 .mg'1 when assayed with 0.6 mM S-orthonitrophenyl-L- cysteine (SOPC) in 50 mM potassium phosphate, pH 8.0, 50 mM KCl, at 30°C (123). Prior to a push, the enzyme was diluted with dialysis buffer to 4.0 mg-ml'],deactivated by lB—crown-6 (18C6) and subsequ- ently pushed against various concentrations of free K+ as indicated in Table 1V.1. A stock 1 molar solution of lB-crown-6 was used to reduce the free K+ concentration in the enzyme solution. All soectra were scanned over the wavelength range 315-540 nm. The experiments were carried out between 10 and 40 minutes after addition of l8- crown-6 at the ambient temperature of 23:l°C. 8.2. Results The kinetics of activation were studied in both scanning and fixed-wavelength modes. Figure IV.5 shows the spectral changes that occurred when a solution of freshly deactivated tryptophanase was pushed against a saturating concentration of K+. Concentrations of the enzyme and free K+ after mixing were 2.0 mgoml'1 (36 uM) and 33.0 mM, respectively. The spectra show the simultaneous growth of the active enzyme (at 337 nm since pH = 8.70) and the decay of the 109 Table 1V.1. Concentration of Various Species (After Mixing) in the Stopped-Flow Studies of Tryptophanase Reactivation by K+ (K+ Jump). E0 = 2.0 mg.ml' (36 uM) for all experi- ments. lB-Crown—6 K;ree (initial) K;ree (final) (mM) (mM) (NH) 50.5 0.7 3.0 50.5 0.7 7.5 62.5 0.5 11.6 67.0 0.5 16.0 69.5 0.5 18.7 70.0 0.5 19.2 70.0 0.5 24.2 70.0 0.5 33.0 aaaaaaaaaa 111 "inactive" enzyme (420 nm). The difference spectra taken from Figure 1V.5 are compared with similar spectra during K+ removal (deactivation) in Figure 1V.6. As shown in this figure, the overall spectral changes are essentially the reverse of those which occurred during the K+ removal with one important difference. Even in the presence of saturating amounts of K7, only about 50 percent of the 337 absorption was receovered and a corresponding fraction lost at 420 nm. Similar experiments by using a Cary 17 spectrophotometer where the activation was allowed to proceed for longer times showed only a small additional recovery (less than 10 percent) in a period of about 1 hour. In spite of this apparent spectral irreversibility, however, separate experiments showed that 100% of the enzymatic ac— tivity could be recovered by adding K+ to the deactivated enzyme. The rate data at 420 and 337 nm were analyzed by the program K1NFIT4 using appropriate rate equations. B.2.l. Absorbance Change at 337 nm - Inspection of the difference spectra, obtained by subtracting the Spectrum of the inactive enzyme from other spectra, showed no detectable fast change at this wave- length at the start of the reactivation. The overall process is slower than K+ removal so that the reaction is not complete in over 4 minutes of data collection time. At saturating K+ concentrations (above 16 mM), the growth in absorbance at this wavelength was fit to within random errors by three exponentials with the rate constants k], k2 and k3 essentially independent of the free K+ concentration. Equation IV.2 was used 112 .AIIIQ mucoumm mew ucm o.mm .w.m_ ccm Auuiv mucoumm om_ ucm m.m_ .o.v III ogpumam m>wusuwmcoo Io mmEII .A v 25 o.mm .+¥ 50:0 6:6 .IIIV z: mep mmiczogu Twp I_E\ms o.~ .mmocm::OIqxgu .IIIZ mcwst :muwm mcowpmgucmucou .0111v acme TILmaxm =aszn Inc :I mmmcmcu = 6:6 AIIIV acmEILIme egocu +¥= 5:0 mcwgsu cm>gmmno mo:mn:om :Ipcmmmgq moswp ucmngIIu mags» In ocuumam 60:5:50va umIUIIIm .e.>: eesmId H3 o.>H mg=m_u AES 59.2995 000 00¢ - q own ONm \/ \ / \ I x x \ ‘... s \. .1 \ \ . ~ \ s\\ \\|’ \\ \ . x \\ [Nil \\ [Ill \\ \~ I I. x. x ’ / .x‘x \ I, ,x/ x. x I I....\ ~ I x I \ z \ / \ ONO: O_.O .. 0.0 9.0 ONO. aouquosqv ouag 114 to fit the data at saturating K+ concentrations. 3 Aobs = Aco - 12 0A1. exp (-k1.t) (IV.2) AA],AA2, AA3,k1, k2 and k3 were the six adjustab1e parameters. The f011owing relation was used for Aco to reduce by one the number of adjustabie parameters for the purpose of data fittings. Aso = A0 + 2 AA. (IV.3) The A0 vaiues were obtained from the experiments. At a concen— tration of 16.0 mM free K+, the va1ues of AA1 and k1 were fixed at 0.0085 0.0.auu10.39 sec'] (the averages of AA] and k1 at saturating K+ concentrations), respective1y, to get a reliabie fit. Figure 1V.7 shows a computer fit of the data at 337 nm for the enzyme and free K+ concentrations of 2.0 mg.m1"1 and 18.70 mM, reSpective1y (after mixing). At the concentration of 11.6 mM free K+, the two faster processes decreased in amp1itude and/or rate so that a two-exponentia1s equation simi1ar to Equation IV.2 (i=2) fit the data to within the experimenta1 random errors. At this concentration, one of the expon- entia1s accounted for over 80% of the tota1 change in absorbance. Fina11y, at the two 1owest concentrations of free K+ (2.3 mM and 7.0 mM), the three phases were inseparabie and a sing1e exponentia1 cou1d account for the tota1 change in absorbance. Resu1ts of the fitting precedure at saturating K+ concentrations are tabu1ated in Tab1e IV.2 whi1e those beiow saturation are given in Tab1e IV.3. .m_m>wuuwammg .25 ~.mp ucm A2: mmv Ps\ms o.N ”mew: +x new mex~cm mg» mo mcowumgucmu -coo .m>g:u umum_:upmo mg» mw mcwp cw—Om mg“ new mumu mg» mew m.x .N.>H cow“ smacm xn ”gash +xv +1 xn cowum>wpum wmmcmgaopqxgu com 5: mmm pm mumo mg» we aw; .m.>H mgamwu «0mm» octs ohm oeu o.u on. on. on. om om on o F n _ h — p P P — .P _ n - P by b b L .— no.6 io_d r~.d no.6 im.d . loud aouquosqv I —N.o . Tumd I mud .Ist.o 116 Table IV.2. Kinetic Parameters for the Reactivation of Tryptophanase by KT at Saturating Concentrations of the Cation. ~These Parameters were Obtained by Fitting the Absorbance Changes at Each NaveTength to Equation IV.2. E0 = 2.0 mg/ml'1 (36 uM) after mixing. Concentration ----- 3 Exponentiais ----- + K (fina1) free mM k§b),s“ kéb)x102.S-1 kgb)x103.5'] 33.0 0.39:.05 2.08:.22 4.72:1.32 24.2 0.38i.03 2.57:.15 5.58i1.31 19.2 0.38:.04 2.21i.12 3.20i .91 18.7 0.57:.14 2.01i.34 3.06i2.09 16.0 0.39a 2.06i.28 4.95i1.07 + . Kfree(fina1) Nave1ength __- A ___ -__ A _-- --- A _-- (mM) (nm) 1 2 3 33.0 337 0.009i.001 0.053i.009 0.065i.004 420 0.014i.001 0.077i.001 0.060i.001 24.2 337 0.008i.001 0.055i.005 0.050:.002 420 0.010:.001 0.072i.001 0.057:.001 19.2 337 0.009:.OO1 0.058i.004 0.071i.006 420 0.016i.001 0.075i.001 0.049i.001 18.7 337 0.008i.001 0.040:.010 0.066i.011 420 0.008i.001 0.047i.001 0.065i.001 16.0 337 0.0085a 0.028i.007 0.065:.003 420 0.005i.001 0.049:.001 0.063i.001 aVa1ues were fixed, see the text. bki are the "apparent" rate constants. 117 Table IV.3. Kinetic Parameters for the Reactivation of Tryptophanase by K+ at Concentrations of the Cation Below Saturation. A Two Exponential Equation (11.65 mM) and a Single Exponen- tial Equation (7.5 and 3.0 mM) were Used in the Fit. £0 = 2.0 mg.mi-l (36 an) after mixing. Kfree(fina1) Wavelength ( ) 2 1 (mM) (nm) k]a x10 , S'] kéa)x103 S-_ 11.65 337 6.59:1.00 7.76: 43 420 6.88:1.19 8.55: 74 7.5 337 1.37i 04 -------- 420 1.32: .02 -------- 3.0 337 1.21: .20 -------- 420 1.12: .04 -------- K; (final) Wavelength ree (mM) (nm) AAgb) AA2 11.65 337 0.013:.001 0.063i.002 420 0.012i.001 0.072i.003 7.5 337 0.034i.001 ---------- 420 0.053:.001 ---------- 3.0 337 0.0090:.ooo3 ---------- 420 0.018:.001 ---------- ak1 and k2 are the "apparent" rate constants. bValues are corrected for the slight difference in the enzyme concentra- tion. 118 8.2.2. Absorbance Change at 420 nm - The absorbance change at the start of the activation at 420 nm is different from that at 337 nm. At saturating K+ concentrations (above 16 mM), an exponential fast growth was observed at this wavelength (centered at N430 nm) which lasted about 600 mSec; no significant change occurred at 337 nm during this period as indicated earlier. Figure 1V.8 shows the difference spectrum obtained at the end of the fast growth along with a partial time course of the absorbance change at 420 nm. Concentra- tions of the enzyme and free K+ after mixing were 2.0 mg-ml'1 and 19.2 mM, respectively. The data during this time period were fit to a single exponential by KINFIT (Figure IV.9) and the results are presented in Table IV.4. The absorbance change during the same time at lower potassium concentrations was not large enough to allow a reasonable fit. From the data in Table IV.4, the rate constant k0 for this process is 9.5:.5 sec-1. Following the fast exponential process, the growth of absorbance at 337 nm is quantitatively mirrored by the decay at 420 nm. The data at this wavelength were again fit to Equation IV.2 and the results are reported in Tables IV.2 and IV.3. From the data at saturat- ing K+ concentrations (Table IV.2), three exponentials with k1 = 0.43:0.09 sec", k2 = (2.2:o.2) x 10'2 sec", k3 = (4.3il.l) x 10‘3 sec", and relative amplitudes of AA1 = 7.5i2.0%, AAZ = 44:8% and AA3 = 49i8% can be calculated. From the data at the two lowest con- centrations of K+ (Table IV.3), a single rate constant (obtained by averaging the results at both 337 and 420 nm is 1.3:.1 x 10'2 sec". Delta Absorbance Absorbance 119 0.02 l l g l 1 l l I O.C)1 -* . - . ._ h 0 C C O . . . 0.00 4W.. .=; , .fi '- -o.01 - IK — -0.02 I 1 7 1 1 1 T 1 320 360 400 440 480 Q2“ Wavelength (nm) (DJZS -* 'H~E‘ ‘. 0.22 - \g B 0.21 - K. 0.20 “ ....o.. 0.19 "" ...... (3518‘ l I I I I l 5 10 15 20 25 3O Thne (sec) Figure 1V.8. (A) Difference spectrum at completion of the fast growth at 430 nm in tryptophanase activation by K+. (8) Partial time course of the absorbance change at 420 nm. Concentrations were; trypt0phanase, 2.0 mg- ml"1 (36 mM); KT, 19.2 mM, respectively. 120 I 3 I : as x rt I X it 0.230 -* 2; . g 0.226- A 4: M c d a: .1: " 0.222- d I 0.218 I T I T I T I I 1 1 I I r I I O 100 200 300 400 500 600 700 Time (msec) 3u0 -' x 4x 20 - x :9 ' . *x 3 $3 1 O X‘ x . -* x¥ x x if, . X X xxx X X Xx XX “’ 0.0 _‘ :x x x x )t ”1 xx ,‘ x xi!!! x:x x x a « :xas‘ . iw * “ ‘0 a q: x °= -2.o - x . x -3.0 I T I I 1 I ‘ r I r 1 I I I I O 100 200 300 400 500 600 700 Time (msec) Figure IV.9. (A) Fit of the fast growth at 420 nm (600 mSec) in "K+ jump" by a single exponential. (B) Residuals of the fit Concentrations were; tryptoohanase, 2.0 mg- mi-1 (36 uM), K+, 33.0 mM, respectively. 121 Table IV.4. Kinetic Parameters Obtained from the Fit of the Early Growth (600 mSec) at 420 nm by a Single Exponential Equa- tion in Tryptophanase Activation by K? at pH= 8.70 (K+- Jump). E0 = 2.0 mg/ml'1 (36 uM) after mixing. K;ree(fina1), mM ----- A ----- --k0,s"-- 33.0 0.0090:.0005 9.7: .9 24.2 o.ooe7:.0003 7.3: .5 19.2 o.ooao:.0004 11.5: .9 18.7 0.0044:.ooo3 8.6:l.0 16.0 0.0035:.0003 10.6:l.8 AVG=9.5:.5 122 The variation of the overall amplitude of the absorbance change at 420 and 337 nm with K+ concentration does not follow a typical saturation function; half-saturation occurs at 9 mM and above 18 mM the value of'AA is independent of the K+ concentration. C. Discussion In this chapter we have reported some basic kinetics data dealing with the effect of monovalent cation, K+, on the transformation of inactive tryptophanase into functional holoenzyme. The kinetics of reactivation by K+ are complex as evidenced by the existence of three distinct phases during the process which can be interpreted in more than one way. Even at saturating concentrations of K+, [above 16 mM (Table IV.2)], nearly half of the enzyme does not convert to the 337 nm absorber (Figure 1V.6). Furthermore, this incomplete recovery of the original absorbance at 337 nm is time-independent. Even after a period of one hour the absorbance at 337 nm is only about half_the initial absorbance (less than 10% additional recovery) as indicated earlier. Yet, the enzymatic activity is completely restored in a few minutes. These observations lead to the following possibilities; i) The enzyme is not homogeneous, i.e., it exists in two dif- ferent conformational forms and that only one of these forms converts to the 337 nm absorber upon reactivation by K+. ii) The holoenzyme dissociates into dimers upon removal of po- tassium ion and that only one dimer converts to the 337 nm ab- sorber (y form) upon addition of K+. 