OVERDUE FINES: 25¢ per day per item RETURNNB LIBRARY MTERIALS: \- Place in book return toremo charge from circulation records // filll\\\\h\‘ g ‘ I \A 11m '14"; IMPORTANCE OF DIMERIZATION IN THE ADENOSINE 5' MONOPHOSPHATE ACTIVATION OF BIODEGRADATIVE L-THREONINE DEHYDRASE FROM ESCHERICIA COLI and DETERMINATION OF ENZYME KINETIC PARAMETERS BY CONTINUOUS ADDITION OF SUBSTRATE TO A SINGLE REACTION MIXTURE AND ANALYSIS BY A TANGENT-SLOPE PROCEDURE By David Joseph LeBlond A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Biochemistry 1980 A simple biodegradativu ted by using 1 order of the I a rate-limitir gress curves y SW at 28°c. TDH was r 1'"e. This rad bound to CUB r-a 0f mat"I"~t>oun.< A” (matrim fer WSUIted I." WIN-bound. I characteristic | l §//é (6.03 ABSTRACT IMPORTANCE OF DIMERIZATION IN THE ADENOSINE 5' MONOPHOSPHATE ACTIVATION 0F BIODEGRADATIVE L-THREONINE DEHYDRASE FROM ESCHERICIA COLI and DETERMINATION OF ENZYME KINETIC PARAMETERS BY CONTINUOUS ADDITION OF SUBSTRATE TO A SINGLE REACTION MIXTURE AND ANALYSIS BY A TANGENT-SLOPE PROCEDURE By David Joseph LeBlond A simple affinity purification procedure has been developed for the biodegradative threonine dehydrase (TDH) of Eschericia coli. TDH isola- ted by using this procedure is estimated to be 87-96% pure. The protein order of the AMP activation of TDH was found to be 2.01, consistent with a rate-limiting subunit dimerization step. Analysis of activation pro- gress curves yielded a dimerization rate constant of 8.8 x 105 M’1 sec‘7 at 28°C. TDH was radioactively labelled by growing E, 9911 on 3[Hprridox- ine. This radioactively-labelled enzyme has been used to quantitate TDH bound to CNBr-activated Sepharose. The specific activity and 50.5 of matrix-bound TDH, in the presence of AMP, were similar to those of the soluble enzyme. when TDH was attached to CL-Sepharose in the presence of AMP (matrix-bound, associated TDH), washing the matrix with AMP-free buf- fer resulted in removal of 50% of the natrix-bound TDH. The resulting matrix-bound, dissociated TDH possesses an activity in the absence of AMP characteristic of soluble unactivated TDH. It is capable of binding near]! of AMP a‘ bound de These ob quaterna bound, (1‘ however, failure 0 strongly of the en; In Si. provides r tion progr substrate 4 WIN gener were fit to (U) a tang ferentlated anaiyzed as estimates of At least ten tiai guesses The tangent-g of 1.5 to 10; during the as. Cement" dti on David Joseph LeBlond nearly an equal amount of soluble TDH when placed again in the presence of AMP and this treatment raises the specific enzyme activity of the bound dehydrase to 83% of that of the matrix-bound, associated TDH. These observations correlate with the effects of AMP on the activity and quaternary structure of soluble TDH. When AMP is added to the matrix- bound, dissociated TDH, a fraction (38%) of the TDH is activated; however, the remaining dehydrase is not significantly affected. The failure of AMP to activate the major fraction of immobilized TDH monomer strongly suggest that dimerization of TDH is required in the activation of the enzyme by AMP. In support of these studies, a new method has been developed which provides reliable estimates of enzyme kinetic constants from single reac- tion progress curves recorded under conditions of continuously increasing substrate concentration. The approach was first investigated using com- puter generated data containing known amounts of random noise. Such data were fit to the Hill equation by (i) direct nonlinear curvefitting, and (ii) a tangent-slope technique in which the raw data are numerically dif- ferentiated, transformed into substrate versus velocity data, and then analyzed as linear plots. Both procedures provided accurate and precise estimates of the Hill parameters. However, the tangent-slape method was at least tenfold faster to compute and was not dependent on accurate ini- tial guesses of the Hill parameters or integration of the rate equation. The tangent-slope method was reliable over a range of Smax/50.5 of 1.5 to 10; the optimal value was 3. Slow enzyme inactivation (4% loss during the assay), or product competitive inhibition (maximum product concentration 30% of the inhibitor dissociation constant) do not produce serious errors in the Hill parameters. eters a Gilf to a S“ on papa from th agreemer rabbit m Sepharosi enZymes a David Joseph LeBlond This approach for semi-automated evaluation of enzyme kinetic param- eters was tested in a newly devised instrumental system. It consists of a Gilford spectrophotometer modified for continuous addition of substrate to a stirred enzyme mixture, and for recording of absorbance data coded on paper tape. The Hill parameters for a number of enzymes, obtained from these data by tangent-slope or curve-fitting procedures, are in good agreement with published or manually determined values. Experiments wfith rabbit muscle lactate dehydrogenase covalently linked to Sephadex 6-50 or Sepharose 4-B examine the feasibility of this approach when applied to enzymes attached to solid supports. I am more than the atoms tho I am of atoms made. For no atom ever fell in love nor on his guitar played. Neither has a symmetry of only space and time heard the yearnings of his soul and answered back in rhyme. - D.J.L. ii IGWU HIIE, Ch: “VIEd through ' ‘° and fount DEDICATION To my wife, Christine, and my little children, Scott and Cherie, who waited through their lonely nights so I could live out a boyhood daydream . and found me with their smiles. l i would “if: E'iii'uurag‘er‘ier ACKNOWLEDGMENTS I would like to thank my advisor Dr. H.A. Hood for his confidence and encouragement. The help and warm friendships of John Reibow and Doris Bauer will be long remembered. I would like to acknowledge the substantial contributions of Curt Ashendel who wrote the original version of the TANKIN program and whose careful initial studies of substrate addition methodology gave direction to my own. The support of NIH Training Grant number GMlO91 from Michigan State University, and of NSF Research Grant number PCM08586 is gratefully acknowledged. iv thT ”Di r LI)I SF T'HIUL: l'f' r.‘ P'l' ' L.,l UI f'LJ. "\“M Hi . an . t, A. ,4 "7"P';r‘vvrn A 1| \IlJLJl" I... 1 A “fir ft. I A 0 A {L '«AI‘ITf‘t ‘. HP". "Cr-QR: Am. A ‘l.,\‘ Viln'filfi‘.‘ L.;'1K§-J.i (H) POEM . . . . . . DEDICATION . . . ACKNOWLEDGMENTS . LIST OF TABLES . LIST OF FIGURES . SYMBOLS AND ABBREVIATIONS TABLE INTRODUCTION 0 O O C O O O O O O I. IMPORTANCE OF DIMERIZATION IN MONOPHOSPHATE (AMP) ACTIVATION or L-THREONINE DEHYDRASE (TDH) FROM ESCHERICIA COLI OF CONTENTS THE ADENOSINE 5' BIODEGRADATIVE A. LITERATURE REVIEW 0 O O O O O O O O O O C O O 1. Regulation of Activity Through Subunit Interaction O O O O O O O O O O O O O O O a. Models of Allostery Involving Subunit Interaction O O O O O O O O I O O O O b. Ligand-Regulated Oligomerization . . 2. Assessing the Importance of Subunit Asso- CTat‘ion I O O O 0 O O O O O O O O O I O I a. Equilibrium or Steady State Methods . b. Association Kinetics c. Immobilized Subunits d. Stabilized Subunits . . . . . . . . . 3. Regulation of the Biodegradative TDH of Eschericia coli . . . . . . . . . . . . . V .xiii . xvi a. Role in Energy Metabolism . . . . . . . b. ktivation 0f TDH by MP 0 O O O O O O c. Inhibition of TDH by a-Ketobutyrate aid Pyruvate . . . . . . . . . . . . . Allosteric Models Applicable to TDH . . . . a. Ligand Induced Oligomerization-Deoligo- merization . . . . . . . . . . . . . . b. Changes in Quaternary Structure Catalysis . . . . . . . . . . . MATERIALS AND METHODS . . . . . . . 1. 2. Bacteriological . . . . . . . . Determination of TDH Activity . a. Standard Catalytic Assay . b. Assays Employing Rapid Mixing Determination of Protein . . . a. Soluble Proteins . . . . . b. Inmobilized TDH . . . . . . Determination of Radioactivity a. Aqueous Solutions . . . . . b. Sepharose Suspensions . . . c. Polyacrylamide Gel Slices . . Purification of TDH by Affinity a. Preparation of Crude Extract b. Chromatography on N6-linked AMP- During Chroma- tography l O O O O O O O O I O O O O O O O sepharose C O O O O O O I O O O O O O O c. Concentration and Final Centrifugation d. Production of 3H-labelled TDH . . . . . Production of AMP-Free Dehydrase vi 15 16 16 20 22 22 25 25 25 26 26 26 27 27 28 28 28 28 29 3O 3O 3O Pt Cl 10. ll. 12. A 1. 2. L. RES Polyacrylamide Gel Electrophoresis of TDH . . a. Native Gels . . . . . . . . . . . . . . . b. Electropliresis in the Presence of SDS . Reduction of TDH by NaBH4 . . . . . . . . . . Immobilization of TDH . . . . . . . . . . . . a. Quantitation and Handling of CL-Sepharose SuspenSionS O O O O O O O O O O O O O O O b. Immobilization of TDH to CL-Sepharose . . Collection and Analysis of Reaction Progress cur\les O O O O O O O O O O O O O O O O O O O a. Instrumental System . . . . . . . . . . . b. Absorbance Calibration . . . . . . . . . c. Determination of Hill Parameters by Sub- strate Addition . . . . . . . . . . . . . d. Data Collection and Differentiation . . . e. Analysis of Activation Curves by First or Second Order Kinetic Plots . . . . . . . Least Squares Treatment of Data . . . . . . . Analytical Ultracentrifugation . . . . . . . AII-TS O O I O O O O O O O O O O O O O O O O O 0 Improved Purification Procedure for TDH . . . a. Chromatography of TDH on AMP-Sepharose . b. Gel Filtration of AMP Sepharose Purified TDH 0n sephadex 6-200 0 o o o o o o o e o c. Electrophoresis of TDH on $05 Polyacryl- amide GEIS O O O O O O O O O O O O O I 0 d. Polyacrylamide Gel Electrophoresis of Nati ve TDH O O O O O O O 0 O O O O O O 0 Preparation of 3H-PLP-Labelled TDH . . . . . vii 32 33 34 34 34 35 35 36 37 38 39 39 39 40 4O 44 45 a. Affinity Chromatography of TDH Labelled LllVIVO With H'PyridOXIne o o o o o o o o o o o o 45 b. Association of 3H~TDH Radioactivity with the PLP CnfaCtor O O O 0 O O O O O O O O O O I O O 46 Activation of Soluble TDH by AMP . . . . . . . . . . . 54 a. Kinetic Properties with ReSpect to L- Threonine . . . . . . . . . . . . . . . . . . . . . 54 b. Protein Order Dependence of the Activa- tion Process . . . . . . . . . . . . . . . . . . . 57 c. Nature of the Process of AMP Activation . . . . . . 66 i. Analysis of Progress Curves of AMP ktivation O O O O O O O O O O O O O O O 0 O I 66 ii. Pre-established Polymerization as an Alternative Hypothesis . . . . . . . . . . . 74 iii. Rate constant for the Activation Process 0 O O O O O O I O O O O O O O O O O O O 77 d. Effect of Sucrose on the Rate of Reac- tivation O O O O O O O O O O O O O O O O O O O O O 87 e. Effect of Temperature on the Rate of ktivation O O O O O O O O O O O O O O O O O O O O 91 Activation of Immobilized TDH by AMP . . . . . . . . . 94 a. Properties of TDH Immobilized on CL- Sepharose O O I O O O O O O O O O O O O O O O O O O 94 b. Removal of AMP from Matrix-Bound, AS SOCIatEd TDH O O O O O O O O O O O O O O O O O O 97 c. Treatment of Sepharose Bound TDH with urea and NaBH4 O O O O O O O O O O O O O O O O O O 103 i. Measurement of Radioactivity . . . . . . . . . 103 ii. Measurement of Enzyme Activity . . . . . . . . 103 d. Uptake of Soluble TDH Monomers by Matrix- Bound, Dissociated TDH in the Presence of TDH . . . 107 e. Kinetic Behavior of Immobilized TDH . . . . . . . . 110 viii lifl’t‘piri . a :, '..LlLIMI‘| Filming; i [17, r_I- iinwn; , A. III; I. 019.: 1. 2. 3. i. Hysteresis in the AMP Activation of Matrix-Bound, Dissociated TDH . . . . ii. Effect of L-Threonine on the Activity 0f MatTlX-BOUHCI TDH o o o o o o o o o USSJIII o o o o o o o o o o o o o o o o o o 0 Improved Purification Procedure . . . . . . . In Vivo Labelling of TDH Using 3H-Pyridoxine Activation of Soluble TDH by AMP ...... II. DETERMINATION OF ENZYME KINETIC PARAMETERS BY CON- TINUOUS ADDITION OF SUBSTRATE TO A SINGLE REACTION MIXTURE AND ANALYSIS BY A TANGENT-SLOPE PROCEDURE . . A. \N d LITERATURE REVIEW ..... . . . . . . . . . . . 10 The H11] Equation 0 O O O I O O O O O O O O O 2. Kinetic Analysis of Single Reaction Progress curves 0 0 O O O O I O O O O O O O O O O O 0 3. Independent Control of Substrate Concen- tration . . . . . . . . . . . . . . . . . . . 4. Automation in Enzyme Kinetic Analysis . . . . MATHEMATICAL ANALYSIS OF THE METHOD . . . . . . . 1. MATERIALS AND METHODS o o o o o o o o o o o o o o o 1. Control of Substrate Concentration by Con- tinuous Addition 0 O I O O O O O O O O O O 0 Analysis of Raw, Undifferentiated Data (curve—Fit MethOd) O O O O O O O O O O O O 0 Analysis of Differentiated Data (Tangent- Slope MethOd) C O O O O O I O I O O O O O O 0 Computer Programs . . . . . . . . . . . . . . . a. Optimizing Experimental Variables (SSOP) b. Generation of Simulated Data (SIMUL) . . c. Integral Analysis of Data (MARQ) . . . . d. Differential Analysis of Data (TANKIN) . ix Page . . . . . 110 113 119 119 119 120 123 123 123 124 125 126 128 128 128 132 136 136 136 137 138 139 Page e. Weighting in the Analysis of Differ- entiated Data 0 O O O O O O O O O O O O O O O O O O 143 2. Experimental . . . . . . . . . . . . . . . . . . . . . 147 a Biochemicals . . . . . . . . . . . . . . . . . . . 147 b. Immobilization of LDH . . . . . . . . . . . . . . . 147 c. Enzyme Assays . . . . . . . . . . . . . . . . . . . 148 d. Instrumental System . . . . . . . . . . . . . . . . 152 e. Operation of the System . . . . . . . . . . . . . . 155 f. Absorbance Correction and Data Storage . . . . . . 156 0. RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . 161 1. Analysis of Simulated Data . . . . . . . . . . . . . . 161 a. Determination of Optimal Window Size for the Tangent-Slope Method . . . . . . . . . . . 161 6. Determination of Optimal Substrate Concentration Range . . . . . . . . . . . . . . . . 164 c. Comparison of the Tangent-Slope and Curve-Fit Methods . . . . . . . . . . . . . . . . . 165 d. Time or Product-Dependent Effects . . . . . . . . . 17C 2. System Performance and Analysis of Real Data . . . . . 178 a. Preliminary Evaluation of the System . . . . . . . 178 b. Kinetic Constants Estimated for Solu- bIe Enzmes O O O O O O O O O O O O O O O O O O O O 181 c. Kinetic Constants for Imnobilized LDH . . . . . . . 191 E. DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . 196 1. Analysis of Simulated Data . . . . . . . . . . . . . . 196 2. Analysis of Real Data . . . . . . . . . . . . . . . . . 198 SYNOPSIS AND CONCLUSIONS 0 o o o o o o o o o o o o o o o o o o o o 204 PPENDIX O O O O O O O O O O O O O O O O O O O O O O O O O O O O I 205 FO()1.h"()T-IES O O O O O O O O O O O O O O O I O O O O O O O O O O O O O 212 'riEFEREh‘CES . Page REFERENCES . . . . ........ . . . . . . . . . . . . . . . . 216 xi L13 ,4 . Lu.) Table 1 1 12 123 14 LIST OF TABLES Importance of Subunit Association in the Catalytic Activity of Enzymes . . . . . . . Importance of Subunit Association in the Allosteric Functions of Enzymes . . . . . . . Dissociation Constants for Subunit, Sub- state, and Activator Equilibria for TDH . . Comparison of the Affinity Purification Procedure of TDH used in these Studies with a Non-Affinity Procedure used in Preliminary Studies . . . . . . . . . . . . Labelling o TDH with 3H-PLP by Growth of £0 C011 0n H‘PyridOXine 0 0 0 0 0 o o o o 0 Kinetic Constants for Soluble TDH . . . . . Optimized Linear Fits of Activation Progress Curves to Either a First or Second Order Processes O O O O O O O O O O O O O O O O I Effect of Urea or AMP-Free Buffer Nash on Untreatgd or Reduced Matrix-Bound, Asso- ciated H-PLP-Labelled TDH . . . . . . . . . Specific Uptake of Soluble TDH . . . . . . . Michaelis—Menten Parameters of Various Forms of Matrix Bound TDH . . . . . . . . . . . . Protocols for Enzyme Assays . . . . . . . . Noise of Spectrophotometric System and Cuvet Contents . . . . . . . . . . . . . . . Kinetic Constants for Soluble Enzymes . . . Kinetic Constants for Soluble and Innmbil- ized LDH I O O O O O O O O 0 O O O O O O O O xii Page 10-11 19 43 51 55 71 104 108 117 149-151 179 188—189 192-193 LL) . («1 Link». vatOr Setha Puri.‘ Chl‘g. Llrll‘leg rP-‘y J 1() 1 1 112 13 LIST OF FIGURES Linked TDH Subunit, Substrate and Acti- vator EQUilibr‘ia O O O O O O O O O O O O O O O O TDH Induction Kinetics . . . . . . . . . . . . . Sephadex G-200 Gel Filtration of TDH Purified by N6-Linked AMP Sepharose . . . . . . Chromatography of 3H-Labelled TDH on N6- Linked AMP Sepharose . . . . . . . . . . . . . . Nat ve Polyacrylamide Gel Electrophoresis 0f H-PLP-Ldbélled TDH o o o o o o o o o o o o o Sephadex G-25 Gel Filtration in 8 M Urea of 3H-PLP Labelled TDH with and Without NaBH4 Pretreatment . O O I C O O O C O O O O O O Hysteresis in the Activation of TDH by AMP . . . Activation of TDH by AMP as a Function of Time with Variation in Enzyme Concentration . . Determination of the Order of the Initial Rate of TDH AMP-Activation with Respect to Protein Concentration by the Differential Method . . . . Inverse Time Plot Showing Approach to Com- pletion of Activation of TDH by AMP . . . . . .~ Extent of Reactivation by AMP as a Function of the TDH Concentration and of the Procedure used to Determine Maximum Reactivation . . . . . . . Boundary Sedimentation Velocity of TDH in the Absence of AMP as a Function of Enzyme Concen- tration O O O O I O O O 0 O O O O O O O O O O 0 Second Order Kinetic Plot of TDH AMP-Activation Progress Curves . . . . . . . . . . . . . . . . xiii 17 23 41 47 49 52 58 61 64 67 72 75 78 20 22 23 27 29 30 31 14 15 16 17 18 19 20 21 22 23 24 25 265 237 ZEES 23$? 3() 31 Determination of the Apparent Order Rate Con- stant for Activation of TDH by AMP . . . . . . . 81 First Order Kinetic Plot of TDH AMP-Activation Progress Curves . . . . . . . . . . . . . . . . 83 Determination of the Apparent First Order Rate Constant for Activation of TDH by AMP . . . . . 85 Dependence of Second Order Reactivation Rate Con- stant on Viscosity . . . . . . . . . . . . . . . 88 Determination of the Apparent Arrhenius Activa- tion Energy for the AMP-Activation of TDH . . . 92 Effect of CNBr Concentration on the Specific Activity of Matrix Bound, Associated TDH . . . . 95 Release of TDH Activity from Matrix Bound, Asso- ciated TDH Upon Removal of AMP from Wash Buffer 98 TDH Remaining Matrix Bound After Hashing the Matrix with AMP-Free Buffer . . . . . . . . . . 101 Renaturation of TDH from 9 M Urea . . . . . . . . 105 Reduced Total Activation and Hysteresis in the AMP Activation of Matrix Bound, Dissociated TDH 111 Substrate Saturation Steady State Kinetics of Various Forms of Matrix-Bound TDH . . . . . . . 114 A Hypothetical Substrate Addition Experiment . . 129 Graphic Illustration of Tangent-Slope Estima- tion of Reaction Velocity . . . . . . . . . . . 133 General Flow Chart for the Computer Program TANKIN O O O O O O O 0 O O O O O O O O I O O O 0 O 140 A Semi-Automated System for Kinetic Analysis of Enzyme Reactions used in the Present Studies . . 153 Correction of Raw Absorbance Data . . . . . . . 157 Determination of Optimal Window Sizes for use in Tangent-Slope Estimation of Velocities at Three Data Noise Levels . . . . . . . . . . . . 162 Determination of Optimal Substrate Concentration Range for TANKIN Tangent-Slope Estimation of Hill Parameters O O O O O O O O O O O O O O O O O O O O 0 O O O 166 xiv 34 35 36 37 38 Comparison of the Accuracy and Precision of the MARQ and the TANKIN Methods . . . . . . . . . . . . Effect of End Point Deletion on the Final Correl- ation Coefficient (A) and Apparent Hill n (B) at Various Levels of Simulated First Order Enzyme Inactivation . . . . . . . . . . . . . . . . . . . . Effect of Varying tf (A and C) or Pf (B and D) During a Simulated Substrate Addition . . . . . . . Typical Results of Single Cuvet Assays of Hill Parameters for LDH (A and B) and B-Galactosidase (C and D) C C O C O O O O O O O I O O O O O O O O 0 Proposed, Fully Automated System for Kinetic Analy- sis of Enzyme Reactions . . . . . . . . . . . . . . CD Observed During the Exchange of Denterium into a- Ketobutyrate from 020 Catalyzed by KDPG-Aldolase . . CD Observed During the TDH Reaction in 020 as a Function of Buffer Conditions and the Presence or msence Of AMP O O O O O 0 O O O O O O O O O O O O O XV 172 . 176 183 . 202 207 210 A AMP,ADP,ATP C C Ci Cl,C2,C3,CC DTT EDTA E f (subscript) F FDP FTHF H i (subscript) SYMBOLS AND ABBREVIATIONS absorbance adenosine mono-, di-, tri-phosphate concentration of substrate solution being added (M) cosubstrate concentration (M) curie apparent linear correlation coefficients dithiothreitol ethylenediaminetetraacetate molar extinction coefficient for 1 cm light path (M'lcm'l) final value convergence criterion for the program TANKIN fructose diphOSphate formyl tetrahydrofolate concentration of activated TDH subunits (M) the ith value first order constant for enzyme inactivation (min'l) second order rate constant for dimerization (M'lseC'l) inhibition constant of product (M) thousand counts per minute Z-keta-3edeoxy-6-phosphogluconate liter xvi LDH n N NAD,NADP o (subscript) 0 ONPG PEP PLP PMSF concentration of the unactivated TDH subunits (M) lactate dehydrogenase Hill coefficient number of data points per run nicotine-adenine dinucteotide, nicotine-adenine dinucleo- tide phOSphate initial value observed absorbance ortho-nitrophenyl~3-D-galactoside product (moles) phospho-enol pyruvate pyridoxal phosphate pheyl methyl sulfonyl fluoride order of dependence of activation rate on subunit concen- tration rate of substrate addition (1/min) root mean squared deviation of noise seconds substrate concentration (M) S at Vmax/Z sodium dodecyl sulfate S-o-nitrophenyl-L-cysteine time, time interval between points (min) trichloroacetic acid biodegradative threonine dehydrase of E, gglj_ biodegradative threonine dehydrase of £3.2211 catalytic reaction velocity (micromoles/min) expected V if all subunits activated xvii expected V if all subunits inactivated expected V if all active sites are saturated variance of V number of data points in window (odd number) xviii INTRODUCTION The tenuous rhythm of the living state is maintained by a complex system of information processing. The transducers of this system are proteins that sense their environments and adjust their activities in symphony. As the spectrum of protein activity is wide, so the patterns of regulation of that activity are diverse. Some generalizations, how- ever, seem possible. Regulation appears where and when it is needed: at key points in metabolism that irreversibly commit biological resources, or whenever homeostatis requires modulation of certain processes. These control mechanisms may act at the level of protein synthesis, degradation, com- partmentalization or structure-function. Structural alterations are often the result of binding of small mole- cules in the environment. Such regulatory ligands act via the tertiary or quaternary structure to communicate information in the form of confor- mational adjustments. Subunit interfaces are evidently quite vulnerable to this kind of disturbance and often the attachment of ligands will change the strength of association between subunits. The importance of this subunit structure in regulation of protein function has been recognized since x-ray analysis failed to confirm the concept of direct heme-heme interaction in hemoglobin (1). Indeed, regu- latory proteins are often found to possess complex quaternary structures. In some instances ligand binding may thus lead to a change in oligomeric 1 state of a regulatory protein which can offer some unique opportunities for metabolic control. The biodegradative threonine dehydrase from Eschericia coli catalyzes the first step in the utilization of L-threonine for ATP generation. The synthesis of this enzyme is mediated by cyclic AMP with glucose and oxy- gen as repressors and amino acids as inducers (2). Its activity is fur- ther regulated by AMP activation (3), product (a-ketobutyrate) inhibition (4), and pyruvate (5) and serine (6) inactivation. This enzyme is a prime example of regulation by ligand-induced oligo- merization-deoligomerization. Inhibition of the enzyme by a-ketobutyrate pyruvate, or sulfhydryl oxidation is accompanied by subunit deoligomeri- zation (4,5,7), while activation by AMP correlates with an increase in molecular weight (3). It is clear that both activity and oligomeric state are related to ligand binding (8,9,10), but it is less certain whether quaternary structure alterations act in concert with ligand bind- ing to alter enzyme activity or whether Oligomerization is merely a by- product of ligand binding, possibly with some other metabolic function. The research to be described was undertaken to further clarify the role of Oligomerization in the AMP-induced activation of biodegradative L-threonine dehydrase of E, £911. At low enzyme concentration, AMP induces a dimerization of the enzyme. Previous studies of pre-steady state kinetics of AMP activation have suggested that dimerization was necessary for activation (11). These studies were re-examined over a much wider range of enzyme concen- tration using an improved analytical instrument. The present results are 3 in substantial agreement with earlier findings (11) and prompted further characterization of the hysteretic1 activation process. The progress of activation was examined and found to be consistent with either a first or second order process. However, a first order fit to the activation time course required restrictive assumptions