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Tutti ~‘3 LIBRARY Michigan State University This is to certify that the thesis entitled PART I: CRYSTAL STRUCTURE DETERMINATION OF A FLUORESCENT PROBE, 1-ANILINONAPHTHALENE-8-SULFONATE, ITS COMPLEX WITH a-CHYMOTRYPSIN AND THE NATURE OF pH DEPENDENCE ON THE COM- PLEX. PART II: PROTEIN DERIVATIVE PHASE REFINEMENT BY DIFFERENCE ELECTRON DENSITY MODIFICATION presented by Lawrence D. Weber has been accepted towards fulfillment of the requirements for Ph-DL degree in _Chemisj;r;L ‘ '__— u l 1' lu‘XCut Major profesin Date \o[$\l7§’. 0-7639 OVERDUE FINES ARE 25¢ PER DAY PER ITEM Return to book drop to remove this checkout from your record. '. .- PART I CRYSTAL STRUCTURE DETERMINATION OF A FLUORESCENT PROBE,l-ANILINONAPHTHALENE-B-SULFONATE, ITS COMPLEX WITH a-CHYMOTRYPSIN AND THE NATURE OF pH DEPENDENCE OF THE COMPLEX PART II PROTEIN DERIVATIVE PHASE REFINEMENT BY DIFFERENCE ELECTRON DENSITY MODIFICATION By Lawrence D. Weber A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements‘ for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1978 O CK \ J fl,\O \ “J ABSTRACT PART I CRYSTAL STRUCTURE DETERMINATION OF A FLUORESCENT PROBE,l-ANILINONAPHTHALENE-8—SULFONATE, ITS COMPLEX WITH a-CHYMOTRYPSIN AND THE NATURE OF pH DEPENDENCE OF THE COMPLEX PART II PROTEIN DERIVATIVE PHASE REFINEMENT BY DIFFERENCE ELECTRON DENSITY MODIFICATION By Lawrence D. Weber The structure of the fluorescent probe l-anilino- naphthalene-B-sulfonate (ANS) was determined by three dimensional X-ray crystallographic techniques. The mole— cule crystallized in space group P21/c with four molecules in the unit cell and cell dimensions of a = 6.150%, b = 9.5uufi, c = 26.773, and B = 90.350. The structure was solved by use of the program MULTAN. The unit cell contained one ammonium counter ion and one water molecule per ANS. The carbon-nitrogen bonds in the latter were found to be shortened significantly from expected single-bonded values. Inspection of independent crystallographic structures of ANS (1,2) revealed that such shortening persists regardless of anilino geometry Lawrence D. Weber or conformation. The naphthyl moiety of ANS demonstrated the geometric distortions typical of periesubstituted naphthalenes. The 2.83 resolution X-ray crystallographic structure of the complex between ANS and c—chymotrypsin (a—CHT) was studied at pH 3.6 and 6.6 with the difference Fourier method. At pH 3.6, the ANS binds on the surface of the enzyme close to the amino terminus of the A—chain and interacts intimately with the disulfide bond of Cys 1-122. The ANS is exposed to polar residues and possibly some ordered water molecules. Thus, the fluorescence enhance- ment at low pH (3) does not reflect a hydrophobic site but rather a polar one. It has been demonstrated that the ANS binding site in the crystal is the same as that in solution (3). The ANS and its protein environment remain practically the same at pH 6.6. The structural changes which occur attendent to a-CHT pH 5.“ conformer formation (A) are essentially the same as those which take place in the ANS-c-CHT complex at pH 6.6. Substituent—protein contacts and protein structural changes were summarized by use of the difference diagonal plot representation (DDP). A "multiplicity" characterization of the DDP contacts was developed to supplement this technique. The pH fluores- cence dependence observed in solution (3) may be due to a proton-disulfide interaction which prevents the disulfide group from quenching the ANS fluorescence at low pH. Lawrence D. Weber Another likely mechanism is an increase in the degree of mobility of water molecules as the pH is increased. The results suggest the need for caution in the interpretation of spectral characteristics of fluorescent probes that are interacting with biomacromolecules. The difference Fourier method used in protein crystallo— graphy relies on the phases of the native protein to approxi- mate those of a protein-derivative structure. A difference electron density modification (DDM) procedure was developed to refine the phases of a derivatized protein from the native starting set. The DDM procedure is an iterative 'sequence of alternating difference density modification and Fourier inversion calculations. Greater computational efficiency was achieved by use of a Cooley-Tukey Fast Four— ier Transform (5). The criteria for effective difference density modifications were delineated. Primary among these is that, in contrast to electron density modification (6,7), the modifying function must take into account that the majority of the difference density is frequently below background. REFERENCES 1. Cody, V. and Hazel, J., J. Med. Chem., gg, 12 (1977). 2. Cody, V. and Hazel, J., Acta Cryst. B33, 3180 (1977). 3. Johnson, J. D., Ph.D. Thesis, Michigan State University, 1976. Vandlen, R. L. and Tulinsky, A., Biochem., lg, H193 (1973). Ten Eyck, L. F., Acta Cryst., A29, 183 (1973). Collins, D. M., Brice, M. D., LaCour, T. F. M. and Legg, M. J., "Crystallographic Computing", Ahmed, F. R., Huml, K., Sledlacek, B., ed., p. 330, Munks- gaard, COpenhagen (1976). Raghavan, N. V., Tulinsky, A., Acta Cryst. (1978) in press. ACKNOWLEDGMENTS To Dr. Alexander Tulinsky, for his guidance, support and encouragement throughout this study, the author ex- presses his sincere gratitude. The author would like to thank Dr. N. V. Raghavan, and Dr. S. R. Ernst for their many helpful contributions to this study. For their many stimulating discussions, their collaboration in the fluorescent probe work, and for imbuing the author with a portion of their enthusiasm for fluorescence methods, the author wishes to extend his appreciation to Dr. M. A. El-Bayoumi and Dr. J. D. Johnson To Dr. D. L. Ward, the author is thankful for the use of a data collection facility, many computer programs, and useful discussions. For many helpful discussions the author is indebted to Dr. B. A. Averill, to Dr. M. N. Liebman, especially for his suggestion of the difference diagonal plot, and to Dr. I. M. Mavridis, Dr. A. Mavridis, Dr. L. S. Hibbard and Mr. M. Frentrup. Thanks are ex— tended to Dr. D. J. Duchamp for the use of a computer graphics facility. The author expresses his gratitude to Ms. C. Britton for her technical and general assistance. Support of the National Science Foundation and the National Institutes of Health is gratefully acknowledged. ii To the memory of Samuel S. Abrams iii TABLE OF CONTENTS Chapter Page LIST OF TABLES. . . . . . . . . . . . . . . . . . vii LIST OF FIGURES.... . . . . . . . . . . . . . . . x PART I. Crystal Structure Analysis of the Fluorescent Probe l-Anilinonaphthalene- 8-sulfonate, its Complex with a-Chymo— trypsin; and the Nature of pH De- pendence of the Complex I. INTRODUCTION. . . . . . . . . . . . . . . . . l A. Fluorescent Probes. B. Review of Excited State Processes C. Solvent Polarity and its Effect on the Fluorescence Properties of N-arylaminonaphthalene Sulfonates . . . . 6 D. Fluorescence of ANS in the Pres— ence of a-CHT . . . . . . . . . . . . . . 18 E. Structural Studies of ANS. . . . . - . - 22 II. STRUCTURE DETERMINATION OF ANS . . . . . . . 23 A. Experimental. . . . . . . . . . . . . . . 23 B. Structure Solution and Refinement . . . . 25 C. Results . . . . . . . . . . . . . . . . . 27 D. Discussion. . . . . . . . . . . . . . . . 27 III. STRUCTURE OF THE ANS-a-CHT COMPLEX, AND THE NATURE OF ITS pH DEPENDENCE . . . . . MD A. Experimental. . . . . . . . . . . . . . . A0 1. Crystal Preparation . . . . . . . . . A0 2. Data Collection . . . . . . . . . . . A3 3. Data Reduction. . . . . . . . . . . . A7 A. Difference Electron Densities . . . . A9 B. Results . . . . . . . . . . . . . . . . . 52 l. ANS Substitution at pH 3.6. . . . . . 52 2. ANS Binding Site. . . . . . . . . . . 5U iv Chapter Page 3. Independent Evidence for the ANS Binding Site. . . . . . . . 6A A. Changes in Protein Structure of ANS-a- CHT, pH 3. 6, Use of the Difference Diagonal Plot. . . . . 65 5. Changes in the ANS Binding Site at pH 6. 6. . . . . . . . . . . 7A 6. Changes in Protein Structure of ANS-a- CHT, pH 6. 6. . . . . . . . . 78 7. Comments on the DDP . . . . . . . . . 82 C. Discussion. . . . . . . . . . . . . . . . 8A 1. Comparison Between ANS-a-CHT and Solution Studies of ANS Fluores- cence . . . . . . . 8A 2. Disulfide Protonation Mechanism for Dependence of Fluorescence. . . . 86 3. pH Dependent Solvent Structure Mechanism for Fluorescence Dependence. . . . . . . . . . . . 91 A. Conformation of ANS . . . . . . . . 95 5. Secondary Binding Site of N- formyl Tryptophan . . . . . . . . . 96 PART II. Protein Derivative Phase Refinement by Difference Electron Density Modification IV. INTRODUCTION . . . . . . . . . . . . . . . . 98 A. Advantages and Disadvantages in Using the Difference Fourier. . . . . . . 98 B. Phase Refinement by Electron Density Modification With a View Toward Difference Electron Density Phase Refinement. . . . . . . . . . . . . 100 V. EXPERIMENTAL. . . . . . . . . . . . . . . . . 111 A. The Fast Fourier Transform Algorithm . . . . . . . . . . . . . . . . 111 B. Determining the Appropriate Grid Size for FFT Calculations . . . . . . . . 115 C. Difference Electron Density Modification Applied to a-CHT Derivatives . . . . . . . . . . . . . 117 Chapter D. Data Processing. . . . . . . . . . E. Trial Refinements. VI. RESULTS VII. DISCUSSION REFERENCES APPENDIX A. Computational Details of DDM Refinement at MSU. . . . . . . . . . APPENDIX B. Details of Calculation of Phase Change Between Native Protein (ON). and Derivative (aD). . vi Page 123 12A 130 lUS 152 160 165 Table II III IV VI VII VIII LIST OF TABLES 2* and ET(3O)** Values for Some Selected Solvents. . Fluorescence of ANS in Various Solvents Crystal Data of ANS. Fractional Coordinates and Thermal Parameters (A2) for ANS Non-hydrogen Atoms. Thermal Parameters are of the form [-1/AXiXJ(a*ia*JhthBij)] where a*i is a reciprocal Ce11 Edge and hi is a Miller Index . . . . . . . . . Fractional Coordinates and Thermal Parameters (A2) for ANS Hydrogen Atoms. . . . . . . . . . . . . . . . . . Geometric Parameters of the Hydrogen Bonding Scheme in ANS. Atoms Con- stituting the Ammonium Ion are Designated with an Asterisk. Conformational Parameters of ANS Ob- served in Several X-ray Crystallographic Structure Determinations . . . . . . . Unit Cell Parameters of Native and ANS- a-CHT pH Conformers. vii 10 11 2A 28 29 31 35 U2 Table IX XI XII XIII XIV XV XVI XVII XVIII XIX Page Data Reduction Parameters for Several a-CHT Derivatives. . . . . . . . . . . . . 50 Coordinates of Bound ANS Molecules . . . . 58 Close Protein Contacts with ANS. . . . . . 59 Comparison of Conformations of ANS . . . . 63 Coordinates of Points Chosen to Represent the Finite Volume of the ANS Substitution . . . . . . . . . . . . . 69 Difference Electron Density Peaks 1 [0.17eA-3l in the Vicinity of ANS Binding, Other Than the ANS Substitution . . . . . . . . . . . . . . . 71 Peak Heights of Non-Polar Cavity Difference Density in Various Dif- ference Maps . . . . . . . . . . . . . . . 77 Difference Electron Density Peaks 1 IO.l8eA-3| Representing Protein Structural Changes in ANS-c-CHT, pH 6.6 . . . . . . . . . . . . . . . . . . 8O Chronology of DDM Refinements. . . . . . 127 Statistical Results of DDM Refine- ments. 131 Non-Substitution Ap Peaks, ANS- a-CHT, pH 3.6. . . . . . . . . . . . 136 viii Table XX XXI Page Non-Substitution Ac Peaks, ANS— a—CHT, pH 3.6; Random Selection . . . . .. 137 Peak Heights for the 8 Non—Substi— tution Features (Table XIII) of ANS—a-CHT, pH 3.6 as They Appear in Two Difference Maps Calculated Using Refined Phases . . . . . . . . . . . . . . 139 ix Figure LIST OF FIGURES Skeletal formula of l-anilino- naphthalene-B-sulfonate, with numbering scheme. (a) Schematic electronic state energy level diagram: S is singlet and T is triplet. The S0 state is the ground state and the subscript numbers identify individual states. (b) Summary of processes in a, in- cluding approximate time ranges Lowest energy electronic absorption transition in 1-ethy1-U-carbomethoxy- pyridinium iodide . . . . . . . . . Plots of the transition energy of fluorescence as a function of the empirical solvent polarity scale, Z, for ANS(a) and 1,5-ANS (b) (9). The data for ANS are taken from Table II. . . . . . . . . . . . Plot of fluorescence emission maxima (in cm'l) versus the solvent polarity standard ET(3O), for 2,6-ANS and two derivatives labeled in the Figure Page 11 Figure Page (25). The notations Slnp and Slct are explained in text. All measure— ments were performed in dioxane—water mixtures except for those indicated by filled rectangles for which the solvent mixture was ethanol-water. These latter data were not included in the correlation lines. . . . . . . . . 15 Fluorescence spectra of 10-“ M a-CHT in the presence of 2x10’5 M ANS (2A) at various pH values: (2.A, 3.6, H.75, 7.0 and 8.0). Successive red shifts of the emission maxima occur as the pH value is increased. Since the spectra were recorded at various sensitivities, relative intensities are not reported. . . . . . . . . . . . 20 Relative fluorescence intensity of 2x10'5 M ANS in the presence of 10'” M a-CHT (2A); fluorescence intensi- ties were measured at the emission maxima. . . . . . . . . . . . . . . . . 21 (a) Bond lengths (A) of ANS. Standard deviations are in parentheses. (b) Bond angles (deg.) of ANS. Standard xi Figure 10 Page deviations in parentheses . . . . . . . . 30 Deviations (A) of naphthyl carbon atoms from best least squares plane of several ANS structure determinations. Addi- tional parameters are: S=[( 0.17eA-3) accompanying substitution blocked at 1 9A and enclosed by broken lines; interactions with molecule I below and with molecule 1' above diagonal . . 68 DDP between ANS-a-CHT, pH 6.6 and a-CHT pH 3.6. Substitution proper same as Figure 12 blocked at 3 12A; 29 changes (|Ap| > 0.18eA-3) accom- panying substitution blocked at xiii Figure 1A 15 16 17 Page 1 9A; interactions not common to pH 5.“ conformer enclosed by broken lines; molecule I below, molecule 1' above diagonal. . . . . . . . . . . . . 79 Average relative peak height of un- known atom in a Fourier map, as a function of its relative scattering power, ¢, in centric case, XC, and acentric case XA' At 0 + w, XC + 1.00 and xA + 0.5 (63). . . . . . . . . 101 (a) Graphical representation of the function given in Equation (19), after Collins (112). The symbol 00 represents the observed electron density, and is normalized to unity. The symbol 00 represents the calculated electron density (pMOD). (b) Same as (a), but with tangential addition (113) explained in text . . . . . . . . . . . . . . . . 109 Modification of A00 as applied to protein derivative phase refine- ment. . . . . . . . . . . . . . . . . . 119 Hypothetical arrangement of FN, (J) (J) IFNDI, “ND , and AFD in phase (J) space. Once IFNDI, “ND and FN are xiv Figure 18 Page specified, AFEJ) follows as a geo- metrical consequence. . . . . . . . . . 121 Modification function (tangential line segments) used to provide an exclusively enhancing modification. . . 