123 iii) The enzyme remains as a tetramer in the inactive form but only two of the four protomers convert to the y-form upon reacti- vation by K+. The other two subunits convert very slowly, not contributing much to the 337 nm growth over the time of the experiment (over 4 minutes). The first possibility can be ruled out due to the fact that trypto- phanase purification from Escherichia Coli Blt7/A yields essentially 95% homogeneous enzyme as judged by polyacrylamide gel electrophoresis and its high specific activity when assayed with the substrate, 5- orthonitrophenyl-L—cysteine (123). It does not seem likely that re- moval of K+ ion causes significant inhomogeneity in the enzyme. The dissociation of holoenzyme into dimers (possibility ii) is not feas— able under our experimental condition. Morino and Snell (59,60) have shown that dissociation of holotryptophanase into subunits re- quires strong denaturing agents such as sodium dodecyl sulfate or urea. Furthermore, Raibaud and Goldberg showed that dimeric trypto- phanase is not functional under conditions where the tetrameric enzyme is perfectly active (71). These studies, along with the fact that the growth of the quinonoid absorbance (508 nm) upon mixing L-ethionine and saturating concentration of K+ with the deactivated enzyme is complete in 5 minutes or less (Chapter V), strongly suggest that holo- tryptophanase is not dissociated into dimers under the reactivation experimental conditions. Dissociation of pyridoxal-p from the holo- enzyme in the absence of K+, which may lead to partial dissociation of the apoenzyme into dimers, does not occur either. This is concluded from the facts that the deactivation rate remained unchanged in the 124 presence of excess pyridoxal-p (Chapter III) and that the spectrum of pyridoxal-p under similar (to reactivation) experimental conditions did not fit as an absorber in the PCA analysis of the reactivation (Chapter VII). These observations, thus, suggest that tryptophanase remains as a tetramer in the inactive conformation and that two of the four subunits remain "inactive" upon activation by K+ alone. The initial fast rise at 420 nm, which amounts to 0n1y'L6 Per- cent of the total absorbance change (decay) at this wavelength at the highest K+ concentration (Table IV.4), is probably due to a change in 420 nm absorbance upon K1 binding since it shows no change at 337 nm. Alternatively, a small fraction of the enzyme which does not contribute to the absorbance at 420 nm is readily converted to the 8 form upon addition of K+ with the rate constant, k0, 9.5:.5 sec']. This fraction may be present in the original preparation or it may have been produced by the 18C6 deactivation (perhaps indicated by the very slow exponentia1 changes at the completion of the deactiva- tion,Chapter III). The initial fast first order process (k1, Table IV.2),which also accounts for only 7.5:2% of the overall change at both 337 nm and 420 nm, could then be due to conversion of the form 8 to the v-form at 337 nm. This can be represented by; k1 B :Y (420 nm) (337 nm) The rate constant for this process obtained in these experiments, 0.43:.09 sec"1 (Table IV.2), compares reasonably well with the value 0.8010.2 sec'lobtained by June et al. (82) for the same process at a 125 similar pH from the pH jump and drop studies on the spectral forms of tryptophanase. The second and third phases in the three exponential process of reactivation (Table IV.2) have comparable changes in absorbance with values of AA2 = 44:8% and AA3 = 49:9%, respectively. However. the rates of the two phases differ by a factor of 5. The apparent first order rate constants for the two processes are 2.2:.2 x 10"2.sec"1 and 4.3:1.1 x 10'3 sec", giving half-lives of 0.52 min and 2.7 min, respectively. Above 16 mM, both processes are independent of potas- sium as indicated earlier. Since both of these phases remove 420 nm absorbance and simultaneously replace it by 337 nm absorbance; they cannot represent conversion among various forms of the inactive enzyme or a single bottleneck step. One way to interpret these results is given by the two following assumptions; a) Two sites per subunit saturate in binding by potassium ions in order to obtain the functional holoenzyme b) Two inactive (a) forms of comparable concentration exist. Our results on tryptophanase deactivation in the presence (Chapter VI) and absence (Chapter III) of L-ethionine strongly suggest that two potassium ions per subunit are required for activation, consistent with the binding of two Tl+ per subunit as reported earlier (77). To account for this and the second assumption together in the reactiva- tion of the enzyme by K+, one possibility is that each of the subunits of the enzyme converts from a to y at a "different rate" according to the following simple model; 126 k2 k3 O‘4 ._ Y10‘3 ._ t Y20‘2 (Tetrameric a) (Tetrameric ) inactive 50% y recovered with the rate constants k2 and k3 represented in Table IV.2. Even though tetrameric holotryptophanase shows no cooperativity, it has already been demonstrated that the enzyme exhibits a strong "kinetic antic00perativity" in the binding of its cofactor, pyridoxal-p (63). Raibaud and Goldberg showed that a strong structural coupling between the protomers is involved in the binding of the coenzyme; such that fixation of the first two pyridoxal-p molecules to the apoprotomers results in a decrease in the binding rate of the two remaining sub- units (71,72). In view of this, it may also be possible that potas- sium binding to the first protomer induces a change in the conforma- tion of the second protomer and renders it less reactive to the po- tassium ion. By "less reactive" it is meant that the rate of potas- sium binding is slower, i.e., "kinetic anticooperativity" exists in K+ binding to the enzyme protomers. The "invisible” very slow step, which at saturating K+ concentration contributes only about 8 percent to the absorbance recovery at 337 nm after a period of 1 hour, could then be due to the two remaining subunits slowly converting into the y-form according to; very slow Y20‘2 ‘ i *4 The data in Table IV.2 indicate that above 16 mM free potassium, the activation process is K+-dependent. This suggests that K+ 127 binding must either be fast and complete or else occurs after the rate- determining step. From the effect of monovalent cations on the enzym- atic activity of tryptophanase, Raibaud and Goldberg suggested that addition of potassium ion to a solution of the enzyme (in the presence of 0.1 M triethanolamine-HCl, pH 7.5) might induce a transition in the tetramer from an inactive form not fixing the cation, to an ac— tive form with affinity for the same ion (63), i.e., K+ binding occurs after such transition. The data obtained in our experiments do not permit us to discriminate between these two possibilities, even though fast K+ binding seems more probable. As the concentration of free potassium falls below saturation (16 mM) in the reactivation experiments, the three processes gradually decrease in amplitude and/ or rate so that a single "effective" rate can account for the overall change in absorbance as indicated in Table IV.3. 0. Conclusions The results presented here suggest a multistep interconversion of the K+-depleted (inactive) enzyme into the functional (v form) holo- enzyme. The kinetic results, by themselves, are not sufficient to propose a detailed scheme for this interconversion. Further experi- ments, such as the enzyme dependence of the activation, and pH- dependence of the process,in particular, are needed to gain more information on the possible individual steps involved in the mechan- ism. The stability studies indicate that the enzymatic activity, in contrast to the enzyme spectrum, is fully recovered upon reactivation of the enzyme by K+. This suggests that substrate in addition to K+ 128 is required to regenerate the spectrum of the enzyme. The stopped- flow results are interpreted in terms of ”kinetic anticooperativity" between the subunits of the enzyme upon K+ binding. Such kinetic anticooperativity has been reported in binding of pyridoxal-phosphate to tryptophanase (72) and aspartate aminotransferase (150). CHAPTER V TRYPTOPHANASE ACTIVATION BY K+ IN THE PRESENCE OF ETHIONINE-"QUINONOID FORMATION" A. Introduction An absorption band centered around 500 nm appears following addi- tion of certain amino-acid inhibitors such as L-ethionine, or true substrates such as L-tryptophan, to several pyridoxal-p dependent enzymes (7). This band is due to a quinonoid complex at the enzyme active site formed by the loss of a labile group from the a-carbon of the inhibitor (or substrate)-pyridoxal-p complex. In the presence of true substrates a leaving group from the B-carbon of the quinonoid complex is labilized causing the disappearance of the 500 nm band as the substrate is converted to products. Morino and Snell (65) demon- strated that a stable quinonoid complex characterized by an intense absorption band with Amax at 502 nm and a prominent shoulder near 470 nm is produced immediately upon mixing the competitive inhibitor, L-alanine, with tryptophanase. They further showed by experiments in 2H20 and 3H20 that the o-hydrogen of L-alanine was labilized in the process. Watanabe and Snell (149) later identified a number of inhibitors that formed quinonoid complexes with tryptophanase. In this chapter we will focus on the interaction of the inhibitor, L- ethionine,with inactive tryptophanase in the presence of K+. 129 130 Formation of the enzyme—quinonoid complex with ethionine requires activating monovalent cations. Suelter and Snell (77) proposed that in the absence of such cations, ethionine formed a Schiff's base with the enzyme, but that this complex did not proceed to quinonoid until KCl was added. The K+-complexing agent, lB-crown—6, was used in the present work. to reduce the concentration of K+ in the enzyme solution prior to the push for subsequent rapid scanning stopped-flow spectrophotometry (see Experimental Section). The purpose of this study was to examine the kinetics of quinonoid formation of the K+-depleted enzyme with the inhibitor, L-ethionine. A further goal was to correlate the results with those of activation in the absence of the inhibitor (Chapter IV) in an attempt to gain some insight into the mechanism of the interconversion of the active and inactive enzyme forms. B. Experimental Section Tryptophanase from E-Coli B/lt7-A was prepared as described pre- viously (123). Holoenzyme in bicine buffer at pH - 8.70 with a total K+ concentration of 17 mM was prepared from the stock apoenzyme as described in Chapter III. The enzyme had a specific activity of 46.0 pmole-min'l-mg'1 when assayed with 0.6 mM SOPC as before. A stock lM solution of lB-crown-6 in dialysis buffer was used to reduce the concentration of free K+ in the enzyme solution to ml mM just before the stopped-flow experiments. Similar to reactivation experio ments in the absence of the inhibitor (Chapter IV), all experiments 131 were carried out within 10 to 40 minutes after addition of 18-crown-6 at the ambient temperature of 23:l°C. The experiments were performed in two different ways: i) The enzyme was deactivated by 18-crown-6 (a-form) and then pushed against similar bicine buffer solutions containing in addition; 16 mM L-ethionine (saturating concentration, KI = 0.52 mM) and sufficient KCl to give final free K+ concentrations of 2.3, 7.0, 12.0, 16.0, 25.0, and 42.0 mM, respectively; (a-Enz) vs. (K+-Ethionine) experiment. ii) The enzyme was deactivated by 18-crown—6, then mixed with the inhibitor (16.0 mM before push) and pushed against the bicine solutions with similar free K+Oconcentrations as in i; (a—Ethionine) vs.(K+) experiment. The results of these studies are described in sections C and D of this chapter, respectively. C. Activation of Inactive Tryptophanase by a K+ Mixture- (a-ENZ) vs (K+-ETH) C.l. Spectral Shape Analysis Figure V.1 displays a 30 plot of the overall spectral changes from 320 to 550 nm which occur when inactive tryptOphanase is mixed with a solution of L-ethionine and K+. Concentrations of the enzyme, ethionine and free K+ after mixing were 1.25 mg.ml'], 8.0 mM, and 16.0 mM,respectively. The difference spectra, obtained by subtracting 132 .cowpowm _mucwEwLmaxm as» cw .25 0.0— .+¥ m25 o.w .mcecowzpm mE: mmv F-_E.ms .c nonvgumou wee m:o_uwu:ou emcpo .A.;pm-+x .m> 5v meaux_5 m: owgum mN._ .mmmnp “mew: m=_xwe tween meowueepcwucoo 1+! m an mmmcmcqopaxgu eo cowue>_pomme mg» to» womeesm weep-;umcm_m>e3-mu:eneomn< ._.> wezmwm A55 59.2263 eon can 9:. 2n 3». can w J a. D U 3 O (‘7 Nu“ 133 the first spectrum collected from the spectra at the various time points, are displayed in Figure V.2. These spectra were selected from 55 spectra collected by the scanning stopped-flow system described in the experimental chapter. The principal changes of absorbance are the decay of the inactive form(s) of the enzyme at 420 nm, and the growth of the quinonoid complex with an intense peak at 508 nm. Due to the fact that the 337 nm absorbing form of the enzyme is not formed under these experimental conditions, the spectral contributions are only from the a-form(s) and quinonoid chromopnores. The changes in absorbance at m3OO nm are precisely parallel to those at 508 nm. C.2. Kinetics The kinetics of the reaction were studied in both scanning and fixed wavelength modes by stopped-flow spectrophotometry. Kinetic analyses were done on data collected in the scanning mode as well as on data from the fixed wavelength mode. The scanning mode analyses were done in order to get a more precise estimate of the values of delta-absorbances at each wavelength for comparison. This is due to the fact that the fixed wavelength pushes at various K+ concentra- tions may have been at slightly different wavelengths because the scanning monochromotor is mechanically set to a particular wavelength. Non-linear least-squares data fittings were carried out by program KINFIT. 134 .mem new .m.mm .o.~ .m.m "mew E: mom pm souuon one sage .umm cw .mcuumqm an» to; was?» ._.> meamwm :_ mm mamm mew mew: mcowu_ccou __< .A53Luumam pmewwv mechm m>wuumcw an» we Ezepuoam ecu mcwuumeunsm »n _.