about the quaternary structure and activity of the inactivated dehydrase. A second order fit did not require such assumptions and was consistent with a rate limiting dimerization process in AMP activation. From these data, a second order rate constant for dimerization was calculated. From the value of this rate constant and its dependence on viscosity it was felt that the dimerization process may itself be diffu- sion controlled. However, it was not possible to obtain strong support for this possibility from temperature dependence studies. To obtain more direct information about the importance of oligomeri- zation, the enzyme was immobilized on Sepharose 48 under conditions which produced minimal alterations in kinetic properties. Evidence is present- ed that the AMP-activated dimer becomes attached to the matrix via only one subunit. This product is referred to as the “matrix-bound associated enzyme" since its properties appear to resemble those of the soluble TDH dimer. Nhen AMP is removed from wash solutions, non-covalently linked monomer can be eluted from the matrix in a process resembling the de-oli- gomerization2 which takes place in solution. The remaining "matrix- bound, dissociated enzyme" will also reassociate with soluble monomers in the presence of AMP to form a "matrix-bound reassociated enzyme". The matrix-bound, dissociated enzyme shows a reduced AMP activation and no significant hysteresis in the activation process. The steady state kinetics of this enzyme form show that this reduced activation is 4 due to a fraction of enzyme which can be fully reactivated while the majority of the enzyme appear unaffected by AMP. It is argued that this smaller fraction represents subunits attached to the matrix in adjacent positions allowing rapid dimerization and activation while the remainder of the protomers cannot be activated because they are unable to dimerize. The matrix-bound reassociated, enzyme is fully activatable, lending weight to the concept that dimerization is necessary for AMP activation. In support of this main theme, a new enzyme preparation was developed based on affinity chromotography which is simpler and more reproducible than a previous protocol. In addition, in order to quantitate immobil- ized threonine hydrase a method was developed to radioactively label the PLP requiring enzyme in 1119 with 3H-pyridoxine. These techniques sim- plified isolation of the large quantities of labelled enzyme needed for these studies and are described, along with the examination of AMP acti- vation, in Chapter I of this dissertation. To aid in the kinetic analysis of threonine dehydrase, a new method was developed for obtaining kinetic constants from a single reaction mix- ture. The method was validated statistically using artificial data and further tested with a variety of enzymes both soluble and immobilized. As this project developed, it became largely removed from studies of TDH and consequently it is treated independently in Chapter II. The Appendix of this dissertation presents the results of a prelimin- ary investigation of the effect of AMP on the stereospecificity and mech- anism of TDH. CHAPTER I IMPORTANCE OF DIMERIZATION IN THE ADENOSINE-5'—MONOPHO$PHATE ACTIVATION 0F BIODEGRADATIVE L-THREONINE DEHYDRASE FROM ESCHERICIA COLI A. LITERATURE REVIEW 1. Regulation of Enzyme Activity Through Subunit Interaction a. Models of Allostery Involving_§ubunit Interaction The complex tertiary and quaternary structure of some proteins allows them to govern the interaction of a set of dissimilar molecules or ligands. The indirect nature of these interactions is best illustrated in proteins such as hemoglobin (13) or aspartate transcarbamylase (14) where communication must occur between ligand binding sites on different peptide chains. Conformational alterations wrought at one site must, in these cases, be translated to distant sites through subunit interfaces. The discourse of structurally related (homotropic) or unrelated (hetero- tropic) ligands through the language of protein conformational change has come to be called allostery. An early model of allostery (15) considered proteins to be bistable elements with the relative populations of the two tautomeric states per- turbed by the energetics of ligand binding. All subunits of a given pro- tein molecle were postulated to occupy the same state. Allostery was thus the result of functional differences in the two tautomers. This model satisfactorily described the coooperative homotropic binding of oxygen to hemoglobin and the allostery exhibited by phosphofructokinase. The symmetrical nature of the equilibrium between states, however, was admittedly (15) unrealistic. A more flexible formulation (16) postulated that tautomeric changes were not necessarily pre-extant, but were induced by ligand-protein 5 6 interaction. In addition, allowance was made for intermediate tautomer- ic states depending upon the subunit arrangement and the sequence by which subunit binding sites take up ligand. This seguential model could account for the anti-cooperative binding of NAD to glyceraldehyde-B-phos- phate dehydrogenase (17)., Both the symmetrical and sequential models are themselves limiting cases of even more general models (18). However, the utility of such general models is restricted by the multitude of tautomeric equilibria that must be analyzed. Simplified models have contributed conceptual viewpoints from which to consider allosteric phenomena. However as the diversity of enzyme regulation has become clearer, it seems much less probable that any one mechanism can ever unify our concept of allosteric behavior. b. Ligand Regulated Oligomerization It has recently been argued (19,20), that mechanistic interpretations are misleading and that allostery is better characterized in terms of energetics. In this view, cooperativity results from the need to balance the free energy changes that define variously liganded states of oligo- meric proteins. Further, ligand binding site interactions should be described by changes in subunit-subunit dissociation constants which may be more readily detectable than changes in tautomeric states. Subunit equilibria have been used to probe the allostery of hemoglobin (21) and CTP-synthetase (22). A consideration of subunit association-dissocia- tions is particularly appropriate since such equilibria may be important regulatory features of many enzymes (8). 7 The kinetic consequences of ligand regulated enzyme-Oligomerization have been extensively examined from a theoretical point of view (23). The kinetic properties of such systems appear to have the potential for great regulatory flexibility with a minimum expenditure of energy. Lists of enzyme which exhibit ligand regulated Oligomerization have been given by Frieden (12), Lavitsky and Koshland (17), Klotz (24), Kurgonov (25) and more recently by Dunne and Hood (8). Although the phe- nomenon is apparently widespread in nature, few detailed characteriza- tions have been made. In particular, it is rarely clear whether allostery is dependent upon -- or merely coincident with -- the observed changes in oligomeric state. 2. Assessing the Importance of Subunit Association a. Equilibrium or SteadyAState Methods The techniques used to examine the importance of quaternary structure on enzyme activity have classicially involved equilibrium methods. Such methods, which probe only isolated states of Oligomerization, are poorly suited for probing causeeeffect relationships important in mechanistic investigations. In addition, in order to demonstrate that the functional state at equilibrium reflects the quaternary structure rather than merely the degree of ligand binding, it is necessary to simultaneously monitor (a) enzymatic activity, (b) quaternary structure and (c) stoichiometry of ligand binding. It would be fortuitous if subunit and ligand dissocia- tion constants as well as intrinsic catalytic rate were all of the proper magnitude to allow such simultaneous measurements. Nhile specialized 8 rapid reaction or active enzyme centrifugation techniques may prove use- ful, the above constraints probably account for the dearth of studies where such direct correlations have been attempted. An example of such a study concerned the effect of glutamate dehydrogenase concentration on enzyme activity and effector binding (26). These authors, using light scattering, direct equilibrium binding, and rapid steady-state kinetic techniques, provided data consistent with an important role for oligomer- ization in determining enzymatic response to effectors. These results implied that subunits may themselves behave as effector "ligands". The information from these equilibrium experiments was less than definitive, however, and data from acetylated (non-oligomerizing) enzyme was needed to strengthenthis conclusion (27). This example illustrates the weakness of equilibrium/steady state techniques in elucidating the importance of subunit interaction in allo- steric interactions. The most satisfying answers to the question of the importance of subunit association in the catalytic and regulatory func- tions of enzymes have come from experiments employing one of the follow- ing techniques: (1) Association Kinetics, (2) Inmobilized Monomer, or (3) Stabilized Monomer (see Tables 1 and 2). b. Association Kinetics If subunit associations are required for the catalytic or regulatory functions of an enzyme, then changes in enzyme function should be observed when isolated subunits of an enzyme~polymerize into the associ- ated form. If isolated subunits can be obtained under conditions where association proceeds spontaneously, and if the association step is rate- liniting, then the association process can be studied by observing .eeee_e ee_e o» »o___ee mg» m_ a_>_eee eeeameexe .mwmwgucmgoq cw ummopucu men assuaemuwa on maocosmvomo Anny no» omucvx ucpunosu heev e: “may e: ee_u..< Amev we» afieveeee =95 Aoev no» emacmmoeuxgma mum—u: Aomv mm» Ammv no» amou_mouua—~uia Ammv o: Asmv Loeocoe .uoacv emacomoeua;oa manganese m «wasmupueouapo Ammv we» mmnuugamozg m:__ux_< Ammv mm» mmaeosomm muagamogm «morph Acmv «a» a emu—auo=nmogm Ammv o: «mo—ocpumcmeh ANMV oe afimv ee Acme ee eme_ee_« Amuv o: omucpme< nawwv no» mmacmmcguagmo .ogou_< eweocoz eoeocaz mupuocpg mea~cm vapppamum vmnp~_nOEE~ cowuupuomm< ~»u_>_oe< Lee eoe_=ae¢ eo_be_eeem< eweeesm massage ee »u_>_ue< u_b».eueu me» e. comuu_uomm< u_::a=m ea mucoueoasu H «pooh 10 Ammv we» .Ex—on ..>waua .eumaam wmo_o=w Aemv mm» Aemv mo» .sa—oa ..uuu:. mom omucwx Foeou»_o Ammv no» .eapoa ..>.uum += umupugucxw m1»; .sxpoa ..>+uuu amazon Ammv we» Afimv we» mz\eeeeeeeemH -oeeSeeo maeeepeomu own—xxoneou Acmv no» .Es—oa ..>.pun mum wan>=e~mipocmognmczm .oommvu Amev we» ..eeee. eue\eh< emee.x eeeeeeeeameea H anacomoeuas .Eapoa loo ocpeomoeo: Awev we» ..>*uou ocwcooegpig immucwxousoam< omuAPQEan Asev no» Acvv ma» .pamo¢.mh<\m»u euumcuep muoueaam< Lueocoz eoeoco: muwuocwx copuuezm mea~=m .pwnmmmi .noeeu .oomm< ucovuuczm so» vaepaaoa covuowuomm< upcsnsm «mea~=m we m=o_uu:=m opeaumo__< as» =_ copuovoomm< upcaasm mo mucoueoaeu w m—auh 11 .eo_eebeemmwe mweee “my mm» Ao.HHV mm» .Ezpoa ..>wuuo mz< :9» ANmV mm» .sxpoa ..>wuum mz\ama wmcwx muu>aexa Aomv waxes .esgoa ..>wuum aumumo< mmucwx mcwpmmeu amazon ioeuagmo opusgmozm Aemv eases .eemm_e ..peeee .ee< -m-ee»eee_eeeea_u Remy ee .e»_oe ..>_oee ae< ANNV mm» Ammv o: .uommpv ..uou=w aou\a»o mmmcmmoeu»;mo becamuapm eoeccoz Legacoz murumcpx caravan; mexucm “pumMMMT .neesH .UOmmKi unopuucam Lop voewaama coFuuwuomm< pecansm mmsxucm mo meowuucam upcmumopp< on» =_ cowumPoOmm< upcsnam yo mucuucoaem A.eeeeuv N apeee 12 changes in enzyme catalytic or regulatory function with time. Since associations proceed at a rate which is second order or greater in sub- unit concentration, a catalytic or regulatory change whose appearance is at least second order in subunit concentration may require subunit asso- ciation. Thus association kinetics have been used to determine the requirement for association of a large number of catalytic (Table 1) or regulatory (Table 2) functions of enzymes. For enzymes known to undergo ligand mediated changes in oligomeric state (e.g. glycerol kinase, aspartokinase-homoserine dehydrogenase I, isocitrate dehydrogenase or TDH (Table 2)), association from isolated subunits can be made favorable by rapid changes in ligand concentration. In other cases isolated subunits must be obtained under more drastic con- ditions such as urea or guanidine-HCl denaturation or by temperature or pH changes (e.g. aspartate transcarbamoylase (Table 2), aldolase, triose phosphate isomerase, or avidin (Table 1)). In these latter instances significant subunit refolding often occurs and detailed kinetic schema must be considered. c. Immobilized Subunits A significant problem with equilibriun methods (described above) is that often the equilibrium constant for subunit association is so great 'that isolated, stable subunits cannot be examined at the concentration required for catalytic enzyme assays. Thus a general method whereby association can be prevented would be very useful. The technique of enzyme immobilization is such a method. The use of enzyme immobilization to investigate the significance of subunit associations has been pioneered by Chan (58). His work has lead 13 to methods for handling and assaying Sepharose-bound enzymes, and condi- tions under which relatively unmodified matrix-bound monomer Species may be obtained. He has used enzyme immobilization to examine the properties of aldolase, transaldolase, and lactate dehydrogenase (Table 1) and aspartate transcarbamoylase (Table 2). In an interesting combination of approaches, the inactive LDH monomer was bound to Sepharose through a reducible disulfide bridge. Kinetics of reappearance of LDH activity upon reduction suggested that reassociation was required for appearance of catalytic activity (42). d. Stabilized Subunits An alternative to immobilization would be to stabilize the monomeric form of the enzyme in some way. Occasionally this can be done by mere dilution (e.g. glycerol kinase, Table 2). However more often, a very specific chemical modification is required. Glutamate dehydrogenase subunits can be stabilized by acetylation, and become insensitive to the effects of guanine nucleotide (Table 2). On the other hand, aldolase subunits acetylated during renaturation are unable to tetramerize, yet still retain catalytic activity. The more drastic the dissociation procedure, the more uncertain is the meaning of the observed results on catalytic or regulatory activity. Thus the implications of observed inactive subunits of acid dissociated LDH (42) is best judged only in the light of other studies of reassocia- tion kinetics or of the immobilized monomer. 14 3. Regulation of the Biodegradative TDH of Eschericia coli a. Role in Energngetabolism ‘ TDH3 catalyzes the production of a—ketobutyrate and ammonia from L-threonine. g, £911_synthesizes two TDH forms: a biosynthetic TDH, active in the biosynthesis of isoleucine and a biodegradative TDH which seems to represent the first step in catabolism of L-threonine for the generation of ATP (59). The latter dehydrase is synthesized only during anaerobic growth on a complex amino acid containing medium devoid of glu- cose or similar energy source (60,61). Conditions which result in a tem- porary energy deficit in the E, 5211 cell accentuate TDH synthesis appar- ently through an elevation in the level of cyclic AMP (2). An analogous enzyme from Clostridium tetanomorphum appears linked to ATP generation via the intermediates a-ketobutyrate and propionylphos- phate (62). It appears possible that the TDH of g, gglj_may be similarly linked to ATP formation since propionate is produced by anaerobically grown E, gglj_cells on a medium devoid of glucose but high in L-threonine (63). b. Activation of TDH by AMP Further evidence implicating TDH in an energy generating role is its activation by AMP. AMP lowers the $0.5 value of the enzyme for threonine 20-50 fold (64). AMP may also increase the Vmax of the enzyme (7) although this latter effect remains uncertain due to the reported instability of the enzyme in the absence of AMP (64). The process of activation has been shown to involve both changes in quaternary structure of the enzyme and facilitation of substrate binding in the reaction mechanism (11,65). 1% At TDH concentrations above 1 mg/ml, the enzyme appears to be a tet- ramer (66). At lower concentrations (i.e., those found under catalytic assay conditions) and in the absence of AMP, TDH dissociates ultimately to a monomer (11). However the smallest structure observed in the pres- ence of AMP is a dimer (8). A study of the kinetics of AMP association of TDH indicates that a dimerization of the monomer species in some way facilitates the AMP activation (11), however an absolute requirement for dimerization in the AMP activation of TDH has not been established. whether or not AMP affects the terminal steps in the reaction mechanism is also not known. c. Inhibition of TDH byggketobutyrate and pyruvate In the absence of AMP, TDH is inhibited by both o-ketobutyrate (4) and pyruvate (5). The inhibition of both of these a-ketoacids is similar in some respects and highlights the importance of AMP and Oligomerization in the regulation of TDH. The inhibition by a-ketobutyrate is competitive with respect to the binding of AMP, and the degree of inhibition is more marked at low con- centrations at which the tetrameric enzyme dissociates to a dimeric or monomeric form (4). Furthermore o-ketobutyrate itself can cause the enzyme to dissociate to its subunits, and conversely AMP counteracts this product-induced dissociation. The mechanism of‘TDH’inactivation by pyruvate involVes covalent attachment to the active oligomeric form of the enzyme followed by dis- sociation of the oligomer to yield inactive enzyme (5). Increasing dehy- drase and/or AMP reduces the rate of pyruvate inactivation. 16 Thus these inhibitors alter the enzymes association-dissociation equilibrium in favor of dissociation, whereas the AMP activator alters it in favor of associatjon. This observation suggests that the oligomeric state may well be a determining factor in the activity of the enzyme and that activators and inhibitors may act in part by influencing the quater- nary structure. Thus the quaternary structure may play more than merely a passive role in the allosteric regulation of TDH. 4. Allosteric Models Applicable to TDH a. Iglgand Induced Oligomerization - Deoligomerization The interdependance of activity, quaternary structure and AMP concen- tration as described above have led Dunne and Hood to propose a ligand induced Oligomerization model for TDH regulation (8). They have analyzed this model in terms of substrate, activator, and subunit binding equili- bria which are linked thermodynamically (67). This analysis correctly predicts (a) that the affinity for AMP should increase with increasing TDH and/or threonine concentrations (b) that subunit binding should be enhanced by AMP and reduced by L-threonine (c) that the enzymes affinity for L-threonine should be increased by AMP but lowered at elevated pro- tein concentrations. There are 12 equilibria that describe subunit, substrate, and activa- tor associations (see Figure 1). Thus a rigorous test for consistency of 'this model requires accurate measurement of a large number of equilibrium constants. Table 3 lists the values of those equilibrium constants for which information is presently available. Only two tests for consistency of the model can presently be made. These involve comparison of calcu- lated values for K1 and K5 with the probable ranges for these l7 Figure 1. Linked TDH Subunit Substrate and Activator Equilibria. M, TDH monomer; D, TDLH dimer; T, L-threonine; A, AMP. 18 ¥ . “ \“‘ $333322" “\ — V\\“\\\\\\\\\\:/ eeees 2'5 K 2 l9 Table 3 Dissociation Constants for Subunit, Substrate and Activator Equilibria for TDH Binding Dissociation 'Method of Constant Equilibriuma Constant(M) Determination Ref. K1 2M 0 5 - 50 x 10'7 Ultracentrifug. b (1.1 x 10‘7) Calculation c K2 2A+D 0A2 5 x 10-5 Equilibrium Dialysis 69 K3 ZMA 0A2 K4 A+M MA K5 2A+DT2 DT2A2 , 2 x 10-5 Steady State Kinet. d (0.7 x 10'5) Calculation e K5 21+o 0T2 2.2 x 10-1 Stopped Flow 11 K7 2MT 0Tb 6.7 x 10‘6 Active Enzyme A Centrifug. f K3 T+M MT - 6.0 x 10-2 Steady State Kinet. 11 K9 A+MT MAT x10 2T+DA2 DTZAZS 3.0 x 10-3 Steady State Kinet. 64 K11 T+MA MAT K12 2MAT DTZAZ <1o-8 Active Enzyme Centr. 63 r aM, D, A and T represent the dehydrase Monomer, dehydrase dimer, AMP and L-threonine respectively. bThis dissertation: see Discussion associated with Fig. 11. CCalculated from thermodynamics: K1 = K7 ° Kg/KG dBased on steady statg kinetic measurements made at elevated TDH concen- ‘tration of 1.6 x 10‘ M where the dehydrase may have been highly dimerized (4). eCalculated from thermodynamics: K5 = K2 ° KID/K5 prproximate value obtained by extrapolation (68). 20 constants based on experimental work. As seen in Table 3, calculated values are within an order of magnitude of measured values. Information is not presently available for equilibria in which the species MAlor MAJ are involved (see Table 3) because the monomeric spe- cies has not yet been observed in the presence of AMP. Using active enzyme centrifugation, Menson has shown that in the presence of AMP, TDH exists as a dimer at concentrations as low as 10'3M (0.4 ug/ml) (68) and thus K12 must be less than 10'3M. One of the purposes of this dissertation was to establish some of the properties of monomeric dehydrase in the presence of AMP. b. ghggges in Quaternary Structure During,Catalysis A very different view of the significance of TDH quaternary structure is presented by Hayaishi (10). Based upon spectral measurements and steady state kinetic determinations at high TDH concentrations (71), he has proposed that the oligomer formed at high protein concentration or in the presence of AMP is catalytically inactive although it possesses a high affinity for L-threonine. The monomer on the other hand is catalyt- ically active but has a poor affinity for substrate. While only the steady-state/equilibrium aspects of this model have been tested with any rigor (71), the model is discussed at length in terms of kinetic predictions (10). The overall TDH reaction supposedly requires substrate binding by the oligomer followed by dissociation and catalysis. Reassociation then completes the reaction cycle (10). In order for this model to be viable the reassociation rate must be at least as great as the observed catalytic rate. At TDH concentrations of 0.1 1.U./ml and in the presence of AMP, where this reaction scheme is 21 supposed to occur (71), a reassociation rate constant (monomer to dimer) of 1011M"15ec”l would be required‘. Such a rate constant approaches the diffusion limit for second order reactions (72). It is shown in the Results that the association constant of TDH monomers is about 8.8 x 105M‘lsec'1, raising doubts about the applicability of this model. 8. MATERIALS AND METHODS 1. Bacteriological TDH was obtained from an isoleucine-requiring mutant of Eschericia £911 (ATCC9739) which lacks the biosynthetic dehydrase. The mutant was re-isolated from stab cultures by combining individual colonies from Levine EMB agar plates. The isoleucine requirement was verified by observing growth on Davis and Mingioli agar plates with and without iso- leucine. The organism was best maintained at 37°C on slant cultures of nutri- ent broth in 2% agar. Bimonthly transfers on this medium ensured viabil- ity. Liquid cultures were grown at 37°C in 2% N-Z amine NAK (Humko-Shef— field Chemical Co.), 1% yeast extract (Gibco Diagnostics) and 0.5% diba- Sic potassium phosphate and distilled water. Starting cultures were pre- pared by loop-transfer from slants into 10 or 100 ml of this medium. Successive transfers were made using 1% innocula. Starting and intermed- iate cultures were incubated without agitation for 8-12 h. Final cul- tures were grown under argon with minimal strirring. Large scale cul- tures (120L) were grown in a New Brunswick Scientific Co. fermentor. The profile of growth and TDH induction in final culture is shown in Figure 2. Absorbance of the culture at 660nm was taken as a measure of g, 2211 growth. Prior to assay for TDH activity, a culture suspension was vigorously agitated with a 1% volume of toluene: ethanol (1:9:v/v), then incubated on ice for 15 min. An aliquot of the cell suspension was then added to the standard catalytic assay (see below). 22 23 Figure 2. TDH Induction Kinetics. Twelve liters of medium were innocu- lated with 120 ml of a stationary culture of E, coli. The culture was incubated under argon at 37°C and 50 to 100 ml aliquots were taken at intervals and placed on ice. The assay procedures for TDH activity an) and cell growth «3) are given in Materials and Methods. 