1U“ XV PART I CRYSTAL STRUCTURE DETERMINATION OF A FLUORESCENT PROBE,l-ANILINONAPHTHALENE-B—SULFONATE, ITS COMPLEX WITH a-CHYMOTRYPSIN AND THE NATURE OF pH DEPENDENCE OF THE COMPLEX I. INTRODUCTION A. Fluorescent Probes The use of fluorescent probes of macromolecular struc- ture has been motivated in part by the precision with which spectroscopic quantities can be measured. Fluores- cence methods can also offer a distinct advantage in terms of time and cost, compared with other structure-probing techniques such as electron and nuclear magnetic resonance, and x-ray crystallography. Although virtually non-fluorescent in water, naphthyl- anilines and related dyes undergo a dramatic fluorescence enhancement upon addition of bovine serum albumin or heat- denatured proteins, as was first reported by Weber and Laurence in 195“ (l). The emission enhancement of these dyes in non—polar solvents was also noted. Stryer subse- quently found that 1-anilinonaphthalene-8-su1fonate (ANS) (I) (Figure I) adsorbed specifically to the non-polar heme- binding site of apomyoglobin and apohemoglobin, with a bind- ing constant on the order of 105 M"1 (2 ). A two-hundred fold increase in the quantum yield of ANS fluorescence accompanied the binding, along with a 60 nm shift to higher energy (from green to blue) of the emission maximum. Not- ing the striking correlation between these results and the spectroscopic properties of such dyes in solvent systems of varying polarity, Stryer suggested that they could be Figure 1. Skeletal formula of 1-anilinonaphtha1ene-8- sulfonate, with numbering scheme. used as probes of non-polar sites of proteins. Thus, an inferential model was conceived that initiated use and elucidation of the properties of probe molecules (3-12). B. Review of Excited State Processes The electronic energy levels of a hypothetical molecule are represented schematically in Figure 2a. Straight arrows indicate electronic state transitions in which radiation is absorbed or emitted, and wavy arrows indicate non—radiative transitions. Figure 2a illustrates the pro— cesses of absorption, fluorescence, phosphorescence, and deactivation. These processes, together with approxi- mate time scales, are summarized in Figure 2b. The times indicate the high probability that environmental fluores- cence sensitivity will be determined by the interactions which involve states S1 and T1 since these are by far the 3 longest lived excited states. An electron spin selection rule AS = 0, taken into account in Figure 2, where S is the electron spin angular momentum quantum number, applies rigorously to electronic transitions in conjugated molecular structures that contain atoms of a mass lighter than or comparable to bromine (13). An excited singlet state which can decay only through an emissive process will show first order fluorescence decay behavior: S4 ‘ ,l ‘l ‘l 83 A 1 Radiationless ’1‘ transitions— l a V S: 1‘ InteTnal conversion T: S; I Radiationless - _ - T ‘ transition- "‘9'“ "'P'“ . . absorption h mtersystem crossmg E * 1 T1 in Fluorescence I " Phosphorescencel, Internal Ab t' lntetnal Absor tion ers'on sorp ron . lp conv ' (forbidden) conversion s. 1 1 So ————> S,l (absorption) l0""-10'“ sec . . ,, w w) S, (internal conversron) I0"-—lo”sec » > So + hv (fluorescence) IO" sec . . 5'l — wwwww w» T, (mtersystcm crossmg) .wwwwy 50 (internal conversion) nod-104 sec Io-io"scc , So + by (phosphorescence) T — . . ’ “wwwww So (Internal conversron) l0-l0-3sec Figure 2. (a) Schematic electronic state energy level diagram: 8 is singlet and T is triplet. The SO state is the ground state and the subscript numbers identify individual states. (b) Summary of processes in a, including ap- proximate time ranges. (Figure 2a,b used by permission of publisher (13).) I = I e (l) where I is the fluorescence emission intensity at time t, I0 is the intensity at the onset of decay (at t = O), and I; is the intrinsic or "natural" lifetime of the excited state. The natural lifetime is thus the time required for I to fall to l/e times its value at t = O, and we can define the fluorescence decay constant kF as _ 1 kF ‘ t° . (2) F In the event that other deactivation processes are opera- tive, the observed mean lifetime, TF,Of the excited state is kF IS TF- +k )Tg (3) (kF+k IC where kIS is the rate constant for intersystem crossing and kIC that for internal conversion, both of which are defined in a manner analogous to kF. Another useful measure of emission efficiency is the quantum yield, ¢F, which can be shown to relate to the emission lifetime. The quantum yield of fluorescence is defined as ¢ = number of fluorescence quanta emitted F number of quanta absorbed to a singlet excited state’ (A) and is equal to the intrinsic fluorescence quantum yield, ¢%, when external quenching processes (e.g., deactivation by collision) are absent. For excited singlet state emis- sion, k F ° = (5) F kF+kIC+kIS ’ so that TF = ¢%T% . (6) Since ¢§ takes all internal deactivation processes into account, a longer observed mean fluorescence lifetime necessarily implies more effective competition by the fluorescence process as a deactivation pathway. C. Solvent Polarity and its Effect on the Fluorescence Properties of N—Arylaminonaphthalene Sulfonates Investigation of the spectral properties of fluores- cent probe molecules has been aided by establishment of spectroscopically based empirical measures of solvent polarity. Prominent among these are the Z (lu, 15) and ET(3O) (16) parameters. The value of the Z parameter of a solvent, expressed in kcal/mole, is the energy of the charge transfer band (the lowest energy absorption) of the solute l—ethyl-u- carbomethoxypyridinium iodide (II). The transition is represented in Figure 3, and is essentially of the dipole annihilation type. This description pertains due to the relative orientation of the molecular dipole moment, which is perpendicular to the 6-membered ring (between atoms of the ion pair) in the ground state, but parallel to the ring (and smaller) in the excited state. The equilibrium configuration between solvent molecules and the ground state of the solute defines the Franck-Condon (or "cybo- tactic") environment of the excited state. In this case it is an environment possessing a net dipole moment per- pendicular to that of the excited solute. Such a circum- stance leads to the absence of a net dipole interaction (in the ideal limit of point charges) and a destabiliza- tion of the excited solute relative to its energy in an environment of unorganized solvent (1A). The energy of II in the ground state will also vary significantly, depending on the characteristics of its solvent shell. Thus the higher a solvent is in polarity, the more effectively it can solvate the ion pair, and this will produce an absorption band at higher energy. The ET(3O) parameter is measured in the same manner, but utilizing the transition energies of pyridinium- phenolbetaine (derivative No. 30 (17)) and its methylated form (betaine), the latter for solvents of the lowest polarity. The relationship between Z and ET(3O) is COOCH3 COOCH3 _ h ' . MI I ” > I II N+ N I CHZCH3 012m3 A CED Figure 3. Lowest energy electronic absorption transition in 1-ethy1-A-carbomethoxypyridinium iodide. fairly linear over the range of solvent polarities between that of benzene and water (15). Values for Z and ET(3O) are given in Table I for some selected solvents. An analogous solvent-solute interaction sequence for initial and final electronic states can be operative for the fluorescence process if we impose the constraint that the lifetime of the excited state is longer than that needed for equilibration of surrounding solvent molecules (solvent "relaxation"). A graphical representation of the behavior of ANS emission maximum in response to solvent polarity is pre- sented in Figure Ha, the latter as measured by the Z param- eter. An identical plot for 1-anilinonaphthalene—S-sul— fonate (1,5-ANS) is given in Figure Mb. The degree of qualitative agreement between these plots is typical for the isomers of ANS. The data used in plotting Figure A are listed in Table II. It is clear that a red shift of the ANS emission maximum is observed in more polar solvents, and that this is accompanied by a dramatic quenching of fluorescence intensity (small oF). A theoretical formulation, attributed to Lippert (l8) and Mataga, et__l. (19,20) describes the electrostatic effects of permanent and induced dipole-dipole interaction between solvent and solute, under the constraint of "rapid" solvent relaxation mentioned earlier. These authors have successfully employed it to relate the energies of the lO * ** Table I. Z and ET(30) Values for Some Selected Sol— vents. Solvent z(kcal/mole) ET(30)(kcal)mole) Water 9U.6 63.1 Methanol 83.6 55.5 Ethanol 79.6 51.9 l-propanol 78.3 50.7 1-butanol 77.7 50.2 t-butanol 71.3 U3.9 Pyridine 6A.0 “0.2 l,A-Dioxane ---- 36.0 Benzene 5A. 3A.5 * Reference 15. ** Reference 16. 1" I '0‘ km") 11 13 e 2 2 A I ’ 22- ° au— ' . ' €‘ 6 o 0 ' 3 tr— 3 2.0 i- .. '9 o. e . 0 O o a .520- . I ’ r- . l .. . l . use . . a +— 1 L L l l .1 1 l 1 l A l 65 70 75 .0 05 90 93 .5 70 75 00 05 ’0 95 Z 2 Figure A. Plots of the transition energy of fluorescence as a function of the empirical solvent polarity scale, Z, for ANS(a) and 1,5—ANS (b) (9). the Data for ANS are taken from Table II. Table II. Fluorescence of ANS in Various Solvents. ANS Quantum 3% (310" Solvent (S) Yield (e) cm'l) Hater 0.0032 1.802 £thanol(20) 0.0072 1.876 Ethanol(h0) 0.020 1.931 Ethenol(60) 0.050 1.953 Ethan01(80) 0.11 1.996 Ethanol' 0.u0 2.083 Dioxenc(20) 0.012 1.908 Dioxanc(fl0) 0.038 1.93u Dioxene(60) 0.099 1.980 Dioxene(80) 0.23 2.028 Dioxane 0.57 2.118 Hethenol(50) 0.029 1.93" Nethenol(80) 0.077 1.96h Methanol 0.17 2.032 Acetone 0.39 2.137 Dlmcthylformamide 0.39 2.11u Ethylene glycol 0.12 1.968 l2 excited (pre-emission) state of fluorescent molecules with that of the ground state, and thereby to explain fluores- cence properties. This theory has also been successfully applied to ANS isomers and derivatives (11,21). For ANS— like molecules the Lippert-Mataga expression is 2 — — z 2 5-1 1'} -l + —> 2 A F hCOa3 2c+l 2,12,l e a where the constant, a sum of additional terms arising from different kinds of induced dipole interaction is, at maximum, only 10'3 as large as the lead term (20). In Equation (7), U and JF are the wavenumber values A (cm-l) for the lowest energy singlet absorption maximum and fluorescence maximum respectively, so that their dif- ference represents the non—radiative energy loss of the emitted photon. The explicitly written lead term, which accounts for the orientation effect between the permanent dipole of the solute and those of solvent molecule, contains h, Plancks constant; co, the speed of light in a vacuum; a, the Onsager cavity radius of the solute (22); c, the dielectric constant of the solvent; n, the refractive index of the solvent; E the dipole moment of first excited e, singlet state of the solute; and fig, the dipole moment of the solute ground state. (€‘l 112‘]. U ____ - _____ F 2c+1 2n2+1 a value for the apparent dipole change accompanying the A plot of V - vs ) can be used to obtain 13 emission process. Such graphical analysis for 2,6-ANS and its derivatives, performed with spectral data measured in ethanol—water mixtures, yielded plots of high linearity (11). A value (ue-ug) = HOD was reported for 2,6-ANS, a higher apparent dipole moment in the excited state. A simple explanation for sensitivity of emission maximum to conditions of solvent polarity can now be presented. The constraint requiring relatively short solvent relaxation times is amply satisfied in many or— ganic solvents. Dielectric relaxation times measured for primary alcohols, attributed to hydrogen bond break— ing followed by ROH rotation, were found to range from 0.“ ns in n-propanol to 2.0 ns in n-decanol at 20°C (23). In contrast, the observed mean lifetime for ANS in n— propanol is 10.2 ns (2A). Thus, the emitting fluorophore is in transition from a solvent equilibrated condition to a Franck Condon or cybotactic region. The excited state is more polar than the ground state, and undergoes a relative stabilization in polar solvents. The relative destabilization of the ground state, which is experiencing the Franck Condon en- vironment, is also greater in more polar solvents and the result is a red shift of fluorescence maximum. ANS-like molecules will fluoresce with anomalously high energy and fluorescence intensity in polar media such as glycerol (11) or ice (25), where solvent relaxation is retarded. 1A The spectroscopic response of 2-anilinonaphtha1ene-6- sulfonate (2,6-ANS) to solvent polarity and that of two of its derivatives, as measured by the ET(3O) parameter, is depicted in Figure 5 (26). The behavior of 2,6-ANS is readily seen to manifest distinct high and low polarity sensitivity regions (26,27). The onset of high sensi- tivity is displaced to lower polarity with a methyl sub- stituent (Me-2,6-ANS*), an electron donor. With methoxy, a stronger effective donor (due to conjugation effects), only a high sensitivity is observed. If 3% in Figure 5 is expressed in kcal/mole the high sensitivity slope is near unity at approximately 0.7. The ET(30) parameter is based on an intramolecular dipole annihilation transition and, in consideration of the substituent effect, intramolecular charge transfer is postulated to give rise to the highly polar (ll) excited singlet (labeled Slot in Figure 5). The fact that the fluorescence of 2—aminonaphthalene-6-su1fonate is nearly solvent insensitive (23) underscores the importance of the aryl substituent. It has been suggested (27) that a rela- tively planar molecular configuration must be achieved to facilitate electronic communication between the phenyl and naphthyl ring systems. Also, due to the insensitivity of the absorption spectrum to the aryl substituent when * Also referred to in the literature as 2-p-toluidinylnaph- thalene-6-sulfonate (TNS). 26 25 24 23» 22 2| FLUORESCENCE MAXIMA , v, . r03 , cm" 20 I9 Figure 5. l5 - NH __ 0,3” 0x X __\ (3 S» ‘- \ \g‘"" H 3 2,6-ANS \ e b ‘o (SH-50 Me-2,6- ANS _ \q \9 01,0. Moo-2,6-ANS t1 ‘0 4‘ do, “ A \X X ”b‘ if... ‘9 051a r- \\ \ \ t‘ \ o _. \‘ \ #- LlLlllllLJllLilllllilJllLLLlllJJ 30 4O 50 60 7O 80 90 ET(30),Kcol Imole Plot of fluorescence emission maxima (in cm’l) versus the solvent polarity standard ET(30), for 2,6—ANS and two derivatives labeled in the Figure (25). The notations Slnp and Slct are explained in text. All measurements were per- formed in dioxane—water mixtures except for those indicated by filled rectangles for which the solvent mixture was ethanol-water. These latter data were not included in the correlation lines. 