> we:m_e sage umuuzeumcou meuumnm mocmewmw_u umuumpmm .N.> mczmwu AEcV 593.963 8» our. one o3 o3 can can Seal P P I —( P b b — b — b — ”FoOII O 8.0 L , T 8.0 a c a nu nn 0 .. .. o w o w s 86 1 T 3... s b o A J a. a. . r nu nu “u e o D 8.. 1 I on... a I T 8: . a J _ a _ a _ . _ . a 96 135 C.2.l. Absorbance Change at 508 nm — The change at this wavelength is triphasic at all except the lowest K+ concentration. The data at this wavelength were best fit to a three "lst-order" exponential equa- tion (similar to Equation IV.2) by KINFIT. The rates of the three processes were sufficiently different for KINFIT to separate them. At the lowest K+ concentration a two "first-order" exponential equation described the data. A typical fit of the overall absorbance change at this wavelength is shown in Figure V.3. The results of the fit at this wavelength are summarized in Tables V.1A for the rate constants (ki) and V.2A for the delta-absorbances, AAi' The results in Table V.lA indicate that the rate constant for the second phase, k2, is the most sensitive to the K+ concentration while the rate constant for the last phase, k , is relatively independent 3 of K+. An average value of (6.79:0.63) x 10'3 sec-1 can be calculated for k3 at this wavelength. At the lowest K+ concentration the last two phases were inseparable indicating that the two slower processes have decreased in amplitude and/or rate. The magnitude of the absor- bance change for the first process is strongly K+ dependent while the change contributed by the second phase is practically independent of K+ (Table V.2A). The delta absorbance for the third phase shows a slight increase at the lower K+ concentrations. C.2.2. Absorbance Change at 420 nm - The absorbance change at this wavelength was also triphasic, again, with the exception of the change at the lowest K+ concentration. The magnitude of the absorbance change at the latter concentration was very small, only 0.008 0.0. 0.70 0.” 0.50 0.30 Absorbance 0.10 0“ 136 030 0.10 Residuals (x102) é O 1 210 T 105 1 140 175 240 Time (sec) Figure V.3(A). I 140 1 175 l 210 l 245 1 we no Time (sec) Fit of the data at 508 nm in "a-Enzyme" vs. "K+—Ethionine" experiment by a three "first-order" exponential equa— tion. (K+)f was 12.0 mM. Other conditions were the same as Figure V.1. B. Residuals of the fit. 137 Table V.1. Apparent Rate Constants at 508 and 420 nm for the Activa— tion of Tryptophanase by a Mixture of Ethionine and K+ in Bicine Buffer at pH=8.70. Concentrations of the Enzyme and Ethionine (After Mixing) were 1.25 mg.ml'1 (23 uM),and 8.0 mM, respectively. (a-ENZ) vs. (KT-ETH). A. A=508 nm [K+],mM ki,Sec'] ké,$ec'] ké,Sec'] 42.0 .88:.05 .151:.006 (7.73:.13)x10‘3 25.0 .61:.03 .133:.005 (6.60:.08)x10'3 16.0 .36:.03 .083:.004 (6.17:.11)x10'3 12.0 .41:.o3 .070:.002 (6.37:.10)x10'3 7.0 .60:.30 .035:.002 (7.10:.74)x10'3 2.3a .50:.20 .015:.001 ------- AVG=(6.79:.62)x10'3 B. A=420 nm 42.0 .60:.O6 .150:.003 (6.76:.6O)x10'3 25.0 .56:.04 .133:.002 (4.97:.80)x10'3 16.0 .40:.02 .106:.003 (6.35:.50)x10’3 12.0 .30:.03 .O64:.OlO (8.0:1.3)x10'3 7.0 .52:.12 .045:.003 (5.34:.95)x1o"3 2.3b - .062:.015 -------- AVG=(6.28:1.20)xlO'3 aTwo exponentials equation used in the fit. bOne exponential equation used in the fit. 138 .pww any cw new: cowpmzcm pmwpcmcoaxm econ .pwm any cw new: cowumzcw mpmwpcmcoaxm 03pm -- -- n2: ----- ----- _oo.eooo. nm.~ _e mm N _oo.ammo. .oo.ameo. _oo.nmoo. 0.“ mm we w_ _oo.nmmo. .oo.nomo. _oo.nomo. o.~_ mm om m_ Poo.aomo. _oo.n~mo. _oo.ammo. o.o_ mm we NN moo.nmmo. Foo.n_mo. _oo.ne~o. o.mm om Ne mm _oo.nemo. _oo.n_mo. Poo.nemo. o.~e 2: omena .m mom o_ ----- eoo.nooe. o_o.neeo. em.~ we we op mpo.n~_e. NNo.amNe. o_o.neo_. 0.“ mm wv my moo.momv. o—O.Hm_@. —_0.Hom—. o.NF om we _N eoo.nmwm. _No.no_o. mmo.nmm~. o.o_ am Re em moo.hw©m. m_o.hmoo. mpo.nmom. o.mm mm _e om moo.n_Pe. mpo.neom. _No.nmme. o.~e m< w_amp :_ mm mem any mew m:o_u_u -coo Fmpcmswemaxm .Azhm-+x .m> sziav mcvcowzpm ccm +1 mo mezaxwz a An wmmcmzaouaxek eo cowpm>wpu< mg» Low 5: owe use mom um mmmcmgo magnetomn< as“ we mmmucmueme new musuwpas< asp .N.> mpnmp 139 (03 times the noise level at this wavelength), and, thus, the three phases were inseparable. A single “average" rate constant of (6.2:1.5) x 10'2 sec'1 was calculated at this concentration by KINFIT. The re- sults of the fit at this wavelength are summarized in Tables V.lB (rate constants) and v.28 (delta absorbances). As can be seen from these tables, the data at this wavelength are quantitatively in agreement with those at 508 nm. Specifically; (a) k2 and AA] are strongly K+ dependent; (b) 0A2 is independent of K+; (c) The rate constant of the third phase, k3, is independent of + K . The average value of k3 at this wavelength, (6.28:1.28) x 10'3 sec-1, compares favorably with that obtained at 508 nm, (6.79:0.63) x 10'3 sec'], which indicates that they represent the same process. A fit of the data at this wavelength for the K+ concentration of 25.0 mM is shown in Figure V.4. 0. Activation of Inactive-Tryptophanase-Ethionine Complex by K+ (or ETH) vs. E) 0.1. Spectral Shape Analysis The spectral changes were identical to those described in Section C of this chapter. The principal changes of absorbance were again the decay of the inactive form at 420 nm and the growth of the quinonoid complex at 508 nm with no substantial change at 337 nm. However, the 1L2: can 0 O C 0.10 O .0 L. O m 0.10 ..D <( 0.14 0.12 0.15 (L10 A N S 0.05 >< v 12 (L00 8 m 12 a) [g -0.10 -4L15 Figure V.4. 140 x x iii”: 1:”: E3 x x x x x x X X X "x Xx x x X xx xa?‘ at x a: x W fig” XX X): x "xx x ‘x x gas: 1 1 1 1 1 1 o 10 20 30 40 no Time (sec) A. Two-exponential fit to the first 50 seconds of the ab- sorbance-time data at 420 nm in ”a-Enzyme vs. KT-Ethionine" experiment at 25.0 mM free KT. Other conditions are the same as Figure V.1. Dots (°) are the data and solid line is the calculated curve. (B) Residuals of the fit. 141 overall process appears to be somewhat slower in this experiment and it is not completely over during the same time period as the a-enzyme vs. K+-ethionine experiment (Section C). The difference in extrapolat— ed final absorbance between the two experiments at a K+ concentration of 42.0 mM is about 20 percent of the quinonoid absorbance peak. Sim- ilar differences in total absorbance change were also observed at all. + . other K concentrations. 0.2. Kinetics The kinetics of this experiment were again studied in both scanning and fixed-wavelength modes and the data were analyzed by the program KINFIT4. D.2.l. Absorbance Change at 508 nm - The absorbance change at this wavelength was again triphasic at and above K+ concentrations of 12 mM. At a K+ concentration of 7.0 mM, it appears that the first process decreased in amplitude so that a single exponential could account for the absorbance change of the first two phases (Table V.3A). At the lowest K+ concentration, the three phases were completely inseparable and a single exponential with a rate constant of (1.78:.02) x 10'2 sec"1 accounted for the total change in absorbance. The fit of the data at this wavelength for a K+ concentration of 16 mM is shown in Figure v.5, and the results are summarized in Table V.3A (rate con- stants) and Table V.4A (delta absorbances). Comparison of the results in Table V.3A with those in Table V.lA at this wavelength reveals that the rate constants for the first and 142 Table V.3. Apparent Rate Constants at 508 and 420 nm for the Activa- tion of KT-depleted-Tryptophanase-Ethionine Complex by K+ in Bicine Buffer at pH = 8.70. Concentrations of the Enzyme and Ethionine (After Mixing) Here 1.25 mg.ml-1 and 8.0 mM, respectively. (a-Ethionine) vs (K+). A. A=SO8 nm [K+],mM k",Sec'] k",Sec'] k",Sec'1 1 2 3 42.0 .70:.03 .086:.003 (6.95:.13Ix10'3 25.0 .50:.02 .073:.002 (5.16:.21)x10'3 16.0 .40:.02 .064:.002 (5.32:.06)x10'3 12.0 .43:.02 .085:.012 (7.30:.15)x10'3 7.0a .13:.01 (6.77:.09)x10’3 2.3b (1.78 .02)x10‘2 ------- AVG=(6.3:l.O)xlO'3 B. A=420 nm + -1 -1 [K ],mM k],Sec k2,Sec -3 42.0 .25:.02 (4.92:.13)x10 25.0 .24:.04 (5.28:.40)x10'3 16.0 .2o:.03 (4.96:.18)x10'3 12.0 .12:.02 (6.83:1.2)x10‘3 7.0b (1.19:.10)x10'2 ---- 2.3b (.cs4i.12)><10'2 ---- Ave=(5.47i.92)x10‘3 aTwo exponentials equation used in the fit. bOne exponential equation used in the fit. 143 .m>e=u umum_:u_mu as» m? m:__ uw—om any new mean as» men A.v mace .om.m mm: In .Amcwxwe memmv zE o.m .mcwcowzum 14 mAzn mmv P1ps.ms mm._ .mmmeh ”mew: meowumeucmucou cacao .+¥ mace ze o.m_ pm .m.> masmwe “sweeteaxm =+ = .m> =eeeeo_;em-a= cw 5: mom pa meme new ea e_e _ewe=m=oexe-emeee «can» 0E2. on“ a.“ o.« a». ca. no. as an a _ i. p r _ _ _ _ _ cog. . .1 ace. 1 .1 one .1 one. fi1 «as. aauquasqV 144 .pww 0:: :w new: :o_um:cm _mwu:m:o:xm m:o: .uwm m:p :: :mm: :owwmzcm m meu:m:o:xm 03E: 2: -- £8988. ---- am.~ 2: -- £8938. ..--.. no: Em m_ moo.nmmo. _oo.nmoo. o.N_ w: EN moo.nomo. _oo.nm_o. o.m_ —m mm moo.nomo. moo.nmmo. o.mm mm _m Foo.nmmo. Poo.nomo. o.~: NE: :24. NE :2 :5 .C: E: omen: .m 11 :00: 1-111 Noo.nomm. nm.~ co co, Noo.nkom. Poo.nomo. to.“ _~ mm o moo.nmmm. _—o.nmup. :Po.n_mo. o.m~ we om N_ Noo.nmeo. moo.nmm_. woo.no__. o.m_ mm my mp moo.n:_o. ooo.nom_. Koo.n0w_. mm om om om Noo.0:mm. ooo.nmom. “00.0mm—. o.~: )2: NZ: :2: m2 9: :2 z: . Fa: E: mom": .< .m.> m_:mp :: mm mEmm m:: m:m m:owuw::ou _mu:mE_:m:xm .A+¥ .m> .:EM1av +x »: xmpanu =m:::ow:um1mmm:w:aoa:x:E1cmuwFamou+¥= 0: car: 1m>wpu< m:u :o: E: om: ::m mom a: mam:m:u mo:mDLOm:< m:: :o ammu:mu:m: :cm musawpaE< w:» .:.> mFQmE 145 third phases, k; and k3, are essentially the same as ki and k5, however, in contrast to the former experiment (a-Enzyme vs. K+-Ethionine mixture) kg is independent of potassium. An average value of 0.077:.Oll sec-1 can be calculated for k; from the data in Table V.3A. Comparing the absorbance changes in the two experiments, presented in Tables V.2A and V.4A, shows AA] to be similarly K+ dependent, 0A2 is K+ independent at least above 12 mM, and AA3 shows a gradual increase with increasing K+ concentration. The significant difference between the two experi- ments is that in the latter case (a-Enzyme-ethionine vs. K+) the over- all absorbance change is only about 75 to 80% of that in the former experiment (a-Enzyme vs. K+-Ethionine). Moreover, the absorbance change during the third phase in the latter case contributes more than 60% of the total absorbance change compared to m25% in the previous experi- ment. 0.2.2. Absorbance Change_at 420 nm - The absorbance change at this wavelength was biphasic, two first order processes, at K+ concentra- tions of 12.0, 16.0, 25.0 and 42.0 mM. The change at the two lower K+ concentrations was small and a single rate constant was calculated by KINFIT for the overall process in both cases. Results of the analyses at this wavelength are summarized in Tables v.38 (rate constants) and V.4B (absorbance changes). The results in Tables V.3 and V.4 together reveal the following information regarding this experiment; i) The rate constant for the slower process at 420 nm, k2. is essentially the same as the rate constant for the third 146 phase at 508 nm, kg, (Table v.3). ii) The relative percentage of the absorbance change due to the slower process at 420 nm, %AA2 in Table V.4B, is also compar- able to the %AA at 508 nm (Table V.4A) and they both show 3 similar K+ dependence characteristics. iii) The rate constant for the faster of the two phases at 420 nm, k], appears to be an average of the two faster processes at 508 nm, k; and k5 (Table v.3). iv) Finally, the magnitude of the change in absorbance due to the faster process at 420 nm, %AA] in Table V.4B, is again strongly K+ dependent, similar to that at 508 nm (V.4A) and the changesirithe a-enzyme vs. K+-ethionine experiments (Table v.2). E. Discussion The results presented in this chapter on activation of tryptophanase in the presence of L-ethionine are again multiphasic. As discussed earlier (Chapter IV), it does not seem likely that inhomogeneity of the enzyme is responsible for the multiphasic kinetics observed in these experiments. Such inhomogeneity would have to be significant, in particular, in these experiments to account for the triphasic be- havior of the reactivation. The significant difference between the activation in the presence of ethionine described in this chapter and that in the absence of the inhibitor is that the growth of the quinonoid absorbance upon mixing ethionine and saturating concentration of K+ with the deactivated enzyme is complete; whereas only about 50 percent 147 of the original absorbance at 337 nm is recovered in the absence of the inhibitor (Chapter IV). Once again, the results can be interpreted in terms of "kinetic anticooperativity" between subunits of the enzyme. Hereafter, the reactivation of the inactive (a) enzyme by a mixture of K1 and ethionine (Section C) will be referred to as experiment 1 and reactivation of the inactive-enzyme-ethionine complex by KT (Section D) will be referred to as experiment 2 for the sake of brevity. The variation of the amplitude of the absorbance change at 508 and 420 nm in the first phase of experiment 1, AAl in Table V.2, shows a saturation behavior that depends on the square of the potassium concen- tration as indicated in Figure V.6; half-saturation occurs at about 14 mM K+ concentration. The (K)2 dependence again strongly suggests that two sites per protomer need to be saturated by potassium for the appearance of activation. In this experiment, AA1 contributes an av- erage of 25 percent to the overall absorbance change. In addition, 4A2 and AA contribute about 48 percent (”50%) and 30 percent (”25%) to 3 the overall absorbance change in experiment 1 as indicated in the same table. Since the quinonoid growth in this experiment is complete and no enzyme inhomogeneity is believed to be present, the data might in- dicate that the rate of quinonoid formation depends upon the subunit conformation, i.e., kinetic anticooperativity is responsible for the complex kinetics in these experiments. The contributions of the three phases to the overall absorbance change in experiment 1 suggest that one protomer in the first step, two in the second, and one in the third phase convert to the quinonoid at different rates by virtue of the kinetic anticooperativity. 