24 25 2. Determination of TDH Activity a. Standard Catalytic Assay The coupled Spectrophotometric assay described by Dunne £2.21: (64) was used to measure TDH catalytic activity. The standard 0.2 ml cataly- tic assay contained 5 mM DTT, 5 mM AMP, 0.3 mM NazNADH, 20 mM L-threo- nine, 50 ug/ml beef heart LDH and 75 mM potassium phosphate pH 8.0. This concentration of LDH insured that a steady state reaction rate was attained within 1.5 min (73). The assay was performed in a Gilford 2000 recording spectrophotometer at 288C. The reaction was initiated by addi- tion of TDH to the reaction mixture. The TDH activity of Sepharose beads was determined using the method of Chan (74). The Standard catalytic assay was modified by increasing the assay volume to 2.0 ml and by employing a continuous stirring mechan- ism (Gilford Model 2445 Spectrostir). Stirring was at the maximum rate of 1000 rpm. 4 b. Assays EmployingRapid Mixing When the time course of AMP activation of TDH was studied, the con- centration of LDH used in the catalytic assay was increased to 1 mg/ml. This insured attainment of steady state reaction rate within 2 sec (73). AMP was initially abSent but was added from a Hamilton syringe by inject- ing 0.05 ml of a 200 mM potassium AMP, solution pH 8.0 into the 1.95 ml stirred reaction mixture. Usually, absorbance measurements were made at 340 nm employing an extiiiction coefficient of 6220 M'lcm'l. Hhen elevated concentra- tions of NADH were required, absorbance measurements were made at higher wavelengths. Relative extinction coefficients at 372.5 nm (2080 26 h-l), 382.5 nm (1150 n-1) and 384 nm (988 M-l) were determined by comparison of the absorbance of NADH solutions at these wavelengths to that at 340 nm. V 3 Other variations of the standard catalytic assay for rapid mixing experiments were made as described in Results. 3. Determination of Protein a. Soluble Proteins For the most part, protein determinations were made by a small scale modification of the Lowry procedure using crystalline bovine serum albu- min as a standard (75). However, this procedure ws unreliable when the DTT concentration in the final Lowry mixture exceeded 10 uM. In these cases a method based on fluorescamine was used (76). Unfortunately, this procedure was also found unsuitable if the sample contained excess ammo- nium ion. 2 In later work, a Coomassie blue-G procedure (77) proved very conven- ient. It was not affected by elevated levels of either DTT or ammonium ion. Both the fluorescamine and Coomassie blue procedures were calibrat- ed using a solution of TDH standardized by the Lowry procedure (75). b. Imobilized TDH Determinations of the protein content of matrix bound TDH were made by Ms. Doris Bauer of the Department of Biochemistry, Michigan State Uni- versity on a Beckman 120 C amino acid analyzer according to published methods (78). 4 A 0.6 ml sample of sepharose suspension (1:1(v/v), determined as described below) was placed in a thick glass walled hydrolysis vial and l 27 lyophilized. To the vial was then added 0.5 ml of 6N HCl. The vial was evaculated, sealed and incubated for 24 h at 110°C. The solutions were centrifuged for 15 min. at 2000xg to remove charred debris, and the supernatant was evaporated to dryness. The solid material was resuspend- ed in 0.7 ml of sample application buffer containing norleucine as an internal standard and 0.5 ml of this solution was submitted to quantita- ‘tive partial amino acid analysis. The isoleucine content of suspensions of matrix-bound TDH was corrected for that of Sepharose blanks (activated with CNBr and blocked with ethanolamine as described below but not exposed to TDH). The blank content was 50-100%. The protein content of the matrix was then calculated from this isoleucine content, and the known amino acid composition of TDH (69). 4. Determination of Radioactivity a. Aqueous Solutions The tritium content of aqueous solutions was determined by liquid scintillation counting at ~53C in a Packard instrument with a gain set- ting of 75% and a counting window of 50 to 1000. The scintillation cock- tail was prepared by mixing 500 ml of toluene, 500 ml of triton X-IOO, 4 g PCP and 0.1 g dimethyl POPOP. Ten milliliters of this cocktail was mixed with 1.0-2.0 ml of aqueous sample. This level of H20 produced a stable clear solution at room temperature and at -5°C. In some cases the salt content of the sample was lowered by dilution in H20 to avoid pre- <:ipitation in the cocktail. Basic samples were acidified with 0.05 ml of 20%»TCA.in order to avoid phosphorescence background during counting. All samples were counted until the statistical error in the count (2 .S.D.) was less than 5%. Quench corrections were made by addition of an intel Counl 56le ml 0' ing l desu in ill 30% l scin' cult Ing‘ Pinc‘ 28 internal standard consisting of 0.02 ml of 3H-toluene to each sample. Counting efficiencies ranged from 5 to 13% depending upon the sample vol- ume and salt content. b. Sepharose Suspensions To determine the tritium content of matrix-bound TDH, 0.4 ml of a Sepharose suspension (1:1 (v/v), as determined below) was mixed with 0.4 ml of concentrated HCl and incubated at 70°C for 10 min. To the result- ing clear solution was added 0.8 ml of H20. This sample was counted as described above for aqueous samples. c. Polyacrylamide Gel Slices Polyacrylamide gel slices (6 mm diameter, 2.5 cm length) were placed in marble capped test tubes and incubated for 3 h at 70°C with 0.2 ml of 30% H202. The resulting clear solution was then transferred to a scintillation vial and counted as described above for aqueous samples. 5. Purification of TDH by Affinity Chromatography a. Preparation of Crude Extract The frozen cell paste (about 144 g wet weight) from a 120 l liquid culture was brought to 2-6°C by suspension in 170 ml of a buffer consist- ing of 1 mM Nag EDTA, 2 mM DTT, 0.05 mg/ml PMSF5, 0.01 mg/ml bovine pancrease deoxyribonuclease I, and 0.1 M potassium phosphate, pH 6.8. The cold suspension was placed on ice and sonicated for 3 min using a Branson sonicator fitted with a half-inch tip, and a power setting of 80 watts” This process was repeated 10 times with intermittent cooling to maintain a temperature of less than 10°C. 29 The sonicate was immediately centrifuged at 2-6°C for 3 h at 31,000 x g in a Beckman J-21C Centrifuge using a J-21 rotor. The resulting clear yellow supernatant was further purified by affinity chromatography. b. Chromatography on N5-Linked AMP-Sepharose A column (9 cm height, 2.5 cm width) of NG-linked APP-Sepharose (P and L Biochemical Col, 5.2 umoles of phOSphate per ml of bed) was precy- cled by first washing with 35 ml of 8 M urea solution, then by resuspen- sion, repacking and equilibration with 2 mM DTT, 1 mM Naz EDTA 0.1 M potassium phosphate, pH 6.8 (Nash buffer). The column was equilibrated, used and stored at 2-6°C. The same bed was reused 7 times over a period of 6 months with no apparent changes in binding or flow properties or in the final dehydrase specific activity. The crude E, ggll_extract was carefully applied to this column (at 2-6°C) followed by 10 l of wash buffer at a flow rate of 300 ml/h. The column was then washed successively with the following buffers and vol- umes at about 100 ml/h: (1) wash buffer contaiing 1 M KCl, 100 ml, (2) wash buffer, 20 ml, (3) wash buffer containing 20 mM NazATP, 20 mM Naz ADP, 2 mM NADP, and 4 mM NAD, pH 6.8, 40 ml, (4) wash buffer 40 ml and (5) wash buffer containing 5 mM AMP, pH 6.8, 1 1. During the last wash the effluent was monitored for the first sign of yellow color or fluorescence (using a long-wave UV lamp). As soon as color or fluorescence was visible, the effluent was collected into a sep- arate container. Altotal of 450 ml of effluent was collected. 30 c. Concentration and Final Centrifugation The eluted dehydrase was concentrated for 5 h under 50 psi argon using an Amicon concentrator fitted with a PM-30 membrane. The solution was concentrated to a final volume of 7 ml and centrifuged at 30,000 xg at 2-6°C for 1 h to remove denatured protein. The solution was stored frozen at -20‘C in 0.5 ml aliquots until needed. When stored this way no loss in enzyme activity was observed over periods up to 1 year. d. Production of 3H-Labelled TDH For production of 3H-labelled TDH, the cell paste from a large scale E, £911_culture was combined with that from a smaller (1/10th scale or 12L) culture. The two cultures were grown and harvested simultaneous- ly under identical conditions, with the exception that upon innoculation of the smaller culture, 0.5 to 1.5 ml of G-3H pyridoxine hydrochloride (Amersham Co., 0.6 - 2.1 Curies/mmole) was also added. 3H-TDH was iso- lated from this combined'cell mass exactly as outlined above for unla- belled dehydrase. 6. Production of AMP-Free Dehydrase AMP was removed from TDH solutons by Sephadex G-25 gel filtration exactly as described by Rabinowitz gt_gl, (65) with the exception that the column length was increased from 4.8 cm to 20 cm. This column pro- vided excellent resolution of TDH from AMP and no significant levels of AMP could be detected in gel-filtered solutions of TDH by either absor- bance at 260 nm or by adding 140-»? as done by Rabinowitz gt 91. (65) (data not presented). 31 TDH solutions lacking AMP were prepared for catalytic assay by first adding a 2.5% volume of 200 mM AMP, pH 8 to an aliquot, incubating at room temperature for 30 min prior to addition to the standard catalytic assay. Such assays showed that recovery from the G-25 procedure was greater than 90%. 7. Polyacrylamide Gel Ejectrophoresis of TDH a. Native Gels Native polyacrylamide gel electrophoresis was conducted at 4°C according to the method of Ornstein (79) and Davis (80). Minor modifica- tions of this method are described in detail by Menson (68) and will not be repeated here. These gels were stained for protein exactly as described by Blakesly and Boezi (81) and for activity exactly as given by Menson (68). Color development in this latter stain was found to be highly non-linear with time (data not shown) possibly due to TDH inacti- Vation during the staining reaction (82). The stain was therefore not used to quantitate TDH activity on gels. Enzyme activity was quantiated on native gels by cutting the gels into 2 mm sections. The.sections were gently crushed and suspended in an equal volume of buffer containing 2 mM AMP, 2 mM DTT, 1 mM EDTA, and 0.1 M potassium phosphate, pH 8.0. The suspension was incubated at 4°C for 24 h and the eluted activity determined using the standard catalytic assay. b. Electrophoresis in the Presence of $05. SDS polyacrylamide gel electrophoresis was performed employing the : ugh .muoguoz can mpowemuaz :v.p*opou a. co>pm my ogsuoooea aupcpweo one .Ammv cameo: we one» no: can: ugauoooea Aupcpeeulco: aged cu A :e an a 32 s . 5 32:? m2 « am we A «.8 a v 5 . 32:: .3: @541: $88 :8 $3.8 5.: couscous: .u.m « Aup>puu< . .u.m « ppm?» u_wwouam peep; mucuewcoaxm agecpeepaea :. vow: oczuouoea »p_:_mh ._.Z._._>_._.O.—._>_._.o< wwxwo o CON 00. mm Om wk. 00_ We) NOILVHLNBONOO HAIR/131:1 Figure 5. 49 Native Polyacrylamide Gel Electrophoresis of 3H-P5P-labelled TDH. 3H-PLP labelled TDH (407 I.U./mg, 1.5 x 10- I.U.ldpm) was electrophoresed, as described in Materials and Methods. The volume applied to 2 identical gels was 0.025 ml containing 0.1 mg of protein. One gel (solid line) was stained as described in Materials and Methods and scanned at 600 nm in a Gilford spectophotometer fitted with a linear transport. The other (C) was sliced in 0.2-0.25 cm sections and counted as described in Materials and Methods. 50 . 500.0000... 00: oooooooooorooooooooooooi - (WdOM) x1lAl10v0lovu Ed? do 20E mozqema m m L. m m a m N _ o - — q _ 4 Od (mu 009) BONVBHOSBV 51 ODE\ 0:0H owe we auw>wpuo onceuxzmu quFUmam use ooo.o¢ agave: empaoopos mo pecanzm Lon 34a H mcvsammc nouepzupwu pecansm uopponep use mo xpv>wuocovnme owepomama .Aemeqazm an co>vm .m ooH\me H.HV uuoeuxm ammo» cw ucowoea acaosm ogp mqu woven ocpxoueeag umppmnop we uc305o on» Eoee uoamp=o_auc wepxoupexmi: cpxocw >9 mom-1m m co wpoo .m.»0 u 3: Ice Lo me_,.oeep m opamp m.mm m.~m~ m.m¢~ mm.o m m.aHH o.m¢~ ¢.mo~ eo.o e m.mHH o.m¢o o.wmm Nm.o m o.om m.-m ~.mmm an.“ N o.oHH o.mmm N.mmm mm.~ H Ade.xoceexa ea av Aupoe\.ov Au.ee\.uv In» axe» oepxcu_c»a Accpoeocoezv ocoeuaeucoocoo ucosweoaxw muw>wuumowuum ovmvomam o:_xouweam Figure 6. 52 Sephadex 0-25 Gel filtration in 8 M Urea of 3H-PLP-labelled TDH with and without NaBH4 as described in Materials and Methods. To the reduced dehydrase was added solid penicilla- mine to a final concentration of 50 mM and solid urea to a final concentration of 8 M. After incubation at room tempera- ture for 30 min, the solution was gel filtered through a col- umn (0.7 x 20 cm) of Sephadex G-25, equilibrated with 8 M urea, 1 mM DTT, 1 mM EDTA, 50 mM penicillami e, 0.1 M potas- sium phosphate pH 7 GD). Another sample of H-PLP-labelled TDH was treated identically but was not exposed to NaBH4 (O). Chromatography was at room temperature in the dark. Material was eluted using the above buffer at a flow rate of about 0.1 ml/min. Five min fractions were collected into gradient tubes. A 0.05 ml aliquot from each tube was counted as described in Materials and Methods. 53 :EV m2340> Hzgjm m v . u I I O W .( 2888283 aImez c: o 2.858285 vim 62 o _ _ p — . P ON 9» 0m 0m (IN/WdOM) All/\ILOVOIOVH 54 radioactivity was contained in the low molecular weight fraction. This result would be expected if the great majority of radioactivity was asso- ciated with PLP. The PLP on TDH may be covalently attached to the enzyme by borohy- dride reduction (97). When 3H-labelled TDH was treated with NaBH4 prior to gel filtration in urea, 92.3% of the radioactivity remained associated with the large molecular weight fraction. This behavior sug- gests that 92-97% of the radioactivity is in a form which can be both resolved by denaturation in urea and covalently attached to the enzyme by NaBH4 reduction. These properties are to be expected for the PLP cofactor of TDH. Because urea denaturation and borohydride reduction may not be complete, it is likely that nearly 100% of the radioactivity is in the form of 3H-PLP. 3. Activation of Soluble TDHgby AMP. a. Kinetic Properties with Respect to L-threonine. To learn more about the role of Oligomerization in the AMP activation of TDH, the hysteresis of the activation process was studied. To ensure 90% of steady state reaction rate within 2 S, 0.5 mg/ml of lactate dehy- drogenase was required (see Methods). Because the coupling enzyme is stored in concentrated ammonium sulfate, the final ammonium sulfate con- centration in the experimental solution was 0.11 M. Attempts to remove this salt by dialysis or gel filtration resulted in large losses in lac- tate dehydrogenase activity and instability of the desalted enzyme. Because the 50.5 of TDH is affected by ionic strength (64), these values were re-determined under conditions to be used in studies of the activation process. Table 6 presents the parameters of the Hill 55 . .o:—m> omoeo>m co macaw imeqme ucmwowemoou co_umpoeeoo .HH Luggage cw umnpeumou mo :oPpFUUQ museum loam eo vaguoe on» an meme mcopuecwscouou e soc» vomoeo>e «to: mma—u>n .HH tonnage :* wonpeumou Eoemoea szz e=< are» o_e=.om Lee neeeenepg oeoue_¥ o o_aae 56 equation which describe saturation of TDH by its substrate, L-threonine at elevated ammonium sulfate. The Hill coefficient is very near unity whether determined in the presence or absence of the activator as previ- ously reported (64). If significant homotropic interaction, substrate protection or inactivation of TDH were present, this value might be expected to deviate markedly from 1.0 In the presence of AMP, the $0.5 value was 6.7 mM (see Table 6). This value is approximately 2-3 fold greater than that determined by others at reduced concentrations of ammonium sulfate and coupling enzyme, and is consistent with expected effect of ionic strength on TDH kinetic parameters (64). In the absence of AMP, 50.5 was about 264 mM which is 2-4 fold greater than that determined previously in the absence of elevated salt. The Vmax value in the absence of AMP was nearly half that obtained in the presence of the activator. Dunne gE,gl. have explained this phenomenon on the basis of enzyme instability in the absence of AMP and have shown, using an internal correction procedure, that Vmax is independent of activator concentration (64). As shown below in the Results Section, under the assay conditions employed in the present work, it seemed unnecessary to make such corrections. The kinetic constants in the presence of AMP were also determined using a rapid, single cuvet assay technique described extensively in Chapter II of this dissertation. This "reaction progress" method is more sensitive than the usual multi-cuvet technique to anomalous effects such as coupling enzyme inadequacy, product inhibition, enzyme inactivation, hysteresis, etc. However, as shown in Table 6, single suvet derived val- ues agree reasonablywell with those obtained by the standard method. No 57 hysteresis was observed in the multi-cuvet reaction progress curves, sug- gesting that this effect is probably absent under similar conditions employed in the single cuvet assay. The kinetic constants for AMP were not determined. Throughout these studies AMP, where present in diluents and assays, was 5 mM. Reaction rates of activated TDH were not significantly affected by halving or doubling the AMP concentration. b. Protein Order Dependence of the Activation Process Gerlt g; 21- (11) were the first to study the transient-presteady state period observed upon addition of AMP to otherwise complete reaction mixtures. These authors measured initial rates of TDH activation and found these to have a second order dependency on enzyme concentration. This indicated that a subunit dimerization was rate limiting in the acti- vation reaction. These studies were limited by the available instrumentation which required manual mixing upon addition of AMP. Although absorbance data were collected automatically at is data intervals, the information which could be gathered during the initial phases of activation was limited. Because of these limitations, only reduced enzyme concentrations in the range of 0.005-0.02 I.U.lml could be examined6 (11,98). Therefore, it lwas not determined whether different processes (i.e. first order confor- rnational change) became rate limiting at elevated enzyme concentrations. The improved Spectrophotometric system described in Materials and Methods was capable of relatively rapid mixing and data collection rates (75.75‘1). The initial activation time course, measured with this improved system at two enzyme concentrations is shown in Figure 7. The Figure 7. 58 Hysteresis in the Activation of TDH by AMP. Changes in the absorbance of a stirring cuvette containing 1 mM DTT, 0.275 mM NADH, 1 mg/ml bovine heart LDH, 0.1 M potassium phosphate pH 8.0 and either 0.035 or 0.35 I.U. of TDH (designated by 1 or 10 in the figure) were measured before and after the addition of 0.05 ml of 200 mM KAMP, pH 8.0 (at the spike). Data were collected and stored as described in Materials and Methods. The solid lines represent tracings of data plotted using an HP 7200 flat bed plotter interfaced to the HP9815A. 59 1 S l 1 l N O. (”“0179 BONVBHOSBV MINUTES 60 initial linear portion of the curves represents the reaction rate in the absence of AMP. AMP was added to the stirring cuvet solution at the spike and activation was observed subsequently. With this system it was possible to add as muCh as 1.1 I.U. of dehydrase per ml in the kinetic assay or about 50-fold above that used in previous studies (11). The data for the lower curve.in Figure 12 were collected at a TON concentra- tion of 0.26 I.U./ml. At such elevated enzyme levels, the activation process appeared more rapid relative to the catalytic rate than at lower enzyme concentrations (upper curve, Figure 12, collected at 0.026 I.U./ml) and measurments of the maximum extent of activation in a single reaction mixture seemed feasible at elevated dehydrase levels.7 The data from a number of curves such as those shown in Figure 7 were differentiated numerically as described in Materials and Methods and the activation rate at any given time was divided by the rate observed prior to the addition of AMP. These normalized rates representing the fold activation obtained at enzyme concentrations of 0.007-1.1 I.U./ml are plotted vs. time after addition of AMP in Figure 8. The kinetic constants given in Table 6 predict a maximum activation of about 20 fold.8 Only at the highest enzyme concentration (1.1 I.U./ml) was it possible to achieve activation approaching the maximum. .At this enzyme level this value appeared to be at least 20-fold. How- «ever, even at enzyme concentrations of 0.026-0.052 I.U./ml this value reached 13-14 fold and was still increasing steadily. The face that the fiald activation approaches the expected value suggests that irreversible enzyme inactivation is not occuring under these conditions as suggested by the dilution experiments of Dunne g _al. (64). Figure 8. 61 Activation of TDH by AMP as a Function of Time with Varying Enzyme Concentration. To a stirred cuvet containing 1 mM DTT, 0.275 mM NADH, 1 mg/ml bovine heart LDH, 0.1 M potassium phos- phate, pH 8 and various amounts of TDH in a volume of 2 ml, was added 0.05 ml of a solution of 200 mM potassium AMP, pH 8.0. The absorbance was measured at 340 nm and differentiated as described in Materials and Methods. Catalytic reaction rates are expressed as a fraction of that observed prior to the addition of AMP (Fold Activation). TDH was separated from AMP as described in Materials and Methods. The quantity of TDH added to the cuvet was determined by assaying the stock of TDH (1 mg/ml) by spiking it with a 2.5% volume of 200 mM AMP, pH 8 and incubating at room temperature for 1 h before assay- ing with the standard catalytic assay. The TDH levels present in the cuvets were: 2.2 ((7), 1.1 ([5), 0.05 ([3), 0.025 (()), (A) and 0.01 ((7), 0.005 ([5), 0.0025 ([3) and 0.0012 (C)) (B) I.U. The smooth lines through the points were drawn with the aid of a French curve. 62 I T I T l 14- (8| 4 - o ' “£2 - \ Q 4 a 1 4 O 1 o I. . O .' ° N) D. D n O o o N O D P ‘ O O ’ . O —- ’ . i o ' \I\\\ Q \ \ __ 1 L 1 4.3... o ID ID 8 — 9 0 NOILVAILOV 010:1 SECONDS 63 Smooth lines were drawn through the data points with the aid of a French curve9. Back extrapolation of these lines to zero time was made assuming an initial fold activation value of 1.0 (dashed lines of Figure 7). Despite the scatter in the data, it also appeared possible that the initial fold activation was greater than 1.0 (solid lines) suggesting an ilmlediate activation of the enzyme upon addition of ATP. Ad; very low enzyme concentrations these lines back extrapolated to about two, however at elevated enzyme concentrations this value was as high as five. Thus activation by AMP might actually be divided into fast and slow phases, both of which are affected by enzyme concentration. The possibility of a fast phase is examined in the Discussion. The nature of the slow or transient phase was further investigated with the aid of a differential plot as follows. Initial rates of activa- tion were obtained from the initial slopes of the smooth solid lines in Figure 8. These slopes were plotted against TDH concentration on a doub- le log scale (Figure 9).10 The least squares line through the data has a slope of 2.02 1 0.06 (s.d.). This slope is consistent with a rate- limiting subunit dimerization in the activation process and corroborates the conclusions of others (11). The ordinate intercept of this line is 14.49 1 0.5 (s.d.). With this value and with the assumption of a rate- limitng protomer dimerization step in the activation, it is possible to calculate a second order rate constant for protomer association of 2.7 x 105 M'1.11 This value is highly approximate and is the stan- dard deviation of the intercept (1 0.5) suggests, may be in error by an order of magnitude. 64 Figure 9. Determination of the Order (q) of the Initial Rate of TDH AMP-Activation with Respect to Protein concentration by the Differential Method. Initial rates of activation were deter- mined from the data in Figure 8 by estimating the initial slopes of the smooth lines through the points. These data were replotted according to equations given in footnote 11. The dehydrase monomer concentration was calculated from the I.U. added to the cuvet (from Figure 8), a monomer molecular weight of 40,000 (66) and a maximum specific activity of 480 I.U./mg. The Slope of the least squares line through the points in the figure gives a q value and its standard devia- tion of 2.02 1 0.06. LOG INITIAL RATE OF ACTIVATION (I.U.