16 measured in ethanol: 1) the ground state configuration is relatively non—planar (sterically favored to begin with), and 2) the Franck-Condon excited state is non-planar (labeled Slnp in Figure 5) as well. It is from the latter state, Slnp,that emission in the low sensitivity (low polarity) solvent region is assigned, in this two state - non-planar singlet, charge transfer singlet - emission model. These conclusions follow from a line of reasoning similar to that of Seliskar and Brand (11), who also sug- gested the involvement of an intramolecular charge trans— fer process, although they proposed that the Franck- Condon lst excited state was itself of a charge transfer nature. They did not observe a two-fold polarity response as their measurements were carried out in ethanol-water mixtures, which possess a minimum ET(30) value of 51.9 (Table I). However, complete characterization of the emitting states of N-arylaminonaphthalene sulfonates has not yet been achieved. Indeed, wavelength dependent fluores- cence lifetime studies (28) have suggested that the two— emitting state model may be inadequate, although no specific additional states have been proposed. Interestingly, H' NMR studies (29) of ANS that were conducted in D20 and deuteromethanol have revealed a selective relative deshielding in the latter solvent, affecting the chemical l7 shifts of H2, H2,,and H6,(Figure 1). This deshielding has been interpreted as the result of a greater degree of intramolecular hydrogen bonding in the less polar sol— vent (a possibility unique to the 1,8 isomer), and indica- tive of a more planar molecular conformation. Although results of this study contrast with the report of a planar charge-transfer excited state in media of higher polarity (Figure 5), they apply in a direct way only to the ground state. Two hypotheses have been advanced to explain the dram- atic quenching observed for the fluorescence of ANS-like molecules in polar solvents. Brand (11,30) is the chief proponent of the widely accepted intersystem crossing hypothesis. This hypothesis is based on the relation- ship between the dipole moments of states SO, S1 and T1' It has been shown that in aqueous solution the pk values of T1 in 2-aminonaphthalene and N,N—dimethyl-2-aminonaphthalene lie between those corresponding to S0 and 81 (31), this implying an intermediate dipole moment value. Thus, by a mechanism of solvent relaxation, the energy difference between the SI and T1 states will diminish in polar sol- vents, facilitating a greater efficiency for intersystem crossing (32) and subsequent non-radiative decay. A second hypothesis has been advocated by Koscwer and co- workers (27). Pulsed 1aser excitation and chemical techni- ques were used to identify the several absorbing species born 18 of the excitation of 2,6-ANS derivatives in water-dioxane mixtures. In the high polarity range (as in Figure 5), the absorbance attributed to T1 (510 mm) was found to decrease in a fashion similar to that of S this implying 1, that the former is not the intersystem crossing product of the latter. On the basis of additional studies of fluor- escence yield and emission maximum in solvents of varying polarity and viscosity, it was postulated that in the high polarity ranges a charge transfer reaction Slct + SO takes place, at a much lower rate than Slnp + Slct’ but which is favored in higher polarity-lower viscosity media, this accounting for the observed quenching. D. Fluorescence of ANS in the Presence of a—CHT Fluorescence properties of ANS dissolved in water are given in Table II In addition to the quenching effect of water, stronger quenching is observed for 1-anilinonaph- thalene-7-sulfonate (1,7-ANS) when protonation occurs at pH 1.5. Otherwise 8F and 3F are invarient between pH 1.5 and pH 12.0 (9 ). Quenching is also observed in methanolic ANS solutions that have been acidified below pH 3.0 with dry HCl gas (29). When bovine a-chymotrypsin (a-CHT) is added to aqueous solutions of ANS at pH 3.6, a dramatic enhancement of ANS fluorescence intensity and a blue shift in 3? results. At 19 A cm"1 is observed this pH, an emission maximum of 2.05 x 10 (2A) which, referring to Figure Aa, yields an apparent Z value (15) suggestive of a mean environment similar to that of l-butanol. Further, a significant sensitivity is observed as the ANS, a-CHT solution is adjusted toward neutral pH values. This behavior is summarized in Figures 6 and 7 (2U,33). The binding of salicylate derivatives to liver alcohol dehydrogenase has been investigated X-ray crystallograph— ically (3U). Accompanying fluorescence studies demon— strated that ANS competes with salicylate derivatives for the same binding site, located in the hydrophobic adeno— sine-binding pocket. However, no direct crystallographic evidence for ANS binding was presented. The goal of this study was to shed more light on the binding of ANS to proteins, the subsequent fluorescence enhancement, and the mechanism by which fluorescence variability is produced in response to pH-induced or other conformational changes. The molecular environment of ANS has been mapped in crystals of bovine a-chymotrypsin (c—CHT) at 2.8 A resolution, at two pH values. Conditions of pH were chosen such that the fluorescence properties of ANS would vary dramatically. Also taken into account was the fact that pH u.0 and 7.0 correspond to discrete values (among several, higher and lower) at which conformational changes occur in crystalline o-CHT (35). Thus, derivative FLUORESCENCE INTENSITY 400 Figure 6. 20 4E“; 05» I l 40 500 550 600 WAVELENGTH IN NANOMETERS Fluorescence spectra of 10'” M a-CHT in the pres- ence of 2x10'5 M ANS (2“) at various pH values: (2.“, 3.6, “.75, 7.0 and 8.0). Successive red shifts of the emission maxima occur as the pH value is increased. Since the spectra were recorded at various sensitivities, relative intensities are not reported. 21 IOO - 80- 60r- 40- 20- RELATIVE FLUORESCENCE INTENSITY l l l l 1 3456789 pH Figure 7. Relative fluorescence intepsity of 2x10'5 M ANS in the presence of 10' M o-CHT (2“); fluorescence intensities were measured at the emission maxima. 22 structures were investigated at pH 3.6 and 6.6. E. Structural Studies of ANS The crystal structure of ANS itself was also of interest due to the possible conformation dependence of its fluores- cence (27,29). In addition, ANS is a member of the class of periesubstituted naphthalenes, which are known to exhibit a distorted naphthyl ring geometry arising from intra- molecular steric effects (36,37). Cody and Hazel have determined the structure of the ammonium (38) and magnesium (39) salts of ANS. Both crystallized in the triclinic system. In recrystallizing ammonium ANS for the protein work the crystals were found to be monoclinic. Since this suggested an additional conformation for ANS, the crystal and molecular structures of this crystal formwere determined. II. STRUCTURE DETERMINATION OF ANS A. Experimental Crystal Preparation and Intensity Data Collection Ammonium ANS, purchased from the Sigma Chemical Company (St. Louis, MO), was recrystallized by evaporation of an aqueous solution at room temperature. A single crystal of approximate dimensions 0.7 x 0.3 x 0.15 mm was selected and mounted on a glass fiber. Weissenberg and precession photographs indicated that the crystals were monoclinic, space group P2l/c. Diffraction measurements were performed at 20°C using a Picker FACSI computer-interfaced diffractometer with Mo kOl radiation and a graphite monochrometer located between the x-ray source and the crystal. A least squares procedure was used to obtain precise unit cell parameters by fitting the setting angles of twelve reflections with 26 greater than 35°. These data and other characteristics of the crystals are given in Table III. A set of 3073 reflections was measured for 29 S 50°, and of these, 2793 were unique. Intensity data were measured by means of the method of 9-29 scans. A 20 sec background count was performed at the beginning and end of each 6-26 range. Three independent axial reflections, 33° < 29 < 38°, were chosen as intensity standards. Periodic measurement of these reflections during data collection indicated no significant change in intensity. 23 2“ Table III. Crystal Data of ANS. Spaggsgigup Mgnpglinic a 6.150(a)§l b 9.5uu(2)i c 26.77“(7)A e 90.35(2)° z A AND 1.818 cm’1 l.“l3 g cm"1 25 Both background-corrected intensities and their standard derivations contained corrections for Lorentz, polarization, and absorption effects. Values for the absorption correction, after the method of DeMeulenaer and Tompa (“0), ranged between 1.022 and 1.07“ (average 1.036), as calculated by using the atomic absorption co— efficients of Cromer and Liberman (“1). The standard deviations of the structure amplitudes, o(|F|), were calculated as in Wei and Ward (“2) with application of an instrumental instability factor of 0.02. A weight of 1/02 was applied to structure factors during the least squares refinement. B. Structure Solution and Refinement The crystal structure was solved by use of the pro- gram MULTAN (“3). The data set sufficiently over determined the structure so that only the 2077 reflections for which [Fl > 3[o(IF|)] were included in the refine- ment. The positions of the 21 skeletal atoms of ANS were located in the first E—map. After several cycles of full-matrix least squares refinement with isotropic 2I IFol-IFCII thermal parameters (R = 0.18, R = I | ), a X F o 26 difference map calculation showed two peaks which could be possible counter—ion positions. Although it was an- ticipated that one of these was the ammonium counter— ion and one a water molecule, both were favorably placed for hydrogen bonding with sulfonyl oxygen atoms. Each was included in the refinement as a nitrogen atom with an isotropic thermal parameter. After several additional cycles of isotropic and anisotropic refinement (R = 0.07“) the 12 skeletal hydrogen atoms were located in a difference density and were included in subsequent cal- culations at theoretical hydrogen positions (for which an sp2 amilino nitrogen geometry was assumed). A dif- ference map was calculated again after additional refine— ment (R = 0.05“, average parameter shift x 0.010, where o is the standard deviation of the parameter). At this stage, the isotropic E values for the two possible counter ions still agreed within 2% (“.6 A2). However, the difference map revealed one of these to be located in an approximately spherical positive density. This atom was included as an oxygen, and a cycle of aniso- tropic refinement was performed in which the param- eters of these two atoms alone were varied. The R— factor decreased to 0.0“9. Positions of the remaining six H atoms were now obtained in a new difference map, and two cycles of refinement, alternately varying H atom and non-H atom parameters, resulted in a final R-value 27 of 0.035. The final shifts in non-H atom parameters averaged 0.0500. C. Results The final atomic coordinates and anisotropic temper- ature factors of the ANS, its ammonium counter ion and water of hydration are listed in Table IV. The numbering system used is shown in Figure 8(a). The coordinates of the hydrogen atoms and their isotropic thermal parameters are listed in Table V. Bond distances and angles of ANS are given in Figure 8 along with the errors in these quantities based on the standard deviations of the atomic coordinates of the final cycle of refinement. Inter-atomic distances and angles per- taining to hydrogen bonding are listed in Table VI. D. Discussion From an examination of the final bond lengths and angles, shown in Figure 8, it is evident that the ANS structure demonstrates distortions typical of 2221? substituted naphthalenes and other ANS-like molecules. Notable among these are the in-plane deviations of the bond angles about 0(1), 0(8), 0(9), C(1') and the anilino nitrogen. 2253 Table IV. Fractional coordinates and thermal para-eters (:2) for ANS non-hydrogen atone. Theml par-eters are of the (on [4/4111 t.1 (afi1a‘ bib '1 )l where a.1 is a reciprocal cell edge and h1 is a hi1ior index. 5 3 3 “°' ‘ ' z '11 '22 '33 '12 '13 '23 s .osa7(1) .09201(1) .171oa(2) 3.97(3) 3.00(2) 3.1b(2) .23(2) .07(2) .19(2) 0(1) .ssz9(3) .0ta7(2) .16AS9(6) 3.94(a) 4.23(a) b.60(8) .80(6) -.11(6) 1.14(6) 0(2) .6367(3) .2313(2) .19186(6) s.aa(9) 3.31(a) 3.63(7) .52(7) -.51(7) -.63(6) 0(3) .5373(3) -.0107(2) .20017(6) 5.21(9) £.71(8) b.07(8) -.11(7) .67(7) 1.b8(7) 0(1) .7020(() .2790(2) .06S7S(8) 3.3(1) 3.3(1) 3.5(1) -.14(9) .10(9) .37(3) 0(2) .7075(5) .3530(3) .0233(1) 6.1(1) 1.0(1) 0.3(1) -1.3(1) .3(1) 1.0(1) 0(3) .6420(0) .3531(3) -.016£(l) 9.4(2) 5.2(1) 3.1(1) -.6(2) .1(1) 1.1(1) 0(4) .4710(3) .2659(3) -.01649(9) 7.1(2) 5.0(1) 3.3(1) -.0(1) -1.2(1) -.2(1) 0(5) .2605(b) .0043(3) .0268(1) 5.1(1) 6.0(1) 3.3(1) -.£(1) -1.3(1) -.7(1) 0(6) .2210(5) -.0011(3) .0654(1) 3.2(1) 6.2(2) 3.1(1) -2.2(1) -.6(l) -.e(1) 0(7) .35b7(4) .oosa(3) .10751(9) A.3(1) 5.5(1) 4.2(1) -1.0(1) .3(1) .0(1) 0(3) .5234(3) .0950(2) .11093(3) 3.£(1) 2.ss(9) 3.25(9) .10(3) .22(3) -.19(3) 0(9) .5317(3) .1349(2) .06950(8) 3.6(1) 2.7a(9) 3.0b(9) .b0(8) .22(a) -.1s(a) 0(10) .4370(4) .1795(2) .02723(3) 1.3(1) 3.7(1) 3.3(1) .2(1) -.¢1(9) -.32(9) l .9171(3) .2916(2) .103£9(8) A.3(1) 2.97(s) 5.1(1) -.02(3) -.95(0) 1.os(s) 0'(1) 1.0002(3) .6162(2) .11995(0) 3.3(1) 3.3(1) 3.2s(9) -.37(9) .01(0) .57(8) c'(2) 1.2109(4) .4131(3) .1t360(9) 3.6(1) b.1(1) 6.0(1) .1(1) -.01(9) .0(1) c'(3) 1.3006(5) .5326(3) .1630(1) 5.0(1) 5.0(2) A.7(1) -l.6(1) -.s(1) .1(1) 0'(4) 1.1958(6) .0576(3) .1397(1) 3.4(2) a.5(1) 4.2(1) -2.1(1) -.3(1) .1(1) c'(5) .9973(6) .664A(3) .1300(1) 3.0(2) 3.1(1) b.3(1) .6(1) 1.2(1) .6(1) c'(s) .9013(4) .5451(3) .11033(9) 4.0(1) 3.3(1) 4.1(1) .0(1) .3(1) .90(9) It .3716(3) .5537(2) .2t337(a) b.5(1) 5.1(1) ¢.5(1) .02(9) .15(0) .61(8) 0., .7370(3) .umz) .240220) 7.4(1) 0.3(1) 5.0(1) 2.1(1) 1.545(9) 1.311(3) 29 Table Fractional Coordinates and Thermal Parameters (A2) for ANS Hydrogen Atoms. Atom X Y Z iso H(2) .9l7(“) .“13(2) .02l6(8) 6.2(6) H(3) .661(“) .“13(3) -O.“35(9) 7.7(6) H(“) .355(“) .2“6(2) .“583(8) 6.5(6) H(5) .173(“) .079(2) -.0038(9) 6.1(6) H(6) .102(“) .06“(2) .0661(9) 7.3(6) H(7) .319(“) .057(2) .1352(8) 5.7(5) H(N) .960(3) .215(2) .1185(7) 5.2(5) H'(2) .283(3) .330(2) .1“36(7) 5.5(5) H'(3) .“33(“) .528(3) .1799(9) 6.2(6) H’(“) .27A(u) .731(2) .1721(8) 7.5(6) H'(5) .9l7(“) .7““(2) .1327(8) 5.5(6) H'(6) .76l(3) .5“5(2) .0997(8) “.9(5) HN*(1) .79u(3) .375(2) .2212(8) 9.2<5) HN*(2) .87“(3) .539(2) .2259(8) 9.0(5) HN*(3) .983(“) .“20(2) .2u37(9) 8.9(5) HN*(1) .767(“) .“59(2) .26u8(8) 10.1(5) Hw(l) .676(“) .810(3) .2229(9) 8.9(6) Hw(2) .625(“) .737(3) .262 (1) 9.6(6) 3O (0) 0: l.‘52(2) 1.150(2) 0,—5 1.451(2) 0) 1.793(2) 120(2) 113(2) (b) 02 Hum 113.5(1) 3 105.3(1) 100.5(1) 0' \nn ll8(l) 117(1 lZJ(l) 125.0(2) 113.2(2) 120.7(2) 122.1(2) 110.2(2) : 8 3m il 3 Will 110(1) 120(l) Figure 8. (a) Bond lengths of ANS(A). Standard deviations are in parentheses. (b) Bond angles (deg.) of ANS. Standard derivations in parenthesis. 31 Table VI. Geometric Parameters of the Hydrogen Bonding Scheme in ANS. Atoms Constituting the Ammonium Ion are Designated with an Asterisk. Distances (A) Angles (deg) N-O(l) 2.9“2 N-H(N)-O(l) l“8 N*-O(2) 2.95 N*-H*(1)-O(2) 176 N*-Ow 3.09 N*-H*(2)-Ow 133 Ow-O(3) 2.90 OW-HW(1)-O(3) 163 32 A puckering of the naphthyl ring is accomplished by a twist about the C(9)—C(10) bond, and it is accom- panied by a splaying of the perifsubstituents out of the mean plane of the ring system. Another consequence of this deformation is that the normals to the planes formed by 6-membered portions of the naphthalene frag- ment tilt by about 2.5° from their parallel orienta- tions. Similar effects have been noted in previous studies (37,38,39). Distortions of the naphthyl por- tions of ANS are summarized in Figure 9 for several dif— ferent ANS structural determinations. In contrast, Cruickshank and Sparks (“5) found naphthalene to be planar to within 0.010A. The sum of the in-plane expan- sions of the S-C(8)-C(9) and N-C(l)-C(9) angles is seen to bear an inverse relationship to the amount of splay- ing, the latter measured by the sum of the N and S distances normal to the least squares plane. Theoretical considerations anticipate unequal carbon—carbon bond lengths in naphthalene (““). This has been investigated in a number of experimental (“5) and theoretical (“6) approaches. Bond lengths calcu- lated in these independent investigations are in agree- ment within one crystallographic e.s.d. (.0053) re- ported in the former study. In peri-derivatives, the ring bonds involving C(1) ANS S 8.8° 0= .291 A=2.5° 33 -.035 -.007 -.0$3 .075 -.075 ANS fig (39) AN§(2) (38) 0:7. 0 S= .1 0: .AAA = .821 A=3.5° A=6.5° Figure 9. Deviations (A) of naphthyl carbon atoms from best least squares plane of several ANS struc- ture determinations. Additional parameters are: S D [(Hpmz Asvoe.mflm Acvso.mofi Asvmo.mc vaam.sc Amvsm.ms c.m mo .emorcumz< Accom.cam Aevmm.floa Aevso.cc Amvmm.sc Amvmm.o: *w.m mo .emorcrmza Amvom.:am szom.HOH Amvmo.ow szwm.em szmm.m: m.m mo .emouormz< Aoavoo.mam Amvce.HOH Amvsm.mc Acacom.sc AsVsm.ms m.m mo .o>Hooz Amavmoax> ona Axvo Anon Amos K. .mgoELomcoo me Bzololmz< ccm o>Humz mo whopoemhmm Haoo BHCD a . HHH> mHQwB “3 collected. Finally, the pH of the six—month-soaked crystals was increased several times daily by replacement of 0.2 m1 (of a total of 3.0 ml) of soaking solution, with a solu— tion 75% saturated in ammonium sulfate, saturated in ANS, and at pH 6.6. After about one week, the pH of the mother liquor soaking solution had attained a value of 6.6. At that time, all of the storage solution was exchanged. During this procedure the protein crystals were observed to undergo a degree of cracking, but this did not seriously affect their diffraction quality (56). 