148 .:o_u::::mu 1::o +¥ mmLe m:u 0: memzcm oz: :: .N.> m_::E :: _<< .Azpm1+x .m> .N:M1:v P p:mE 1wem:xm :: mm::: “mm: m:u w: mm:::u mo:::::m:: m:: :: wuzpw_:E: m:u mo mo:m::m:m: .o.> mesmw: NASEC NIQNX M~+vC :.:~ :6. o:— :.1 :a. 9:. :.: :.: o... :.u :.: F F _ : : _ _ _ _ p _ 8.: 1 2.: . V V I? I 8.: \I/ n: 1 nu 4‘ 00 4 I on: u . w ( I 9.: 4‘ rl 1 00.0 149 The data in the two experiments do not provide any information about the rates of binding of potassium and ethionine to the inactive enzyme. Such information is not reported in the literature either. However, from our results it is reasonable to assume that both K+ (2 per protomer) and ethionine binding must be complete before any conversion to the quinonoid occurs; and that each protomer may bind either potassium or ethionine at different rates. For a protomer, represented by a, this can be expressed by the following simple scheme; + fast + fast 01 4' 2K——>01K2 + E ——.>01EK2 (V.1) where E represents the inhibitor, L-ethionine. In the absence of ethionine “K2 can convert to the y fonm at 337 nm (Chapter IV); however, in the presence of ethionine the equilibrium lies far to the right. This is supported by the fact that the kinetics of quinonoid growth from the inactive enzyme (this chapter) are dif- ferent than in the absence of ethionine. The absorbance change during the first phase in experiment 1 could then arise from the conversion of one protomer, bound to both K+ and ethionine, to the quinonoid at 508 nm with the rate constant, 0.56:.14 sec'] (Table V.1, ki) prac- tically independent of the potassium concentration. The absorbance change during the second phase in experiment 1 has a relatively constant amplitude above 7.0 mM K+, and contributes about 50 percent to the overall absorbance change as indicated earlier. This 150 was attributed to the conversion of the two other protomers from the inactive form to the quinonoid. The rate constant for the second phase, ké in Table V.1, is directly proportional to the concentration of free K+ which indicates that one potassium ion is involved in the rate- determining step in this process or in a pre-equilibrium process just before this step. 'Assuming that two potassium ions should bind to each protomer, the dependence suggests that the two protomers probably bind one of the two potassium ions more strongly than the other. Conver- sion to the quinonoid does not proceed, however, until the second K+ ion binds to the complex. If a again represents one of the protomers involved in this process, we can schematically fast a + K+.:——>01K+ + E (v.2) . 1 + K + “2 K + uEK+—:——0tEK2.-:':""’QE (508 nm) + It is likely that ké (Table V.1) actually represents two steps, K binding (equilibrium) and conversion to QE (slow). According to Scheme V.2 ké can be represented by; being directly proportional to the free K+ concentration as indicated in Table V.1. This scheme also explains the incomplete recovery of 151 the original absorbance in the absence of ethionine (Chapter IV) since it suggests that the second K+ binding, which is required for the forma- tion of the quinonoid, occurs only after the ethionine binding. No direct experimental evidence is available, however, to confirm this assumption. The absorbance change in the last phase of experiment 1 is probably due to conversion of the last inactive protomer (recall that this phase contributes about 25% to the overall absorbance change) into the quin- onoid with the rate constant k; represented in Table V.l. Once again, the K+ binding to this protomer must be complete before any quinonoid is formed. From the data in Table V.1 an average value of 6.54:.84 x 10'3 sec'], independent of the K+ concentration, can be calculated for kg. These observations together can be explained by the following simple scheme for the activation of inactive tryptophanase by a mixture of potassium and ethionine (experiment 1). 45 + (G)F(?E)4 1 "1 11 kg (v.3) In this scheme potassium ions are involved as described in the text. In experiment 2 the inactive enzyme was first mixed with ethionine followed by pushing the resulting mixture against potassium in the 152 stopped-flow system. Mixing of the inactive-enzyme-ethionine complex with K+ was carried out from 10 to 40 minutes after addition of 18- crown-6, depending upon the time of a particular push. The major difference between the two experiments are that in this case (experi- ment 2); 1') 11) iii) iv) The overall absorbance change extrapolated to "infinite" time is only about 75 to 80 percent of that in experiment 1 as indicated earlier; The rate constant for the second phase, k;, is independent of potassium concentration, K+; The sum of AA] and 0A2 at 508 nm (Table V.4A) compares with AA1 in experiment 1 at the same wavelength (Table V.2A), at least above 12.0 mM free K+ concentration. Furthermore, at 420 nm, where the absorbance change of the first phase represents the "sum" of the two faster processes at 508 nm (Table V.4B), AA1 (at 420 nm) similarly compares with AA] in the first experiment. This suggests that the changes in the first "two phases" in this experiment are due to con— version of only one protomer to the quinonoid. The amplitude of AA3 at 508 nm in this case (Table V.4A) is the same as 4A2 of the first experiment at the same wave- length (above 12 mM). This suggests that the change in the third phase of this experiment probably corresponds to that of the second phase in the first experiment. This is. further supported by the fact that the amplitudes of 4A2 at 420 nm in the two experiments are the same. 153 To account for these observations, it is proposed that the inactive- enzyme-ethionine complex undergoes a conformational transition in the absence of potassium ions, consistent with the suggestion of Goldberg et a1. (63) that the appearance of enzymatic activity of the inactive enzyme by K+ requires a conformational change in the inactive state of the enzyme. In fact in such a transition the conformational state. of each individual subunit might be different from that of the other protomers. If a' represents the conformation of a subunit after such a transition, we can represent the conformational change by; fast(l) (slow)(2) (3) 45 + (0)4; ’ (04514: : (0151(0'513:(a'5)4 (v.4) where the equilibrium lies to the right in favor of step 3 in the ab- sence of potassium. The fact that the rate constants for the first process in the two experiments, ki and k" 0.56:.14 sec'1 and 0.51:.12 1. sec'], respectively, are the same, suggests the existence of both forms in equilibrium for at least one of the protomers as given-in the last step in Equation v.4. Both of these rate constants probably represent conversion of the same protomer in a similar conformation, i.e., con- formation a. In addition, the relative amplitudes of AA] and AA2 (Table V.4A, above 12 mM) at 508 nm indicates that the equilibrium constant for this stepis not far from unity. Since the changes in the first "two phases" in experiment 2 are due to only one protomer as discussed, the second rate constant in the process, k", should represent the conforma- 2 tional change of the same protomer from the gLE state to the g§_state 154 before conversion to the quinonoid. These changes can be represented by Equation V.5 as; K 3 l :::::::::r(a'E) 3 k" 4 2 A Q m V ”A Q m v (v.5) (QE)(Q'E)3 The change in the third phase of experiment 2 at 508 nm (correspond- ing to the 2nd phase at 420 nm, see Table v.3), which accounts for two subunits (as AA2 in experiment 1), can then be attributed to conversion of two other protomers in the a'E conformation to the quinonoid, either directly with the rate constant kg, or via the a conformation. In the latter case the a' to a conformational change should be the rate-deter- mining step. The difference in the overall absorbance change in the two experiments (only 75 to 80% total quinonoid growth in experiment 2 compared to 1) suggests that one of the subunits converts very slowly to the quinonoid in the second experiment. The conversion rate of this subunit is probably further slowed down due to the different conformational states of the other subunits, i.e., the a'E conforma- tions. The results of the two experiments on the activation of trypt0phan— ase by K+ in the presence of ethionine can be represented together by the following model; 155 2K+ Per subunit 2K+ Per Subunit W M 4E + (a)4.-__.——::_-> (faSt (0.94: H510” E (at)(a'e)3—K._:—"-]_* (0.434 2 ll 1.. (QE) (aE)3 (QE)( 0 s)3 t Ké t‘:"n (V.6) (QE)3(aE) WQE) l ., 11:31.0...) (QE)4 (QE)4 in which the slow equilibrium (conformational change) occurs in the ab- sencecfi’pOtassium ions. The left side of this model (with the rate constants k%) represent the first and the right side of the model (with the rate constant k?) represents the second experiment, and potassium binding in individual steps are discussed in the text (Schemes V.1, V 2 and V.4). An alternative model for experiment 2 can also be proposed in which all protomers "anticooperatively" undergo a conformational change to thecxstate (similar to the first protomer) before-conversion to the quinonoid. In this model the a' to a transition should govern the over- all rate to account for the differences in the kinetics of the two experiments. The data obtained in these experiments cannot discriminate between these two possibilities. 156 F. Conclusions The results presented here provide some reproducible experimental information about the interconversion of inactive tryptophanase into the quinonoid in the presence of L-ethionine. In contrast to the ac- tivation by K+ in the absence of the inhibitor (Chapter IV), growth of the original absorbance is complete (experiment 1) which confirms that substrate or inhibitor in addition to potassium is required to completely reverse the deactivation brought about by depletion of K+. Our data again suggest that kinetic anticooperativity governs the rate of con- version of the inactive enzyme into the quinonoid. The data agree with the suggestion of Goldberg et al. (63) that, during appearance of the enzymatic activity in the presence of potassium ion, the inactive enzyme undergoes a change in its confonmation. Our data are also in agreement with circular dichroic experiments (77) which show formation of a com- plex between the enzyme and ethionine in the absence of potassium. A simple model based on the kinetic anticooperativity between the protomers is proposed which describes the results obtained in this chapter. It is worth mentioning here that our data on the deactivation of the enzyme by 18-crown-6 both in the presence and absence of ethionine (Chapters VI and III, respectively) are also in accord with the fact that active holotryptophanase exhibits no cooperativity; as no multi- phasic kinetics is observed in those experiments. CHAPTER VI. REACTION OF THE ”TRYPTOPHANASE-ETHIONINE" COMPLEX WITH lB-CROWN-6-"QUINONOID DROP" A. Introduction The formation of an intense absorption band around 500 nm due to a quinonoid structure upon mixing certain amino acid inhibitors or sub- strates with tryptophanase in the presence of activating monovalent ions was described in Chapter V. In the absence of activating monovalent cations this absorption is absent. The goal of this study was to examine the kinetics of disappearance of this band simultaneously with the growth of the a-form (the reverse of the process described in Chapter V) upon reducing the concentration of free K1. This experiment was an attempt to get more insight into the mechanism of the interconversion of the active and inactive enzyme conformers. For this purpose lB-crown-6 was employed as the K+-complexing agent due to the absence of an effect on the spectrum or activity of the enzyme as described in Chapter IV. B. Experimental Section Holoenzyme from E-Coli Blt7/A with a total K+ concentration of 17 mM in bicine buffer at pH = 8.70 was prepared as previously described (123). The enzyme had a Specific activity of 49.0 pmo1e-min"]-mg'1 157 158 when assayed with 0.6 mM SOPC in potassium phosphate buffer at pH 8.0. Prior to the stopped-flow experiments, the enzyme solution was mixed with a solution of L-ethionine to build up the quinonoid. The enzyme and ethionine concentrations were 2.0 mg-ml'1 and 16.0 mM, respectively, and the K+ concentration was kept constant at 17.0 mM. This solution was then pushed against the various concentrations of lB-crown-6 in- dicated in Table VI.l. The experiments were carried out at 23:1°C. C. Spectral Shape Analysis The spectral changes as a function of the wavelength and time following mixing of the tryptophanase-quinonoid complex with 18-C6 are presented in Figure V1.1. Concentrations of the enzyme and lB-C6 after mixing werel.Omg-ml'1 (18 uM) and 190 mM, respectively. Comparison of the quinonoid spectrum at t=0, prior to mixing, with the first spectrum collected after mixing with l8-C6 (N13 mSec) showed no abrupt changes upon mixing as the two spectra were superimposable. Figure V1.2 displays, in two dimensions, spectra selected from Figure V1.1 as a function of time. As expected, the spectral changes are essentially the reverse of those which occurred during the quinonoid growth from the a-form of the enzyme (Chapter V). Similarly, the change in absorbance at N300 nm was parallel to that at 508 nm. The overall absorbance change at 420 nm is much smaller than that at 508 nm as demanded by the rela- tive values of their extinction coefficients. 