-ml"-min") O 65 ACTIV'N RATE= k [m]° log (ACTIV'N RATEI= q loo (klrnll l 1 SLOPE= 2.0l'q 4 -85 -8o LOG [DEHYDRASE (M)] -75 66 c. Nature of the Process of AMP Activation 1. Analysis of the Progress of AMP Activation As discussed in the Literature Review, the activation process should consist of some combination of (a) pseudo first order binding reactions of AMP or threonine to the enzyme (b) first order conformational changes (c) second order dimerization reactions. The previous results suggest that it is a second order dimerization reaction which is rate limiting for activation. From the data so far presented, however, it is difficult to rule out a process in which the enzyme undergoes a concentration dependent dimerization in the assay system grip: to addition of AMP, while the subsequent AMP activation reaction proceeds by first order to pseudo first order steps. An apparent increase in activation rate would be observed when enzyme concentration was increased if dimers activated more rapidly than monomers. To distinguish between a rate limiting and a "pre-established“ dimerization, the process of activation was analyzed to determine whether it proceeded by first or second order rate limiting steps. When these reaction progress data were differentiated as described in Materials and Methods and plotted on an inverse time axis, plots such as that shown in Figure 10 were obtained. The reaction velo- cities extrapolate to a final activated velocity (VH) at infinite time. However this final velocity is ill-determined because the activation pro- cess is terminated before completion.12 In an attempt to determine the order of the activation process, the velocity-time data in Figure 10 were fit to linear transformations of either first or second order integrated equations as described in Materi- als and Methods. In this fitting method, the VH value was adjusted to Inaximize the strength of the linear fit. Although the fit to the second Figure 10. 67 Inverse Time Plot Showing Approach to Completion of the Acti— vation of TDH by AMP. To a stirred cuvette containing 1 mM DTT, 0.275 mM NADH, 1 mg/ml bovine heart LDH, 0.1 M potassium phosphate, pH 8.0, and 0.12 8 I.U. of TDH activity 2 ml vol- ume, was added 0.05 ml of a solution fo 200 nM KAMP, pH 8.0. The catalytic reaction was followed at 340 nm and reaction rates calculated as described in Materials and Methods. VH values expected for first and second order processes were estimated by a parabolic search which maximized the strength of linear fits to either equation 4 or 5. The VL value for these fits were obtained from the reaction rates observed prior to the addition of AMP. Dehydrase monomer concentra- tion (Lo) was obtained assuming a molecular weight of 40,000 and a specific activity of 480 I.U./mg. Points repre— sent a tracing of differentiated data plotted using a HP7200 plotter interfaced to the HP9815A. Theoretical lines for a second order (dashed line) or first order (dashed-dotted line) were calculated from the optimized fits of equation 5 or 4 to the data. 68 :b. x 852.23 v m N _ O . _ _ _ weigh—59m $895 $20 5.: Lou— ..m .x/a/l/w/H /\/ .\ $805 89.0 9.88 .8 E/ /.u (ZOI x lull 'fl'I) All/\ILOV BSVHOAHBO 69 order equation was slightly better, the data were found to correlate well with either first or second order models, and neither could be rejected on this basis alone. Figure 10 shows that a second order process pre- dicts a continuous rise in the absolute value of the slope of this plot, however a first order process predicts an inflection point at the posi- tion of the arrow, and a leveling off of the velocity to a lower VH value. In the region where data are available the curves are smaller. Although a slight inflection appears in the data near the position of the arrow, it is difficult to rule out enzyme inactivation as a cause for the fall off in rate. Evidence that a second order fit is more appropriate comes from the fact that the optimal VH (0.064 1.0.) for a second order fit is very close to the nunber of units added to the cuvet as measured by the standard assay (0.0638 I.U.), whereas the optimal VH for the second order fit (0.057 I.U.) would require extensive enzyme inactivation to have occured during dilution procedures and/or assay. Such inactiva- tion has been postulated to account for apparent losses in enzyme activ- ity upon dilution into buffers not containing AMP (64), however these studies (64) took the 15-min reaction rate (V15 min) as a measure of the final extent of reactivation. However, as Shown in Figure 10 this Ineasurement underestimates the true VH significantly. This underesti- Ination could be more extensive if assay conditions were not optimized to Inaximize the extent of reactivation during the assay.11 In this connection, although activation appears very nearly complete toward the end of the period in curve 1, Figure 7, an analysis of this I:urve similar to that in Figure 10 shows that the activation may only be 60% comlete if a second order process is involved. This example demon- strates the error of using an apparently linear portion of the activation 70 progress curve as a measure of VH as was done previously (64). This error may be aggravated by slight systematic errors in absorbance mea- surement as discussed in the Methods section of Chapters 1 and II. Table 7 compares the linear correlation coefficients obtained for first or second order fits to a number of data sets similar to that in Figure 10. As the concentration of enzyme in the reaction is increased, a small increase occurs in the % completion attained by the end of the activation curve (see footnote 7). The linear correlation coefficients Of the Optimal first or second order fits do not differ at low enzyme concentrations. However, when the final extent of reactivation enters the region where these curves tend to diverge (about 81% in Figure 10) the first order fit becomes slightly poorer. When the optimal first or second order VH values are plotted as a percentage of enzyme concentration (in V units) added in the reaction (Figure 11) it can be seen that a first order fit (open circles) requires an anomalous loss of 10-30% of the TDH activity during dilution and/or assay in the absence of AMP. Assumption of a second order process, on the other hand, requires no loss at elevated enzyme concentrations and only a 12% loss at the lowest enzyme level. The lower curve shows the percentage of completion after a 15 minute activation period as a percent of added TDH. This curve is similar to one presented by others, as evi- dence for an anomalous loss in enzyme activity upon TDH dilution into AMP deficient buffers, (64). The data presented in Figures 10 and 11 and in Table 7 indicate that tune activation process occurs via a second order process. Figure 11 shows that assunption of an anomalous loss is not necessary at higher 71 .HH we: imwm cw cmnwcummu omega op peuwucouw mew: mm>L=u mmogmoea cowuu>Puu_au< yo cOPumchoocou coco ucowupmwmou soreness zap lemmwwo =o_ua—oecou Loose; mmommouoea Loueo vacuum to umewm a Logupm op mo>esu mmmemoea cowpc>puu< we may; Loo:_4 eo~pevpao s m—noh Figure 11. 72 Extent of Reactivation by AMP as a Function of TDH concentra- tion and of the Procedure Used to Determine Maximum Reactiva- tion. Reactivation experiments identical to that described in Figure 10 were performed but with varying concentrations of TDH in the cuvet. The data were analyzed by either equa- tion 5 (Q) or 4 (0) using a parabolic search routine which varied VH to maximize the strength of the linear fit. Alternatively the VH was taken to be the Observed catalytic activity after 15 minutes Of reactivation as done by Dunne gt ‘31. (64) ([5). The determined VH (I.U./ml) value was expressed as a percent of the concentration (I.U./ml) of TDH in the cuvet (determined by separate experiments as described in Materials and Methods). 73 J l l l 0.12 0.6 0.8 O.|O DEHYDRASE CONCENTRATION (I.U./ml) 0.4 0.2 I O O O S 03 co h- 8 We) OBLVNLOVBH BSVHOAHEO 74 enzyme levels if the prolonged nature of this second order process is taken into account. ii. Pre-established Polymerization as an Alternative Hypothesis The possibility that a concentration dependent, pre-established poly- merization contributes to the protein order dependence of activation rate was tested by examining the structure of TDH in the absence of AMP. Dependence Of molecular weight on protein concentration in the absence of AMP has already been demonstrated by sucrose denisty centrifu- gation (7). Boundary sedimentation velocity experiments were performed in the absence of AMP at two concentrations of TDH (Figure 12). The raw sedimentation coefficients were corrected for viscosity and density Of the buffer solution using literature data (93). From the 520w val- ues Of Figure 12 and from available nomograms (99), approximate molecular weights of 40,000 and 100,000 may be estimated at TDH concentrations Of 8.4 and 107 I.U./ml respectively. Since the molecular weight of the TDH protomer is known to be about 40,000 (66), it may be concluded that dimerization was very low at the lower of these enzyme concentrations but that it was complete at the higher enzyme level. From these data, a range for the enzyme dissociation constant can be set between 10 and 100 I.U./ml13 (5-50 x 10'7 M in conventional units, assuming a spe- cific enzyme activity of 480 I.U./mg). The highest enzyme concentraion used in the present studies of the activation process was 1.1 I.U./ml (see Figure 8). It may be shown that at this enzyme concentraion less than 16% of enzyme monomers would have been dimerized in the absence of AMP. It is difficult to imagine how the change in structure of only 16 percent of the enzyme protomers present Figure 12. 75 Boundary Sedimentation Velocity of TDH in the Absence of AMP as a Function Of Enzyme Concentration. Ultracentrifugation of TDH in the absence of AMP was carried out as described in Materials and Methods. The enzyme concentration of the cen- trifuged solutions are given in the figure. The photometer was set to either 280 nm ((3) or to 230 nm ([3). Best fit lines through the points were determined by least squares regression. 76 cm. mM.—52:2 ON_ Cum emuxem _E\.3._ com me "3.8m 25.3.. No. NQ. m2 om._ dad (m0)1ul 77 could account for the large changes in activation rate illustrated in Figure 9. However, the presence of 5-15% protomers already associated might be expected to be rapidly activated by AMP and to produce a rapid increase in reaction velocity if this small percentage was not required to dissociate and redimerize upon binding Of AMP. Such a burst in the activation process was observed in Figure 8 and this hypotheiss is fur- ther considered in later sections of this thesis. It should be pointed out that the above sedimentation experiments yield only an approximate dissociation constant because these measure- ments were not made at elevated concentrations of ammonium sulfate and coupling enzyme nor in the presence of 20 mM substrate as prevailed in the AMP activation experiments. Active enzyme centrifugation in the presence of L-threonine has been performed by others (68). This work suggests that the apparent dissociation constant for the monomer-dimer equilibrium in the absence of AMP increases with increasing L-threonine concentration. At 100 mM L-threonine the value is about 45 I.U./ml14 and is consistent with the results presented here. iii. Rate Constant for the Activation Process When activation time course data, such as those obtained in Figure 10, were transformed and presented as second order plots (see Materials and Methods), using the quantity of enzyme added a a measure of VH9 plots such as those in Figure 13 were obtained. The data appear fairly linear over the ten-fold range of enzyme concentrations examined. As described in Materials and Methods, it is possible to calculate a second order rate constant for activation from a single experiment. Figure 13. 78 Second Order Integrated Kinetic Plot of TDH AMP-Activation Progress Curves. Data from activation progress curves simi- lar to that described in Figure 10 were differentiated as described in Materials and Methods and treated according to equation 4. The numbers adjacent to the lines give the enzyme concentragion during the activation process in units of I.U./ml x 10‘ . The catalytic assay was determined at 382.5 nm (.,0 ,Ij) 372.5 nm (A) and 340 nm (V) as described in Materials and Methods. 79 mM.—52:2 0... ON a. .9 . a . D . a _m . O O o o . a E NM. [‘0 IOVI'ON 80 However the information from all of these experiments may be combined by replotting the SLOPE/INTERCEPT ratios vs. enzyme concentration as Shown in Figure 14. ' As described in Materials and Methods, this plot Should yield a straight line passing through the origin, whose slope equals the second order rate constant for activation. The weighted least squares line in Figure 14 fits the data with a linear correlation coefficient of .967 and passes close to the origin.' The slope of this line is 8.8 (t 1) x 105 M‘lsec‘l providing a measure of the second order activation rate constant. This value agrees well with the value of 2.7 x 105 M‘lseC'1 determined from Figure 9 considering the large error in the determination of the latter value (see discussion in the RESULTS associated with Figure 9). The lines drawn through the data in Figure 13 are theoretical lines calculated assuming a second order rate constant for activation of 8.8 x 105 M'lsec‘l. For comparison, the first order plots Of these data are shown in Fig- ure 15. Smooth curves through these data illustrate the non-linearity of these plots. As described earlier, it was possible to obtain linear first order plots by adjusting the VH value used in the calculation. When optimal VH values were used to transform these data, the slopes of these lines (data not presented) can be replotted as shown in Figure 16. The equations derived in Materials and Methods show that these slopes should equal the hypothetical first order rate constant of activation. Figure 15 shows that this hypothetical rate constant varies with enzyme concentration. This means that the activation process cannot be charac— terized by a single first order rate constant. Figure 14. 81 Determination of Second Order Rate Constant for Activation of TDH by AMP. Slopes and intercepts were obtained from Figure 13 (data from 2 additional experiments are included) and the ratio plotted versus TDH concentration as described in Mater- ials and Methods and Results. The catalytic reaction was determined by measuring the absorbance at 340 nm (O), 372. 5 nm ((3), or 382. 5 ([3). The Bars represent the approximate standard deviation of the SLOPE/INTERCEPT ratio determined from SLOPE and INTERCEPT variances in the least squares fits of Figure 13. The weighted data were fitted to a least squares line and the k2 calculated from this slope accord- ing to equation 5. The kg and its approximate standard ng on determined from this analysis was 8. 8 (t 1. O) x sec‘ 82 AmQ x S: ZO_HIwo m m v m N _ OO A _ — q 4 - L ID 1 l N — r0 (,OI x .968) .LcIElOEIBLNI/BdO‘IS v L (D 83 Figure 15. First Order Integrated Kinetic Plot of TDH AMP-Activation Progress Curves. Data described in Figure 13 were reanalyzed according to equation 4. The numbers and symbols have the same meaning as given in Figure 13. Hand drawn smooth lines through the data are added for clarity. 84 ON mM.—52:2 O. N Figure 16. 85 Determination of Apparent First Order Rate Constant for Acti- vation of TDH by AMP. The same data as described in Figure 13 were re-analyzed according to equation 4. The VH value for each experiment was varied as a parameter in a parabolic search to maximize the strength of the linear fit to equation 4. The least squares slopes and their associated standard deviations (bars) are plotted above according to equation 4. The catalytic reaction was determined by measurin the absor- bance at 340 nm (1|), 372.5 nm (C)) or 382.5 nm ( ). 86 ZOFzmo v m N . _ O - - - fi N (,OI x .998) 3d0‘lS r0 87 d. Effect of Sucrose on the Rate of Reactivation As considered in both Literature Review and Discussion of this chap- ter, a second order rate constant for association of 8.8 x 105 M'lsec'1 is of a magnitude which could be considered diffusion . controlled if the dimerization-is very highly sterically restricted and if the highly charged nature of TDH is taken into account. The upper limit for a second order rate constant may be obtained from diffusion theory as follows (100): k2 ‘ $630403 where N is Avagodro's Number, a is the distance of closest approach of the dimerizing species, D is the diffusion coefficent of the monomer, and e is a factor which takes into account electrostatic interactions between reactants. From Fick's first law of diffusion of spherical particles in ideal solution (100), RT D-«h-f where R is the gas constant, T is temperature, f is the frictional coef- ficient of the diffusing species and h is the viscosity of the medium. Combining these equations gives: k2 . B'MTQ [7] This predicts that a diffusion controlled bimolecular rate constant should be inversely proportional to the viscosity of the solution at con- stant temperature. When the concentration of sucrose was varied in the AMP-activation medium, the second order rate constant, determined from second order plots for activation was affected as shown in Figure 17. As predicted by Figure 17. 88 Dependence Of Second Order Reactivation Rate Constant on Vis- cosity. The apparent kg for reactivation was determined from reactivation progress curve data as described in Figure 10 and in the test. Either 2 (1|), 4 (CD) or 6 0&5) micro- grams Of TDH (specific activity 463 I.U./ml) were added to the stirred cuVet.' Error bars on the data points represent the standard deviations of the determined k2 value and were used to weight the fit of the data to the least squares line indicated in the figure. The numbers adjacent to each point give the concentration in percent (w/v) of sucrose present in the activation mixture. 89 T T T l I F'H-‘O d9 .. 3: -00. o 1;) . _. $.93 -42 O N. N S:- N 0&8 n, V .. N -0 N MK“ 1‘ .. m _N O 1 l 1 L 1 O _o_ 00 ' to <1- N 00 (|_Oes|_w) NOIIVAuovr-Ie 80:1 331 mauveldv I/ RELATIVE VISCOSITY 90 equation 7, the data are reasonable well fit by a straight line (linear correlation coefficient = 0.935) which passes close to the origin. The assumption was made in calculating the rate constants in Figure 17 that sucrose did not raise the dissociation constant for dimerization. Since the AMP induced Oligomerization of TDH is also observed to occur in sucrose density gradients (7), a major effect seems unlikely, at least at the lower sucrose concentrations. The VH values used in calculating the second order rate constants for Figure 17 were obtained by separate measurements of enzyme activity at the given sucrose concentrations. AS the concentration of sucrose was raised, the enzyme activity decreased. At the highest sucrose concentration (37%, w/v) the TDH activity was reduced by 50%. A loss of “activatable“ subunits however, is unlikely to be the sole cause for the effect on the activation rate since at this same sucrose concentration, the rate constant for activation was lowered by a factor of about 5. A reduction in activatable subunits by 50% could only introduce a 2-fold error in the calculation of the rate constant as seen from Equation 5 in Materials and Methods. It was assumed that the effect of sucrose was to decrease the specific activity Of all the threo- Iline dehydrase active sites rather than specifically alter a fraction of 'the molecules. Such a general effect should not interfere with the meth- ods used here to determine the rate constant. To test further whether the effect of sucrose was specific or gener- eil, glycerol was used in place of sucrose to increase the solution vis- (nasity'during activation. At a concentration of glycerol expected to appnuoximately double the solution viscosity (19.5% v/v, see reference 101) , the second order rate constant was reduced from 8.9 (t 0.2) x 105 MT15ec'1 to 4.7 (:t 0.3) x 105 M‘lsec'l. These data 91 suggest that in the case Of glycerol too, the rate constant is approxi- mately proportional to solution viscosity. At this concentration of gly- cerol, the enzyme activity was also reduced by 50%. e. Effect of Temperature on the Rate of Activation If the dimerization process is diffusion controlled as suggested by the above measurements in the presence of sucrose, then dimerization should have a low energy of activation (100). Experiments were conducted to measure the Arrhenius activation energy Of the process of AMP activa- tion. 3 I Measurements of k2 (the apparent second order dimerization con- stant) were made at a Series of temperatures. Calculation of this rate constant was made from second order plots of activation progress curves. VH values necessary for these plots were determined by separate mea- surement of enzyme activity at the various temperatures. The results of these experiments are shOwn in the Arrhenius plot of Figure 18. The slope of this plot yields an activation energy of 6.2 (1 0.4) kcal/mol. This value is slightly higher than 2-4 kcal/mole which would be antici- pated for a diffusion Controlled reaction (100). FrOm this figure, it can be calculated that.the apparent rate constant for activation, k2, varies by a factor of 2 over the 23° K range where data were available. This value is a much larger change than would be expected based upon Equation 7, and is sOmewhat at variance with results from the viscosity experiments described above. However, it is important to emphasize the preliminary nature of these experiments, as these temperature studies assume that the quantity of activatable subunits is not affected by tem- perature. Of course the question of diffusion control concerns the Figure 18. 92 Determination of the Apparent Arrhenius Activaton Energy for the AMP-Activation of TDH. Activation experiments were per- formed as described in Figure 10 except that the temperature was varied as shown on the abscissa. The data was treated according to equation 5 to determine the second order rate constant for activation, kg, and its associated standard deviation (bars). The cuvet contained either 0.038 ([3) or 0.076 ((3) I.U. of TDH as determined by separate catalytic assays. The solid line represents a weighted least squares fit to the data. The Arrhenius activation energy (and its standard deviation) calculated from this line is 6.2 (t 0.4) K cal/mol. 93 mm 1 “no. x 3: $325.25» \ _ in h - O. m. m. 5 mm as mmaeqmmaswe ow ow mm m. .00, e. ID ID ID [.998 .511 )2,” OO'l Q (0 23' 94 mechanism Of the dimerization and does not affect the conclusion that the dimerization is the rate limiting step in the process of activation. 4. Activation of Matrix-Bound TDH by AMP a. Properties of TDH Immobilized on Sepharose The experiments so far presented suggest that a dimerization process is the Slow step in the activation of TDH by AMP. These results were obtained by measurements of the progress of the activation as it occurs with soluble dehydrase. An alternate approach involves observation of the effect of AMP under conditions where dimerization cannot occur. For this purpose TDH was immobilized on cross-linked Sepharose 4-8 activated by cyanogen bromide treatment (86), and the properties Of the covalently bound enzyme were examined. Initially the effect of immobilization upon TDH specific enzyme activity in the presence Of AMP was examined. AS shown in Figure 19, as the quantity Of cyanogen bromide used to activate the matrix was increased, the specific enzyme activity of the resulting immobilized enzyme decreased. In this experiment, activity was measured in the stan- dard catalytic assay, and the quantity of enzyme present on the matrix was determined from the radioactivity of a quantity of matrix containing immobilized 3H-TDH. Figure 19 shows that the Specific enzyme activity (expressed as I.U./dpm) of the TDH attached using low cyanogen bromide concentrations (2-5 mg CNBr/ml Sepharose) is about 75% that of soluble enzyme, but drops to 15% at elevated levels (80-160 mg CNBr/ml). This shows that it is possible to prepare a matrix-bound TDH which possesses a high percentage of the specific activity of the soluble enzyme. The decrease in Specific activity at elevated levels of CNBr may be due Figure 19. 95 Effect of CNBr Concentration on the Specific Activity of Matrix-Bound, Assocgated TDH. Matrix-bound, associated TDH was prepared using H-PLP-labelled TDH as described in Materials and Methods. The concentration of CNBr in the CNBr-Activation step was varied as shown on the abscissa. Dehydrase specific activity in I.U./dpm is expressed as a percentage of that of the soluble TDH (3.51 x 10' I.U./dpm). Dehydrase catalytic activity and radioactivity attached to CL-Sepharose were determined as described in Materials and Methods. 96 120 [CN Br] (mg/ml SEPHAROSE) . l l ' O In C) ID 0 N 10 N (°/o) Ail/\llOV OHIOSdS BSVHOAHBO OO 97 either to diffusion effects on substrate and/or product to and from internal TDH, structural distortions of the enzyme active site caused by multiple linkage of subunits to the matrix, or to loss of catalytically ‘important groups from attachment. The amount of TDH bound to the matrix increased with the concentra- tion of CNBr used for activation and with the Concentration of TDH added during the coupling phase. Usually about 300 I.U./ml was present during coupling. At this level and using Sepharose activated at 2.5 mg/ml CNBr, the resulting matrix bound 2-5 1.0. per ml of packed Sepharose. At high- er levels of CNBr, up to 74 I.U./ml of TDH were matrix bound. Soluble dehydrase in the presence of AMP at the concentrations pres- ent during coupling and washing has been shown to exist as a dimer (68). It thus seems reasonable to assume that the enzyme is bound to the matrix through one or more bonds as a dimer. For this reason, dehydrase bound to the matrix under these conditions is referred to as "matrix-bound, associated TDH". b. Removal Of AMP from Matrix-Bound, Associated TDH Washing matrix-bound associated TDH with 1 M KCl solutions containing AMP as described in Materials and Methods, released less than 5% of the bound enzyme or radioactivity. Concentrations of enzyme activity and radioactivity in AMP containing buffer washes were typically 0.5% Of that (an the matrix. However, if AMP was removed from the wash buffer, a large 'fraction of enzyme activity was released from the gel (see Figure 20). illis activity was released slowly from the matrix. At low degrees of Stflastitution (2-5 mg/ml CNBr), 8 columns volumes of AMP free buffer were required. Three times more was required at high CNBr activation. At the Figure 20. 