2. Data Collection All x-ray crystallographic measurements performed on the a-CHT derivatives utilized an automated Picker Nuclear Corp. FACSI four-circle diffractometer, controlled by a Digital Equipment Corp. (DEC) “K PDP-8 computer coupled to a DEC 32K disc File, and equipped with an AMPEX TMZ Digital Tape Memory System for magnetic tape data storage. The tape system operated with an Eclectic Corp. 6“0 interface. Physical modifications of the diffractometer include a rapidly operating solenoid-actuated balanced filter system, placed between the x-ray source and the crystal in order to reduce sample exposure. Also, a 60 cm helium filled tube intervenes between the crystal and detector, thus improving the resolving power of the instrument and the ““ signal-to-noise ratio of intensity measurements. The associated software package, based originally on that supplied by Picker (57), calculates unit cell parameters and refines crystal orientation by a least squares procedure after the method of Busing and Levy (5“). Substantial modification of the software (55) has introduced a "won- dering" count-six-drop-two w step scan intensity measure- ment protocol, after Wyckoff and co—workers (58), and the capability of periodically revising the crystal orientation matrix, as required by small movements of the protein crystal in its wet capillary mount. Each three dimensional data collection was preceded and followed by axial intensity distribution measurements (run-outs) and by a 6 A resolution (hOA) intensity data collection. The initial run-outs were part of the crystal selection procedure. The final run-outs and (hOA) data collection were used to corroborate the effects of radia- tion induced crystal damage, otherwise monitored auto— matically every one hundred reflections (every 1/65 of the data collection) by measuring three intensity standards. The initial hot data sets (centrosymmetric in P21) were converted to two-dimensional electron densities during the data reduction procedure, under the assumption that the signs of the protein structure factors were unaltered by experimental perturbation of the native structure. Such Fourier maps were used to determine an approximate “5 absolute scale factor for each derivative by comparing them with that of the native enzyme, which was scaled previously (59). Twinning of o—CHT crystals necessitates measurement of the relative scattering strength of the coexistent lattices. As described elsewhere in detail (59), twinning occurs about the 6* direction, withtflu3(0k£) reflections unresolvable. The latter are corrected during data reduc- tion by removal of their intensity component which has originated from the more weakly scattering lattice (re— ferred to as the twin). A ratio of diffraction intensities is calculated between the more strongly scattering lattice (the crystal) and the twin by measuring the intensity of the (600) reflection (readily identified and resolved) for each prior to data collection. The position of * (600) is retained to define the direction of 3 crystal in data collection. The unit cell dimensions and space group of the crystal and twin are the same. Absorption characteristics of a-CHT crystals are some— what complicated by the additional presence of solvent, which can vary in amount and composition, and by the pres- ence of the glass capillary, both of which are bathed by the x—ray beam. A semi-empirical absorption correction technique (60) has been adopted. Our protein crystals are _,,* mounted with b along the spindle axis (0) of the diffrac- tometer, so that the 0 dependence of the intensity of an “6 (0k0) reflection is only a function of the absorption characteristics of the crystal and mount. The method is based on the assumption that the observed absorption co- efficient of a crystal in a given orientation will be the mean of that along the path of the incident and diffracted beam. The 26 dependence is obtained by measuring absorp— tion characteristics for a series of (0k0) reflections, over a range of 0 values (>180°) which include the quad- rant of reciprocal space intended for data collection. During data reduction, in the case of general reflections, the orientation of the crystal with respect to the incident and diffracted beam is related geometrically to a 26 de- pendent (0k0) geometry. Lack of balance between the CuB(Ni) and Cualc2 (Co) filters results from the fact that part of the background radiation is composed of incoherently scattered radiation. For each crystal, prior to data collection, the lack of balance was measured as a function of 20 in a background region of reciprocal space, and has the form ILB = 1Ni(20) — ICO(20) . (8) It is used to augment the background count for each reflection, ICO(hk£ ), during data reduction. In order to extract the most useful information in the most efficient manner, only about 6200 reflections are “7 measured out of 9900 significant reflections at 2.8A resolution (92% of the total). The 6200 that are measured correspond to reflections for which the figure of merit (61,62) is greater or equal to 0.7. In this way, the most reliable phase angle data set can be obtained from one crystal, which will usually experience a decay of its intensity standards by no more than 10%. 3. Data Reduction A set of structure amplitudes is derived from the measured intensity data, I (hkl), as 2 |Fhk2| a I (hkl) . (9) The proportionality constant is composed of several crystal- lographic and instrumental corrections, applied during data reduction. More explicitly the relationship is: t=0 I std )( t=hkl l Istd '2'l:I(¢inc)+I(¢’ref1)J I(hk2)max l+COS2(2e))( 2 = l thkil (sin20)( 2 )' (k2exp(-2Bsin20/12))[INi(hk£)-(ICO(hk£)+ILB(2G))l. (10) The first factor is the Lorentz correction, which takes the finite size of reciprocal lattice points into account. “8 Its form is determined by the geometry of the diffraction experiment. The second corrects for preferential dif- fraction of the component of the incident beam polarized parallel to the reflecting planes. The third factor is t=0 std of three intensity monitors at the beginning of data col— the decay correction, where I is the average intensity lection (measured approximately once per hour during a 65 t=hk£ std intensity at the time of measurement of (hki). The fourth hour data collection), and I is their interpolated is the absorption correction (62), where I(hk£)max is the maximum intensity of an OkO reflection of similar 20 as the general reflection being considered. The inc and refl refer to incident and reflected respectively, and for the four circle diffractometer have the form I<¢inc) = I(¢hki ‘ Ehm) (11a) 1( + 8 (11b) ¢ref1)= I(¢hk2 hkt) where E = 0 = sin-1(sinecosx). The fifth factor contains the scale factor k2 and an exponential temperature nor- malization factor. The latter is determined graphically by averaging the reduced [F]2 in ranges of 20 and fitting the distribution to that of native a-CHT. The k2 is ad- justed simultaneously and includes a factor from the initial (h02) electron density scaling. The final factor “9 written in Equation (10) is I(hk£), as corrected for back- ground and lack of balance. An additional factor is added to correct 0k£ reflections for twinning. A summary of the data reduction parameters used herein is given in Table IX. “. Difference Electron Densities Reduced sets of derivative structure amplitudes were converted to "best" difference electron densities (61,62) for comparison with the native a-CHT structure. The best phase for a reflection is that represented by the centroid of a Gaussian phase-value probability function plotted in complex space ("Argand diagram") (61,62). An assumption is made that the errors arising from the use of a native phase model in conjunction with a figure of merit weight- ing scheme are small and readily characterized (63,6“). We define IAFhkil as ND N lAFhkil = [Fhkfil ’ thki" (12) gkgldGSignates a native protein structure ampli- ND tude, and IFhkAI a derivative structure amplitude. The where IF best difference electron density is l ApBEST(x,y,z)=v%;£m(hk£)IAFhklIexp(-2ni(hx+ky+2z) + io(hk1)BEST) , (13) 50 Table IX; Data Reduction Parameters for Several o-CHT Derivatives. Twin Ratio Decay Ixtal(6oo) Absorp. 2 3.2 Re“ Derivative Itwin(600) Max/Min k B( ) % Range ANS-a—CHT pH 3.6 13.9 1.55 1.26 0.00 6.“ 0-6“08 ANS-a-CHT pH 3.6 (long soak) 2.35 2.00 2.36 l.“0 “.1 0-2626 -6.“ 2627-6A28 ANS-d-CHT 1.29 1.76 1.1“ 0.300 8.9 0-2070 pH = 6 6 0.0 2071—6235 51 where x, y, and z are fractional unit cell coordinates, m(hk2) is the figure of merit, a(hk2) "best" BEST is the native phase angle, and V the unit cell volume. The rms error of the difference electron density (o(Ao)), calculated by the method of Henderson and Moffat (63), with correction (6“), ranges from about $0.02— 0.0“ ei-B in this study. However, previous work on the pH 5.“ a-CHT conformer in this laboratory (65) indicates that 0.05 e3-3 is a more realistic level for 0(Ap). We have adopted a significance level for ADBEST features at approximately three times 0.05 eX-3. An empirical and more conservative calculation with several of the derivatives now under study,of [( 2 [Ao(xyZ)]2/NJl/2, <1“) xyz <1|'—' 0(Ap) = has confirmed the latter as an appropriate significance level. 52 B. Results l. ANS Substitution at pH 3.6 The "best" difference map displayed two prominent saucer-shaped regions of electron density reaching 0.“0 eA-3 in height (m80(Ao)). The map was drawn to a scale of 2 cm 3'1 to correspond to a Kendrew model of o-CHT, and the saucer—shaped regions were readily fitted with models of ANS. An additional corraboration of the excellent overall fit of the molecular model of ANS was provided by comparison with that of p-toluenesulfonyl fluoride which tosylates a—CHT at Ser 195 and establishes an unambiguous sulfonyl location (52). Fluorescence measurements have indicated that the ANS binding site of a-CHT is identical in the crystal to that in solution at pH 3.6 (2“). The saucer—shaped difference electron densities are located in the vicinity of the amino terminus of the A—chain of a-CHT (Cys l-l22) and are situated between dimer molecules related by an ap- proximate local "inter-dimer" 2-fold rotation axis (dyad B of Figure 10). In fact, from only a cursory inspec- tion, it was not clear whether the binding was intra- molecular (ngL, l and l' or 2 and 2', Figure 10) or intermolecular (l—2' and l'-2). However, the anions PtClu= and PtIu= are known to bind intramolecularly in this region near Cys l-l22 (59,66), a moiety with which Figure 10. 53 ->2 Schematic packing diagram of a-CHT viewed down the a” direction. Molecules I and I' form an asymmetric unit and are related by non-crystallographic 2-fold axes A and B; asymmetric units related by crystallographic 2-fold screw axes shown appropriately parallel to y-axis; asterisks denote active-site regions near center of dimer; 1 and 1' denote intra- molecular ANS binding sites; 2 and 2' denote close ANS intermolecular contacts. 5“ the negatively charged ANS makes vanchn~Waals contact. In addition to the ANS density, there were some other smaller regions corresponding to small changes in the structure of a—CHT in the vicinity of the ANS binding. Otherwise, the remainder of the difference map was gen— erally below background level (No.05 eA'3). 2. ANS Binding Site There are only two general close contacts between the ANS and protein molecules in the crystal, and they remain the same following a change in pH from 3.6 to 6.6. The most extensive (nine contacts less than “.“A) and striking of these involves the disulfide bridge of Cys l-l22 (environment 1 or 1', Figure 10) which is also the amino terminus of the A-chain of a-CHT. The other close ANS—protein contact (six contacts less than “.“A) occurs in the vicinity of the side chain of Gln 239' which is located in a 2-fold-related neighboring molecule (mole- cule 1') (environment 2' or 2, Figure 10). The Gln 239 is part of an a-helix formed by residues Val 235—Asn 2“5 at the carboxyl terminus of the C-chain. A drawing of the structure of the environment of ANS in the ANS-a—CHT complex viewed through the ANS toward the Cys l-l22 di- sulfide bridge is shown above the local 2-fold axis in Figure ll, while that viewed in the opposite direction, toward the a-helix of a neighboring molecule, is shown Figure 11. 55 Drawing of vicinity of ANS binding viewed down C-direction of crystal. ANS molecules shaded; local interdimer 2-fold axis shown appropriately; lower part of drawing consti- tutes remaining environment of upper ANS and vice versa; ANS molecules and local 2-fold axis in a plane perpendicular to view; ANS sulfonate and phenyl rotational orientations arbitrary but reasonable (see text). 56 Asn204 LysZOJ Glyz f“ v.13 A 9 Cys] -l 22 6 saw 0 N [30123 O c \J \ >~2 Asn48 '\ .,,. \mzas .— O\ ./ O 0 . . \ mm mass m\ / \ . t’.\ . \ / \. "”237 ‘Kzl mm 1/ o . (5'7 ./ x. . M245 9 mm \‘.’ Q 57 below the local 2-fold axis. The ANS molecules and the interbdimerlocal 2-fold axis are essentially located in a plane perpendicular to the view in Figure ll. The coordinates of the independent ANS molecules of ANS-a-CHT, pH 3.6 are listed in Table X. These were measured visually from the Kendrew model of ANS-a—CHT by use of a grid drawn on clear plexiglass which was suspended perpendicular to the yz plane (Figure 10); and also with the aid of a Richards optical comparator (67). Close ANS-protein contacts are listed in Table XI, from which the close napthyl ring approach of ANS to the Cysl~l22 disulfide can be noted, particularly with respect to ring A (Figures 1, ll). Another prominent feature of this environment is the ion pair consisting of the qua- ternary N-terminal nitrogen atom of Cys l-l22 and its sulfate counter ion separated by about 3.23 (Table XI, Figure 3), the latter having been located previously by a sulfate-selenate exchange experiment (68). Since ANS is a negative ion at pH 3.6, it is somewhat surprising that the binding of ANS in the same general vicinity did not significantly disturb the ion pair. Interestingly, however, the sulfonate group of ANS fits into an alter- nating charge array involving Asp l28—C02-, Lys 203-NH3+, ANS—803-, Cys l-NHu+, sou=-1 (see Figure 11 also). The charge centers are separated by approximately 5.0, 7.5, 5.8 and 3.2%, respectively. These distances appear to be large for strong interactions, but this may be due to 58 Table X. Coordinates of Bound ANS Molecules* Site 1 Site 1' Atom** x y z x y z 1 0.7“1 0.22“ -0.012 0.7“7 0.363 0.006 0.757 0.239 -0.017 0.76“ 0.3“8 0.016 .7“9 0.258 -0.022 0.753 0.331 0.022 :wm O 0.721 0.26“ -0.025 0.726 0.326 0.010 5 0.677 0.253 -0.025 0.682 0.339 -0.012 6 0.659 0.238 -0.019 0.668 0.355 -0.027 7 0.667 0.218 -0.016 0.680 0.373 -0.029 8 0.69“ 0.21“ -0.015 0.706 0.377 -0.015 9 0.713 0.229 —0.018 0.721 0.360 -0.007 10 0.702 0.2“9 —0.021 0.709 0.3“3 -0.001 1' 0.780 0.199 -0.023 0.787 0.393 0.013 “' 0.83“ 0.192 -0.027 0.800 0.“09 0.006 N 0.751 0.203 -0.015 0.760 0.385 0.000 S 0.707 0.192 -0.01“ 0.720 0.397 -0.016 * Coordinates are fractional referred to the crystallographic axes; origin along y defined as in (59); local 2-fold axis approximately parallel to a*—axis at y=0.29l. ** Numbering as in I. 59 * Table XI. Close Protein Contacts with ANS. Site 1 Site 2' Protein Atom ANS d**(A) Protein Atom ANS d**(A) Cys 1 - NH3+ N u.2 Asn “8' — cY uv u.u Cys l - S 2 3.0 Leu 123' - C6 10 “.“ Cys 1 - CY2 1' “.“ Gln 239' - C6 6 3.2 Cys 122 — S 9 2.9 Gln 239' - CG 7 3.1 Cys 122 - S S 3.8 Leu 2“2' - CY 1' “.0 Lys 203 - Ce 6 “.1 Leu 2“2' - CY “' 3.“ Lys 203 — N8 6 “.0 Asn 20“ - CY S “.“ Asn 20“ - 0Y S 3.5 Other Important Contacts Protein Atom ANS d**(A) Cys l - NH3+ S 5.9 so“= - 1 u' “.9 Cys 1 - NH3+-80u=-l 3.2 * See Figure.12for exact nature of site designations. * * Estimated error :(0.6-0.7)K. 60 the fact that hydrogen atoms intervene between the charge centers and limit closest approaches. More im- portantly, the charged array serves to stress the generally polar nature of the ANS binding region 1 and 1'. Other polar features in the binding locale include the side chains of Lys 203, Asn 20“ and the side chain of Gln 239' from another molecule. The only non-polar side chains in the region are Leu 2“2', which makes a minor contact with the phenyl group of ANS, and Val 3 and Ala 206, both of which are relatively small sterically. From the opposite side, the ANS makes a close contact with the carboxyamide side chain of Gln 239' and less importantly, with a methyl group of Leu 123' and CY of Asn “8', all of a neighboring molecule (below local 2- fold of Figure 11). 