159 Table VI.l. Concentrations of K+ and lB-Crown-6 After Mixing in the Stopped-Flow Studies of the Tryptophanase-Ethionine Com- plex Disappearance by 18-Crown-6. E0 = 1.0 mg.ml'1 (18 0M) (L-ethionine)0 = 8.0 mM for all pushes after mixing. [Crown]0, mM (K;ree)final, mM 225 0.30 190 0.39 170 0.48 150 0.69 140 0.84 110 1.13 80 1.63 160 .o1czoeo .uxmu w:u :_ uwnweumm: we: m:owu_::ou :mzuo .mmmcmgqopazep ”mew: mcwwa Lupe: m:owp::p:wu:ou .2: :m: .ezoeu ”:2: :_V _-_e.:e :._ m— »: mu::::m:::mwu :woco:w:: mg: Low womwesm :umcmFw>mz1mep1mu::::0mn< «a :7 y o,::: e ._.H> et=:_: oouoqaocqy 161 .> :m::::u :w :mnweumm: :owuumm: mmem>we ms» :0: we: mm:wp :PFom asp .m:::umm m:m cc: m.m w:: :epumam m>_u:umm:oo w: mmeE ._.H> mesmw: :: m: mE:m ac: we: m::wp:::ou .A111v o-:3::u-w_ :uwz xm_:Eoo w:::o::um1mEx~:mo_o: m:: e: :owaumm: m:: m::::: _.H> mesmw: Eo:: cmpuzepm:ou mguum:m mu:m:memw: :mpumme .N.:> e:=:_: 162 N.:> etamwe 3.5 £05.30; .nvmxu AvnvaAUmu*V hung". 0% Own 0.. .. on. P 1 0 «1 9 aaupcuosqv cue mu- V1010." 0009‘? (DQQ 90'0 1 I r I d ONO... 9.0 1 O. .01 00.0.1 1 J_ l 10 g.- ..O..O 9.0 1 ONO aauoqmsqv mpg 163 0. Kinetics of the Quinonoid Disappearance After Mixing Tryptophanase- Ethionine-K+ Complex with lB-crown-6 D.1. Absorbance Change at 508 nm The absorbance change at this wavelength is biphasic, with an initial fast decay lasting about 200 mSec followed by a slower first-order con- version of the quinonoid to the 420 nm absorbing form(s). The initial fast phase was analyzed by choosing data points covering about the first 200 mSec of the reaction. This phase was best fitted by a single exponential with the program KINFIT4, the results of which are summarized in Table VI.2A. The rate constant for this phase is independent of the crown concentration, k1 = 16.6:2.0 sec-1; however, the amplitude of the absorbance change was inversely proportional to the square of the free K+ concentration. The changes in absorbance in the initial fast phase at concentrations of 18-crown-6 below 140 mM were too small to allow a reasonable fit by KINFIT (AA m 0.006 0.0. at a crown concentration of 140 mM). The analysis also showed that the contribution of the fast phase to the total absorbance change at 508 nm is about 5% at the highest crown concentration. Figure V1.3 shows the fit of the initial fast phase to a single exponential at a crown concentration of 190 mM. The major contribution to the overall absorbance change (>95%) at 508 nm, however, occurs in the slower phase of the reaction. The rate of this slow phase is extremely sensitive to the crown concentration (and thus to the free KT concentration) as indicated in Figure V1.4. The absorbance change in this phase was again described by a lst-order process with values of the rate constants being inversely pr0portional 164 Table V1.2. Analysis of the Fast Phase of the Quinonoid Disappearance by 18-Crown—6 in Bicine Buffer at pH=8.70. k] is the observed lst-Order Rate Constant for the Process. A. A=508 nm + -1 [Crown], mM (Kfree)final AA k],Sec 225 0.30 .072:.001 16.51: .77 190 0.39 .48:.002 16.33:1.82 170 0.48 .035:.002 16.05:3.06 150 0.69 .020:.003 17.57:7.18 140 0.84 .006:.002 ----- AVG=16.6:2.0 B. x=420 nm + -1 [Crown], mM (Kfree)final AA k],Sec 225 0.30 .007:.001 19.1:3.5 190 0.39 .0043:.003a 13.1:3.o 170 0.48 .0032:.003a 17.1:4.4 AVG=15.2:1.8 aAA is very small and it is at the noise level of the experiment. Absorbance 165 ‘5‘ I I I T I 1 I I I 1 0 20 40 00 00 100 120 140 100 100 Time (msec) 0.” '1 x q A x CD F ”X x X X x x x go .1 X X x X X x X X X 2 0.” -1 X x X x 8 O X Xx X X I: x x :9 ‘1‘ .. " " e a) o 4u0- x “ 0: x x ‘ x x '°"° I I I I I 1 1 I I 1 0 20 40 00 00 100 120 140 100 100 Time (msec) Figure V1.3. (A) Fit of the fast decay at 508 nm by a single exponen- tial during the reaction of the quinonoid complex with 18- crown—6. Conditions are the same as in Figure V1.1. (B) Residuals of the fit. 166 .:3::u 2E mmm A: ”:3::: 2E o:_ A: m:z::: 2E op. A: m:zoeu 2E ow A: .pxm: m:p :: :maweumm: we: m:o_uF::oo .E: mom a: 00:: 1::m:::m_: :Po:::_=: :: mum: mg: :: :1:z:::1m_ :: m::_p::u:mucou m:::::> :: pumeem .:.H> meamw: «can» 05:. a.“ can 00' can 00 0v 0 p _ r P p h b _ P — p _ n _ 603v H O O o a U. 0000. o o coo .1 08A— 00 O I :1 eta. uv . . q 0 0 j s o O o O O . . 1..x39 .1 a a q o 0 I D on o a u o 0 old. nu .. "n a a. 00 Mi 0 o O 0000000'18.’ .a. Z _‘ I..lfi— T 167 to the square of the free K+ concentration as shown in Figure V1.5. The results of the fit of this phase at 508 nm are summarized in Table VI.3A. 0.2. Absorbance Change at 420 nm The absorbance change at 420 nm mimics that at 508 nm. An initial fast growth in absorbance which lasted about 200 mSec, was observed at the highest concentration of l8-crown-6, 225 mM, and to a lesser extent at the crown concentrations of 190- and l70-mM. Although the magnitude of this change was very small (AA m 0.007 0.0. at 225 mM crown), it was systematic enough to be resolved by KINFIT. The change was very well described by a first order process, the results of which are presented in Table V1.28. Similar to the results at 508 nm, the rate constant for this process is independent of the crown concentration and its av- ], is essentially the same as that obtained at 508 nm, kl = l6.6:2.0 Sec-1. erage value at this wavelength, k] = 15.2:l.8 Sec- Furthermore, the absorbance change during this phase also contributes only 5-6% to theoverallabsorbance change at this wavelength, which is in agree- ment with that at 508 nm. The slow phase which again gave the major contribution to the overall absorbance change was also fit to a lst-order process by KINFIT. The rate constants obtained are practically the same as those at 508 nm at all concentrations of l8-crown-6 as indicated in Table V1.38. Similar to the results at 508 nm, the apparent first order rate constant is inversely proportional to the square of the 168 .:owu:eu:mu::u +¥ ewe: ms: :: memzcm omem>:_ m:p :o .m.H> m_::E :: we .mm::: 30?: we: we u::um:ou opme em:eo-ume_m ousmm: m:: w: mu:m::m:wa .m.H> mesmw: NimSEV NR.vC\s «. 2 o o e u o _ p _ e _ _ 18.: .. X o 18.“ W .. x l 0 18... Z r. ) S a #8.: a _ 1 Ir ( 18.- 169 Table V1.3. Analysis of the Slow Phase of the Quinonoid Disappearance by lB—Crown-6 in Bicine Buffer at pH = 8.70. k2 is the First-Order Rate Constant for the Process. A. A=508 nm , -1 (Kfree)final’ mM AA k2’ Sec .30 1.054:.003 (8.32:.03)x10"2 .39 1.077:.002 (4.87:.01)x10'2 .48 1.087:.001 (2.98:.01)x10'2 .69 1.034:.001 (1.45:.01)x10'2 .84 .920:.001 (.67:.01)x10'2 1.13 .915: 001 (.36:.01)x10‘2 1.63 .340:.005 (.29:.01)x10'2 B. A=420 nm + . -l (Kfree)fina1’ mM AA k2’ Sec .30 .103:.001 (8.94:.11)x10'2 .39 .103:.001 (5.33:.03)x10’2 .48 .100:.001 (3.21:.01)x10‘2 .69 .096:.001 (1.59:.02)x10‘2 .84 .084:.001 (1.08:.02)x10’2 1.13 .07o:.001 (.56:.02)x10‘2 1.63 .027:.001 (.50:.02)x10'2 170 free potassium ion concentration. Similar to deactivation in the ab- sence of L-ethionine (Chapter III), a very slow decay in absorbance occurs upon completion of the reaction at this wavelength. This change was observed at the three higher concentrations of lB-crown-6 but the magnitude was too small to be analyzed by KINFIT. E. Discussion The data presented in this chapter on the reaction of the enzyme- bound quinonoid complex with l8-crown-6 provides some information about the mechanism of the interconversion of the quinonoid complex, absorb- ing at 508 nm, to the "inactive" a form(s), absorbing at 420 nm. The biphasic growth (at 420 nm) and decay (at 508 nm) in absorbance is cer- tainly indicative of a rather complex mechanism for this interconver- sion. However, the following simple kinetic scheme (Equations V1.1-3, V1.15) is compatible with the observations described in this chapter. k1 k-1 where k (0') _ l = eq K1 _ k (Q) << ] (V1.2) eq Variation of the magnitude of the absorbance change as well as the independence of the observed rate constant to free K+ concentra- tion during the first 200 mSec of the reaction (fast phase) suggest 171 that the quinonoid complex is probably present in two different forms, represented here by Q and Q', in equilibrium with each other. 'The form 0' has a lower affinity than 0 for K+ and is thus present at a very small concentration at saturating K+ concentrations. The fast phase of the reaction can then be expressed as the re- action of the minor species (0', which probably has two K+ ions loosely bound per subunit) with lB-crown-6 in a fast equilibrium step according to Equation VI.3; K QHK; + 20 ——>. 2 . B(H+)+ 2K+C (“'3) (Amax=508 nm) (Amax=420 nm) Previous studies by June et al: (25) on the spectral forms of tYYPtO- phanase suggest that the form (8) is probably protonated at the pH of this experiment. The rate equation for the fast phase of the absor- bance change can then be written as; d (0' + B - . [ {it ( )1 - 14(0) - k_, (0 ) (v1.4) The mass balance on the enzyme Et = (Q) + (0') + (a) (v1.5 together with the equilibrium expression of Equation VI.3 allows the rate law to be rewritten as; 172 2 + 2 . (k + k_ )K (K ) 9L197¥51§lJ-= qut_- { 1 k; ‘3 + k]}*(8) (V1.6) 1 in which K3 = 115 M' (110) represents the equilibrium constant for the formation of the K+-18-crown-6 complex according to Equation V1.7; K3 K + CII::::T K C . (V1.7) Equations VI.3-V1.7 together give the concentration of (Q') in terms of (B) as; (Q') = —————K (a) (VI-8) Substituting (0') in Equation V1.6 yields the following rate law for the fast phase of the reaction; 1 + K§(K+)21 d(B) = k15t - { (k1 + k-1)K§(K+)2 K2 ( dt K2 + k1} (B) (VI.9) If we assume that reaction VI.3 lies far to the right (low K+ affinity in 0'), we can write (0') << (8) (v1.10) eq eq and therefore 173 -——-——-<< 1 (VI.11) This approximation leads to Equation V1.12 for the rate law of the fast phase. 95181 = klEt - 11(8) (v1.12) Equation V1.12 predicts a first-order process for the fast phase of the quinonoid disappearance with the rate constant, k], being in- dependent of the free K+ concentration, in agreement with the experi- mental results presented in Table V1.2. Equation V1.2 together with the equilibrium expression for reac- tion VI.3 also allows calculation of the equilibrium concentrations of the species. The two equations lead to the following relation; ( ) —————K‘K2 (Q) ————K‘K2 E (v1 13) B = = ° ' eq K§(K+)2 eq K§(K+)2 t if (6)eq << (Q)eq Equation V1.13 can be written in terms of the absorbance change as; K K AA , 1 2 T . 1 174 where AAT represents the overall absorbance change. Equation V1.14 predicts the magnitude of the absorbance change in the fast phase to be inversely proportional to the square of free K+ concentration. This is, again, in agreement with the data presented in Table VI 2. From the slope of the fit of the data (absorbance changes at 508 nm in Table V1.2 as a function of inverse square K+ concentra-' tion) a value of K1K2 = (8.6:.4) x 10'5 was determined by KINFIT. The slow phase of the quinonoid disappearance which contributes over 95 percent to the total absorbance change at both 420 nm and 508 nm can be represented by the following enzyme conformational change; k4 B a (V1.15) which gives the rate law; dt dt k4(B)eq (VI'16) Substituting for (8)eq from Equation V1.13 gives K K - 919.1 = ___1_2 d, k, [ 2 . 