98 Release of TDH Activity from Matrix Bound Associated TDH Upon Removal of AMP from Wash Buffer. Matrix bound, associated TDH was prepared as described in Materials and Methods. Four ml of the coupled matrix were washed at room temperature in a 10 ml disposable column supported by a nylon mesh screen. The flow rate was 1-3 ml per min and 1 ml fractions were col- lected. These fractions were immediately assayed for dehy- drase activity. The matrix was initially washed with coup- ling buffer (see Materials and Methods) containing 5 mM AMP. At the position of the arrow, this was replaced by coupling buffer devoid of AMP. 99 l l N -. Q’ 0 (IN/WI) Ail/\LLOV BSVBOAHBO 0,0 O ELUANT VOLUME (ml) 100 lower CNBr concentration, the AMP deficient buffer wash contained 30-40% of the originally bound enzyme activity and 40-50% of the original radio- activity. Recycling this same matrix with AMP-containing, and then AMP- free buffer did not release further activity or radioactivity. The quantity of enzyme activity and radioactivity which remained bound to the marix varied with the CNBr concentration used to activate the matrix (Figure 21). As the concentration of cyanogen bromide was decreased, the amount of radioactivity remaining bound after an AMP-free buffer wash decreased to 50% of that present while the quantity of enzyme activity decreased to about 25%. The protein remaining bound to the matrix was determined by amino acid analysis to be 44% 1 10% (n=3) of that present before the AMP deficient buffer wash. ,The dissociation of 50% of the radioactivity from the matrix with a wash buffer devoid of AMP would seem to resemble the de-Oligomerization of the dimer into a monomer species which is known to occur upon removing AMP from soluble TDH in several ways, including sedimentation into AMP deficient buffer (68). This suggests that the majority Of the remaining bound molecules are monomers. Consequently, matrix-bound, associated TDH treated with AMP-free buffers to remove non-covalently bound subunits is referred to as “matrix-bound, dissociated TDH". The remainder of studies in this dissertation were made using Sepha- rose 4 B activated at a CNBr concentration_of 2.5 mg/ml. The degree of gel activation at this concentration produced a convenient level of «enzyme activity and radioactivity for routine assays, maximized dehydrase :Specific activity, and reduced the probability of double-linkage.15 Figure 21. 101 TDH remaining Matrix-Bound After Washing the Matrix with AMP-Frge Buffer. Matrix-bound, dissociated TDH was prepared using H-PLP-labelled TDH as described in Materials and Methods, except that the concentration of CNBr was varied as shown on the abscissa. Each matrix preparation was washed with coupling buffer devoid of AMP until the TDH activity concentration in the eluant represented less than 2% of that in the matrix bed. The resulting matrix was assayed for TDH activity and radioactivity as described in Materials and Methods. The results are expressed as a percentage of the among present in the matrix-bound, associated TDH assayed immediately prior to washing. 102 Emoquamm .595 Tmzfl OON 09 ON. ON 0v 0 _ _ _ _ _ O . >._._>_._.o._._>_._.o< umzmo o o\ x & 0 ¢ 0 O In 1.0 [x . oo. ONOOS ONINIVWBH .LNBOHHd 103 c. Treatment of Matrix-Bound TDH with Urea and NaBH‘_ i. Measurement of Radioactivity To determine whether significant amounts of non-covalently linked subunits remained on the matrix, matrix-bound enzyme was treated with urea and NaBH4 as shown in Table 8. Urea (9 M) was capable of removing 80% of the radioactivity from matrix-bound TDH labelled with 3H-PLP.16 This was expected from the ability of urea to resolve the radioactive PLP from soluble dehydrase (Figure 6). When the PLP was covalently attached to the protein by reduction with NaBH4 (see Materials and Methods), only 40-50% of the radioactivity was removed while 52.2% remained bound.16 As reported above after washing the matrix with AMP-free buffer, 54.1% of the origi- nal radioactivity remained bound. Thus, washing matrix-bound TDH under highly denaturing conditions (9 M urea) removed only an additional 2% of the subunits than did washing with AMP-free buffer. This suggests that the majority of subunits remaining attached to the matrix after washing in the absence of AMP are bound covalently. ii. Measurement of Enzyme Activity Additional evidence for the conclusion that the TDH bound to Sepha- rose 48 after washing with AMP-free buffer was bound covalently was (obtained by measurement of enzyme activity after urea wash of matrix- bound TDH and subsequent renaturation. As shown in Figure 22, soluble TDH in 9 M urea at room temperature l<>ses 98% of its activity within 30 minutes. However a large amount Of reactivation occurs when the denatured enzyme is diluted 100-fold into a buffer containing 10 TIM AMP, 1 0“ EDTA, 1 TIM DTT, 0.1 II"! PLP and 0.5 M 104 .o.m 1a .uoeeameea esHmmeoca z H.o . use He m.~e. H.¢m ii ucsom gnu: somwam omega az< H.o «.mm venom acme: ume: z m o.em m.mm open—om subspace: eooaeomlaxmez Aucaoa appowuwcH av copuomeu :F umem>ouom auF>Ppumowumm cowuuecm mucosuooch zap pop—mnoHiaoazm wouowuomm< uesom ixweuez noozumm ezmmz so voumoewca co gnu: emwwam omemlaz< go «we: we Hoowmm m as: Figure 22. 105 Renaturation of TDH after Treatment with 9 M Urea. TDH (0.25 mg) in 0.05 ml of 1 mM DTT, 1 mM EDTA, 5 mM AMP, 0.1 M potas- sium phosphate pH 6.8 was brought to 9 M urea by ten-fold dilution into 10 M urea, 1 mM DTT, 1 mM EDTA, 0.1 M potassium phosphate pH 6.8. For assay of urea denaturation aliquots (0) were diluted 100-fold into 1 nM DTT, 5 IIM AMP, 0.1 M potassium phosphate, pH 8.0 and 0.01 ml were immediately assayed in the standard catalytic assay. At the arrows, ali- quots were diluted 100-fold into 10 mM AMP, 1 mM EDTA, 1 mM DTT, 0.1 mM PLP and 0.5 M potassiun phosphate pH 6.8. These dilutions were incubated at room temperature and at various times thereafter 0.01 ml aliquots ((3) were withdrawn and assayed in the standard catalytic assay for assay of renatur- ation. The activity is expressed as a percentage of the ori- ginal TDH present before exposure to 9 M urea as determined in control assays. 106 mpg—[:2 00m OON 00. O _ H _ H H O _ _ _ _ _ _ _ _ __ u __ __ - _ _ _ _ -ON _ _ _ _ __ __ 1.. __ a _. _ _ __ .0? m __ _ _ _ _ _ ._ a _ _ .. loI IIIIIIII Ox _ _ _ Jom _ H 1.. ‘ Illlllllll II. llllll _ i a b llillihnbl . 1 - _ léllllllflk .. om H H E00. (°/o) Ail/\llOV BSVHOAHBO l07 potassium phosphate, pH 6.8.17 As much as 80% of the original activ- ity was regained immediately after denaturation; also, 62% was still recoverable after 2.5 hours. When matrix-bound TDH was extensively washed with 9 M urea activity was completely lost. The renaturation procedure recovered 14.4% of the original bound activity. Since the urea treatments in a column required 3 h to perform, recovery of activity would be expected to be about 60% (Figure 22) if recovery of matrix-bound activity parallels that in solu- tion. Recovery of matrix-bound enzyme following urea denaturation may be lower than that in solution, especially if the TDH is present as isolated subunits. Thus the amount of “potential“ enzyme activity remaining on the matrix is probably greater than 14%]0.6 = 24%. This value compares well with the 25-35% of activity that remains bound when matrix-bound, asSociated TDH on such gels is washed hflth AMP deficient buffer (see Fig- ure 21). This result further suggests that matrix-bound, dissociated TDH is attached covalently to the matrix. d. (Uptake of Soluble TDH Monomers by Matrix-Bound, Dissociated TDH ih the Presence of AMP. De-oligomerization of soluble TDH dimers by either dilution or by removal of AMP can be reversed by re-introduction of AMP (68). The above results Show that freshly prepared natrix-bound, associated TDH can be ' dissociated by removal of AMP. It was of interest to learn whether the Inatrix-bound, dissociated TDH retained the ability to reassociate with soluble TDH in the presence of AMP. As shown in Table 9, matrix-bound, dissociated TDH retained only 65% Of radioactivity and 22% of the enzyme activit of the original 9 108 .muogpmz use mHaHLouc: :H zap voueHoommn .ucaon xpcuca we no.» uncommon com umapeommu mo Hog new Loeman mcHHaaou guH: vegan: cozy mm: xHeuue one .: N Lou mczpmeanmu eooc um oumaaocH op cmonHm mu: Heesz we» con» HHqume emcee mu: m :3 az< :5 com mo HE mHo.o cc emcee mew: Loewsa wash on» we He mo.oiHo.o cH Haav\.=.H eioH x m.~ Hup>Huou OHCHooamv :9» oHnaHom we mucaose vouoowucp one .meaumeoasou sooe pm umeLHHm no: o.m In .mpczqmocn EaHmmouoq z H.o .<~om :2 H .hho :5 H :H He o.o ea wasHo> Hope» a :H amoeccaom ace—n Lo rob canon xHLuoe mo wasHo> umn He m.o ucwmmea ¢z< ccsom x_euoz mo ago; Io» venomichpmz we wagon m:o_cm> eo mcmuoEecmm coucmZmepmozo_z OH wpnmk 118 -Model. The data were fit with the program KINFIT, using a modified Michaelis-Menten model for 2 classes of non-interacting active sites (equation 6). The relative amounts (Vmax values) and the Michaelis constants ($0.5 values) for each site were optimized as parameters of the fit. The $0.5 values for these two sites are remarkably sim- ilar to the $0.5 values for soluble enzyme in the presence or absence of AMP. The higher 50.5 (388 mM) is also close to that of the matrix-bound, dissociated TDH assayed in the absence of AMP, while the lower $0.5 (5.0 mM) resembles that of the associated enzyme forms assayed in the presence of AMP (see Table 10). It was argued ear- lier in this Section that the matrix-bound, dissociated form consists largely of isolated subunits incapable of oligomerization. It would appear that, in the absence of oligomerization, less than half of these matrix-bound, dissociated TDH subunits can respond to AMP (Table 10). From the relative Vmax values of the low and high affinity forms of the matrix-bound, dissociated enzyme (1.22 and 0.74 I.U./dpm, respec- tively) it appears that only 38% of the enzyme subunits present are acti- vated by AMP. If AMP activation results in a 1.5-2.0 fold increase in Vmax: as suggested by Tables 6 and 9, this percentage may actually be only 19%. A percentage of "activatable monomers" of 19-38% agrees with the statistical fraction of subunits capable of reassociating (30- 50%; see footnote 14). Since the matrix-reassociated form of the enzyme appears to be adequately characterized by a single low $0.5 value, addition of subunits to the matrix-bound, dissociated form renders the remaining 62-81% of the subunits AMP responsive. This is in agreement with the kinetic data presented earlier and strongly suggest the concept that oligomerization is required in the AMP activation of TDH. 0. DISCUSSION 1. Improved Purification Procedure The published purification procedures for TDH (68,69) are tedious and lengthy which may account for the lack of studies where large quantities of enzyme are required. The simple, two step procedure described in Materials and Methods makes large quantities of high quality TDH readily available. This procedure was largely developed independently although the use of a nucleotide wash during affinity chromatography was suggested by the work of others (94). Later, it was found that elevated levels of nucleo— tides in the prewash eliminated the need for a final Sephadex G-200 step (94). Although the purification procedure did not remove the contaminant containng TDH activity also observed by others (68,69), it appears from gel electophoresis work, that the contaminant represents less than 3% of the total activity. It appears to be a modified or altered form derived from TDH; however, its nature remains obscure. 2. In Vivo Labelling of TDH Using 3H-Pyridoxine Table 5 shows that the specific radioactivity of the 3H-PLP attached to TDH was nearly equal to that of the 3H-pyridoxine on which the g, ggli_cells were grown. This suggests that under these growth con- ciitions the g, ggli_does not carry out g9 ggxg_synthesis or degradation of’FM.P. The fact that TDH is produced in high yield on synthetic media lacking pyridoxine (68,60) suggests that the synthetic pathway for pyri- >._._oo.._m> LO ZO_._.<2_._.mm maogmfizmozfi. 135 center point was approximated as the slope of the linear least squares line through the points in the window; the slope variance is also calcu- lated. Successive windows were constructed by dropping the first and picking up a subsequent datum to maintain constant w. The result is a set of velocity values - one for each time interval excepting the first and last (w-1)/2 points. These calculations and the subsequent analysis of transformed data were carried out by the computer routine, TANKIN, described below. c. MATERIALS AND METHODS 1. Computer Programs a. Optimizing Experimental Variables (SSOP) In order to insure that progress curve data are obtained over a selected range of substrate concentrations and absorbance values within a given period of time, it is helpful to have a method for calculating the punp rate and enzyme concentration which will produce that result. The pump rate was calculated by rearrangement of equation l7 to give: vQ . [(Sf ' (Ep - Es - Ec) - Aa” Af] [19] r: tf ' c ' (EP - Ec) - 5f ' (EP - Es - Ec) - Af The total quantity 6f product formed in such an experiment can be obtained from equations 8 and 9. Pf = (c - Sf) tf r - Sf v0 [20] Experience with a great deal of substrate addition data, both real and synthetic, suggests that the amount of enzyme needed in units of Vmax may be approximated closely as: Vmax ~ 3:1 ' [21] when Sf as 3 x 50.5 and Hill n a: 1.0. When very accurate knowledge of the required Vmax was needed, equation 21 was used to provide an initial estimate, Vmax'° The final product concentration, Pf pro- duced by this combination of r and Vmax was calculated by applica- tion of equation 16 and 20. An improved estimate of the required Vmax was Calculated as: 136 137 - EL [22] V ii=V I max max Pf' This process was repeated until the desired Pf/Pf ratio was within 0.1% of 1.0, which usually required three iterations. The number of integration intervals used in the Runge-Kutta solution of equation 16 was usually 20. Increasing this value to 100 did not significantly alter the final Vmax value calculated. A computer program (SSOP) was written for a Hewlett Packard Calculator (Model 9815A) to perform these calcula- tions. b. Generation of Simulated Data (SIMUL) In evaluating the new method, analysis by continuous substrate addi- tion, the strategy was to prepare and analyze calculated data which simu- lated a real addition experiment and which contained noise levels expect- ed to be encountered over a range of experimental conditions. In this way it was possible to separate evaluation of the data treatment methods from the evaluation of the instrumental methods. Also, since simulated "data" can be prepared more easily than real data, a larger number of well-defined conditions can be examined and the effect of experimental variables determined. Using this strategy, it was also possible to introduce and study the effects of such anomalies as enzyme inactivation and product inhibition in a controlled way. Artificial data were created by a numerical solution of equation 16 by the method of Runge-Kutta (119) to obtain a series of 120 St values at equal time intervals over a period of 4 min. These substrate concentrations were then used in equa- tion 11 to calculate the respective At values. Known amounts of I38 normally distributed random noise were then superimposed on these At values to form the final simulated raw ”data”. In experiments where it was desired to examine the effects of enzyme inactivation or product com- petitive inhibition during an experiment, equation 14 was modified as follows: 931. . (e-k't) .maL__t_V'n ° 5 n [23] dt St + 50.5 931 V ’ 5t" [24] dt 5t" + 53.5 [ 1 + P {ViI' These calculations were made by the interactive FORTRAN computer pro- gram SIMUL. The program required the input of the following experimental constants: k, K1, v0, r, tf, c, Vmax: 50.5, n, E5, EC, Ep, and A0. The data were stored and analyzed exactly as were real data. c. Integral Analysis of Data (MARQ) A Fortran version (88) of the algorithm of Marquardt was incorporated into a computer program (MARQ) which calculated the best fit of stored absorbance-time data to equation 11. Equation 16 was solved nunerically as described for the program SIMUL. Initial estimates of the 3 kinetic parameters, Vmax- 50,5, and n were necessary to begin the iter- ation; these were provided by the program TANKIN (see below). A minimum 139 improvement in the sun of the squared residuals of 0.01% was used as the criterion for convergence. In a variety of cases examined, only a single minimum was observed. Convergence was reasonably independent of any com— bination of initial parameter estimates over a 1 2-fold range as judged by convergence to parameter values which were identical to 4 or 5 decimal places. The quality of the fit was evaluated principally by examining the magnitude of the standard deviation of the data about the fitted line. Approximate marginal standard deviations and partial and multiple correlation coefficients for each parameter were calculated from the nor- mal and inverse error matrices (120). d. Differential Analysis of Data (TANKIN) The interactive FORTRAN program TANKIN is illustrated schematically in Figure 27. The routine consists of a main program and a sub-routine to perform weighted least squares regressions. At step 1, experimental constants (v0, r, c, E5, Ep, Ec. A0), number of data points, data collection rate and raw Ati values are read from disc resi- dent files created by SIMUL. Using the data collction rate, ti values are calculated and the t1 versus At; values are transformed to Sti: Pt1 values with equations 17 and 18 as described earlier (step 2). A window size is entered at step 3 and used in step 4 for slope-tangent estimation of reaction velocities and their variances as shown in Figure 26. The weighting scheme is selected in steps 5 and 6. Either homogeneous (all VVti = 1) or individual (calculated VVti values) weighting is available. The Sti» Tti, VVti data are further analyzed by linear regression using the familiar linear transformations of the Hill equation: Figure 27. 140 General Flowchart for the Computer Program TANKIN, which reduces raw time-absorbance data (t1, A1) to substrate- velocity data (5;, Vi) by the method of tangent-slopes, and determines the optimal Hill parameters (Vmax: 50.5, n) from the strongest linear fit of the data to equations 25, 26, or 27 and 28. Symbols are defined in Symbols and Abbreviations. N U O N 10 11 12 13 14 15 16 141 @‘D r input constants. data (M's) J‘— I — CIICUIICO: Cg. 31. Pg 1 0 1 to I L enter window size (it) 7 , l » nuerical differentiation of (t1 a P1) toobtain V1 and W 7 i - (Iii 11/2 to I - w - I [i - (widthol- (w- m: l ’ i enter initial «ti—ta ‘ of Mill n (-N) 1 [5:31 I I enter option I I. 2. 3 ('0'?) [[ cell Simmnc.n- on "—7 C2- In-N lu-rll I] callWIlK.TR-0PT I] , I Cl-CC [n-N-(1+F)] I] call MIL. nl - on J] l I ca-cc 1 SUIIOUTIIE pg”. 3 transformation of (sie '1) to 1‘ '1) according to op ion 1. 2, 3. or 4 (-TI) error propagation of VV to VV1 squares fit of 25 l weighted linear least J 25 “. '1. mt VIN!!! calculate CC. SLOPE .andK r1 V 'VIIX p at 5.; i") 1 Mill n (-n) cc . , I call SUBROUTINE. TR - OPT l .061. F _ WWW F- -m.n-lis sil- r n-Elope _J 27 24 23 22 21 [[ call WINE. TR - 4 jzo I [VI-INN J I 19 [r all WINE.Tll-0PT ]]ia 17 142 option 1 [25] . n V Vt = - $0.5 ..§:fi-+ Vmax option 2 [26] s" s" s" ‘ _t._-.-__I‘._+_0..5 option 3 [27] vt vmax vmax Weights were calculated from the Wti values, and the regress- ions were always weighted according to the method of error propagation (88). An initial estimate of Hill n is entered at step 9. This estimate is improved by a search which maximizes the strength of the linear fit (max- imum linear correlation coefficient) to options 1, 2, or 3. The desired option is chosen in step 9, and improved estimates of Hill n are calcu- lated by a parabolic search (88) as shown in steps 10-16. The search is initiated with F = 0.2 (step 8) and is continued iteratively until F < 0.001 (step 17). From the last fit, a provisional Vmax value is calculated (step 19). Using this Vmax’ the Hill n is calculated as the slope of the Hill plot (equation 28). Vt = n log 5t - n log 5 option 4 [28] lo 9 v - Vt 0.5 (Steps 2 and 21). Finally, this Hill n is used to obtain the final i 143 50,5 and Vmax from the slope and intercept of a fit to options 1, 2, or 3 (step 22). The linear correlation of this final regression is reported as a measure of the goodness of fit. This fitting procedure has advantages over previously published meth- ods since it avoids time-consuming non-linear techniques and provides for individual weighting of velocities (106-108). Data analysis was fully automated so that a large number of experiments can be analyzed quickly. In addition, the program can produce crude printer plots of At vs. t, Vt vs. St, or plot of any of the four linear transformations. e. Weighting_in Analysis of Differentiated Data As shown later, the noise in absorbance measurement.is approximately homogeneous. Consequently, in the curve-fit method, raw absorbance val— ues were given equal weight. In the slope-tangent method, two weighting schemes were compared. The first (homogeneous weighting) assuned equal weighting of velocities. ;In the second (individual weighting), the slope variance was used to calculate a weight for each velocity value. In the differential method described above, raw absorbance-time data are transformed into substrate-velocity data. To properly weight the transformed data, it is important to consider propagation of errors. It can be shown (89) that the velocity at the ith data point (see Figure 26) can be calculated from equation 29. . w 1 . w+1) V = - P 29 t:i AT.D§:(J 2 1I’m [1 i=1 Where: Ptj = product concentration calculated at the 1fth data point; t(min) = data collection interval, 144 m-i-"+1+L “EU-"PF If variance in the raw absorbance-time data is due solely to errors in At, it can be shown from equations 9 and 11 and error propagation (88) that: 2 ZS a 0 At 30 o t EP _ ES _ EC 1 J VtozAt [31] 2P EP w ES ' EC at," Since noise in absorbance measurement, At, is homogeneous (see below) and since variation in vt will be slight over the span of w points, from equation 29 and 31. 2" . 2 VVt _ 0 Pt. , Vt_ a At [32] At‘D At(Ep-Es-Ec)VD In the least-squares regressions used in the analysis of transformed data, only Vt is assumed to have error and St is treated as an inde- pendent, error-free variable. For this to be reasonable, ."_".t > .4025 Vt St 145 or, from equation 30 and 32, Vt :—.> l—- or, At’Vt'VTJ- St ___!t__>."_t ' [33] At'fi 51: If an enzyme obeys equation 14 with n = 1, [34] Ui< «In < _V__. 50.5 Combining equations 33 and 34, St can be considered errorless if 11111.11 > 5‘!— [35] 0.5 For the simulated addition experiments described here: vt 2 x 10-3 L, t . 0.033 min, w - 11 (giving 0 10), v,“ax = 10-7 mole/min, and 50,5 10‘4 M. Then from equation 33: 6 x 10-3 gm > 10-3 ynin Therefore, in the studies reported here, St may be considered error- less. It can be seen from the work described below, that inequality 35 can readily be maintained during real substrate addition experiments. Equations 14 and 18 show that both St and Vt are functions of Pt, and thus errors in St and Vt are correlated. As long as St can be considered errorless, these correlations can be ignored. It is 146 interesting to note, however, that examination of equation 29 shows that Vt1 and Stj are not correlated when i a j. A.more serious consideration is the correlation between neighboring Vt; values (121). The statistically correct way to fit such data would involve the use of the inverted co—variance error matrix to provide appropriate weighting (120). The calculation of the error matrix is not difficult; however, its inversion is extremely costly in computer time.19 It is shown in the Results section that assuming zero corre- lation between neighboring Vt1 values need not lead to significant errors in the analysis (St, Vt) data. In the program, TANKIN, weights are calculated from the variance (VVti) of the least-squares tangent slope (Vt1) as shown below: Vt =“'£Pti't1-_Z;L;Z_Pn 1 A1 . 12 and VV = "a 36 ti Ai [ 3 where M = w Ztiz - (xiii)2 0.2 1 l = 2 w - 2 [ apt: + wai + Vt: 2 t - 2a 2P - 2V 2P 2 i i ti ti ti . t + 2a V t ] i itizi 147 a 2 ' 8‘ [ 2111 zpti - Z121 2121 e Pti] /Al and 2: represents a sum over all points in the window. An alternative method of weighting is suggested by equation 32. Since vt varies less than 10% during a typical addition assay VVt may be assumed to be constant. This latter method of homogeneous weighting is also used as described in the text. Because of the correlation between calculated Vt's, the linear cor- relation coefficient obtained in the TANKIN fit is a biased statistic and cannot be used in estimating probabilities for statistical tests. Never- theless, as shown below for real and simulated data, it can be a useful indication of the relative fit to the Hill equation. 