0f the six contacts (Table XI), only three involve the naphthalene portion of ANS. The ANS here appears to span the planar surface of a hemi- spherical non-polar cavity created by the side chains of Ile “7', Leu 123', Val 235', Val 238' and Leu 2“2'. These residues are part of a larger internal spherical non- polar cavity near the center of the molecule (69) between the two cylinders (70) or folding domains of a—CHT. Part of the carboxyl terminal a—helix contributes prominently to this region (Figure 11). However, most of these non- polar features are quite distant to the ANS, especially relative to the proximity of the latter to the disulfide of Cys 1-122. The CS atom of the side chain of Gln 239' 61 is about 3.13 and 3.2%, respectively, from C7 and C6 of the naphthalene ring of ANS. Finally, all the close contacts in this region are far removed from the chemi- cally active anilino and sulfonate groups of ANS (6.0- 8.03). The local 2-fold relationship between the difference densities corresponding to the independent ANS molecules is excellent, both in position and peak height, so that the fit of a model of ANS in each case leads essentially to an identical molecular orientation and conformation (Figure 11). Since the density corresponding to the phenyl group of ANS possessed axial symmetry about the I 1 conformation and thus determine the coordinates of the N-C direction, it was not possible to assign a rotational * C2', 03', C5. and C6. atoms of the ring. However, since a rotation about the Cl—N bond displaces the phenyl ring, it was possible to assign Cl' coordinates and to calculate a C '-N—Cl-C2 torsion angle. Parameters which characterize 1 the conformation of ANS can be compared among: (1) The high resolution ANS structure determination reported in the previous chapter (ammonium salt, monoclinic form), (2) another high resolution ANS structure determination (ammonium salt, triclinic crystal form) with two mole- cules per asymmetric unit (38) and, (3) with parameters * The phenyl-naphthyl dihedral angle in Figure 11 was chosen to optimize the vanmhn7Waals contacts within the ANS molecule. 62 obtained from the ANS-a-CHT complex. The torsional angle and the angle between the planes of the phenyl and napthyl rings of the foregoing are listed in Table XII from which it can be seen that the Cl'-N-Cl-C2 torsion angle of ANS in the complex is similar to that in ANS (1) (38) but different from that of ANSMSU and ANS(2). In any con— formation, as observed by space filling models, the anilino hydrogen and the sulfonate oxygen atoms are sterically crowded. This precludes classical linear hydrogen bond- ing although it does not preclude an interaction among these atoms.* While the changes in protein structure accompanying ANS binding will be discussed in detail below, it can be mentioned that the difference map of ANS-a-CHT, pH 3.6 shows a pronounced density gradient associated with the side chain of Gln 239'. Upon ANS binding, there is a rotation of the side chain of Gln 239' about the C 6 and C atoms such that the polar end of the side chain is Y removed from the close proximity of the napthyl ring of ANS. This shift is of the order of 1A and may be restrain- ed by a possible interaction of the side chain with that of Lys 203 of another molecule. The side chains of Lys 203 and Lys 203' also move away from the fluorescence probe but to a lesser degree. Changes in structure on * The rotational orientation of the sulfonate group about the S-C8 bond is arbitrary in Figure 11. 63 Table XII. Comparison of Conformations of ANS. * Parameter ANS-a-CHT ANSMSU ANS(l) ANS(2) c -N-C -c ** m10° u3° 22° -uso 1' 1 2 *** a ? 61° 63° 127° * Chapter II. ** Defined as zero when CT is coplanar with N, C and C 56* 1 2' * Angle between planes of phenyl and napthyl rings. 6“ the opposite side of the ANS, near Cys 1-122, are restrict- ed to those apparently involving solvent and do not always show local 2—fold equivalence. The region leading away from the quaternary terminal nitrogen along the local 2-fold axis (Figure 11) is generally composed of solvent. From all appearances, the ANS probably approaches the protein binding sites from this direction in the crystal. 3. Independent Evidence for the ANS Binding Site Since the ANS binding site lies in an intermolecular region of the crystal, deduction of its intramolecular binding mode was based on the closeness and extent of vanckn°Waals contacts. (Such a binding mode was also dramatically illustrated by the difference diagonal plot as outlined below.) Although these clearly showed that ANS contacts the protein more intimately in the Cys 1-122 region than in environment 2 or 2' (Figure 10), nonethe— less, the possibility existed that the binding site in solution was associated with the more non—polar a—helical region, even though the vanckn~Waals contacts there were fewer. This is especially so because complicated non- polar or hydrophobic interactions are still not under- stood well theoretically or in detail, and in any case, the entropic contribution to the free energy of complex formation is not known. In order to establish the ANS binding site more definitively, use was made of the fact 65 that PtClu= and PtIu= are known to bind near Cys 1-122 in crystals of a—CHT (59,66). PtIu= was found to strongly quench ANS fluorescence in solution studies of ANS-a-CHT, and this was accomplished via a mechanism of competitive binding (2“,71). If the fluorescent probes were binding near the non-polar a-helical region of the protein its fluorescence would have been essentially unaltered by the presence of PtIu=. “. Changes in Protein Structure of ANS-a-CHT, pH 3.6; Use of the Difference Diagonal Plot The ANS binding and subsequent perturbation of the protein structure may be conveniently examined by means of a difference diagonal plot (DDP) (72,73). This plot is an extension of the well—known a-carbon diagonal dis— tance plot (7“—76) and is a way of expressing a differ- ence electron density in a diagonal distance plot format. An NxN matrix is formed with elements r that are the 13 sum of moduli of vectors given by -> -> + r(k) = [61 - akl + ch - ak|, (15) 11 where Ci’ CJ and 5k are coordinate vectors of the i and 3th a-carbon atoms of a—CHT and the kth peak of the difference density, respectively, and N is the number of amino acid residues of a-CHT. This is then contoured at 66 some convenient distance or distances. Moreover, since r13 = r31, only half of the DDP is unique so that the entire plot may be used to represent the changes occurring in both molecules of a-CHT dimer by plotting the respec- tive interactions above (molecule I', Figure 12) and below (molecule I, Figure 12) the diagonal. We have found that 9.03 was a meaningful lower limit for representing the rij of protein structural changes attending ANS binding but that a level of 12A was better to represent the ANS molecule contacts since the latter binds on the surface of the protein. Early in this study it was recognized that information may be lost in the DDP when several difference peaks satisfy riJ < 9% or generate the same 13 block (Figure 12). The number of peaks generating a given block will thus be referred to as the "multiplicity" of the block. The DDP calculation was modified to produce a table listing the multiplicity and all of its contributing difference density peaks for each block, as well as to produce a "multiplicity plot" in which the multiplicities were plotted. The multi- plicities can be used in identifying regions of the protein which are most susceptible to structural change under varied chemical conditions. They can also be used along with the DDP as a more sensitive index of asymmetry in the a-CHT dimer. An examination of the multiplicities of the DDP's of 67 the a-CHT derivatives investigated in this study revealed that only a few of these were greater than or equal to two. They are discussed appropriately in text as they were not numerous enough to warrant presentation of a multi- plicity plot in each case. However, the plot can be val- uable and has been used in representing structural changes of partially denatured derivatives of a-CHT (73), where the multiplicities were of higher order and more numerous. The DDP corresponding to contacts made by the ANS substitution and the difference peaks accompanying the substitution is shown in Figure 12 where broken lines are used to enclose the latter.* In an effort to approxi— mate the shape and the volume of the saucer-like difference density of ANS substitution for the DDP calculation, the ANS was represented in terms of eight appropriately spaced points around its perimeter. The coordinates of these are given in Table XIII. In Figure 12, it can be seen that the substitution shows excellent local two-fold symmetry and that the principal ANS-protein interactions (ngL, Cys 1-122, Lys 203 locale and Gln 239') are clearly revealed. Moreover, of the “0 interactions (13 blocks) occurring below the diagonal due to the ANS (molecule 1), all but nine are generated by the N-terminal binding * The DDP maps are reproduced from a line printer plot (10 characters per inch, 8 lines per inch). This results in a slight distortion and hence a rectangular shape for the DDP. 68 50 IOO 200 I I I I T'— so IOO I50 200 Figure 12. Diagonal plot of difference density between ANS-a-CHT, pH 3.6 and a-CHT, EH 3.6. Substi- tution proper blocked at i 12 ; 8 changes (IApI > 0.17eA-3) accompanying substitution blocked at :39A and enclosed by broken lines; interactions with molecule I below and with molecule 1' above diagonal. 69 Table XIII. Coordinates of Points Chosen to Represent the Finite Volume of the ANS Substitution. Point x y Site 1 1 0.711 0.208 .000 2 0.72“ 0.179 .015 3 0.750 0.198 .015 0.8“2 0.189 .023 5 0.776 0.198 .023 6 0.737 0.27“ .038 7 0.750 0.255 .015 8 0.711 0.2“5 .000 Site 1' 1 0.711 0.396 .031 2 0.737 0.“15 .015 0.829 0.“15 .023 0.789 0.377 .023 5 0.750 0.330 .015 6 0.763 0.“06 .000 7 0.737 0.330 .015 8 0.711 0.3“9 .031 70 environment; with molecule I', the corresponding numbers are 3“ and five. The nine and five-block features are associated with the a-helical C-terminal region of the enzyme. Thus, it is clear that, in addition to being generally closer, the ANS maintains a more extensive contact with the protein in the disulfide region and that contact with the helical region is relatively minor and simply represents an intermolecular contact arising from packing of molecules in the crystal. The ANS difference map contained 8 small peaks in the vicinity of binding in addition to the substitution itself. These ranged from 0.17 eA'"3 (m3o) to 0.25 eA'3, and are listed in Table XIV. Their effect on the DDP calculation was to give rise to those features enclosed by broken lines in Figure 12. These features occur exclusively in cylinder 2 (70) or the B folding domain (sequence > 122) of a-CHT (72). Moreover, since they are close to the diagonal of the DDP, they are necessarily localized near these par- ticular main chain positions. As can be seen in Figure 12, only three regions are involved (near Pro 12“, Lys 203; Lys 203-Asn 20“; and Gln 239), and all are located in the vicinity of the ANS binding site. These features also show a complete lack of local 2-fold symmetry, but this may be partially due to their nature as side—chain struc- tural perturbations which occur closest to atoms not directly accounted for by the DDP. Thus, a large gradient 71 Table XIV. Difference Electron Density Peaks 3 l0.l7eA—3| in the Vicinity of ANS Binding, Other Than the ANS Substitution.* Peak Peak Height x y z 1. a. 0.18ei'."3 0.632 0.387 0.012 *x b. 0.23 0.6“5 0.377 0.008 c. 0.25 0.658 0.377 0.012 d. 0.23 0.671 0.377 0.015 2. a. -0.20 0.618 0.368 -0.031 b. -0.2“ 0.632 0.368 -0.031 c. -0.21 0.6“5 0.373 -0.027 3. a. -0.18 0.618 0.132 0.023 b. -0.22 0.632 0.132 0.023 -0.18 0.6“5 0.127 0.027 “. a. 0.19 0.6“5 0.217 -0.062 b. 0.21 0.658 0.217 -0.062 5. a. 0.19 0.605 0.217 0.008 6. a. -0.18 0.72“ 0.212 —0.069 7. a. -0.18 0.868 0.193 —0.0“6 b. -0.18 0.882 0.193 -0.050 8. a. -0.18 0.6“5 0.203 -0.023 * Coordinate system as defined in Table X. ** Extended peaks are represented in three—dimensionstnrseveral point densities. 72 such as is found at the side—chain of Gln 239 on the surface of the protein may Just satisfy the r distance 13 condition in one of the a-CHT monomers, but not in the other. This is precisely the case observed here. The asymmetric feature in the Lys 203 region is generated by two peaks individually and in combination with two of the resulting blocks possessing a multiplicity of 2. Due to the Asn 20“ position being at the pivot of a hair—pin turn in the C-chain, wherein the carbon atoms of consecu- tive amino acids are more closely spaced, it is not unusual for the two difference peaks to record 16 interactions. 0n the other hand, the difference peaks at Lys 203' did not reach the significance level. The foregoing changes correspond to small movement in the sidechain Lys 203 and the peptide chain between Lys 203-Asn 20“. The movement of Gln 239' away from the ANS alters the environment of Lys 203, which in turn moves toward Asn 20“, thus causing it and the main chain in that region to undergo small shifts in position (ml.0“). A compact, approximately spherical difference density was observed with a peak height of 0.25 eA-B, and with coordinates virtually identical to those of U02+2 substi- 2+2 to a-CHT was characterized during heavy atom multiple isomorphous replacement (MIR) tution. The binding of the U0 phase determination of the native enzyme (59). The 0.25 eA-3 feature was present only in the (ANS-a-CHT, pH 3.6 — a-CHT, pH 3.6) "best" difference map. It occupies a region 73 exhibiting a striking lack of two-fold symmetry that results in one uranyl binding site per asymmetric unit, and which has been observed to manifest a high sensitivity to per— turbations of the native protein (73,77). This location is approximately 25“ distant from the ANS binding site 1 (Figure 10). At first, possible sources of metal contam- ination were considered in order to account for the peak, which existed only in the most isomorphous of the deriva- tives under study, ANS-a-CHT, pH 3.6; the geometry of the binding site is disrupted above pH 5.“ (77). However, new phases for native a-CHT became available in the later stages of this study and form the basis of the work presented in Chapter V. The new phases were the 2.83 subset of the 1.8“ a—CHT refinement-extension structure obtained (78) by using electron density modification techniques (79). After convergence, the average phase change for the 2.83 subset was :28°. This is on the order of the expected error of the starting MIR set, which is :“0°. It should be noted that the new phases are not associated with a figure of merit weighting scheme, the latter of which scales the peak heights in the "best" difference map approximately by a factor of (63), or 0.79 in the present study. Thus it was noteworthy when substitution of the new phases into the calculation induced a 25% decrease in the uranyl site difference- peak height. After four cycles of difference electron 7“ density modification phase refinement (ChapterVVIL the uranyl site difference-peak height was reduced below background. These observations underscore the need for care in the interpretation of protein derivative structural changes in this site that are located using the original phase model. Several smaller features were also sup- pressed by the refinement procedure, but the major features associated directly with ANS binding were enhanced. Lastly, other difference peaks in the ANS binding region, but on the borderline of significance, would indicate small changes in the location of solvent mole- cules, some changes being symmetric, some not. Other- wise, no significant changes appear elsewhere in the protein. 5. Changes in the ANS Binding Site atng 6.6 The difference density corresponding to ANS in the ANS-a-CHT, pH 6.6 map is nearly identical to that ob- served at pH 3.6 and only a few small changes were ob- served in the binding environment upon comparison of difference Fourier syntheses of ANS-a—CHT, pH 3.6 with c-CHT, pH 3.6 and ANS-a-CHT, pH 6.6 with a-CHT, pH 3.6. The previously discussed Gln 239 difference gradient underwent a diminution at pH 6.6. There were also some smaller changes involving the Lys 203 peaks. Since the 75 0-CHT pH 5.