21 (4) (v1.17) K3(K) The rate law of Equation VI.l7 again predicts a first-order inter- conversion of the quinonoid complex (form Q) to the inactive form(s), a, for the slow phase with the pseudo lst-order rate constant given by; 175 k K K k' = 4 1 2 1 (V1.18) 3 f Equation V1.18 is supported by the experimental data for the slow phase presented in Table VI.3 (see also Figure VI.5). From Equation v1.18 and values of 115 M“ for K3 (110) and 8.6 x 10'5 forKJK 1 2 (de- termined by KINFIT), a value of 1.1:.1 sec' was calculated for k4. The change in the slow phase of the quinonoid disappearance can be further investigated to see whether the (8) to (a) interconversion occurs directly or via the y (337 nm) form. As indicated earlier, from June et al. (82,89) the 8 form of the enzyme is mostly protonated at the pH of the experiment, 8.70 (PK0 for protonation of the B-form is 9.70, see Scheme III in Figure 1.4). However, the deprotonated v-form is dominant at this pH (PK4 = 6.75 in Scheme III). Furthermore, the values of k1 (rate constant for the conversion of deprotonated B-form to deprotonated y-form in the scheme and k_3 (rate constant for the con- version of protonated B-form to protonated y-form in the cheme) were determined by June et a1. (82) to be 8.3 sec'] and 0.03 sec'], respec- tively. Therefore, the relative magnitude of k] and k_3 along with the high pH of the experiment suggest that conversion of the protonated B-form to deprotonated y-form is favored to proceed through the route with the rate constant k], if the (8) to (a) interconversion is to proceed through the y-manifold (Scheme III). If this is the case, then, an effective first-order rate constant for such a process at 9 pH = 8.70 (11+ = 2.0 x 10' M) is (V1.19) 176 Substituting for the values gives; keff = 0.83:.16 Sec-1 This value is similar to the value of the rate constant for the slow 1 and,_ phase of the quinonoid disappearance by 18-C5, k4 = 1.1:.1 sec- thus, seems to suggest that the (8) to (a) interconversion proceeds through the v-manifold. So, the slow phase of the quinonoid disappear- ance may be explained more precisely by the following process; 1 1 1.1 sec- 2.8 sec- B(H+) :: Y : a (V1.20) (420 nm) (337 nm) (420 nm) with the first step being rate—limiting with a rate constant k4 — l 1 1.11.1 sec” . The rate constant for the second step is 2.8:.2 sec" determined from the deactivation of the enzyme by 18-crown-6 (Chapter III). Reaction V1.20 predicts the concentration of the v-form at steady state to be k1 ms...“ = —2- (B) = 0.4 (6) However, since (B)eq << (Q)eq, one does not expect a significant build up of the v-form at 337 nm. 177 F. Conclusions The simple scheme discussed above satisfactorily explains the results presented in this chapter. The biphasic changes in absorbance at 420 nm and 508 nm are explainediriterms of this scheme and the 1 are obtained for the rate constants of 16.6:2.0 sec-1 and 1.1:.1 sec- fast and slow phases of the quinonoid disappearance, respectively. The inverse second-order dependence of the rate of the slow phase on the concentration of free K+ again strongly suggests that two potassium ions per subunit are required for activation. This is consistent with the deactivation results discussed in Chapter III and binding of two thallium (1) ions per subunit as reported earlier (77). The data also suggest that the interconversion of the (B) to (a) in the slow phase probably proceeds through the v-manifold which absorbs at 337 nm. More kinetic experiments at different pH values and enzyme concentra- tions as well as some information on the nature of the "inactive" enzyme form(s) are, however, needed to present a detailed model clearly. CHAPTER VII PRINCIPAL COMPONENT ANALYSIS OF TRYPTOPHANASE ACTIVATION/DEACTIVATION PROCESSES A. Introduction Optical absorption spectroscopy has been widely used in the characterization of tryptophanase spectral forms and catalytic re- actions. As described earlier, the holoenzyme has peaks at 337 and 420 nm due to bound pyridoxal-p and at 508 nm due to a bound amino acid substrate or inhibitor that has undergone a-proton abstraction. In this chapter, the method of Principal Component Analysis (PCA), also known as principal factor analysis (PFA), will be described first. This will be followed by its application to the scanning stopped-flow experiments of tryptophanase activation/deactivation by the monovalent cation, K+, in the presence and absence of the dead-end inhibitor, L-ethionine. The purpose of this study was to determine the number of optically absorbing species present during the reactions and to resolve the scanning data into the individual static spectra and concentration-time profiles of such species in order to propose appropriate mechanisms for the reactions. 178 179 B. The Method of Principal Component Analysis (PCA) As described earlier, in a typical scanning wavelength experi- ment, a selected wavelength region is rapidly and repeatedly scanned as a function of time while a spectrophotometric response such as absorbance is measured at a fixed number of wavelength channels dur- ing each scan. The result is then a PXN data matrix A_composed of N consecutive spectra measured at P wavelength channels. Such a data matrix is suitable for the application of principal component analysis. Although PCA has been applied to a variety of physical techniques such as analysis |3> Zl—I For an errorless experiment, the goal of M analysis is to obtain rM, the rank of M, which also equals rA, the rank of A_by a standard matrix theorem (147). Since rA §_q, rM is a lower limit to the num- ber of absorbers in the reaction. r is determined by diagonalizing M M, which is done by solving the eigenvalue problem OY‘ A: = 9A. 011.4) where A_is the eigenvalue matrix, 183 A: diag (61.62, . . ., 6p) (v11.5) with 6] 3_62 3_63 . . . 3_dp, and g_is a (pxp) matrix whose columns are the p orthonormal eigenvectors: 9i 913' = 513' (VII.6)' For errorless data, there are two ways to determine rm: 1. The rank of M, rM, is equal to the number of non-zero eigen- values in Equation VII.5; 6]. 52, . . . érM' 2. rM is also the lowest value of r for which Er’ the reconstruct- ed experimental surface, defined b, (V11.7) is exactly equal to A, where_g(r) is the (er) matrix whose r columns are the first r eigenvectors of M, B(r) is called the prin- cipal component estimate of A. The fact that EICM) = A_for an error- less experiment is shown in Appendix A of R. Cochran's Ph.D. disser- tation (98). 8.1.2. S Analysis - Sample covariance matrix PCA, or S analysis, gives for q the number of absorbers whose concentrations change in- dependently of one another during the experiment. §_is defined by 184 _s_ = [1701-1118 - EMA - ET (v11.8) 1 N where A - - Z A. is the average absorbance at wavelength 13 N k=1 1k channel i. An_§ analysis gives rs, the rank of S, which is also the rank of (A_- E). The procedure to determine rS is similar to that of M analysis, i.e., the rank of §_equals the number of non— zero eigenvalues of.§ and is also the lowest value of r for which A (A(r) - E) defined by (80.1 - A) = 2),.) ‘12:) (A - A) 011.91 is an exact r principal component estimate of the experimental (A_— A) difference surface. 8.2. Effect of Random Measurement Errors-Actual Case B.2.l. Inclusion of Error in the Absorbance Model — Each experi- mentally measured absorbance has a random measurement error associ- ated with it which must be considered in order for PCA to give correct results. Thus a more realistic model for A_than Equation v1.2 is defined by _A=_F_£T+_e_ (VII.10) where A_is the matrix of measured absorbance, and §_isai(PxN) error matrix whose element Eij is the random measurement error of the 185 absorbance measurement Aij' To complete this model, it is necessary to make some reasonable statistical assumptions about the error matrix Q, Cochran and Horne (98,139) assumed that the noise in absorbance measurements obtained by the scanning stopped-flow used in this study can be ap- proximately factored into two major contributions: (1) a time- dependent component which is minimized by signal averaging, and (2) a position dependent component which depends upon the position of a channel in the spectrum and its nominal absorbance. They thus pr0posed that the i,th_element of g, which is assumed to have an expectation value of zero, has varianceirithe form of Equation v11.11, _ 2 _ Var(g..)-o-. -x.z. (v11.11) where Xi is a function of the peak position (or wavelength channel number) and Zj is a function of the spectrum (group) number. The Zj contribution in our case is attributable to the nature of the data collection scheme used in our stopped-flow instrument. In order to optimize the allocation of a finite number of computer storage locations and at the same time scan the full dynamic range of a reaction, the stopped-flow system averages a number of con- secutive scans and stores the average as a single spectrum. The number of scans averaged into each stored spectrum is increased with time during the reaction; so at early times, where fast changes occur in the reaction, there is little or no averaging while at 186 longer times, where the changes are slow, the signal to noise ratio is greatly improved by increased averaging. The averaging scheme is fully described in Coolen's Ph.D. dissertation (134). Using this scheme, Coolen points out that the Zj contribution for this in- strument is given by Equation VII.12 23. = 90%) (v11.12) where gis the group factor (modulus for increasing the averaging) and hi is the stored group number. The Xi component in Equation VII.11 accounts for three major noise contributions to the absorbance at channel i: (l) the wave- length corresponding to this channel (mainly photomultiplier tube noise); (2) the actual value of absorbance; and (3) the rate of change of absorbance with wavelength at the particular channel i. The last contribution originates from errors in the precise wave- length reproducibility at each channel due to mechanical vibrations of the mirror system used. A method previously used to calculate the values of Xi for each channel was to use a flat absorber, e.g., a neutral density filter. However, while the method accounted for the Xi contribution originat- ing from the photomultiplier tube response, it failed to correct Xi for contributions arising from the latter two sources. To cor- rect for this, a new method was adopted by F. Halaka which uses two “scanning" experiments that represent the major reactant chromophore(s) anc inose of the final products with no reaction occurring in either 187 experiment. These two "weight" files must be collected with the same scanning parameters used for the reaction under study (i.e., same wavelength region and number of points per spectrum), but without averaging. An “average weight" is then calculated from the standard deviations in each weight experiment for every wavelength channel by Equation VII.13 = __L = 1 (VII.13) 1 av 2 2 1/2 0'1 [1/2(O11+021)] where 011 and 021 are the standard deviations of channel i from the two weight experiments. This new method gives a much better weight for each channel over the previous one because it accounts for the charac- teristics of the scanning monochromotor used in this study. That is, if a chromophore has a sharp peak, the "sides" of the peak are most sensitive to irreproducibility in the scan synchronization and to scanning mirror mechanical artifacts and hence have the highest measurement errors. This new method particularly should be a good approximation for reactions that do not produce intermediates with spectral shapes greatly different from those of reactants or products. 8.2.2. Weighted Principal Component Analysis - The model for variance given by Equation VII.ll leads to statistically weighted absorbance matrices defined as A“ = LAI (v11.14) 188 =LEI (VII.15) where L_= diag (l 12, . . . 1p) and I = diag (t1, t2 . . . t 1. 