2. Experimental a. Biochemicals Rabbit muscle lactate dehydrogenase, pig heart mitochondrial malate dehydrogenase, E, 2911 B-galactosidase, and their substrates were obtain- ed from Sigma Chemical Co. TDH was isolated as described in Chapter I. Tryptophanase of £3.2211 (122), SOPC, KDPG-aldolase from Pseudomonas ‘pgtigg, were gifts of David S. June and Paul Kuipers of the Biochemistry Department at Michigan State University. All other chemicals were reagent grade from Sigma. b. Immobilization of Lactate Dehydrogenase Sepharose 4-8 and Sephadex G-50 were activated according to the unethod of Axen gt_gl. (86) with 70 mg of cyanogen bromide for each ml of 148 packed matrix. The coupling solution containing 10 mg of lactate dehy- drogenase (in ammonium sulfate suspension) and 5 ml of activated matrix in a total of 7 ml of 0.05 M sodium phosphate, 1 mM dithiothreitol, pH 7.0, was incubated overnight at 4°C. The matrices were washed in columns with 10 ml of buffer containing 1 M sodium chloride, and then with excess buffer. The resulting derivatized support contained 8.8 and 1.92 I.U. of lactate dehydrogenase, respectively, per ml of packed matrix. Soluble activity in both cases was less than 5% of the total. c. Enzyme Assays Substrate addition assays were carried out according to the prin- ciples outlined above. Each reaction required (a) an enzyme-cosubstrate solution in the stirred cuvet and (b) a concentrated substrate solution in the motor-driven syringe. The cuvet and syringe solutions were chosen to give a composition similar to that for conventional assays given in the literature (see references in Table 11). The concentration of added substrate was adjusted so that the total volume change and mixing noise were minimized. Mixing nbise due to continuous addition from the syringe was reduced by using identical buffers in cuvet and syringe solutions. The syringe solution also contained reducing agents where used, but not activators or coupling enzymes. All solutions were prepared fresh daily. The computer program, SSOP, was used to calculate the rate of sub- strate addition (pump rate) and the amount of enzyme needed to achieve 'the specified final absorbance, final substrate concentration, and dura- tion of the experiment. 50,5 and Hill n estimates needed in this 149 .umm H cw mpopm Anewum mo amm mcw>wm .=.H :_ machmomH acme; eowmu “are mmocezqmm umNHum>Hemu umxoma H m.mu momiu xmeozaom omNHum>Hcmv umxumn H omn Hucmmmcq mew; pm>=o coe exocm meowpeeucmucoo He “came mc_u=umc nee cmewzn .mumcumnnm op cowuwuue :He .HH mHnmh 150 uo.omm emacumocuxsmu uHuueH o.m age N3. :22 o.me o.m :a .ooeeamcea +3 o.~ «.9 omeoeeeaeoe eeeeceee uo.m amocomoceagou oppon— Nmé :22 o.e~ o.m Ia .Hu: oHO~He_eH o.m v.0 emcheH< mace o.om o.w :a .mpagamoga +¥ o.~ mso.o mmecugaouaALP o.ooH H.e ze .ooegemcee +ez m.~ mH.o emeeeaceoeHae-a 25 :22 o.ooH m.~ In .ouagamoga +x m.~ mo.o mmecmmocea:mu oumHmz omo.o m-e omceeeaom ea oe.o-~m.o zo ucaoe< ruwuwcH mupm>=u cH «cauxvz :oHuunoz i mxdmm< osa~cm co» mHououoca HH mHnnh 151 m5... m-m .ececea eceo_eeao HEEE flaw/Puma mega - i 5.55 _ oz ww<50> $25.6 - - H . eos..m >~.<~.On=2m.. 155 1 temperature-controlled sample compartment of the spectrophotometer. Con- centrated substrate in a Hamilton microliter (25 to 250 ul) glass syringe mounted on a precision syringe drive (Sage, model 255-1) was added con- tinuously to the cuvet solution (see Table 11) via a polyethylene tube (length, 40 cm; i.d., 0.023 in), which passed through a small opening in the top of the sample chamber. The tubing was cut to extend about 1.5 cm below the initial volume meniscus, but to remain above the light path. Noise from stirring or substrate addition was minimized by using the full aperture of the monochromator and offset control on the photometer to make zero adjustment. ‘ The analog photometer output was digitized with absorbance digitizer, (Gilford model 410), which was linked to a digital multiplexer (Gilford model 402) and a paper tape punch (Gilford model 4010). The digitizer converts the voltage analog of absorbance to four binary-coded decimal digits; 0.000 A. The multiplexer converts the binary data into ASCII- coded characters, adds a prefix character to each set to signify an absorbance value, and punches the prefixed set on paper tape. e. Operation of the System The cuvet solution'(Table 11) was given 5 min equilibration with max- imum stirring (1000 rpm). During this period, the syringe was filled vvith concentrated substrate and advanced to fill the plastic tubing until tJ1e liquid meniscus was flush with the end to be immersed in the cuvet. Tliis step minimized any syringe drive backlash and subsequent delay of substrate delivery at the start of the experiment. Noise due to bubble formation during stirring was eliminated by carefully precleaning the strir-pellet and insuring that all solutions were pre-equilibrated at room _ 156 temperature. Before substrate addition, the end of the tubing was care- fully wiped free of substrate solution. Then 10-15 absorbance values were collected at two second intervals to provide an accurate zero.time by simultaneously: (a) lowering the pump tubing into cuvet solution, (b) turning on the syringe drive;-and (c) switching to a different channel identification character on the multiplexer to signal the start of substrate addition. Data collection was continued at 2 sec intervals for the specified time in the range of 3.5-5.0 min. Data on paper tape was later read by Teletype paper tape reader, transferred via telephone line modem to a CDC 6500 computer, and processed and stored as disc files (see below). f. Absorbance Correction and Data Storagg The photometer was largely linear over the range of 0-2.5 A. However, the nature of the diode linearizing network (87) in the instrument caused minor deviations of observed absorbances from the true values. Plots of 0; (observed absorbance) minus A; (true absorbance) versus 0i were sinusoidal corresponding to the conducting ranges of linearizing diodes, with a period of 0.5 A and maximal deviatons of t ().005 A (Fig. 29A). Although such errors have little effect on individual absorbance measurements, they had a cumulative effect when tangent slopes were calculated for the TANKIN analysis. The curvature of the plots of 01 - A; vs. 01 (Fig. 29A) obscured any simple relation between A and 0. However, plots of (01 + 1 - Ofi/(Ai + 1 - Ai) vs. 01 were sawtoothed (Fig. 298) and obeyed the following rel ation: 157 Figure 29. Correction of Raw Absorbance Data. (A) Plot of error in observed absorbance (Oi-A ) as a function of observed absorbance (01). (B) Var ation in relative instrument response (Oi/Ai) as a function of observed absorbance. Least squares lines through segments of points were calculated to obtain at and b- values (see Appendix). (C) Plot of true absorgance ( 1) vs. observed absorbance (0.). A1 values were calculated at arbitrary 01 values us ng equation 2 and the aj b values obtained from (B). The O- values are measured as gescribed in the text using a solution of ferricyanide with an absorbance of 0.077 A at 370 nm. 158 &. N — O l i 1 N v- -( war in med 0 ment 1 1 ince- 'e l . l X)o + C ”bance e Hues ' m {B)' '- C. -( P- usW’y ' l Aat .‘ : e e e i— . .1 i— -i — e e e e < e f— : I- d e e e e . m . l O +0.0l - A OVA) 0.00 -00| - |05 _ 100 095 AOI AA, 159 DUI "’ 0110.1” . ‘0 03+] 1.. flglojtl 3 a10 + bi [37] A1.” - MIOJ AA1 OJ dA 03 , over contiguous intervals, j (a 0, 1, 2, 3,. . . .). Such plots of measured values for a particular spectrophotometer may be constructed by the method of cumulative addition of small absorbances, AAi (= Ai+1 - A1). This is accomplished by zeroing the instru- ment with solvent and measuring 01 of a solution with a low concentra- tion of some chromophore (true absorbance 8 AA) togive A01 (8 01 - 0.0). The slit is then closed so that solvent has the same 01. Then the absorbing sample is again measured to give 02 and a second A02 (- 02 - 01), and so on, across the absorbance range. Thus, AA is con- stant and dO/dA ( AO/AA) is evaluated as a function of increasing 0,. In practice, the value of AA was between 0.03 - 0.1 A. AA was taken as the average of A01 values from 01 = 0.0 A to 2.0 A. Since slopes (a1) and intercepts (b1) could easily be measured from such plots (i.e., Figure 298), for contiguous intervals from 00 (00 = 0.0 A) to any observed absorbance, (< 2.5 A), it was possible by integration of equation 37 to calculate the correct absorbance, A, cor- 1~e5ponding to any observed a (01-1 < a < 01+1) as follows: 9 1-1 A=Z d0 + d0 aj°0+bj 0. a]’0+b] i=0 1 -11 a .0 e 0 A=:_ln *1 j+1+b1+Lln°‘.°+b‘ [38] j=0 aj aj ' Oj + bj a] a] 01+ b] 160 Raw observed absorbance values, a, were thus corrected by comparison with a table of 50 true and observed absorbance pairs using linear interpola- tion. The absorbance table for a given instrument was established using aj, bj values and equation 38 (Figure 29C), and was found to be valid over a period of at least 1 year. Absorbance correction by FORTRAN pro- gram, CATLOG, reduced by half the standard deviation in recorded absor- bance during addition of dye, improved the appearance of substrate-velo- city plots, and increased by 0.02 the apparent linear correlation coef- ficient in the TANKIN analysis. True absorbance vs. time data sets were stored sequentially in disc files along with all the experimental parameters (pump rate, initial volume, extinction coefficients, number of absorbances, data collection rate, initial absorbance, and substrate concentration in the syringe). D. RESULTS 1. Analysis of Simulated Data a. Determination of Optimal Window Size for the Tangent-Slope 02202.4 It was to be expected that as the number of points in the window used for data differentiation was increased, estimation of reaction velocities would become more reliable. Yet at large window sizes, the tangent-slope method should introduce bias errors. In order to determine: (a) the extent of such biases, (b) the overall precision of the differential method, and (c) the optimal window size, SIMUL was used to generate noisy “data" which simulated a substrate addition experiment with lactate dehydrogenase. These data were analyzed with TANKIN, employing option 1 (equation 25); the results are shown in Figure 30. The 1 error in each evaluated constant was calculated and results are expressed as mean 1 1 standard deviation of six individual determinations. Window sizes from w = 3 to w = 19 were tested and three simulated noise levels are compared. When three data points are used, the tangent slope method for calcu- lating reaction velocities reduces to that of Balcom and Fitch (113), iuhich has been criticized on statistical grounds (121). The large stan- 52 omomovomONQ < 0.8.0 8.0 So .8 mac . mmo - OO._ 174 in correlation coefficient suggests that differentiated data, transformed according to equation 25, deviated from linearity when enzyme inactiva- tion was present. These deviations were regular and could be revealed in most cases where the inactivation constant is independent of S by TANKIN analysis in which raw data points were progressively deleted from the end of the data set, i.e., from the highest S or longest time. As the data set was shortened, the correlation rose (Figure 33A). The rate of in- crease was greater with an increased inactivation constant. Under the same conditions, Hill n decreased correspondingly until the Hill napp approached the true value of 1.0. When product competitive inhibition was simulated using equation 24, very similar biases were introduced into the Hill parameters and the cor- relation coefficient decreased as Ki (in these tests Pf = 50.5 = 0.1 mM). A product inhibition constant of 0.3 mM (three times the final product concentration produced errors in $0.5, Vmax: and Hill n of ~20%, -10%, 9%, respectively. When Ki equaled 0.1 mM, the errors rose to -50%, -35%, and +20%. Correlation coefficients for no product inhibition, and for the cases when K1 equals 0.3 mM and 0.1 mM were 0.995, 0.992, and 0.980, respectively, for data with RMS noise levels of 0.45 mA. Unlike enzyme inactivation, end point deletion did not signifi- cantly improve the Hill parameters, or the correlation coefficients when there was product inhibition (data not shown). This observation relates to the fact that competitive inhibition does not alter the form of the rate equation (129), making it impossible to detect this type of inhibi- tion in a single run. To determine whether product competitive inhibition could be distin- guished from enzyme inactivation in a series of runs in which 175 experimental variables were systematically altered, the TANKIN-determined Vmax (Vmaxapp), was compared with the Vmax used in con- structing the data set (theoretical Vmax) (Figure 34). Eleven ex- perimental conditions were defined using the SSOP program in which either the duration (Figures 34A and C), or the final product level (Figures 343 and D) were varied. For each of these 11 conditions, various levels of either enzyme inactivation (Figures 34A and B) or product competitive in- hibition (Figues 34C and D) were simulated. All other experimental vari- ables including total nunber of data points and final substrate concen- tration were held constant. As expected from Figure 33, as the overall duration (tf) increased, so also did the effect of enzyme inactivation on Vmaxapp (Figure 34A). The effects of product inhibition on Vmaxapp, however, were not significantly changed by increasing tf (Figure 34C). Similar- ly, increasing Pf, which accumulated during the assay, increased the effects on Vmaxapp due to product inhibition (Figure 34A), but not due to enzyme inactivation (Figure 348). It should be noted that back extrapolation of the fitted least-squares lines to zero tf (Figure 34A) or zero time Pf (Figure 34D) results in a much better approxima- tion to the true Vmax- Very similar results were found with 50.5 and Hill n (data not shown). The results from Figures 33 and 34 suggest that serious deviations from the Hill approximation can be expected when there is greater than 4% loss in enzyme activity or when the final product concentration is higher than 30% the Ki for product. Changes in correlation coefficient or Hill n caused by point deletion serve as indicators of excessive (22% loss during assay) enzyme inactivation (Figure 33). It is possible to Figure 34. 176 Effect of Varying tf (A and C) or Pf (B and 0) During a Simulated Substrate Addition Experiment on the Ratio of VmaXa to Its Theoretical Value (Vmax)- Simu- lated data were computed as described in the legend of Figure 30 except that either equation 16 or 17 were substituted for- equation 7 in the program SIMUL. The simulated noise level was 0.45 mA. The data were analyzed by TANKIN using indivicr- ual weighting and an 11-point window. Lines represent least, squares regressions through the data. 177 1 ob 0T5 oéo 0725 0.30 035 Pf (umoles)—" 178 detect lower levels of enzyme inactivation (<10%) and also product inhi- bition (K12> S-fold final product concentration) by systematically varying either the duration of the experiment or the final product con- centration. 2. System Performance and Analysis of Real Data ( a. Preliminary Evaluation of the System Initial tests of the instrument system were made to determine the nature and extent of errors in absorbance measurement in a substrate addition experiment. In addition to spectrophotometer noise, drift, and nonlinearity, errors in absorbance measurement could result from inhomo- genieties of stirring, mixing, or addition rate. Therefore, the contri- butions of these factors to overall absorbance error wee closely examin- ed. As shown in Table 12, RMS error in the absence of stirring, mixing, or substrate addition (static cuvet) were about t 0.6 mA and largely independent of nominal absorbance. A significant portion of this noise was due to truncation error in recording absorbance, since the readout is to the nearest mA. Another component of this noise was spectrophotometer drift which amounted to 0.43 mA.over a 3-min period. The increase in noise due to stirring was about t 0.24 mA. As expected, this noise was also nearly homogeneous in distribution with respect to nominal absor- bance. No special precautions were taken to remove small suspended par- ticles which are probably the major contributors to the noise increase during stirring. Since some of the experiments discussed later involve assay of immobilized lactate dehydrogenase, background absorbance and noise levels were also measured with graded amounts (0 to 60 pl) of pack- ed Sephadex G-50 beads in the stirred cuvet. Under these conditions, 179 .cwe m Low m~m>cmucw umn N um umuumppou mam: open .mo=_m> mucmncomna _Po mo .o.mn .om: umcpamm umxcapn mew: xoumgamm ;p_z =o_p:~om .mueancomno po:_eoc m>wm op zaau .e: oem p mpcmpcou um>=u new Empmxm occumeouocaocuomam we mmwoz NM mFDQH 180 increases in background absorbance (due to light scattering in the bead suspension) in response to added Sephadex G-50 was nearly linear. Even under such extreme conditions, RMS error never rose above 1 3.32 mA; nearly identical results were obtained with Sepharose 4-8 (results not shown). Further evaluation of the effects of mixing and substrate addition was made in two ways: (a) concentrated bromphenol blue, 2 mg/ml, was added dropwise above the meniscus to cause step changes in absorbance; i.e., from 0 to 1.5 A. Strip chart recordings and analysis of data on tape showed that complete mixing occurred in 1.5 sec. (b) NADH (10 mg/ml) bromophenol blue (0.05 to 2 mg/ml), or ferricyanide (24 mg/ml) were added from the syringe pump and the increase in absorbance recorded. Relative increases in absorbance with time (corrected for dilution) were compared with those predicted by Beer‘s Law. These data revealed no lag in the onset of linear absorbance increase. Calculation of pump rate at various times during chromophore addition from the slope of absorbance vs. time line revealed a relative error of 1 4.1% within individual experiments. When correction for absorbance nonlinearity (see Materials and Methods) was applied, this value dropped to 2.2%. For this reason, the absorbance correction procedure was used in all experiments. When chromophore addi- tion data were fit to theoretical equations (assuming Beer's Law and cor- recting for dilution), the RMS error depended upon chromophore concentra- tion. For instance, with dye concentrations of 0.5-4.0 mg/ml, this value was 0.55 mA; but it increased to 1.1 mA at higher concentrations, presum- ably due to a swirling of the dense solution directly into the light path before mixing. Residuals signs tests and residuals distribution plots 181 (120) showed that error distribution was approximately Gaussian, although some systematic deviations remained. The above results suggested that the RMS error for substrate injec- tion experiments should be 1 0.5-1.0 mA. However, larger errors may be expected if dense substrate solutions or immobilized enzymes are used. The major component of this noise is probably spectrophotometer instabil- ity and nonlinearity, and truncation error. Stirring, mixing, and pump- ing appear to contribute far less error than had been expected. b. Kinetic Constants Estimated for Soluble Enzymes An analysis of simulated data suggested that both nonlinear curvefit- ting and the tangent-slope methods can be used reliably to analyze reac- tion progress data with a noise content in excess of that expected from the above evaluation of system performance. (While the curvefitting meth- od can provide more meaningful statistical information, the computation time for the tangent-slope analysis is 10-fold shorter and does not re- quire highly accurate initial guesses of the Hill n. Real data differs from artificial data in that additional biases may come from errors in: (a) the measuring system (instrumental bias); (b) experimental parameters, pump rate, initial volune, etc. (experimental bias) and (c) the experimental model (model bias). To assess the effects of these factors on the reliability of both methods of analysis, sub- strate addition experiments were performed on a number of soluble en- zymes. Initial observations indicated the need for absorbance correction prior to tangent-slape analysis whenever the total absorbance change was greater than 0.4 A, or when absorbance measurements spanned more than one 182 absorbance correction interval. Use of absorbance correction improved the appearance of TANKIN-generated substrate-velocity plots and increased the apparent correlation coefficient of the final fit by about 0.02 (e.g., 0.96 to 0.98) in analysis of typical experiments with a number of enzymes. For these reasons absorbance correction was always used for both tangent-slope and curve-fit analyses. The profile of a typical corrected absorbance-time curve for a pyru- vate addition with lactate dehydrogenase is shown in Figure 35A. Absor- bance at 340 nm decreases as NADH is consumed by the reaction. The solid line through the data points represents the HARD-generated curvefit to the data. The RMS error for this curvefit (1 1.08 mA) is slightly higher than expected (0.5-1.0 mA). The extra error may be accounted for by the additional biases introduced in the real experiment as discussed above. However,-this error level is well within that required for valid analysis (see Figure 32). From the computer program MARQ, the multiple correla- tion coefficients given for this fit revealed that all three parameters are highly coupled (950.5 = 0.9998, Pvmax = 0.9998, pn = 0.9855). Partial correlation coefficients (120) showed that this was due mainly to a high correlation between 50.5 and Vmax (pg,O 5’ Vmax = +0.9944). Despite this high correlation, percent marginal standard deviations were low (30.5, +2.7%; Vmax» 1.3%; Hill n, t 1.0%). This indicates that the optimal para- meters are very well defined by the data; this is also indicated by the fact that convergence from a number of combinations of initial guesses, with i 30% or more deviations from the optimal value, produced the same parameters within 5 significant digits. Figure 35. 183 Typical Results of Single Cuvet Assays of Hill Parameters for LDH (A and B) and s-Galactosidase (C and D). Corrected absorbance data were analyzed by either the MARQ direct curve-fitting procedure (A and C) or by the TANKIN tangent- slope procedure (8 and 0). Conditions for the assays are given in Table 11. Lines through the data are theoretical and are derived from the optimal kinetic parameters obtained from the MARQ (A and C) or the TANKIN (B and 0) analyses, respectively. 184 1.5 w- LACTIC DEHYDRUGENASE 'Ubserved Absorbance “Curve—Fit LACTIC UEHYURUCENASE . 1 .L V(Slope'Tongent) v8.151'1 ‘Linear-Fit l .1.2 1. 4 A B (a. 9 A83 l/V 1.2» i’ r 10.6 Sts=U.ZBSmH Sas=0.192mH Vmax=0. 119 1. U. Vmox=0. 114 1. U. 1.m H111 n=1.08 , , H111 n=1.14 10,3 RMS Error=1.@36mA Linear C.C.=U.991 3&9 as to a} a} at «a an a} ae L2 to 10 MINUTES 1/[Pyruvate(M)r1(*1fls) 3.5 v v - . * rgi - r V 1.3 BETA-CALACTOSIUASE BETA'CALACTUSIDASE °Ubserved Absorbance . 1 vs ;L 8.4 " V(Slope-Tongent) [51'q 0.8 -Corve-F1t -L1near-Fxt a. 3 C < . D «a. 6 A83 l/V 0.2 ‘ 1 10.4 'Sts=0.129mM Sts=0.122mM Vmax=g.1281.U. Vmox=0.1251.U. 3.1 H111 n=1.@1 1 H111 11:1.02 3.2 RMS Error=0.483mA Linear C.C.