“ conformer (77) falls in the same range of structural stability as that of a pH 6.6 structure with- out the presence of ANS (35) and since examination of the (a-CHT, pH 5.“ — a-CHT, pH 3.6) "best" difference map showed no significant peaks in the probe binding region, one concludes that it was not the presence of the ANS in conjunction with the higher pH which depressed the Gln 239 changes originally observed at pH 3.6. Moreover, the pKa values for the key polar side-chains in the binding region are much higher than 6.6, so that their behavior in these derivatives should not be influenced by any signi- ficant change in extent of ionization. As for the ANS molecule itself, appreciable zwitterion formation is not observed above pH 3.0 in methanol (29), nor between pH 1.0-2.0 in water (71). Therefore, one concludes that alteration in the appearance of the difference peaks ac- companying the pH change involving protein moieties closest to the ANS probably results from a poorer phas- ing approximation for the higher pH conformer. 0f some interest is a feature of difference density located about 9A from the ANS in the non-polar cavity of environment 2' (Figure 10). This feature resolved into three peaks in a line roughly parallel to the crystallo- graphic y—axis in the (ANS-a-CHT, pH 6.6 - ANS-a-CHT, pH 3.6) (Map 1, Table XV) difference map. A summary of the behavior of the region in various difference maps is 76 given in Table XV. In two of the maps, where the feature is at a maximum of 0.16 eA-3, it is only slightly above background. From inspection of Table XV, it appears these peaks are a product of both the pH increase and the ANS binding. One possible source of their origin may be a greater accessibility of the cavity to solvent with in— creased pH. However, even if this were the case, the additional molecules of solvent in this part of the protein would not be close enough to the bound ANS mole- cule to affect quenching as observed in solution by a mechanism of solvent relaxation. If it were postulated that binding in environment 2' could alter the fluores- cence, it would also be assumed that better solvent ex- clusion is provided at low pH in the crystal than is found in solution. This would by the same reasoning re- sult in a longer fluorescence lifetime in the former medium, which is not observed. Finally, a number of small difference density peaks are located in the solvent region of the ANS binding site. However, with one exception, they hover around the sig- nificance level. The largest is a peak —0.18e3'3, appear- ing in map 2, Table XV, and it has neither a positive counterpart nor a local 2—fold equivalent. This feature also appears at background level in map 3. It is situated approximately 23 distant from C“' of ANS along the direc- tion of the local 2-fold axis (Figure 11), and may have 77 Table XV. Peak Heights of Non-Polar Cavity Difference Density in Various Difference Maps. f Peak Height Difference Map (eK'3) 1. (ANS-a-CHT, pH 6.6 - ANS-a-CHT, pH 3.6) +0.20* 2. (ANS-c-CHT, pH 6.6 - a-CHT pH, 5.“) +0.16** 3. (ANS-a-CHT, pH 6.6 - a-CHT, pH 3.6) +0.16** “. (ANS—a-CHT, pH 3.6 - a-CHT, pH 3.6) Background 5. (a-CHT, pH 5.“ - a-CHT, pH 3.6) Background * Three resolved peaks. xx One broad maximum. 78 been induced by the combination of pH change and ANS .4. binding. This peak is not associated with the Cys l-NH3 - SO“= ion pair, and may signify a small asymmetric solvent loss or readjustment. In summary, we have observed only very small altera- tions in or related to the ANS binding site region which accompany a change in pH from 3.6 to 6.6, and which are unique to the protein-probe complex. These do not seem directly related to the fluorescence properties of the probe, either from the point of View of solvent acces— sibility or of the conformation of the ground state of ANS. 6. Changes in Protein Structure of ANS-a-CHT,_pH 6.6 Another difference in structure between ANS-a-CHT, pH 6.6 and a—CHT, pH 5.“ is a peak of -0.18 eA-B located near dyad A in a solvent region of the dimer interface. The peak is mid-way between the side chains of Leu l“3 and Leu l“3'which are separated by about 8%. A DDP of the most significant peaks (:I0.18 eA-Bl) between ANS-a- CHT, pH 6.6 and c-CHT, pH 3.6 (map 3, Table XV*) is shown in Figure 13, and the peaks themselves are listed in Table XVI. Since the structure of q-CHT, pH 5.“ (77) is an * This map is practically the same as the superposition of maps 2 and 5 of Table XV. 79 r": In. L--. IOO”' I50F- ZOOi’ I c.- I I ' 50 IOO I50 200 Figure 13. DDP between ANS-a-CHT, pH 6.6 and a-CHT pH 3.6. Substitution proper same as Figure 12 blocked at 3 12K; 29 changes (IApI > 0.1 efi'3) accompanying substitution blocked at :_9 ; interactions not common to pH 5.“ conformer enclosed by broken lines; molecule I below, molecule I' above diagonal. 80 Table XVI. Difference Electron Density Peaks 1|0.18ei-3| Representing Protein Structural Changes in ANS-a-CHT, pH 6.6.*** Peak Peak Height x y z 1. 0.18efi 3 0.0 0.300 0.650 2. * 0.053 0.067 0.“17 b **** * 0.066 0.067 0.“17 3. -0.18 0.079 -0.033 0.55 h. -0.18 0.211 -0.033 0.617 5. a. * 0.276 0.067 0.367 b. * 0.289 0.067 0.367 6. a. -0.18 0.316 -0.083 0.583 b. -0.18 0.329 -0.083 0.600 7. a. 0.18 0.368 -0.067 0.600 b. 0.18 0.382 -0.067 0.600 8. a. 0.20 0.553 0.267 0.“67 b. 0.22 0.566 0.267 0.“67 9. 0.18 0.566 0.117 0.633 10.a. 0.18 0.618 0.“3u 0.u00 b. 0.18 0.632 o.u3u 0.“00 11 * 0.671 0.175 0.538 12. -0.18 0.671 0.“17 0.uoo 13. * 0.68“ 0.175 0.5u2 l“.a * 0.711 0.567 0.633 b. * 0.72“ 0.567 0.633 15. -0.18 0.763 0.333 0.u83 16. -0.18 0.789 0.“67 0.383 17 0.22 0.868 0.325 0.600 18. 0.18 0.868 0.083 0.883 1 .a. 0.2“ 0.882 0.317 0.608 b. 0.18 0.895 0.317 0.617 20. -0.18 0.921 0.333 0.583 21. * 0.93“ 0.133 0.583 22. -0.18 0.93“ 0.“00 0.“50 23. * 0.9u7 0.133 0.583 2“.** 0.18 0.72“ 0.300 0.133 25.a. 0.20 0.72“ 0.367 0.133 b. 0.20 0.737 0.367 0.133 26.a. 0.18 0.72“ 0.“67 0.133 b. 0.18 0.737 0.“67 0.133 27.a. 0.18 0.776 0.300 0.667 b. 0.20 0.763 0.300 0.667 28.a * 0.72“ 0.233 0.667 b. -0.18 0.737 0.250 0.617 29. -0.18 0.730 0.300 0.250 t_l Peak < -0.20eK'3. *“Peaks 2“-29 are unique to Map 1, Table XV. *¥*Coordinate system as defined in Table X. ****Extended peaks are represented in three-dimensions by several point densities. 81 excellent model for the structure of a-CHT in the protein- probe complex at pH 6.6, the interactions generated by the ANS binding (map 2, Table XV) are enclosed by broken lines in Figure 13 and specifically represent the interactions of the non—polar cavity peaks, a negative peak near Gly 196, and their local two-fold counterparts. From Figure 13 it can be seen that at pH 6.6, much of the structural change in the protein is asymmetric. The features enclosed near the diagonal in the A folding domain (sequence < 122) result from contributions of all the difference peaks Just described. They represent contacts with a segment of chain from Gln 30—A1a 55. This portion of the backbone forms three strands of beta sheet by winding back on itself twice forming two discrete seg- ments. The Junction of both beta strand segments is near Ser “5. The sheet segments run from Gln 30-Ser “5 then form another strand from Ser “5 through Thr 5“. This conformation brings consecutive amino acids in this region close together into a structure dependent on inter- chain hydrogen bonding, the sidechains of which define part of the nonpolar cavity in the Ser “5—Thr 5“ region. As an illustration of the size of this nonpolar cavity, and the location of the difference peaks, the largest and most developed positive peak of the triplet in monomer I contributes no interactions to the DDP. The features fairly symmetrically placed in the 82 off-diagonal corners result from difference peak con— tacts with the beta sheet segment Just described as it passes near the active site region. The feature in molecule I is generated solely by contacts with the negative difference peak near Gly 196, whereas the one in molecule 1' arises from contacts with both positive and negative peaks. The former contains 12 blocks, and the latter 25. Of the 25, 15 arise from the positive peak of molecule I' and 16 from contributions of the negative peak (there are six blocks with a multiplicity of 2). Moreover, the interactions of molecule 1' arising from the negative difference peak do not have one—to-one cor- respondence with molecule I. Thus, approximate symmetry in the DDP can entail a large degree of asymmetry in the detailed steric interaction of a difference peak. In summary, from Figure 13 it appears that the A folding domain of a-CHT is somewhat more sensitive to pH change in the ANS—a-CHT complex than the B domain. 7. Comments on the DDP Features in the ApH DDP may also be used to point out some of the limitations of the technique as presently constituted. Specifically, the alterations in protein structure which accompany the pH change are, in the maJority, surface changes, changes involving amino acid side-chains, and changes located in the dimer interface 83 (77). The DDP calculation is currently restricted to the consideration of c—carbon-difference peak contacts thus limiting its use for summarizing side—chain movements. This is especially so on the surface of the protein where there are necessarily less contacts.* Further- more, the calculation does not include riJ between the different monomers in the dimer interface region. There- fore, a number of changes, which have been characterized by detailed analysis of the pH 5.“ conformer of a-CHT, are underrepresented in the DDP. Conversely, the DDP accurately represents any lack of maJor perturbation in tertiary structure, and the involvement of certain amino acids in regions of im- portant changes. In the latter category, one observes features in the Tyr l“6, and Tyr l“6', the Ala l“9, Asp 6“, and Phe 39 regions which have been described and discussed in detail previously (77). A difference peak which generates interactions in the Ser 217-Ser 218 region also generates a block at Ser 217'-Ser 218', thus demonstrating a close contact between monomer polypeptide chains (69). Along similar lines, the DDP calculation between pH con- formers (5.“ - 3.6, map 5, Table XV) contains a total of 51 blocks, of which “7 have a multiplicity of one, two * Since solvent does not enter into consideration, its volume is excluded from the calculation thus generally giving rise to fewer riJ satisfying the 9.03 limit. 8“ of two, and two have a multiplicity of three. All of the higher multiplicity interactions involve Tyr l“6 and Tyr l“6',which indicates the sensitivity of this carboxylic B chain terminus to pH change in both monomers. C. Discussion 1. Comparison Between ANS—a-CHT and Solution Studies of ANS Fluorescence The crystallographic and fluorescence results (33) present several interesting contrasts to solution studies of N-arylaminonaphthalene sulfonates and other fluores— cent molecule. For instance, the naphthalene ring system of a-CHT-bound ANS is within vanckn~Waals contact of the Cys 1-122 disulfide, yet ANS fluoresces intensely at low pH. Disulfides are known to quench tryptophan fluores- cence in proteins, and have been shown to quench indole emission in solution by collision (80). Further, fluores- cence enhancement of the probe-protein complex in solu- tion has been observed to increase continuously with decreasing pH, along with a modest blue shift in ANS emission maximum, to the lowest pH measurement, pH 2.“ (33). Yet fluorescence of ANS alone in solution is un- affected in the pH range we have studied, alth0ugh quenched below pH 1.5 in water (71) and below pH 3. in anhydrous methanol (29). These contrasting properties are present 85 in the protein complex even though solvent accessibility to the probe binding site has been amply demonstrated by the accessibility of the site to ANS itself, and by the effectiveness of PtIu= quenching. Although the wavelength dependence of emission decay has not been studied, the excellent fit of a single ex- ponential to the fluorescence decay curve at “90 nm (2“) appears to indicate a single emitting state of ANS at pH 3.6 in the protein. Because of the nature of the protein environment that has been observed (which combines charged groups, the disulfide and water accessibility), this would imply either that the relaxation time for local dipoles is very long on the fluorescence time scale, or that specific interaction with the protein dominates fluorescence charac- teristics of the probe or both. The nature of the pH effect provides further evidence for a specific inter- action. Plausibility is also given by the fact that the relatively hydrophobic environment 2' (Figure 10), which is encountered by the probe only in crystals of 0-CHT, has had no measureable effect on its emission at low pH. In either case, this result contrasts measurement of 2— anilinonaphthalene-6-sulfonate (2,6-ANS) fluorescence in a viscous medium (glycerol) where more complex decay kinetics were observed (81). Fluorescence lifetime data, required for direct com- parison of the ANS fluorescence properties of ANS-c-CHT 86 in solution and in crystalline environments at pH 6.6 is presently unavailable. However, the solution (33) and crystallographic studies agree that affinity of the ANS for its binding site is not significantly different at pH 6.6 than it is at pH 3.6. Crystallographically, the region of the protein in which ANS binds at the higher pH was observed to be the same as at the lower. Thus, a quenching mechanism requiring separation of ANS is ruled out, and the high pH ANS-binding region in solution is very likely the one encountered at low pH. Surprisingly, the nature of the ANS-binding region was observed to change very little with pH change in crystals of 0-CHT, and no definite structure-linked basis for the fluores— cence dependence can be assigned. However, two possible mechanisms for the pH dependence can be proposed, the first involving direct proton-disulfide interaction at low pH, and the second involving the nature of the inter- action between the fluorophore and locally ordered solvent. The Justification and shortcomings of each are discussed below. 