'I’ As pointed out by Cochran and Horne (140), the elements of L_and I are given by 1/2 -1/2 Ir— 1 X - a (VII.16) = b”Z 2'1/2 (VII.17) l—i where a and b are arbitrary constants (set equal to 1) and X's and Z's are defined by Equation VII.11. With the above definitions of weighted absorbance matrices, Equations VII.3 and VII.8 become, respectively, _ l_ T and s =._l_ (A - A') (A - A')T (v11 19) —w N-l —w —w —w —w ' and principal component analysis is performed using MN and §W to determine the essential ranks, m and s, of MN and S”, respectively. The inclusion of §_in Equation VII.10 makes the matrices M_and S'of full rank P. In other words, the eigenvalues in Equation VII.5 are gll_non-zero. For statistically weighted PCA, Cochran 189 points out that the weighted sum of the squares of the residuals, defined by Equation VII.20 gives the condition for the value of r that equals the essential rank of M“, m. N x Z LiTi (A 0 = .. lj=l ‘3 2 r (r) - A“) (VII.20) IIM'U 1 When r=m, the value of the function Qr/(N-r)(p-r), should be approxi- mately unity (140). This function also approaches unity for weighted S analysis when r=s, and Aij(r) and Aij in Equation VII.20 are re- placed with the appropriate difference surfaces. Similar to the errorless case, the essential rank, m, in weighted M analysis is also determined by finding the lowest value of r for . which A(r)’ now defined by (r) L) A (VII.21) fits the experimental matrix A_to within its random errors. Likewise in S analysis, 5 is the lowest value of r for which (£(r) - E) de- fined by A — _ -1 ' IT __ (A(r) - A) - (L 90‘) 910”) p) (_ - A) (VII.22) fits the experimental difference surface (A_- E) to within its ran- dom errors. In Equations VII.21 and VII.22, M_and pf are the eigen- vector matrices of MN and §W’ respectively. The most straightforward procedure for determining when A(r) fits 190 A_to within experimental error is to examine the residual surface (A(r) - A). For a fit to within random experimenta1 errors, points on the weighted residual surface should fluctuate randomly about zero and thus the residuals should not be highly patterned when plotted vs time or wavelength. If there is no pattern we have chosen the value of r equal to the essential rank. 8.3. PCA Determination of Real Components As described earlier, the two kinds of principal component analysis, M analysis and S analysis, yield, respectively, the minimum number of absorbers required to interpret the experiment (m) and the minimum number of absorbers whose concentrations must have changed independent of one another during the experiment(s). In addition, PCA provides a tool by which one can test whether a proposed spectral shape or a concentration profile fits as one of the column vectors of the f and C_matrices in Equation VII.2. This is called "Target Testing". If the measured static spectra of known reactants, products, and catalysts fit and account for the m required absorbers, then one has resolved the experiment. The starting point uses an identical but more useful equation than Equation VII.21 for 9(r) given by T -1 (VII.23) 191 9(r) = diag(w],m2,....,mr) (VII.24) - 1/2 and ) = T -1 1m ‘ (Arty-~11: 4w 3(1‘) 90) 011.25) where the r columns of 0(r) contain the first r eigenvectors of M&, defined by (appendix A in Ref. (98)) n; = (1/p) A; Aw (VII.26) The model for M analysis estimate of_[ and §_is T |>> k5> (m) = E_ (VII.27) where 3(m) is given by Equation VII.23 and E_§T is an error-containing estimate of [_CT in Equation VII.10. Equation VII.27 is used to estimate for each absorber the shape of its static spectrum, the shape of its concentration profile, and its contribution to the meas- ured experimenta1 (absorbance-wavelength-time) surface. Equations VII.23 and VII.27 together give “T = L-1 1 x _ A T - A("1) - £2 - fl>—(m) 8m) £(m) I (VII.28) 192 solved for E, Equation VII.28 gives E = (_L_'1 Am) 0 (VII.29) where M is an (mxm) matrix defined by E = 9.0") 5121",) _T_ f; (ET :0)" (VII.30) solved for :6, Equation VII.28 gives 5 = (1'1 34m) 1 (VII.31) where !_is an (mxm) matrix defined by _V_ = .00“) 61,") L" E (ET 31'] (VII.32) Resubstitution of Equations VII.29 and VII.31 into Equation VII.28 - gives the following condition on M and 1. T U = . __ g0“) (VII 33) It follows from Equations VII.29-33 that if the in2 elements of either 9.0".! are known, then both E_and C can be computed directly from Equations VII.29 and VII.31, respectively. Thus, the strategy for obtaining E and §_is to estimate enough elements of M and M_separately so that all of M_and M_are given by 193 Equation VII.33. By partitioning U_and M, _l_’ = (111.1-12.....flm) _Y = “1:1/2.....1m) (VII.34) where each_Mj and Vi is an m component column vector, Equations VII.29 and VII.31 become respectively 4,) I - (L4 40,109,. i=1, 2. m (v11.3s) 10> ll (1.] 11m) 3.1 .1 =1. 2. .... m (VII.36) which shows that the j M columns of M_and M_depend only on the jth static spectrum and concentration vector, respectively. For a given reaction there is usually a set of suspected absorbers. For example, in an enzyme-catalyzed reaction the suspected absorbers are any light-absorbing substrates, inhibitors and enzymes that were mixed to initiate the reaction. Equations VII.35 and VII.36 can then by used as models against which suspected static spectra or kinetic profile can be tested. If a suspected absorber is one of the m linearly independent absorbers in the experiment, its static spectrum and concentration vector must satisfy Equations VII.35 and VII.36, respectively. Cochran and Horne (98) presented the least squares criterion for determining whether a suspected absorber fits as one of the m linearly independent absorbers. In Equation VII.35, we see that every spectral shape that fits to within random error as one of the components, provides an estimate of the th_column of M, 194 Md, and hence gives m elements of M, Finding all the m static ab- sorbers, i.e., all 15's, provides all the m2 .M_and from Equation VII.33 the matrix M can then be directly computed. elements of the matrix Equation VII.31 can then be used to compute directly from the matrix M_the concentration vectors of the m linearly independent absorbers, i.e., all Cj's, and thus completely resolve the experiment. Similar arguments hold for every concentration profile that fits, within the least squares conditions, as one of the components in the experi- ment. For an "absorber" in the experiment, even if a limited wave- length region is used for the spectral shape proposed (in case the complete spectrum is not available), the spectral shape of that absorber which best fits that surface, is calculated for the gptigg set of experimental wavelength channels by PCA. A note of caution is also necessary regarding the correct inter- pretation of the term “absorber“. The fit of a suspected absorber as one of the m linearly independent absorbers shows that the experi- ment can be interpreted by using the suspected absorber as one of the absorbers, however, it does pgt_prove that the suspected absorber is 22 "absorber" in the experiment. In other words, the term "ab- sorber" may in fact refer to several species that are not independent in their rates (S analysis), concentration-time profiles (M analysis), or spectral shapes. An example of the first case (linearly dependent rates) was previously given in Chapter II. The following example is intended to show the effect of linear dependence of the latter two points on the determination of the number of "absorbers" by PCA. Suppose we have a two absorber reaction that follows the simple 19S kinetic mechanism k1 A1 + A2—>non-absorbing products (I) with the initial concentrations of A1 and A2 in the experiment being equal (4,10 = (4,10 (11) Mechanism (I) imposes the constraint d d 3; [A1] = EE'[A2] (III) and Equations (II) and (III) together give the constraint [A1]: = [A2], (Iv) so thatfl.1 and‘Am2 are linearly dependent. Performing M analysis PCA on such a system would give m to be unity even though there are two absorbers. Even if the static spectra;1 and f2 are linearly in- dependent, they do not individually satisfy Equation VII.35, and by testing them as proposed static spectra one would correctly conclude that A1 and A2 are not linearly independent absorbers in the re- action. In fact the information in the experiment lumps A1 and A2 together as one absorber. This can also be seen by noting that Beer's law contribution to this experiment may be written as 196 T ._ T T ‘ C-§h+£% M 3.- 2 but Equations (IV) and (V) together would give f T = 1:, + :2) 9.1 W” from which it can be seen that the combination ?jprop = (f, + :2) would fit as a proposed static spectrum for an "absorber". Detailed discussion of PCA along with more examples and its ap- plication to the stopped-flow studies of LADH-catalyzed reduction of NDMA by NADH can be found in R. Cochran's Ph.D. dissertation (98). Also, application of the technique along with the results obtained on reduction of cytochrome oxidase by MPH is discussed in the Ph.D. dissertation of F. Halaka (99). The application of the steps sum- marized above to the present work is discussed below. C. Principal Component Anglysis of Tryptophanase Deactivation by 18-C6 The characteristics of this reaction are discussed in Chapter III. PCA was performed on data collected in the wavelength region 300-500 nm. The data contain information on the spectral shapes and kinetic profiles of the active and inactive enzyme. We here des- cribe the steps taken to resolve the independent components in this region. 197 C.l. Number of Absorbers Figure V11.2 presents the three dimensional wavelength-time- absorbance experimental surface obtained on mixing 6.0 mg/ml trypto- phanase in the presence of K? with 300 mM 18-crown-6. Principal com- ponent analysis surfaces were reconstructed for [_values from 1 to 5 (Equation VII.23). Careful visual comparison of the reconstructed absolute surfaces, §(r)’ with the experimental data surface, 5 showed that the surface was quantitatively reproduced by three ab- sorbers. Figure VII.3A shows the reconstructed surface for r=3 (this is to be compared with Figure V11.2). For comparison, the reconstructed surface with one eigenvector (r=l) is displayed in Figure VII.3B, which clearly indicates that it does not reproduce the experimental surface. Inspection of the residual surfaces, (9(r) - A), which should be random at r=m, provides a better visual comparison of the fit. In Figure VII.4A, the residual surface is shown for r=3, which confirms the assignment of 5m=3 since the residuals are small and fluctuate around zero. The small and relatively non-random pattern observed for the late time spectra of the surface may be indicative of yet a fourth absorber which contributes slightly to the surface at the last phase of the reaction. The residuals constructed by using two eigenvectors are shown in Figure VII.4B for comparison. S-analysis of the same data indicated that there are also three components that independently change their concentrations with time, r =3. This, again, was concluded from examination of the recon- —S structed absorbance surfaces and residuals. In addition, the E: \: Ms $3227: :5: 3:: :58 EEEEEE ::§\\\\\\\\ , E: \\ xx: \\ “as 201 Figure VII.4A. Residual surface (3(3) O' A), resulting from subtracting the matrix in 5(3) refers to a recon- A is the experimental surface. Figure VII.3A from the data in Figure VII.2. structed matrix using 3-eigenvectors, 203 of the function Qr/(N-r)(p-r) forlr5 = 1,2,3 and 4 were 20.5, 4.4, 1.6 and 0.9, respectively, indicating 55 = 3. Thus, M-analysis indicates that a minimum of three absorbers with spectrophotometric responses are present in the reaction. The possible target absorbers for the fitting of the eigenvectors are; the active 337 nm absorber, the 420 nm inactive species, and the slow growth at m382 nm at the completion of deactivation. C.2. Concentration Profiles of Individual Absorbers In this step one may fit to the M-analysis eigenvectors for the whole experiment, either the static spectra, or the kinetic profiles of the suspected absorbers. A measured static spectrum or concen- tration profile that fits the absorbance surface may be counted as belonging to one of the m_absorbers in the experiment. We shall focus here on the fit of proposed concentration profiles to the M- analysis eigenvectors. The M-analysis fits to the proposed concentration profiles of the 337 and 420 nm species, two of the suspected absorbers, are shown in Figure VII.5. The concentration profile of the third suspected absorber at 385 nm was obtained by simulating the time course with a rate constant of 1.4 x 10'2 Sec-1 , as determined by KINFIT at this wavelength (Chapter III). Fit of the simulated time course to the M-analysis eigenvectors showed that this species is one of the three absorbers in the experiment. Figure VII.5. 204 (A) M-analysis fit of the 337 nm concentration profile from the data in Figure VII.2. X's are the proposed time course and the solid line is the estimated points. Three eigenvectors were used in the fit. (8) Same fit to the concen- tration profile at 420 nm. Absorbance Absorbance 205 j l ' l ' I r I ' I ‘ I ' an «10 en an we no no Thne (see) I l L L 1 l L b 1- p I I j I T ' I so (0 en in Thne (sec) Figure VII.5. 206 C.3. Spectra of Individual Absorbers Since it was possible to account for all the m(=3) eigenvectors in M-analysis, it was a straightforward problem to calculate the individual spectra of the three absorbers. The results are shown in Figure VII.6 for the three absorbers. The spectra of the 337 and 420 nm are in general agreement with those previously reported. Also, the estimated spectrum of the final product shows a maximum around 382 nm, in agreement with the experimental observation of a small growth at this wavelength at the end of the deactivation. D. PCA Analysis of the Reactivation of Deactivated Enzyme with K1 The characteristics of this reaction are discussed in Chapter IV. Principal component analysis was performed at two free-KT con- centrations of 12 mM and 33 mM, respectively. The experimental ab- sorbance-wavelength-time data surface is shown in Figure VII.7 for the reactivation of 2.0 mg/ml deactivated (K+-free) tryptophanase by 33.0 mM free K+. 0.1. Number of Absorbers M-analysis gave for the rank of M_a value of 3. The values of the function Qr/(N-r)(p-r) in Equation VII.20 were 917.9, 12.8, and 2.7 for the first three eigenvectors. Even though the value of this function for the fourth eigenvector was 1.2, suggesting a value 207 Figure VII.6. Estimated static spectra of the three absorbers in Figure V11.2 (a) 337 nm absorber, (b) 420 nm absorber, (c) the final product. The spectra are normalized to maximum absorbance. Absorbance Absorbance Absorbance 100 can ‘ 0.40 0.20 0.00 1.00 0.80 0.40 0.20 1.” 0.40 0.20 l 1 1 I. l I 0"... [I V e a t . D e .