=B.995 1 egg i5 4 A 1} 1L0 aa ae a} as at .1” 1/[01‘1PC(M)1n (’10 1 3 2.3 27 MINUTES I85 Fitting these data by the method of tangent slopes, resulted in com- parable kinetic parameters (Figure 358). Deviations from linearity in the modified Lineweaver-Burk plot were traced to truncation errors21 (deviations were also present after analysis of artificial data similarly truncated) and to absorbance nonlinearities that were not fully correct- ed. This effect is largest at lower velocities where the effects of truncation are most important. In order to quantitate the effects of experimental bias in TANKIN analysis,~experimental input variables were changed and the resulting Hill parameters compared to those in Figure 358. An error or +4% in initial volune resulted in the following errors: 50.5, -5%; Vmax» +4%; and Hill n, 0%. Error of +1% in pump rate gave errors of +2%, 0.04%, and 0.1%; +16% error in substrate concen— tration produced deviations of +15%, 0.1%, and -2.7%, respectively. Thus 'the results from the tangent-slope method do not appear to be unduly sus- ceptible to experimental bias. Model bias could result from the effects of cosubstrate depletion, product inhibition, or reaction reversibility. Calculations show that the NADH concentration is always 15-fold above the 30.5 for NADH [ca. 10‘5 M (123)]. Assuming the kinetics with respect to NADH to be hyperbolic, the reduction in effective Vmax due to NADH depletion could be no more than 2.3%. Since changes in effective Vmax of less than 4% during a substrate addition experiment may be neglected, NADH can be assumed to be saturating throughout the addition period. When the final absorbance change was held constant at 0.6 A, but the initial NADH concentration was halved to 0.16 mM, a 30% reduction occurred in 50.5 and Vmax: indicating the effects of cosubstrate deple- tion. 186 The analysis of artificial data demonstrated that product inhibition can be detected by varying the final product concentration in an addition experiment. This approach was tested with lactate dehydrogenase, which is known to be subject to product inhibition (123). When the final absorbance change was varied from 0.12 to 0.8 A (equivalent to production of 0.02 to 0.13 mM lactate and NADT), variations in the slope tangent- derived Hill parameters were less than 10%. [Equations describing the kinetics of lactate dehydrogenase (123) can be used to show that reduc- tion in reaction rate due to lactate or NAD+ inhibition would never be greater than 1% for the experiment in Figures 35A and 358. Similarly, it can be shown that the back reaction would always be less than 0.35% of the forward. Thus, small amounts of product inhibition or reaction reversibility do not significantly interfere with these assays. Figures 350 and D show the results of a representative addition experiment with a-galactosidase. In this case, absorbance at 420 nm increases as nitrophenylate is produced. The RMS error for the curvefit (Figure 35C) is low. This may be due to the fact that the entire absor- bance range lies within 1 absorbance correction interval, and deviations due to inadequacies of the absorbance correction procedure are reduced. The Hill parameters obtained by integral analysis (Figure 35C) are in good agreement with those obtained by differential analysis (Figure 350) of the same data. The apparent linear correlation coefficient is higher for this experiment than for that of Figure 358 and is close to that obtained using artificial data with a similar Gaussian noise level and absorbance range (see Figure 32). The calculated 50.5 is in good agreement with literature values (124). Some addition experiments were performed using K+ in place of Na+ as the monovalent cation activator 187 (see Table 11). Under these conditions, the $0.5 rose to 0.8 mM 1 24% (n = 3) with no significant change in Hill n. This effect was ex- pected from the known cation specificities of this enzyme (130). It appears unlikely that product inhibition or back reaction participate since the inhibition constant of galactose is high (9.4 mM) and the reac- tion is essentially irreversible (130). Table 13 compares kinetic constant evaluated for 6 enzymes, including lactate dehydrogenase and B-galactosidase. The data were derived by the ’ substrate addition method and were analyzed by both the differential slope-tangent method (TANKIN) and the integral curve-fit method (MARQ). These results are also compared with kinetic parameters obtained from convential multicuvet assays or with published values. The percentage standard deviations were calculated from replicate experiments. Agree- ment of Hill parameters both between the two methods of analysis and between substrate addition and multicuvet methods is generally good, underscoring the lack of significant bias in the substrate addition technique. Preliminary experiments with yeast pyruvate kinase revealed the expected effects of fructose-1, 6-bisphosphate on 50.5 (0.056 mM to 0.927 mM) and Hill n (0.85 to 1.99). It should be noted that these determinations were made on enzymes whose $0.5 values vary over a wide range (0.02-5.0 mM) and whose Hill n value varied between 1 and 2. TANKIN is written so that determinations can be made when cosub- strate, product, or both substrate and product have absorbance. A com- parison of product inhibition, Michaelis and equilibrium constants with the low maximum product concentrations obtained with malate dehydrogenase 188 .mpouopoca paucmswcmgxm Lo; H m_nm» mom .mocmncomnowpp_e c? coecm mzmm .muwcz PacoppmcemacH cw st>u .25 ca m.omu .vommcm>m mcsc we guess: an» op comm; mammsucmcmq :P namesazn .mcowumcwscmumv mumcmamm we .a.m a w cemza ma.o --- am_o= mzm --- “ma.o aa --- a“ h mo.~ mm a OH.H c why: ~.o um w m~.o no a m~.o . > 3H.o “ON a ofi.o new w OH.o m om Amv amaeamooue_eu-m oe.o --- am_o= mZm --- cem.o do --- am « mH.H am a mo.H e #baz no.0 flew a omo.o son a Nmo.o . > mmo.o was a m~o.o RNH w omo.o m on “av amaeamoceseae agape: ~c.~ --- aam_o= mzm --- Ham.o go we w Hm.” “N w mo.~ we w ao.~ e hwy: we h m~.o we w mH.o aHH w mH.o e . > uo~ w “mo.o am a HH.o mm w NH.o am om afiev amaeamoaeseae weapons M95995“ 5 wuw$im>Lzu mucmmcmh. Macaw—.8 AmcowumcwEqumn—v Lo —e:=cz -maopm mEXNcw mmechm mpnzpom Lee museumcou ovumc_x mH mpnmk 189 .mocmneomampp_we cw coccm mzmm .mpwc: Pm:o_pmccmch :_ xae>u .ZE cw m.omu .ummmcm>m maze eo cones: ms» op Loewe mwmmcpcmcma cw mcmnE=zn .mpououoea Pavemewcoqu Low H m_nmp mom .mcopumcweempmu mumgeqmm mo .o.m a w amaze mo.~ in- mmwoc mzm nu- ~om.o uu mm w mm.o wmfl w ~.H am « ~.H : mw_: “N w mH.o am a m~.o ae w m~.o .e>. am A m.¢ umH w o.m xw « m.¢ m cm Amv mmmuceuagmv mcwcomczp mn.o in- mmpoc max in- Hmm.o uu o.H «H.H HH.H : “my: mao.o No.o mo.o . > mo.o mo.o mH.o m cm RHV amaeaeaopaxce mm.o 111 mmmwo: mzm in- Hum.o uu am A m.H no A m.H um « o.~ c #w&: --- am” w mH.o emfi w mH.o , e . > am w No.o “OH w mHo.o was w mHo.o am om Aev ama_oe_a wage amcauacmuwg upwwuw>czu mucmmcm» penumcou Amcowumcwscmumov co Peace: umaopm msx~=m mmEANCU m—nzpom Low mucmumcou ovum:_¥ A.ea=oav Ma a_aaw 190 (131), and KDPG-aldolase (134) suggest that product inhibition or back reaction could not be significant under the conditions given in Table 11. The values for KDPG-aldolase do not agree with those published previously (135); however, conventional determinations made in this study and the substrate addition methodology gave the same results. Standard deviations of the Hill parameters obtained by the tangent- slope method are also comparable to those obtained by curvefitting. The standard deviations for Vmax are 2- to 4-fold greater than those observed for simulated data (see Figure 32). Part of this increase may be attributed to errors in addition of enzyme in different runs. How- ever, errors in 50,5 and Hill n are also about 2-fold greater than expected from simulated data (see Figure 32), and this may result from experimental biases and the elevated instrumental noise levels. The average RMS error observed about the MARQ-fitted curve are also listed. The value for malate dehydrogenase is about that expected from dye addi- tion experiments; however, for other enzymes this value is slightly larg- er than expected. Comparison of Tables 11 and 13 shows that the largest RMS errors are associated with threonine dehydrase and lacatate dehydro- genase which also have large absorbance changes during the assay. Since this is probably not due to product inhibition or back reaction during substrate addition, it is assumed that residual errors in absorbance re- sulting from incomplete absorbance correction are contributing to errors. The unusually large RMS noise associated with the threonine dehydrase experiments may also be due to the high concentrations of the substrate in the syringe solution (24 mg/ml) and of coupling enzyme in the cuvet solutions (1 mg/ml), which may have produced optical discontinuities in the light path. 191 The average apparent linear correlation coefficients reported for the tangent—slope method in Table 13 do not correlate directly with the RMS errors of the curvefit method. This is because the correlation coefficient is a relative measure of data error and varies with the range of velocity values spanned during an experiment. Since this value will vary between enzymes, correlation coefficients for different enzymes are not directly comparable; and they are presented here only to give their approximate magnitudes. These correlation coefficients were comparable between experiments with equivalent quantities of the same enzyme, how- ever, and could be used to identify unreliable assays. c. Kinetic Constants for Immobilized Lactate Dehydrogenase Tests with artificial data suggested that reliable Hill constants could be obtained even at the higher noise levels encountered in the presence of insoluble supports. To examine this possibility, substrate addition progress curves were obtained for lactate dehydrogenase in the presence and absence of Sephadex G-50 (which excludes lactate dehydrogen- ase). The results in Table 14 show that Hill parameters obtained by sub- strate addition assays were not significantly altered by the presence of Sephadex during the assays. From the data given in Table 12, it was determined that the level of Sephadex added (50 pl packed volume) should produce an RMS noise level of about 2.5 mA. The error obtained from the curvefit of the data obtained in the presence of Sephadex is in close agreement with this value. Similar results (not shown) were obtained with elevated levelS'of Sepharose 4-8. These findings suggest that the elevated noise level in the presence of the matrices does not interfere with the determination of the kinetic parameters. vi... H JM'iaqq. tilt» 32191145? ' w 1614'th _ .9." ' 11. '1511‘ "11"". — -' r V. ammo “wane u .. '_'~”1f!.' 1. H mm 3.\en163dfl1 tmmi'w v nl ‘L39‘1 ';.‘\3 3.11, 'v ‘1. . . . C i fi'. U . . . a. n (a v. 2|. )7 H. 4. 411 u‘ . 1. i . 1 .ca . 'miinpaa . 141 0 “Mr. I II 1 . J 1 V w u I a, :7 A. 1 .q: s a . . J . . ... ) II I a.‘ J“ n1 v 1. In a .. m i w. v 1 . l ... a. A , . .. .. h. r N y .l d .1 1| 6 ..... J an ,_ \I' .3 . . 1 ~ ' n h- 1 f .1 2. V1 h ..1 .. . .. a . . .~ f I . v a ‘1 D. .1. r q .h i .. . y . h , ' . I; 1 i b . .. .f, u\ .. . .9. . . ._ L . ll . It. . . . a .. . . , .. 1 s 1... .H .c . .. .2 . W. o. 1 J» . .1 cl ) t '5 . F .T 1 1 u :1 5 s. .1. o u . .. ). t... m w “I r A. 1:. 11 3 n 1a. 1. # fil- . .. .9. .. .. I k" . ... T . .1 .... .v . , ‘ 1 V . J“... I 11.- I l . l Irv..- 1 . -- 1 lulu v 1' il~i ’1 l | i \OQI ' ‘1l‘l t I, 1 . N 1.11 711.11.. 0.11:... . l1_l.)|.4 192 .ummmcm>m maze we Lmn53c we» op Lowe; mwmmzucmceq cw means: .m_ouopoca Peacoewcmaxo Low H mpnmp mom .mucancomaa___we :_ eoeem mzmm .muwcz chowpeccmucH :_ xme>u .ze cw m.omu z .mcoppmcwscwumc muecmqmm eo .o.m a w :mmzm .vfi open» 193 mem.o --- aoeaa mzx --- “mm.o ca mfi.H am a H~.H a“ w om.H e F: mmo.o «Ha w ao.o mmfi w oo.o hae> Amy m-e amoaagaam- NNH.o ues w m~.o gem w o~.o m om caNPPwaoesH mN.N --- cocoa mzm --- Nom.o do a~.H mm « ~.H mm w mH.H c P: No.0 am a eeo.o em w meo.o ha2> Aev om-u xaeaeaam- mH.o so w HH.o am w OH.o m om ea~w_wnoeec mN.~ --- aoeca mza --- mmm.o do --- ma a H.H mom w o.H c “kg: mo.o a- a wo.o aHH w mo.o > --- an“ w mH.o emu w mH.o m.om Aav om-u xauaeaam+ No.H --- eaoaaa mzm --- Hmo.o up Hm.“ «a w -.H we a m~.H e _M_z wo.o a« w “mo.o am a meo.o ax.s> Nao.o aka w NH.o “mm w -.o am om Amv a_ns_om p_w1m>c:u acumen» acoumcoo Amcowumcchmumov peace: umaorm machw axes ea~___noesH new a_a=_om to» mueapmcou oweac_¥ dfi mwnwh 194 Lactate dehydrogenase bound to Sephadex G-50 (surface coupling) exhibited similar kinetic constants when assayed either by substrate addition or conventional initial velocity methods as shown in Table 14. The $0.5 determined by substrate addition is somewhat lower; how- ever, only one determination was made by the conventional multicuvet method. The 3 kinetic parameters appear very similar for soluble and Sephadex G-50-immobilized lactate dehydrogenase. This lack of immobili- zation effect has also been observed for lactate dehydrogenases attached in a variety of ways (135-138), although large effects have also been reported (139) for others. The effects of immobilization apparently depend upon the species of lactate dehydrogenase, the mode of coupling, and the nature of the insoluble support. When lactate dehydrogenase bound to Sepharose 48 (internal coupling) was assayed by the same procotol, a large Hill n value of 1.7 was obtain- ed (data not shown). Although substrates must diffuse into the bead and products must diffuse to the exterior, the high Hill n value was not due to a prolonged approach to the steady-state reaction rate dictated by the substrate concentration, because initial rate measurement showed that a constant rate was reached in less than 2 sec after substrate addition to lactate dehydrogenase immobilized on either Sephadex G-50 or Sepharose 4eB. Instead, qualitative tests indicated that the 30.5 for NADH was much higher for enzyme bound to Sepharose 48 than for either soluble or Sephadex-bound enzyme. Substrate addition experiments were then per- formed with elevated levels of NADH, and pump rate and enzyme concentra- tion were adjusted so that net change in NADH concentration was much less (see Table 11). The results in Table 14 show that the Hill n value was significantly reduced from 1.7 to a level comparable to the initial rate 195 assays. The discrepancies between 50.5 values determined for lactic dehydrogenase immobilized on Sepharose 4-8 by either substrate addition or conventional initial rate assays appears slightly larger than those observed for soluble enzymes. This probably represents the imprecision of initial rate estimation from tracings containing elevated noise and not any bias inherent in the addition assay. Because the 50.5 for NADH was not determined, it is not known whether NADH was saturating during these assays. E. DISCUSSION 1. Analysis of Simulated Data These results indicate that a tangent-slope method can be reliably applied to the analysis of a reaction progress curve of A vs. t generated by substrate addition. The accuracy and precision of the Hill parameters obtained by this method are comparable to those obtained by direct non- linear curve fitting. The tangent-slope method requires an estimate of one variable, Hill n, rather than all three as in curve-fit method. Valid results may be obtained over a wide range of final substrate con- centrations (1.5-10 x 50.5), and a low degree of enzyme inactivation (> 4% during assay) or product competitive inhibition (K1 > 3x final product concentration) do not seriously bias the analysis. These find- ings indicate that differential methods may have wider application than has been suggested (121). The use of differential methods has been discouraged on the basis of statistical argunents (121). It was thus important to examine more closely the present application of such potentially useful techniques. Using simulated data, we have demonstrated that a differential method, using a tangent-slope approximation to the reaction rate, can confidently be applied to the analysis of substrate addition data using the Hill equation. Others have demonstrated that differential methods for the analysis of reaction time courses compare well with conventional initial rate assays, but are more convenient. Balcom and Fitch (113) utilized a simple difference method to study effects of temperature, pH, ionic strength, and modifiers on kinetic constants. Bizozero g_.al. (114) fit progress curve segments to polynomials from which they calculated veloci- ties and substrate concentrations. Yun and Suelter (115) expanded on the 196 197 approximation of Lee and Wilson (140) to obtain substrate-velocity data across the entire progress curve. These authors demonstrated the relia- bility of their technique using both real and simulated data and provided a sound theoretical basis for its use. Their approach which also consid- ers effects of reaction reversibility and product inhibition, provides a flexible analysis of progress curves in which substrate concentration passively declines by depletion. The addition method has some advantages over conventional progress curve methods. With the substrate depletion method excessive product is present at low, but not high, substrate concentrations; whereas the in- verse is true for substrate addition. For this reason, the effects of competitive product inhibition should be reduced when the substrate addi- tion method is used. Greater control is possible over the substrate and product concentrations encountered in the addition method. The experi- ments can be planned such that product build-up is minimized (perhaps to no more than would occur during an initial rate assay) without changing the range of substrate concentration spanned. The extent to which pro- duct concentration can be attenuated is limited only by the sensitivity of the assay. For inStance, using the program OPT the total activity and pwnp rate parameters can be raised resulting in greater product buildup without changing the final substrate concentration (Figures 34C and D). However, in the present analysis of the Hill equation, it is assumed that product effects are unimportant. Further, a second advantage of the addition method is that it is not limited to the study of substrate kinetics, but can also be applied to analysis of effectors, coenzymes, and cofactors which are not altered by reaction. In addition the tangent slope approach can be used to obtain 198 from single reaction mixtures velocities during a continuous change of pH or temperature to give pH dependency curve or an Arrhenius plot. The speed of the TANKIN analysis and the wide variety of potential applications of addition methodology suggest that these techniques may provide a flexible system for enzyme studies. To be most useful, this system should include a direct, computer-spectrophotometer interface for rapid, on-line processing of raw data. The availability of simplified least-squares procedures for data differentiation (89) makes large, expensive computers unecessary for this purpose. It has proved feasible to program TANKIN analysis into a Hewlett-Packard 9815A calculator which has interface capabilities.22 Incorporation of programs for differ- ential analysis of conventional progress curves (115) should greatly expand the utility of this system. 2. AnaLysis of Real Data The accuracy of kinetic constants obtained by the single cuvet, sub- strate addition method could be diminshed by significant amounts of pro- duct inhibition, enzyme inactivation, reaction reversal, cosubstrate depletion, or of hysteresis. Unfortunately for most enzymes a comprehen- sive rate equation and kinetic constants are not available to aid in eliminating many of the above possibilities as was done herein for lactic dehydrogenase. Also, there are no easily observable signs of these effects in the reaction progress curve as may be observed when conven- tional steady state assays and related plots depart from linearity. To obtain the increased accuracy potentially available with the substrate addition method, it is necessary to determine whether any of the above effects are involved. Diagnostic procedures and an approximation of 199 errors to be expected for enzyme activation and product inhibition have been described. For other interfering effects, separate tests should be run in the usual ways as would be done in ordinary kinetic studies. Thus, one of the major uses of the substrate addition method in the thorough characterization of a reasonably well understood enzyme. ~The data presented show that kinetic parameters for enzymes can be estimated by the described addition-slope-tangent analysis system with a reliability comparable to that of curvefitting to a reaction progress curve, and much above that normally experienced by conventional methods. In view of the degree of control that can be exerted over substrate and product concentrations, as well as the rapidity and convenience of making determinations, it appears that the system described can do much to release the burdensome work normally required in detailed studies of these parameters. Analysis of sources of error has shown that a major segment derives from two instrument-related characteristics. One source stems from the acquisition of absorbance data to only four significant digits (0.000 A) leading to errors in calculations due to the truncation of the 4th significant digit. Since there is now at least one spectrophotometer available in which special precautions have been taken to decrease base- line noise and drift, and which reads to 5 significant digits (0.000 A), there is reason to believe that substitution of such a unit for the ordinary 15-year-old unit used in these studies would significantly decrease noise and attendant error. In this connection the noise can be reduced further by signal averaging; that is, by recording absorbances at very short intervals and averaging n values to give each 2 sec absorbance measurement. Such an approach would reduce random noise by a factor of i" ‘- "r l g. . ' 1 1 1‘ l' I 1 .1 ' ‘ l i 1i“. f‘ '1. "1171‘. l ' ~|r . I ‘ I I iaiamc L ' - wind 9.29: ' . ,{5 000.1. 9*: ‘11?!"1"7‘.1T Ed ”531:4”.1 J 16 asanumv-n 3H; ‘; nusdwz'u ~ r_,. ,. -_. . 5.x,“ 3. . to wit-st s p: semi I .. .- “2'." m hf ffijmk'. . .70 . “ ~115 kw: 93¢.- ( “:- {1 . i .3 . d . 6'. .4. .13 , . 1». ‘éu 15°“: 1. 5‘" M3 1 v-sJ'Ju ‘ 819-qu Q ‘ «moo \ \"1‘: “.146.“ 2 .9. ‘H L a}: ,1} ‘O .3. ,5 I :hr’wu .‘ ' “Wat " 1 'U ‘flhjl't; 5.1, ' - "mm" .' '1 an ..,131 v4!"‘ "74"3110" .1 .A‘ 1” .-~..-~., our 1‘ 91.9, ’ : -_.. 1,131..“{97 _ ‘fi ‘11:; "15v”: A. 200 ‘Vfii For the absorbance digitizer (Gilford 410) and similar digital voltmeters in one of the newer spectrophotometers, data acquisition is at the rate of 7.7 points per sec. Thus for a 2.078 sec interval made up of 16 data points, the.random noise of the averaged interval would be reduc- ed by a factor of 4. A second source of error is the imperfect nature of the absorbance correction. By approximating the sawtoothed error line (see Figure 29). This error behavior derives from use of a set of diodes to correct the systematic departure from the absorbance line (87) which performs well for the usual purposes; however, these small errors have a cumulative effect in tangent-slope calculations. The systematic absorbance error without the diode network, while much greater, can be better corrected by fitting a polynomial to the observed absorbance line and using that expression to make the corrections (see Chapter 1). Another source of error results from temperature drift in the cuvet in the water-jacketed compartment. A higher degree of temperature con- trol can be accomplished by electronically controlled Peltier-effect plates which are directly in contact with the cuvet (141). Such an arrangement would allow determination of kinetic constants over a wide temperature range above and below ambient temperature with greater preci— sion. An experimental combination Peltier effect temperature control and alternating field stirring cuvet holder was used in Chapter 1. Validation of the tangent-slope method makes possible the study of a wide range of variables which in addition to substrates have effects on enzyme activity. For other ligands, whose concentrations are not altered by the reaction, a simple option in the program TANKIN allows calculation of ligand concentration at any time. For other variables such as 201 temperature, pH, and ionic strength, a second data channel utilizing either digital thermometer, pH meter, or conductivity meter together with AmD converter and interface are needed. In addition, a method is requir- eJ to vary smoothly the temperature, pH, or ionic strength from one limit to another. This can be accomplished by the temperature controller sweep control or by the addition of buffers or salts via the syringe drive. Figure 36 gives an improved version of the original system incorpor- ating a spectrophotometer reading to 0.1 mA and a Peltier-effect stirring cuvet. Absorbance can be recorded at high rates and averaged in the Hewlett Packard 9815 desk top programmable calculator. This unit can accomodate two data channels, one of which would alternate with the Hewlett Pakcard X-Y plotter. The HP 9815 also has the capability to initiate the physical tasks needed to initiate a run; i.e., start the syringe pump and immerse substrate input tube in the cuvet, as well as to signify the start of substrate addition. These would be activated by a command from the operator. Although this system and associated programs are only partially develOped and tested, it is clear that the velocity measurements, calcu- lations, and plots of absorbance vs. time and 1/v vs 1/Sn for a deter- mination of the three kinetic parameter can be made in 20 min. ~ino‘ ha. :_.1 1‘2 ,l..J‘Ju15i-‘W. .: ‘ ‘iilzil 'V‘._ -i | K. zevi'Q W ‘ one 963 S) ants. M. H... .73, 0.11 ' 53b.) '. . .. H. 4. l a, .p». r J 7.1.. no. ..... Figure 36. 202 Proposed, Fully Automated System for Kinetic Analysis of Enzyme Reactions. Provisions have been made for calculator control of syringe drive and auxilliary data collection from thermometer, pH meter, or conductivity meter. 203 ‘ >.:>=ODOZOO - 2mm.)— 5.305200 1— >._._>_._.ODOZOU .aZE _l E L 5.5.2 IQ 7 322.5 .3805 _1 E>DU Ewe/55200350 - a 83359 39‘s. 5&3; gage .1 - H E l\\\\\\\| —.