2. Disulfide Protonation Mechanism for Dependence of Fluorescence The pH dependence of fluorescence in the ANS-a-CHT complex is most dramatic at low pH and a hypothetical proton-moderated quenching interaction between the Cys 1-122 disulfide and ANS would have most sensitivity in 87 this region. Proton—disulfide interaction is certainly feasible under these conditions. Whereas the covalent radius of sulfur is 1.0“A (““), S-S bond lengths reported crystallographically in organic disulfides are almost invariably shorter than 2.08A. In tetragonal L-cystine, a s-s bond length of 2.0u3(6)fi is reported (82) which, with use of a standard formulation (““), indicates a double bond character of about l“%. Raman spectra have indicated a significant increase in S-S stretching fre- quency as the R-S-S-R dihedral angle approaches 90° (83) and these results have correlated well with CNDO/2 calculations in which S-S double bond character was varied with dihedral angle (85). The C-S-S-C dihedral angle in tetragonal L-cysteine was 7“° (82) and that of Cys 1-122 is nearly 90° (Figure 11). Furthermore, a model ascrib- ing partial n-bond character to the S—S bond has been successfully used in HMO calculations to predict induc- tive effects upon disulfide ionization potentials in alkyl disulfides (85). Thus, the Cys 1-122 disulfide may be expected to undergo a degree of induced polarization in proximity to the N-terminal amino group, which bears a positive charge at acidic pH values, and to experience a corresponding enhancement in the basicity of one or both of its sulfur atoms. Precedent for such an inter- action has been set by proton interaction with sulfur atoms such as in OH...S hydrogen bonding, inferred from 88 a review of crystallographic data (86). Such an inter- action has also been found to stabilize the eclipsed gas phase conformation of 2-mercaptoethanol intramolecularly (87). In fact, there is evidence that even CH...S hydrogen bonding may occur under appropriate conditions (88,89). A recent survey of x-ray protein crystallographic studies (90) described the regions of eight globular proteins in which striking spatially defined "chains" of alternating sulfur and n—bonded atoms (of aromatic amino acid side chains) were found. In all the metalo- proteins so categorized (five of the eight), the S-n "chains" were found to include the prosthetic group. For example, in rubredoxin the following S-w "chain" was located: 0 in which Cys 6, Cys 9 and Cys 39 are involved in the Fe-Su cluster. It was suggested that these "chains" might serve to help facilitate the flow of electrons. In fact, the quenching mechanism with R-S-S-R compounds (80) has been shown in model compound studies with tyrosine (91) and tryptophan (92) to involve an excited state intermolecular charge transfer from the fluorophore to the sulfur atoms. Even in the ground state, aromatic compounds have been found to interact with disulfides by forming in solution 89 a weak 1:1 complex (93) with an enthalpy of association on the order of -1 Kcal/mol (90), which is roughly one fourth that usually ascribed to hydrogen bond formation. If this kind of ground state interaction is operative in the binding of ANS to a-CHT it may enhance polarity at the disulfide and help facilitate the protonation. However, an important reservation to the foregoing presents itself in the work of Hoffmann and Hayon (9“) who found that model disulfide compounds in aqueous solution react with sol- vated electrons (from a 2.3 MeV electron source), and subsequently with protons: egq + RSSR + (RSSR)- (16) (RSSR)' + ng + RS‘ + RSH . (17) Therefore, protonation of the neutral Cys l-l22 disulfide is required to effectively prevent (RSSR)’ formation (iifiin ANS-disulfide charge transfer) in order to moderate quenching. The rate of reaction (16) was found to exhibit sensitivity to the ionization state of amino groups in symmetrical amino acid disulfides, but Hoffmann and Hayon (9“) ultimately concluded that the rate of anion formation is largely governed at the actual site of electron attack. The degree and effect of RSSR' protonation could be tested in model compound studies by acid titration of asymmetrical 90 disulfides (e.g., x—CH2-S—S-CH2-CH —NH2, x = CH3, H, OH); 2 and by examining aromatic-disulfide binding (8“) as a func- tion of pH, while simultaneously monitoring (RSSR')- formation by absorption spectroscopy (92). The latter binding experiment could also be carried out under condi- tions of aromatic photoexcitation. Spectroscopic detec- tion of (RSSR')' in ANS—a—CHT might be feasible as well. We have had further insights concerning the possible local high microviscosity contribution to fluorescence in the protein complex from the 1.83 resolution electron den- sity map of native a-CHT, pH 3.6 recently computed in our laboratory (78). An examination of the map in the vicinity of the ANS binding indicates a remarkable amount of ordered solvent in the region, in contrast with the 2.83 resolution map where it appeared more diffuse and at a lower level. A large portion of this density with peak heights exceeding 2 eA'3 is clearly associated as an apparent solvation shell with the N-terminal amino group and its sulfate counterion. A smaller disembodied portion of electron density is located “.58 from the disulfide bond. The ANS phenyl ring partially overlaps this density and displaces some of it. This may account for the difficulty we encountered assigning a rotational conformation to the phenyl ring. More importantly, however, it should be noted that this feature could create a high local viscosity for the ANS. 91 Proton exchange in ANS itself is thought to quench fluorescence at low pH by a vibrational coupling mechanism, but it is unknown whether this is directly linked to proton-nitrogen interaction pgr_§g or the accompanying flexibility of the probe molecule (29). Measurements of the pH dependence of fluorescence of ANS-like molecules in organic solvents of high Viscosity are presently un- available. However, studies of ANS fluorescence in con- centrated aqueous MgCl2 solutions, producing a viscous protic medium of high ionic strength, have demonstrated both an increase in quantum yield and a blue shift in ANS emission which increases with salt concentration (29). In view of all the foregoing, our data tend to support the notion that it is a combination of obstruction of the disulfide quenching interaction and a possibly highly viscous environment which are together responsible for the observed fluorescence in ANS-a-CHT at low pH. 3. ,pH Dependent Solvent Structure Mechanism for Fluorescence Dependence The foregoing also engenders the basis for an alter- nately proposed mechanism of quenching regulation. One could postulate that, in the same manner in which an intramolecular charge transfer complex of 2,6-ANS cannot be stabilized and does not form in polar solutions of high viscosity (27), the ANS binding site presents a microviscosity to the probe at low pH which is high enough 92 to inhibit the likely ANS-disulfide charge transfer quench- ing mechanism. Several pH ranges of stability for a—CHT have been observed X-ray crystallographically (35,77). Transitions, between some of these pH conformers take place in the pH range of interest, at pH 3.0, 3.9 and 7.0. These are accompanied by marked unit cell parameter changes. In solution, conformational changes appear to take place more gradually, in a more continuous way, as seen from the pH dependence of dimerization or activation in a—CHT (96-98). Perhaps such changes result in a gradual disordering of water in the ANS binding site, and a reduced microviscosity. Indeed, some small changes in solvent near the ANS are observed in difference maps (Table XV), although they appear near background level. The manner in which and the extent that protein molecules affect surrounding sol- vent is not fully understood. It appears that protein molecules in aqueous solution are to some degree capable of imposing their own rotational relaxation times on water molecules removed from the protein surface as far as the thickness of several hydration shells (98). Although there was no conformational or ionic change in the ANS binding region within the pH range of this study, it may be possible for pH induced changes in other parts of the a-CHT molecule to have an effect on the binding region's solvent structure. 93 Although this is an attractive alternative, it too must be considered with reservation. Recent Raman results (99) and energy modeling calculations (100) have indicated that surface point charges and hydrophobic regions of proteins provide the dominating influence in determining the ordering of surface solvent. In this regard it would be useful to firmly establish the differences, if any, which exist between the solution and crystal ANS-0- CHT fluorescence pH dependence. The pH dependence of the intensity of ANS fluorescence in crystals of a-CHT could be examined for discontinuities at pH values of known conformational transitions (35). The fluores- cence quenching in solution as a function of pH (2“) appears to be independent of the a-CHT dimerization equilibrium, the latter reported by Aune and Timasheff (97). The range of emission maximum (3?) encountered for the complexed probe over the limits of our pH measurements (2“) is only abouttwo-fifthsthe relative variation found to be associated with behavior in mixed solvents which induces a variation in quantum yield similar to that we have observed. The actual 3% values do not seem to be associated with the polar end of the solvent pol- arity dependence plot (biphasic) where emission maximum has greater sensitivity, and resembles that of a di- pole annihilation transition (27). This is consistent 9“ with the view engendered by the crystallographic results that the environment of the probe does not change dram— atically from pH 3.6 to 6.6 and that the pH dependence of fluorescence arises from a subtle effect which can block the quenching reaction. Although it would be speculative to propose specific characteristics for the higher pH 8.8 nm emitting state at this time, the electron donating and withdrawing substituent effect noted for 2,6—ANS fluorescence in mixed solvents (27) can be compared with that expected to result from the present logical alternatives. In comparison with the solution studies, a quenching scheme involving an intramolecular charge transfer process (ictp) in ANS-a-CHT prior to or possibly as a requirement for disulfide quenching would show a greater or equal substi- tution effect. This would be due to the operation of an additional quenching pathway in the complex as the Slct + 80’ for example, and disulfide quenching pathways may compete. A quenching scheme involving non-interactive competition for the excited state between an ictp and (RSSR)' formation would exhibit an equal or lesser sub- stituent effect. If the observed pH dependent fluores- cence properties arise in the absence of an ictp, they would be insensitive to substituent. Additional work will be required to determine whether the ANS emitting state of ANS-a-CHT which appears at the higher pH (2“) possesses 95 any intra— or inter-molecular charge transfer character. 'The chemical relationship of the latter (8.8 ns lifetime state) to the 12.0 ns lifetime state, persistent at both j H values (2“), might also be advantageously studied with Idavelength dependent lifetime data (28). “. Conformation of ANS On the basis of solution studies it has been assumed 'that a planar conformation in the excited state is a inequirement for intramolecular charge transfer in ANS iAsomers and derivatives (27). NMR experiments conducted iri polar and non-polar media have indicated a more planar AIJS conformation in the latter (29), in which ANS fluoresces irrtensely. These results do not necessarily conflict, as tile NMR work applies only to the ground state. Thus, the ifisue of a conformation dependence for ANS fluorescence pleoperties has been the subject of some discussion. The X-sray crystallographic structural evidence, a part of tliis study discussed in detail in Chapter II, has shown tfllat fi-overlap between the phenyl and naphthyl ring systems 1J1 ANS does not depend on their coplanarity, and this ihas suggested a much lesser spectroscopic dependence on conformation. Although models indicate a sterically induced “0° minimum for the dihedral angle between the ring Systems in ANS, structural evidence has also indicated a significant distortion of the naphthalene ring in 96 this and other periesubstituted naphthalenes (Chapter II, 37,39,102) which may allow for the possibility of greater coplanarity in solution media. (The saucer-like shape of ‘the ANS difference density may be a result of such dis— ‘tortion, or may be induced by ground state ANS—disulfide electronic orbital interaction, or both in combination.) In the case of ANS-a-CHT, theC‘lr-N-Cl-C2 torsion angle :reported in Table XII indicates the probe may not assume a liighly planar conformation (Chapter II). Whatever the :specific nature of the ANS quenching reaction, no measur— aible effect involving the C1,-N-C -C torsion angle was 1 2 cybserved as the pH was raised to 6.6. 5. Secondary Binding Site of N-formyl Tryptgphan In a previous study of this laboratory (72) it was nc>ted that a single non-active site substitution of N- fkbrmyltryptophan (form-Trp) is found in crystals of a-—CHT at pH 3.6. It is appropriate to report new details 01‘ the substitution at this time. This secondary site 218 intramolecular and borders that of the ANS site. At Cuie extremity, to which the six-membered portion of the indole ring was assigned, the difference electron density of form-Trp is in contact with dyad B and necessarily has no local 2-fold equivalent.* The indole ring is the Such a 2-fold counterpart would make an unacceptably close van der Waals contact with the form-Trp. 97 most well—defined portion of the difference density, which reaches a maximum peak height of 0.23 e373. The substitu- tion is more interior to monomer I than that of ANS, bind- ing in environment 1 (Figure 10) only, with the indole ring tilted slightly inward from dyad B to the depth of the disulfide. From the perspective of Figure 3, the form-Trp is located to the left of the ANS, at a depth placing it between the disulfide and 5 carbon of Lys 203. The non-indole portion of the substitution electron den- sity is less well defined, but it appears that the mean position of the oxygen atoms is in the same general vicinity as the ANS sulfonyl. The relative peak heights of the difference electron density indicate the form-Trp has a lower affinity for this binding site than has ANS. The fact that the fluores- cence lifetime of ANS is not influenced by form-Trp in solution (53) also indicates that the ANS binding constant is much larger, or possibly that the form—Trp site does not exist in solution. PART II PROTEIN DERIVATIVE PHASE REFINEMENT BY DIFFERENCE ELECTRON DENSITY MODIFICATION IV. INTRODUCTION A. Advantages and Disadvantages in Using the Difference Fourier X-ray crystallographic determination of protein struc- ture proceeds almost inevitably by the well-characterized method of multiple isomorphous replacement (MIR). With a new structure in hand, the crystallographer - molecular biologist wishes to add to the reservoir of knowledge being accumulated concerning the biochemistry of proteins by making further use of this graphic and frequently definitive tool. Fortunately, it is not necessary to solve derivatives of protein structures each as an inde— pendent determination. The standard practice is to utilize difference Fourier maps (Equations (12,13)) in studying substitutions and protein structural perturba- tions such as those which attend ligand or competitive inhibitor binding as well as chemically induced changes in conformation. The power of the difference Fourier method is that the same set of phases may be used to approximate any number of related structures, each of which requires the measurement of only a set of structure amplitudes. Further, the difference electron density is extremely sensitive to small structural changes and can reveal more subtle features than those manifest in an electron density 98 99 calculated with the same native protein phase angles. Fourier series termination ripples, which contribute to the uncertainty of atomic positions in the protein elec- tron density, are virtually absent in the difference density due to cancellation. The three contributing factors to the rms error level, 0(A0), in the "best" difference density are (63): l) underestimation by IAFhkli of the unmeasurable derivative structure ampli- tudes, Inggl, 2) the experimental errors in measurement of IAFhkfil’ and 3) the experimental errors in the native phase angles. It can be shown that these sources of error combine in a manner which produces a C(AO) that is proportional to (IAFhk£|2>l/2 (63 ,6“ ), and that the rms error level in the corresponding "best" native protein electron density is proportional to <|F§k2l>l/2 (62 ). In general, 0(A0) is much lower than 0(0). The major shortcoming of difference Fourier analysis is that the maps are limited in non—centrosymmetric cases (such as 0-CHT) to peak heights which average ap- proximately one half the value, or less, of that expected if ng2 were known exactly. This was shown by Luzzati (102) who derived expressions for the relative Fourier map peak enhancement and suppression for atoms included and not included (unknown) respectively in the phase model of a partially known structure. The entire dif- ference density is in the latter category. In the 100 centric case, all phases are constrained to 0 or n and an unknown atom may approach its true peak height. Some of Luzzati's results are illustrated in Figure 1“. In- dependent of this consideration, Henderson and Moffat (63) have shown that if m can be assumed to be the same for all reflections, the "best" difference density will 2 relative to their values in the have peak heights of m absence of errors in the native phases. The present study contains a good approximation to such a condition, as the 2.8“ resolution data sets are those for which 0.7 g m i 1.0. Thus, the average peak height in the "best" difference Fourier will have a value of l/2 relative to the theoretical value. For d-CHT derivative data sets in this study l/2 z 0.39. B. Phase Refinement by Electron Density Modification With a View Toward Difference Electron Density Phase Refinement Difference densities have been frequently multiplied by a factor of two (103). However, this is only a convenience, which also multiplies the errors by the same factor. In the present study, the prospects of developing an independent method for obtaining protein derivative phase angles have been investigated. Such a set of phases would naturally have the following effects on the derivative difference map: 101 .Amec m.e + ex cam oo.H + ox .8 + o p< .fipmaop mpH mo sofiuoczm m we .awe soapsom m CH Sous czocxcs mo pnwfion xmoa m>HpmHoh owmno>< .aH mpswfim 0n ov on 6 o~ o. o 1 .5 d a a 1:0 «.0 102 1) Enhance peak heights. 