- e e. _ .0......eeeeeeeeO"."L I '7 l I l t j .um («m («m EEO Wavelength (nm) I L l L l 4 .. O b P e . " . h e ' l. e . __ e e. . . . - . D .0 "001- r a I a I I I 35) (“w (“W 5“) Wavelength (um) I l I I I l .0... :- e . c - . .. . .. ‘f‘% , L I '-. . . . O '0. .e e........ . e 0.0 r ' '7 r I j .um «m .«w 1“” Wavelength (nm) figure VII.6 209 of 4 for the rank of [1, the value _rjm = 3 was assumed to be correct. This was concluded from examination of the reconstructed absorbance surfaces. For;m = 3, the reconstructed surface, §(3), faitthlly reproduces the data in Figure VII.7. This is further supported by examination of the residual surfaces for 3h = 2 and 3, which are shown in Figures VII.8A and VII.83, respectively. It can be seen that for 3h = 3, the residual surface is random and non-patterned. S-analysis of the same data indicated that there are only two components that independently change their concentration with time, thus £5 = 2. This, again, was concluded from examination of the reconstructed difference surfaces, (EU) - E), and residuals. The residual sur- face for;S = 2 is shown in Figure VII.86. The suspected absorbers to be used in fitting the eigenvectors in this case (M-analysis) are; the active enzyme (337 nm), the in- active species (420 nm), the exponential fast growth at 420 nm (first 600 mSec of the reaction, see Chapter IV), and pyridoxal-p which may have possibly been released from the deactivated enzyme. 0.2. Individual Absorbers The concentration profiles of the 337— and 420 nm species were found to fit as two of the M-analysis eigenvectors. However, the fits of the exponential fast growth at 420 nm and the spectrum of the 382 nm absorber were unsatisfactory. Also, the static spectrum of pyridoxal—p obtained under the same experimental condition did not fit as one of the M-analysis eigenvectors. It should also be mentioned that no intermediate was observed in the reaction over oooooooooo 212 ’{y. 519.. I, (‘ngI‘ 5’3“ ‘ . ‘ . gills/é ... *0 “it" §f¢ 0‘1 (‘3: O\ *0 ,9‘ O ; éi .' ’s 3' < V ' “S: —, Figure VII.88. Residuals (13(3) - A) of the data presented in Figure VII.7. 214 the wavelength region used in this experiment, thus, ruling out the possibility of an intermediate being the other absorber in the ex- periment. The results probably suggest that K+ binding to the inactive enzyme to some extent perturbs the spectrum of the enzyme, so that in fact two absorbers with maxima close at 420 nm contribute to the absorbance surface. Since the 337 and 420 nm absorbing species are found to be two of the absorbers in M-analysis, we can also check their individual static spectra against S-analysis eigenvectors to see if the two absorbers have linearly independent rates. Such a fit was found to be unsatisfactory in either case, indicating that the time rate of the concentration of the 337 nm absorber is linearly dependent on that of the 420 nm species. For a two absorber system that reacts via the mechanism k A]___...A2 where f5 and;2 (static spectra) are linearly independent, M-analysis gives 5h = 2 whereas S-analysis givesrS = l because of the constraint In such a case, Cochran has shown that the combination :proposed = (Id - :2) would fit as an "absorber" with a linearly independent rate in S-analysis (98). To check this. (£337 - I420) was proposed as an absorber and was tested against S-analysis eigenvectors. The 215 fit is shown in Figure VII.9, indicating that the proposed spectral shape is an absorber with a linearly independent rate. Thus, we can conclude that the 337 nm form is directly produced from the 420 nm species upon reactivation by K+. Once again, this is in agreement with the experimental observation that no intermediate was detected in the experiment and that the growth of the absorbance at 337 nm is quantitatively mirrored by the decay at 420 nm. E. PCA on the Reactivation of Deactivated Enzyme with a(K+- Ethionine Mixture) The characteristics of this reaction are discussed in Chapter V. The major changes in this experiment are at 420 nm (due to inactive enzyme) and 508 nm (due to formation of the quinonoid structure). PCA was performed on data collected in the wavelength region 320- 550 nm at two free K+ concentration of l6 and 42 mM. The results were found to agree with each other. The experimental absorbance- wavelength-time data surface is shown in Figure VII.lOA for the re- action of 2.0 mg/ml deactivated enzyme with a K+-ethionine mixture containing 16 mM free K+ and 8 mM L-ethionine (after the push). E.l. Number of Absorbers M-analysis gave again a value of 3 for the rank of E, This was concluded from a reconstruction of the absorbance surfaces with r = 2 and r = 3 (Figure VII.lOB). It can be seen that for r = 3, the reconstructed surface faithfully reproduces the data in Figure VII.10A. 216 1.00 d 0 .. I I -' P I. . a 0.00 - - a - - 3 o 0.20 - _ - 'e ' ' I I P '0' 020 *- 4: "’ _ < - b -0.“ cl . I h 4 . - ' I -‘ 00 r t f t I 1 I r 320 380 440 500 ' 500 l 1 L 4 l L l L 1.“ ’~ P 0' .' - :- ° b a.” - v . D O a - - ' E .. .- u 0.20 0. a u . I- L . . . e e e e g g . . 8 -o.2o - ' . ' - -° ° N < «- . . . P— -0.” d . . C p O I «In . - e . . . 0 . -1 00 I r I I T I I I 320 300 440 500 500 Wavelength (nm) Figure VII.9. (A) S-analy515 fit of the Iprop = (£3375f420) in trypto- phanase reactivation by K using two eigenvectors. X's are the proposed spectrum and 0's are the estimated points. (B) Estimated spectrum (:337-f420). The jfs are the static spectra of the two absorbers. aaaaaaaaaa 219 Furthermore, examination of the residual surfaces for rM = 2 and rM = 3, shown in Figure VII.llA and Figure VII.llB, respectively, confirms the assignment, 3h = 3. Also, the values of the function Qr/(N-r)(p-r) were 2972.2, 34.3, and 1.5 for the first three eigenvectors. The value of this function for the fourth eigenvector was 0.90, indicat- ing that 3h = 3. S-analysis of the same data indicated that there are also three components that independently change their concentra- tions with time, thus r ._5 = 3. This, again, was concluded from ex- amination of reconstructed absorbance surfaces, shown in Figures VII.lZA and Figure VII.lZB for the experimental difference surface and three eigenvector reconstructed difference surface, and residuals, shown in Figures VII.lBA and VII.lBB for = 2 and):5 = 3, respectively. I; This value of;5 was further confirmed by the values of Qr/(N-r)(p-r) for;S = l to 4, which were 59.5, 5.3, 1.4 and 0.6, respectively, indicating 35 = 3. The possible absorbers in this case are the quinonoid species, the 420 and 337 nm absorbing species and pyridoxal- p. E.2. Individual Absorbers Since L-ethionine is a dead-end inhibitor, it binds the enzyme without further reaction. Thus, the final spectrum collected in a scanning experiment (infinity spectrum) was used as the proposed spectrum for the quinonoid. This spectrum was found to fit as one of the M-analysis eigenvectors (Figure VII.l4). The fit of the spectra of pyridoxal-p and the 337 nm absorber' were, however unsatisfactory. The fit to the 420 nm absorbing spectrum 22] Figure VII.llB. Residuals (21(3) - A) of the data presented in Figure VII.lOA. 225 ' I ’ I k” r I ‘s ‘ “0 V \ . ‘ \ . ~ - I, "A - 4' . ‘3’" l M’ . ‘4 - \ ‘ 1‘ \ ‘Hllto \‘ \\\ I v; , \ s \_ l k l e :2 ‘If “P ) {‘7‘ VII.lOA. Figure VII.l3B. Three eigenvectors S-analysis residuals of the data represented in Figure Absorbance Absorbance 1.00 0.00 0.00 0.40 0.20 11“! OJKI (LOO (l40 OJHJ Figure VII.l4. 226 vectors were used in the fit. trum. The spectra are normalized. Wavelength (nm) ' e ‘ e . a ' 0 C C " a C . . a . \ . . . Wan-IOOIC""IOIO'. . . r t | I T u r '44—” - 320 300 440 500 500 Wavelength (nm) 1 n l n I 1 l " i. . . P '3 . [- 4 .. q . P - . O I- . \ e . 0.0.0.000....00000.. . . I ' 1‘ F l ' I ...j"- 320 300 440 500 500 M-analysis fit of the quinonoid spectrum from the data presented in Figure VII.lOA. Three eigen- (B) Estimated spec- 227 was acceptable, but it was not as good as the quinonoid fit. The same fit using four eigenvectors, however, was completely randomized. This may be explained in two ways: l. The experiment contains four independent absorbers. 2. The K+-free enzyme may have partially formed a Schiff's base with the inhibitor, L-ethionine. The first possibility can be ruled out based on the discussions in the previous section (E.l). However, formation of a Schiff's base between K+-free enzyme and the substrate has already been reported for tryptophanase (77). Such a reaction is accompanied by a change in the circular dichroic spectrum but no major change in the absorp- tion spectrum of the enzyme occurs. Therefore, the proposed spectrum used in the fit may in fact be a composite spectrum of two absorbers, namely the Kf-free enzyme and the enzyme-ethionine complex, each of which has a maximum at or near 420 nm. The S-analysis fit to the quinonoid spectrum was also satis- factory, indicating that it is one of the absorbers with a linearly independent rate. The K+-free enzyme and the enzyme Schiff's base complex may be the other two probable absorbers in S-analysis. More information about the nature of the absorber(s) at 420 nm is needed in order to sufficiently and completely resolve these data. F. Conclusions The work presented here demonstrates the application of PCA to three different stopped-flow experiments. In the deactivation with 228 l8-crown-6, PCA provides resolution of the independent spectral shapes of the components of tryptophanase. These spectral shapes, which were deduced from PCA without any mechanistic assumption, agree well with the reported assignments for the components of the enzyme. In the M-analysis for the reactivation experiment, three independent absorbers are required to allow reproduction of the absolute experimental surface. S-analysis gave only two components that change concentration independently with time. This was in— terpreted by postulating that K+ binding to the inactive 420 nm ' perturbs the spectrum of the enzyme which in turn is dictated as two absorbers in PCA analysis. In the reactivation experiment with L-ethionine present, three independent absorbers were again the minimum number required by both M- and S-analysis. The quinonoid species was found to be one of the absorbers in each case. The Kf-free enzyme and the enzyme (K+-free)-ethionine Schiff's base complex are suggested as the other two absorbers. A final point regarding the power of the PCA method is worth mentioning here. In fitting a suspected absorber to the PCA eigen- vectors, one does not need the spectrum of the absorber over the whole wavelength region of the experiment. However, once a given absorber has been shown by principal component analysis to appear in the experiment, its spectral shape across the entire wavelength re- gion of the experiment is estimated by PCA. This is particularly use- ful in cases where only a limited range of wavelength channels is available for the proposed spectrum. CHAPTER VIII SUGGESTIONS FOR FUTURE WORK The work presented here demonstrated the potential of using crown-ethers (and to some extent cryptands) as complexing agents for inorganic monovalent cations instudies of enzyme activation/de-r activation by such cations. Application of this work to other enzy- matic systems which require these cations, such as B-tyrosinase, should further test the usefulness of this new method for the studies of enzyme activation-deactivation by monovalent cations. Structural information coupled with the kinetic data on activation/deactivation of the enzyme by monovalent cations should provide an in depth picture of the specific role of the cation in the enzyme structure as well as its role in enzyme catalysis. Binding of 2 K+ ions per subunit of tryptophanase as shown in this work proves a specific role for the cation, rather than a nonspecific conformational effect. Since the spectral forms of tryptophanase are pH-dependent as discussed in the text, the activation/deactivation experiments should be carried out at several pH values. The practical pH range in such studies is, however, limited because of the fact that the 420 nm form of the active enzyme dominates the absorption spectrum (absorb- ing in the same wavelength range as the inactive enzyme. Thus, the 229 230 overall absorbance change is drastically reduced (83). The enzyme concentration dependence of the activation and de- activation (in the presence of ethionine) should also be examined to see what effect the enzyme concentration might have on the rate constants. Application of PCA to this and other systems mentioned above should be useful in understanding the activation mechanism of these enzymes. PCA, when supplied with sufficient target absorbers (spectral shapes or concentration profiles), can completely resolve scanning stopped-flow experiments. It is known that tryptophanase forms a Schiff base, a5, with ethionine in the absence of activating monovalent cations. Even though the absorption spectrum of the inactive enzyme and the Schiff base are similar, their CD spectra are different (77). In order to clearly propose a reliable model for the enzyme activation by the cation, some experimental data on the rate of such SB formation is needed. 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