~_m._.m_20h01a —l liailuililu E :1 H 3205 _4 :a _ -4 OFSZOQIU. .OZOS. . mmahémaimh - 4 mama hi mvaE>m _, mZO=0._m ommOmOmn. SYNOPSIS AND CONCLUSIONS The research described herein has depended heavily on development of new techniques and approaches. Improved TDH purification, in vivg radio-labeling techniques, the ability to renature the dehydrase from urea and resolve it with urea-penicillamine, optimization of TDH immobil- ization methodology, and the soft and hardware development of the analy- tical instrumentation have been the sine qua non in these studies. The single basic hypothesis tested in Chapter I of this thesis con- cerned the requirement for subunit dimerization in the AMP activation of TDH. This hypothesis was tested using both kinetic and immobilization methodologies. These methodologies have been extensively used by others to answer similar questions about the importance of subunit structure in other enzymatic systems. The behavior of both soluble and matrix-bound TOH is consistent with dimerization being a required, integral part in the activation process. The substrate addition methodology described in Chapter II of this work, largely removed from studies TDH, represents a significant depar- ture from conventional steady state kinetics, and as such required a more extensive analysis than the other procedures utilized. Although its efficacy seems proven, quality control must always be considered when evaluating the results obtained with this technique. 204 APPENDIX APPENDIX STEREOSPECIFICITY OF DEUTERIUM INCORPORATION INTO THE PRODUCT OF THE TDH REACTION Previous work has shown that one deuterium is incorporated from 020 into the product of the TDH reaction during tautomeric rearrangement and hydrolysis of a-aminocrotonate (97). The chirality of the product, l-D-a-ketobutyrate, has implications for the catalytic mechanism of TDH since any asymetry in the deuterium incorporation requires that the rear- rangement occur on the enzyme surface rather than spontaneously in solu- tion. The method presently available for determination of the chirality of 1-D-a-ketobutyrate involves the large scale formation of l-D-a-ketobutyr- ate, oxidative decarboxylation to propionate with H202, isolation and crystallization of sodium propionate and determination of its specific rotation. This procedure has been used to investigate the mechanisms of KDPG-aldolase (142), pyruvate kinase (143) and cystathionase (144). How- ever this procedure is insensitive, inconvenient and not amenable to a large number of experiments. An intensive effort employing this technique to confirm the partial chirality of l-O-a-ketobutyrate produced when the TDH reaction is carried out in 020 proved unsuccessful. It was suspected that chirality of l-O-a-ketobutyrate may only be partial and was somehow lost during the oxidation process. Ainore direct and sensitive assay for the chirality of l-D-a-ketobutyrate was therefore desired. 205 206 The molecule a—ketobutyrate possesses an absorbance maximum at 320 nm due to the aeketo group. It would not be unexpected for an asymetric carbon neighboring the keto group (e.g., in I-D-a—ketobutyrate) to induce a chirality into the absorption band at 320 nm. If this occurred, a CD signal would be expected at this wavelength (145). Such a CD signal might allow a direct assay of chiral l-O-a-ketobutyrate. To investigate this possibility 1-D-a-ketobutyrate was produced by a KDPG-Aldolase which is known to catalyze a stereospecific exchange of position 1 hydrogen with deuterium in 020 (142). Figure 37 shows that a transient positive CD is produced when KDPG- Aldolase and a—ketobutyrate were incubated in 020 but not in H20. As the enzyme concentration is increased both the rate of appearance and disappearance of the signal appears to be increased. Such behavior might be expected if KDPG-Aldolase catalyzed incorporation of deuterium into the I-proR and l-proS positions of a—ketobutyrate at 2 different rates. To corroborate the possibility that chiral I-D-asketobutyrate is present at the peak of the CD signal, a reaction mixture was prepared identical to the one in Figure 37 containing 0.1 mg/ml of KDPG-Aldolase but in a 25 ml volume. ,After 1.5 h incubation, propionate was formed, isolated, crystallized and quantitated exactly as recommended (144). Relative intensities of the position 3 and 2 hydrogens determined by proton NMR in 020 suggested that the propionate was 40% deuterated in the 2 position. 0RD measurements indicated a 14% excess of S-3—2H,H propionate (0230 = 2.8 degrees, see reference 144). The chirality is lower than expected (142), but indicates that a positive CD signal may be associated with l-S-D-a-ketobutyrate. 1"” ‘l 1.1 Y? n . _, :1 1 . - :1 . o‘b'ivgutk39‘m . ~. . '8‘] r - .. m 13.43». H .qqu'G ‘b; v _ - . . ._ .. «a mi 9. -. L ‘ _'.' ’11-. a!” 0”}: It 'I {g . L. ;".""'1 ". J5 'lflfiquiQD‘I‘ r."'" 3191“, i" J I .. "1‘ aiobf'I . ~ 1 mm uni: \YII L mf‘lfi-CI w "I? . l. ili’itum I’.‘ , . - at; ‘u ,3 ‘ -a“nn if . I . '- ‘W'I mI_:.III a 1 Ohm , l . T 3' - . H - 4 - 4 lo can out. ‘? "I ‘ 4",." .‘I - . 4.4 . I I ’ ‘1. 'f 9 0‘3 Iv I‘ . man'- ‘ 5 5» “J M"- " rm ‘ - 4.1,!- ) Join? bum-writs: ' 1 ' ,, , 4 '- .35’ fit) J I vd i611?1:~':e.37~ . 4 m ,- ' - .‘ '9' 2‘11 ‘1 or 09161931:’ « 4' : _-_. '2: an i ' I "gHS'§ “" ~I" TL ' ‘. . .1'." ‘3’ g'; "0.. ILL?I:'_"‘"A "Rio ( , (him: 1-- '." - 1 ' -..,.e' w... sew...»- 5.; 4* gs ' a . I” I "‘ ~ - , . , . ,. r‘", l " "v 1 . _J- {an iinef? ad 72" -, n ‘-w' :2 :n-g . .. , ..-. b43393: $~yl l " , ‘3' '9‘ - . x.‘ 'V&. "A? : "- ‘ ‘ ‘J'u -\ lucm‘JA-iv-L-d'l .4_ -« I ' I' L ‘J‘ ‘ Q-V'Ia i “I”, I i 51 1),}. -' _ Figure 37. 207 CO Observed During the Exchange of Deuterium into a-Ketobu- tyrate from 020 Catalized by KDPG-Aldolase. The reaction was started by addition of KDPG Aldolase at the indicated concentrations (mg/ml) to a 1 ml solution containing 0.1 M Na a-ketobutyrate and 0.1 M potassium phOSphate in 98% 020 solution (solid lines) or H20 solution (dashed line). Final pH was 7.7 uncorrected for the presence of 020. The solution was inmediately mixed and transferred to a water jacketed cylindrical fused silica cuvet. The CD measurements were made at 28°C and 320 nm with a Durrum-Jasco ORD/UV_5 spectropolarimeter with a CO attachment. 208 HOURS <1- ro N -— A (saelfiepmw) xuouama Mva 209 A positive CD signal was also produced at 320 nm when the TDH reac- tion was carried out in 020 but not in H20 (Figure 38A). The well documented CD change between 400 and 450 nm due to the PLP cofactor is also shown in this figure. Figure 388 also indicates that the chirality produced depends upon the buffer conditions and the presence or absence of AMP in the TDH reaction mixture. Chirality increased slightly in the absence of AMP, and even further when pH is elevated and potassium ion removed in addition. - Because no attempt was made to isolate and positively identify the chiral species produced by KDPG-Aldolase and TDH in the experiments of Figures 37 and 38, it would be inappropriate to draw strong conclusions. However the CD signals observed in Figure 38 raise the possibility that the terminal stages in the mechanism of TDH occur on the enzyme surface, and may be regulated by AMP. Figure 38. 210 CD Observed During the TDH Reaction in 020 as a Function of Buffer Conditions and the Presence or Absence of AMP. Reac- tions were started by addition of 0.01 mg of TDH (specific acitivty 401 I.U./mg) to 1 ml solutions containing either 200 nW1(Figure A) or 100 mM (Figure B) L-threonine, 1 mM DTT, am either (Figure A), 5 nM AMP and 0.1 M potassiun phosphate pH 7.7 (uncorrected), or (Figure B) the indicated buffer and AMP conditions (5 "M where indicated). Measurements were made as indicated in Figure 37. 211 2:: < 0 9.3 00v 0mm 8m E. In Ex .852. y E In av. £44K... II" mm In maflazhazq- m om? \ on. (999159P!II!U1)A.LIOIJ.dI'l‘lI-l MVH HAW-Ba LIST OF FOOTNOTES In this dissertation, the terms hysteresis and hysteretic effects (12) are used to refer to changes in kinetic or molecular properties of TDH upon the addition or removal of AMP, which occur slowly rela- tive to the rate of the catalytic reaction. In this dissertation the terms "oligomerization" and "deoligomeriza- tion" refer to changes in quaternary structure of soluble enzymes. These terms are to be distinguished from "associated", “dissociat- ed", and "reassociated" which describe the states of matrix-bound enzyme forms. TDH will henceforth refer to the biodegradative TDH of E. coli. For reassociation to be significant during catalysis, Rate of association zsRate of catalysis or k2M2~ ch OI" k2 a: kc/M Where k2 is the second order rate constant for association, k is the catalytic turnovr rate and M represents the concentration of TDH monomers of molecular weight 40,000. Under typical assay condi- tions, where kc = 480 I.U./mg and M = 5 nanomolar, k2 may be shown equal to 1011 M'lseC'l. PMSF is best added to the buffer from a 25 mg/ml lébutanol solution. All solutions containing this chemical must be handled with gloves since PMSF is a deadly poison. The enzyme concentration (I.U./ml) used in previous studies (11) may be calculated by dividing the observed AA/min by the extinction coefficient of NADH (6,220 M‘lcm' ). At a given extent of activation by AMP, the catalytic rate should be proportional to enzyme concentration. However, if dimerization is the rate limiting step in activation, then the rate of activation will be proportional to the s uare of enzyme concentration. Thus a greater extent of activation 5 ould occur at elevated dehydrase lev- els, for a given extent of catalytic reaction. Substituting the Hill parameters given in Table 6 into the Hill equation (equation 14) yields a value for the ratio of the AMP acti- vated to the unactivated catalytic rate of 19.8. 212 9. IO. 11. 12. 13. 213 In this somewhat subjective procedure low weight was given to appar- ent outliers and account was taken of the fact that rates at very short times (3-5 seconds) may be low due to coupling lag in the assay. Assuming an 9th order dependence on TDH concentration, activation rate = k ' [TDH]9 log (activation rate) = 9log k + a ° log [TDH] where k is the 8th order constant for activation. If V is the rate of the dehydrase reaction (I.U./ml), L the TDH protomer molar concentration at zero time, and rL and rH the specific reaction rates (I.U. ° nmol'l) of the protomer in the monomer and activated dimer forms respectively, then: V = L (rL - rH) + L0 EH dV dL at‘at “1”“) but since dL = k2L2 for a second order process, where k is thelsecond order rate constant for protomer association (M' S‘ ) %¥-= kzL2 (rH - FL) log %¥-= 2 log L + log k2 (rH - rL) since it is shown in the text that .EH = EL 20, rH >> rL intercept log k2 rH 10intercept - 1014.49 I.U. ml'1 min-1 rH ' (480 I.U.7mg) (40,000 mg7mmol) (50 57min) 2.7 x 105 M-1 s--1 k2 = The reaction must be terminated because NADH becomes limiting. To overcome this problem, and to increase slightly the extent of acti- vation within the assay period, the increased and the reaction observed at a wavelength of reduced sensitivity. This was done in the experiment of Figure 13 (see Figure Legend for details), however completion was still not obtained. It can be shown that a dimerizing species will be 50% dimerized when present at the level of the dissociation constant. In the above experiment, little dimerization has occurred at 8.4 I.U./ml so the dissociation constant must be above this value. Conversely also, the value must be less than 107 I.U./ml. 14. 15. 16. 17. 214 In conventional units, the dissociation constant was 2.34 x 1 '5 M (68). To convert to agtivity unitg, 2.34 x 10-6 M) (4 x 10 g/mol) (480 I.U./mg) (10 mg/g) (10' l/ml) = 44.9 I.U./ml. Upon addition of AMP, "neighboring“ bound monomers could conceivable reassociate. Such closely spaced subunits could arise by “pair coupling" of a dimer species to the matrix leaving both subunits covalently attached. Although each subunit might acquire a new sol- uble partner during the coupling period, they could reassociate after the AMP-free buffer wash when AMP is re-introduced during assay. For such pair couplings to occur, cyanogen bromide activated groups must be within a TDH molecular diameter, d, of each other. For the TDH dimer of molecular weight 80,000 (66) and partial specific vol- une 0.738 (66), d=5 A, The probability (4) of such occurrences is (44): . _ _d.C1/3 4 - 1 - EXP "‘774" where C is the molar concentration of CNBr activated sites. At 2.5 mg CNBr/ml, c =1.1x 10-3 M (44) and 4: 0.54 The actual number of twin couplings will be lower than 54% for the following reasons: (1) A fraction of these closely spaced linkage points (about 17% from the above equation) will be within a subunit radius and thus too close to bind to the adjacent subunit; (2) not every potential linkage point pair will have the appropriate orien- tation to link both subunits. The above equation may also be used to estimate the probability of independently attached subunits still being close enough to recom- bine due to matrix flexibility. With uncrossedlinked Sepharose 4B, monomers may be able to move though distances of 200 A (44). The concentration of such monomers at 2.5 m /ml CNBr would be about 1.3 x 10-7 M. For this situation, d = 200 and 4 = 0.17. This precentage would be greatly reduced with the crosslinked Sepharose 48 used in the present studies (44). These argunents suggest that 30-50% of the subunits may be able to reassociate. Solutions counted in the presence of urea were not fully corrected for quenching. Thus solutions of released radioactivity contained fewer detectable counts than actually present. Dependence of rate or extent of reactivation on the components of the renaturation buffer was not extensively investigated. However, the rate of renaturation was much slower when PLP was omitted from the mixture. 18. 19. 20. 21. 22. 23. 215 Assuming that attachment to the matrix does not raise the specific activity of the dehydrase or in some ways preferentially bind only more highly active TDH molecules. Analysis of rate data using the Hill equation presupposes that reac- tion velocity is proportional to ligand or substrate binding. 0. LeBlond and H.A. Hood, 1978 unpubished data. The mean chi-square for these curve fits was 0.997 t 0.05 (s.d.) suggesting that parameters evaluated by this method were indeed optimal for the data (88). Errors in reaching absorbance at the 4th digit (0.0000) due to the use of an analog-to digital converted with only four significant digits (0.000). H. Pawlowski, D. LeBlond, S.A. Douglass, H.A. Hood, 1977 unpublished data. LIST OF REFERENCES 4. 5. 6. 7. 9. 10. 11. 12. 13. 14. 15. 16. 17. LIST OF REFERENCES Perutz, M.F.; Rossman, M.G.; Cullis, A.F.; Muirhead, H.; Hill, G. and North, A.C.T. (1960) Nature 185, 416-422. Phillips, A.T.; Egan, R.M. and Lewis, B. (1978) g, Bacteriol. 135, 828-8400 Phillips, A.T. and Hood, H.A. (1964) Bioch. Bioph. Res. Commun. 15, 530'5350 Shizuta, Y.; Kurosawa, A.; Ioue, K.; Tanabe, T. and Hayaishi, 0. (1973) 9, Biol. Chem. 248, 512-520. Feldman, D.A. and Datta, P. (1975) Biochemistry 14, 1760-1767. Hood, H.A. and Gunsalus, 1.0. (1949) g. Biol. Chem. 181, 171-182. Hhanger, P.D.; Phillips, A.T.; Rabinowitz, K.H.; Piperno, J.R.; Shanda, J.D. and Hood, H.A. (1969) g, Biol. Chem. 243, 167-173. Dunne, C.P. and Hood, H.A. (1975) Eur. 1223.10 Cell. Regul. 9, 65’1010 Phillips, A.T. (1974) Crit. Rev. ifl_Biochem. g, 343-378. Shizuta, Y. adn Hayaishi, 0. (1976) Eur. 1gp. 1Q_Cell. Regul. 11, 99‘1460 Gerlt, J.A.; Rabinowitz, K.H.; Dunne, C.P. and Hood, H.A. (1973) g, Biol. Chem. 248, 8200-8206. Frieden, C. (1971) Ann. Rev. Biochem. 59, 653-698. Baldwin, J. and Chothia, C. (1979) 0. Mol. Biol. 129, 175-220. Chan, H.H.-C. (1975) 9. Biol. Chem. 250, 668-674. Monod, 0.; Hyman, J. and Changeaux (1965) g, M91. Biol. 12, 88-118. Koshland, D.E.; Nemethy, G. and Filmer, D. (1966) Biochemistry 5, 364-385. Levitzki, A. and Koshland, D.E. (1969) Proc. Nat. Acad. Sci. U.S.A. 62, 1121-1128. 216 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 217 Heber, G. (1972) Biochemstry 11, 864-878. Weber, G. (1975) Adv. Protein Chem. 99, 1-83. Noble, R.H. (1969) 93-HQl- Biol. 99, 479-491. Levitzki, A. and Koshland, D.E. (1972) Biochemistry11, 247-252. Nichol, L.H., Jackson, H.J.H. and Hinzor, 0.0. (1967) Biochemistry 9, 2449-2456. Klotz, I.M. (1974) Accounts Chem. Res. 1, 162-168. Kurganov, 8.1., Dorozhko, A.I., Kagan, 2.5. and Yakovlev, V.A. (1976) 9, Theoret. Biol. 99, 247-269. Cohen, R.J., Jedziniak, J.A. and Benedek, G.B. (1976) 9, M91. Biol. 199, 179-199. _— Colman, R.F. and Frieden, C. (1966) 9, Biol. Chem. 241, 3661-3671. Rudolph, R., Gerschitz, J. and Jaenicke, R. (1978) £99, 9, Biochem. 91, 601-606. Carvajal, N., Martinez, J., de Oca, F.M., Rodriguez, J. and Fernandez, M. (1978) Biochem. Biophys. Acta 527, 1-7. Chan, H.M.-C., Mort, J.S., Cong, D.K.K. and Macdonald, P.D.M. (1973) 9, Biol. Chem. 248, 2778-2781. Chan, H.M.-C and Mawer, H.M. (1972) Arch. Biochem. Biophys. 149, 136-1450 Chan, H.M.-C., Kaiser, I., Salvo, J. and Lawford, G.R. (1974) 9, M91, Biol. 91, 847-852. Chan, H.M.-C., Schutt, H. and Brand, K. (1973) £99, 9, Biochem. 99, 533-541. Feldmann, K., Zeisel, H. and Helmreich (1972) Proc. Nat. Acad. Sci. U.S.A. 6_9, 2278-22820 McVittie, J.D., Esnouf, M.P. and Peacocke, A.R. (1977) E99, 9, Biochem. 91, 307-315. McKarcken, S. and Meighen, E. (1980) 9, Biol. Chem. 255, 2396-2404. Bartholmes, P. and Jaenicke, R. (1978) _E_u_r_. 9. Biochem. 91, 563-567. 38. 39. 40. 41. 42. 43. 44. 4s. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. S7. 58. 59. 60. 218 Nagradova, N.K., Golovina, T.O. and Mevkh, A.T. (1974) FEBS Letters 99, 242-245. Pollard, H.B. and Steers, E. (1973) Arch. Biochem. Biophys. 158, 650-661. Jaenicke, R., Rudolph, R. and Heider, I. (1979) Biochemistry 19, 1217-1223. Jaenicke, R. (1974) £99, 9, Biochem. 99, 149-155. Chan, H.M.-C. and Mosbach, K. (1976) Biochemistry 19, 4215-4222. Green, N.M. and Toms, E.J. (1972) Biochem. 9, 199, 707-711. Green, N.M. and Toms, E.J. (1973) Biochem. 9, 199, 687-700. Bickerstaff, G.F. and Price, N.C. (1976) FEBS Letters 91, 319-322. Chan, H.H.-C. (1975) 9, Biol. Chem. 250, 661-667. Chan, H.M.-C. (1974) FEBS Letters 91, 178-181. Fontan, E. and Bachi, P.T. (1978) 9, Biol. Chem. 253, 2754-2757. Frieden, C., Gilbert, H. and Bock, P.E. (1976) 9, Biol. Chem. 251, 5644-5647. Hohl, R.C. and Markus, G. (1972) 9, Biol. Chem. 247, 5785-5792. Carlier, M.-F. and Pantaloni, D. (1978) E99, 9, Biochem. 99, 511‘5160 LeJohn, J.B., McCrea, B.E., Suzuki, I. and Jackson, S. (1969) 9, Biol. Chem. 244, 2484-2493. Harmony, J.A.K. and Himes, R.M. (1975) 9, Biol. Chem. 250, 8049-8054. deRiel, J.K. and Paulus, H. (1978) Biochemistry 11, 5134-5140. Gawronski, T.H. and Hesthead, E.H. (1969) Biochemistry 9, 4261-4270. Bickerstaff, G.F. and Price, N.C. (1978) Biochem. 9, 11E, 85-93. Tuominen, F.H. and Bernlohr, R.M. (1971) 9, Biol. Chem. 173, 85-930 Chan, H.M.-C. (1976)‘§99,I9, Biochem. 99, 521-528. Hood, H.A. (1969) Curr. L9. 111 Cell. Regul. _5_, 151-181. Egan, R.M. and Phillips, A.T. (1977) 9, Bacteriol. 199, 370-376. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 219 Yui, Y., Hatanabe, Y., Ito, S., Shizuta, Y. and Hayaishi, O. (1977) 9, Bacteriol. 199, 363-369. Tokushige, M. (1972) Proteins: Structure and Function, pp. 141-2010 Beitz, 0., Hhangar, P. and Hood, H.A. (1971) unpublished experiments. Dunne, C.P. Gerlt, J.A., Rabinowitz, K.H. and Hood, H.A. (1973) 9, Biol. Chem. 248, 8189-8199. §_2_, 162-168. Rabinowitz, K.H., Niederman, R.A. and Hood, H.A. (1973) 9, Biol. Chem. 1739, 8207-8215. Sacki, Y., Ito, 5., Shizuta, Y., Hayaishi, 0., Kagamiyama, H. and Hada, H. (1977) 9, Biol. Chem. 299, 2206-2208. Hyman, J. (1964) Advanc. Protein Chem. 19, 223-286. Menson, R.C. (1976) Ph.D. Thesis. Department of Biochemistry, Michigan State University, East Lansing, Michigan. Shizuta, Y., Nakazawa, A., Tokushige, M. and Hayaishi, 0. (1969) 9. §____iol. Chei___1_1. 2_4__4, 1883- 1889. Dunne, C.P., Menson, R.C., Gerlt, J.A. and Hood, H.A. (1973) in Metabolic lnterconversion of Enzymes. Third International Symposiun held in Seattle, Hashington, June 5-8, 1973, ed. Fischer, E.H., Krebs, E.G., Neurath, H. and Stadtman, E.R. Springer-Verlag, New York. Shizuta, Y., Kurosawa, A., Tanaba, T., Inone, K. and Hayaishi, O. (1973) 9. Biol. Chem. 919, 4213-4219. Gutfreund, H. (1972) Enzymes: Physical Principals, p. 159, John Hiley and Sons Ltd., NeinorR. McClure, H.R. (1969) Biochemistry 9, 2782-2786. Mort, J.S., Chong, D.K.K. and Chan, H.H.-C. (1973) Anal. Biochem. Lowry, 0.H., Rosenbrough, N.J., Farr, A.L. and Randall, R.J. (1951) 9, 8191. Chem. 193, 265-275. Bohlen, P., Stein, 5., Dairman, H., Udeufriend, S. (1973) Arch. Biochem. Biophx . 155, 213-220. Spector, T. (1978) final. gjochem. 86, 142-146. Spacmn, 0.H., 51:31", "0 HO and More, So (1958) Ma]. Chem. 39, 1190-1200. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 102. 220 Ornstein, L. (1964) Ann. N.Y. Acad. Sci. 121, 321-341. Davis, B.J. (1964) Ann. N.Y. Acad. Sci. 121, 404-427. Malik, N. and Berrie, A. (1972) Anal. Biochem. 99, 173-177. Feldman, D. (1973) Ph.D. Thesis, Department of Biochemistry, University of Michigan, Ann Arbor, Michigan. Steck, L. (1977) Anal. Biochem. 19, 459-465. Heber, K. and Osborn, J. (1969) 9, Biol. Chem. 244, 4406-4412. Riebow, J. (1978) M.S. Thesis, Department of Biochemistry, Michigan State University, East Lansing, Michigan. Axen, R., Porath, J. and Ernback, S. (1967) Nature 214, 1302-1304. Hood, H.A. and Gilford, S.R. (1961) Anal. Biochem. 9, 589-609. Bevington, P.R. (1969) Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill, New York. Savitzky, A. and Golay, M.J.E. (1964) Anal. Chem. 99, 1627-1639. Frost, A.A. and Pearson, R.G. (1961) Kinetics and Mechanism. John Hiley and Sons, inc. Hilkinson, G.N. (1961) Biochem. 9. 99, 324-332. Dye, J.L. and Nicely, V.A. (1971) 9, Chem. Educ. 99, 443-448. Svedberg, T. and Pedersen, K.O. (1940) The Ultracentrifugg pp. 277-283. Bhadra, R. and Datta, P. (1978) Biochemistry 19, 1691-1699. Datta, P. and Bhadra, R. (1973).§E£-.Qr Biochem. 91, 527-532. Tokushige, M. (1967) 9, Vitaminology 19, 165-172. Phillips, A.T. and Hood, H.A. (1965) 9, Biol. Chem. 240, 4703-4709. Rabinowitz, K.H. (1970) Ph.D. Thesis, Department of Biochemistry, Michigan State University, East Lansing, Michigan. Holleman, A.B. (1966) Ph.D. Thesis, Department of Biochemistry, Michigan State University, East Lansing, Michigan. Handgook of Chemistry and Physics (1974) p. D-231, Chemical Rubber Co. Press, Cleveland, Ohio. Goldstein, L. (1979) Methods 19 Enzymology 99, 397-443. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112. 113. 114. 115. 116. 117. 118. 119. 120. 121. 122. 123. 221 Hyman, J. (1964) Advan. Protein Chem. 19, 223-286. Cornish-Bowden, A. and Koshland, D.E., Jr. (1975) 9:.5219 Biol. 99, 201-212. Dunne, C.P. and Hood, H.A. (1975) Curr. Top. 19_Cell. Regul. 9, 65-1010 Hieker, H.-J., Johannes, K.-J., and Hess, B. (1970) FEBS Letters 9, 178-1850 Mkins, G.L. (1973) Ell-£011.. BiOChen‘o 32, 175-1800 Nimmo, I.A., and Bauenmeister, A. (1977) Anal. Biochem. 99, 468-472. Philo, R.D. and Selwyn, M.J. (1973) Biochem. 9, 199, 625-530. Bates, D.J. and Frieden, C. (1973) 9, Biol. Chem. 248, 7878-7884. Duggleby, R.G. and Morrison, J.F. (1977) Biochim. Biophys. Acta ‘991, 297-312. Atkins, G.L. and Nimmo, I.A. (1973) Biochem. 9, 199, 779-784. Balcom, J.K. and Fitch, H.M. (1970) 9, Biol. Chem. 245, 1637-1647. Bizzozero, S.A., Kaiser, A.H. and Dutler, H. (1973) 999, 9, Biochem. 99, 292-300. Yun, S.-Y. and Suelter, C.H. (1977) Biochim. Biophys. Acta 480, 1'13- Jordan, F., Kuo, D.J. and Monse, E.U. (1978) Anal. Biochem. 99, 298-3020 Blasier, R.B., Hilson, J.E. and Holland, J.F. (1974) Anal. Biochem. 91, 336-342. Lucas, 0. (1978) Anal. Biochem. 91, 394-402. Carnahan, B. and Hilkes, J.O. (1973) Qigital Computing and Numerical Methods, pp. 389-391, John Hiley, N.Y. Hamilton, N.C. (1964) Statistics in Physical Science, p. 124-185. Ronald Press, New York. Cornish-Bowden, A.J. (1972) Biochem. 9. m. 637-639. Suelter, C.H., Hang, J. and Snell, E. (1976) Anal. Biochem. 19, 221 -2320 124. 125. 126. 127. 128. 129. 130. 131. 132. 133. 134. 135. 136. 137. 138. 139. 140. 141. 142. 143. 222 Hallenfels, K. and Heil, R. (1972) in The Enzymes (editors . . .) Vol. 7, pp. 617-663, Academic Press, New York. Bergemayer, H.U., Gawean, K. and Grass], M. (1974) in Methods of Enzymatic Analysis, (H.U. Bergemayer, editor) Vol. I, p. 425-522, Academic7Press, New York. Suelter, C.H., Hang, J. and Snell, E. (1976) FEBS Letters 99, 230-232. - Meloche, H.P., Ingram, J.M. and Hood, H.A. (1966) Methods Enzymol. 9, 520-524. Dunne, C.P., Gerlt, J.A., Rabinowitz, K.H. and Hood, H.A. (1973) 9, Biol. Chem. 248, 8189-8199. Cornish-Bowden, A. (1976) Principles of Enzyme Kinetics, p. 144. Butterworths, Boston. Kuhy, S.A. and Lardy, H.A. (1953) 9, Amer. Chem. Soc. Z9, 890-896. Raval, D.N. and Holfe, R.G. (1962) Biochemistry 1, 1112-1117. Hatanabe, T. and Snell, E.E. (1972) Proc. Nat. Acad. Sci. U.S.A. 99, 1086-1090. Rabinowitz, K.H., Niederman, R.A. and Hood, H.A. (1973) 9, Biol. Chem. 248, 8207-8215. Meloche, H.P. and Hood, H.A. (1964) 9, Biol. Chem. 239, 3511-3514. Kovachevich, R. and Hood, H.A. (1964) 9, Biol. Chem. 197, 745-756. Hilson, R.J.H., Kay, G. and Lilly, M.D. (1968) Biochem. 9, 168, 845’8530 Stolzenbach, P.E. and Kaplan, N.0. (1976) in Methods Enzymol. 99, 929-936 0 Daka, M.J. and Laidler, K.J. (1978) 999, 9, Biochem. 99, 774-779. Levi, A.S. (1975) Arch. Biochem. Biophys. 168, 115-121. Lee, H.-J. and Hilson, I.B. (1971) Biochim. Biophys. Acta 242, 519-522. Douglass, S.A. (1978) Amer. LEE'.lQ: 123-127. Ingram, J.M. and H00d, H.A. (1966) 9, Biol. Chem. 241, 3256-3261. Bondinell, H.E. and Sprinson, 0.8. (1970) Bioch. Bioghy . 999, Commun. 99, 1464-1467. 223 144. Krongelb, M., Smith, I.A. and Abeles, R.M. (1968) Biochim. Bioghys. _ILc_t_a_ 191, 473-475. ‘— 14s. Duffield, 0.0. and Shunays, A. (1966) Anal. Chem. 91, 29A-58A.