2) Eliminate spurious peaks resulting from artifacts in the native phase set. 3) Improve the signal—to-noise ratio. As greater sophistication in computer hardware and programming techniques has rapidly evolved in the past years, so has the variety of protein structure refine- ment techniques. Considering that complicated difference densities frequently require 'interpretation', a method of improvement was sought which would render such maps more reliable without the use of model structures. Least squares and potential energy refinement were avoided in this study, although much work is being conducted along these lines in refining protein structures. Instead, a technique which would treat the electron density or crystallographic data set as a whole was pursued, and the method of choice was electron density modification. Refinement techniques have been developed which use the principle of density modification and operate in real or reciprocal space. The earliest such method in the latter category was that of Sayre (10“), who postulated that the electron density function and its square were very nearly alike in structures of like atoms, and acceptably like in practice for structures containing only C, N, O and H. Bochner and Chandrase- kharan had shown that as a general result of Fourier theory the Fourier transform of the convolution of two 103 functions is the product of their transforms (105). This led Sayre to represent the squared structure as the "self-convolution" of its structure factors and led to the following relationships: 2 F(p,q,r)F(h-p,k—q,£-r) = VS(h,k,£)F(hk£), pqr for all h,k,£. (16) In these equations, the left hand side is the convolution of the structure with itself, V is the volume of the unit cell and S is a function to account for the change in atomic shape on squaring. Sayre later amplified this method in a least squares phase refinement and extension technique for protein structure (106,107). Phase refine- ment is achieved when (h,k,2) in Equation (16) is within the set (p,q,r), and phase extension when it is not. Not withstanding its promise in protein crystallography, this method possesses what are presently considered prohibitively large computational requirements. However, it is worth noting that it constitutes the first applica- tion of direct methods to protein phase extension (106,107). Barrett and Zwick (108) applied the squaring modifi- cation of Sayre (10“) in cycles of a real space phase extension of myoglobin, from 3.08 to 2.03 resolution. Prior to squaring the electron density they set its 10“ negative regions to zero. This noise elimination pro- cedure cannot be accomplished by reciprocal space methods. The 8E map was used in their study instead of the con- ventional 8F in order to better satisfy the equivalence requirement between the normal and squared structure. The pF is the Fourier transform of the Fhkk’ and DE is that of the coefficients Ehkx’ where 2 F 2 _ hkl Ehkg - fi———— (triclinic), (17) 1‘3 j hkz and fJ is the atomic scattering factor of the jth hkz of N atoms and contains the 8 (or (hk£)) dependent thermal factor. Thus, the E values depend only on the arrange- ment and atomic number of the atoms in the unit cell, as the thermal effects have been removed. This makes pE sharper than the corresponding pp. With the myoglobin phases extended and refined to 2A resolution, the most . _ = o reliable subset of E values gave <|acal “MIRI> 78 . Although a random change in phase angle predicts .. O _. (lacal'aMIR|> - 90 , pEcal was found to favorably com pare with p (108). SMIR One of the difficulties in the application of this method is the problem of calculating E values for use in protein structure refinement. This is generally difficult because a frequently large fraction of the unit 105 cell volume is composed of solvent. In addition, 8E exhibits more severe series termination effects than does 9F (108). In the case of difference density refinement, a simple squaring procedure would be inapplicable because the negative peaks are equally important. Although this difficulty can be overcome in real space, the difference density fundamentally violates the central axiom of the squaring method: The structure is to be composed of identical atoms. Hoppe and Gassmann (109) outlined the criteria by which the electron density of a partially known struc- ture may be Judged improved by a modification process: 1) Reduction of the enhanced maxima at known atomic sites. 2) Enhancement of the reduced maxima at unknown atomic sites. 3) Reduction of the reduced maxima at incorrectly placed atomic sites. “) Reduction of background. It is clear that 2, 3 and “ are directly analogous to the goals of difference density improvement of protein deriva- tive structures. A modification or density weighting func- tion developed from a Taylor series was designed by Hoppe and Gassmann (109) to accomplish the four objectives. The form of this modification, in contrast to more intuitively 106 designed functions, was suited in this way for reciprocal space conversion, since the latter calculations require an analytical relationship between structure factors. In real space the relationship is of the following kind oMOD =a0 + 002 + 003, (18) where p and OMOD are the observed and modified electron densities respectively, and a, b and c are constants. These terms correspond to the following convolutions (see Equation (16) also) in reciprocal space Fh = th + hsh hX'Fh,Fh_h, + cshhz,hz,,Fh"Fh'-h"Fh-h" (19) where Sh is the scattering vector and h, h' and h" repre- sent the indices (hkz), (h'k'z') and (h"k"£") respectively. The procedure is the same in both real and reciprocal space refinement: calculate an 'improved' phase angle set (by inverse Fourier transformation in the former case), and combine the new phases with the experimental structure amplitudes to form Fh for the next cycle. A simple linear modification, designed to promote more rapid convergence in real space calculations was also proposed (110). Our results show that extreme care must be exercised in DDM in order to avoid overly severe modifications. 107 Ito and Shibuya successfully applied real space dif— ference density modification to refine the lone pair electron distribution in a two-dimensional projection of NaNO2 (111). The modification was accomplished by zero- ing large regions of the difference map such that QMOD corresponded only to selected peaks which were otherwise not modified. Refinement proceeded by cycles of alternat- ing difference density modification and Fourier inversion, for which the difference density at cycle zero was the free atom X-ray structure (containing electron deforma- tion information in IF I) minus the neutron spherical obs atom structure. In each cycle the phase of F was cor- obs rected by adding FC to extracting the new phase 7: ‘obs’ and applying it to [F for subsequent calculation of the obsl modified difference map. After ten cycles, excellent agree- ment was obtained with the difference density of the X- 2 scattering factors for ray structure calculated using sp the N and O atoms, minus the same neutron structure as above. Convergence had been essentially achieved at cycle 5, for which the average phase change was only 15% that of cycle 1. The average change after cycle 10 was 8% that of cycle 1. This result is encouraging, although such a modifica- tion cannot be generally utilized in protein derivative density refinement. This is due to the complexity of protein derivative difference maps. Individual selection 108 of significant difference peaks would be subjective and difficult. The process of choosing which peaks are significant and which are not would introduce an un— acceptable level of bias. However, the studies cited in the preceding discussions have demonstrated that there is considerable freedom in choosing a useful modifica- tion function. On the basis of test phase refinement calculations with an artificial 17 carbon atom single- bonded structure, Collins (112) demonstrated the utility of a weighting function applied to the electron density in the equal atom case given by: 2 300 — 203; 00 > 0 pM00 = (19) 0; p0 < 0 In this modification, pO is normalized to a maximum value of one. The relationship is plotted in Figure 15a. However, real structures rarely qualify for even a quasi— equal atom classification. In order to prevent the strong- est electron density features from dominating the phases at the expense of lower lying detail, Collins and co- workers (113) prOposed a tangential addition to Equation (19), which is shown in Figure 150. By the choice of the factor X (Figure 15b),which scales the function of Equa- tion (19), an appropriate decrease in modulation of the higher electron density can be obtained. This latter function, with appropriate values for X: has been used 109 l1)- (a) PC .J 0 LG l’o LC)- (b) 1°C 5 I I I i J x LO Po Figure 15. (a) Graphical representation of the function given in Equation (19), after Collins (112). The symbol 00 represents the observed electron density, and is normalized to unity. The symbol pc represents the calculated electron density (pMOD)' (b) Same as (a), but with tangential addition (113) explained in text. 110 with success in several protein structural refinements (78 ,113) and has suggested itself as a suitable modifica- tion function to meet the unique requirements of protein difference density refinement. V. EXPERIMENTAL A. The Fast Fourier Transform Algorithm Practicality has been realized in iterative cycles of electron density modification with large structures by application of the Cooley-Tukey (11“) fast Fourier trans- form algorithm (FFT). The economies of the FFT result from the manner in which the Fourier series is factored. A factorization which is in wide-spread use for con— ventional calculation of crystallographic Fourier trans- forms is that of Beevers and Lipson (for example, see (115)). Their method represents a drastic reduction in the number of arithmetic operations required for the evaluation of the three dimensional transform: <00 0(xyz) = Z F(hk£)exp[-2ni(hx+k2y+zz)J, (20) k h where Friedel's rule is assumed to operate and the sums are only over the positive indices. In practice, Equations like (20) are evaluated by considering a set of F(hk£) belonging to a limited sphere in reciprocal space, and although p(x,y,z) is a continuous function, it is calculated at the points of a regular network corresponding to division of the crystallographic directions x, y, and 2 into Nx’ Ny, and NZ equal increments respectively. A 'trivial' evaluation of Equation (20) would involve NX°N ~NZ-NF y 111 112 operations, where NF is the size of the set F(hk£), and one operation is defined as a complex product followed by a complex sum. For example, if a grid of 76 x 100 x 100 were chosen for a map of an c-CHT derivative associated with a data set of 6300 reflections, a total of “.8 x 109 operations would be required. However, the Beevers-Lipson factorization results in three one-dimensional transforms, evaluated serially (115,116): T(h,k,z) = Z F(hk£)exp(-2wi£z) (21) Q U(x,k,z) = g T(hkz)exp(-2nihx) (22) R(x,y,z) = Z U(xkz)exp(-2wiky), (23) k where p(x,y,z) = % R(x,y,z). The sums are only over positive indices, and the only condition is that Friedel's rule holds (115). Equations (21), (22) and (23) each represent a one-dimensional transform for every h and k value, k and z value, and every x and 2 value, respectively. The number of operations is determined by (NkNx)(NlNz + (Nsz)(Nth) + (Nsz)(NkNy)' Since in practical cases N < Nx’ N < Ny and N < N this will always be less than h k A Z’ 8 (NxNyNz)(Nx + Ny + NZ) which for the example is 2.1 x 10 . Thus, an improvement by a factor of 20 is achieved. After completion of each summation over A in Equation (21), those values of F(hk2) no longer require storage 113 and are replaced by T(hkz). Such a replacement operates through each succeeding step and results in a major reduc- tion of computer storage requirements. In 'trivial' calculations, with Equation (20), the entire sets of F(hk£) and 0(x,y,z) need to be stored at all times. Finally, both the 'trivial' method and the Beevers- Lipson method benefit from fewer operations and lower storage requirements when additional crystallographic symmetry relates classes of F(hk£). A further factorization of the Beevers-Lipson type of one-dimensional transform is utilized by the Cooley- Tukey FFT. By way of example, one of the elementary one- dimensional transforms calculated in Equation (21) can be represented as NQ-l T(z) = F(£)exp(—2nilz). (2“) 2:0 The number of operations required is NQNz < Ni. Note that in the case of the inverse transform, 9 + F, the F(£) can be replaced with p(z), the exponential with its complex conjugate, and T(z) with T(z). Defining j 5 zNz, let us re-write equation (2“) in the Cooley-Tukey notation: N T(z) = E 1: 1 A<2>w32 (25) 0 11“ where A(l) = F(£) and W = eXp(-2ni/NZ). If N2 is equal to a power of two, J and 2 can be represented by binary numbers. For the general case where Nz = 2M, we can write M-2 j = JM_12 + jM_2 2 + ... + 312 + 30 (26) 2M"1 2M‘2 + + z 2 + A . (27) 8 = 2III-1 + gIII-2 °°° 1 0 Equation (25) can now be re-written: 1 1 1 T(j)=T(JM=l,JM_2,...,jO)= 2 Z ... Z_ A(2M_l,RM_2,...,20)x 20=0 21=0 2M_1- M-2 M‘2 2 +...+2 M-1 M-1 (JM_12 +3M_22 +...+jO)(£M_12 +gM_2 0) w (28) It can be shown (117) that the following recursive rela- tionships result: A1(JO’£M-2’£M-3""’£0) M-1 1 j z 2 0 M-1 (29) 2 {_OA(2M_2,2M_1...2O)W M-l" A2(jO’Jl’£M-3""’£O) - 1 (3121+30)2M_22M’2 (30) Z=OA1(JO’£M-2’£M-3’°’°’£0)w 2III-2 115 AM(JO’J]_’ °° °:Jm_1) = l (jM_l2M‘l+...+jO)20 2_ AM-l(jO’Jl"'°JM-2’£0)w . (31) 70-0 Finally, T(jM=1,jM_2,...,jO) = A(J0,jl,...,JM_l). (32) A reordering operation is necessary after completion of the calculation due to the bit reversal. This set of recursive equations corresponds to the original Cooley-Tukey FFT formulations and requires on the order of Nilog2N£ opera- 2 R Lipson type transform. For comparison with the example given previously, 1002 = 10“ tions for completion, in contrast to N for the Beevers= and 100 log2100 = 66“, or an improvement of about a factor of 15 over the Beevers- Lipson type transform. In fact, the FFT is rapid enough so that when N, is not an exact power of 2, the extra terms may be added as zeroes without a prohibitive increase in the cost of calculation. B. Determining the Appropriate Grid Size for FFT Calcula- tions It was mentioned previously that in practice the choice of Nx’ Ny and N2 is such that each is greater than Nh’ Nk’ 116 and N2 respectively. The reason for this follows from Shannon's sampling theorem (118): If a function f(t) contains no frequencies higher than wcps, it is completely determined by giving its ordinates at a series of points spaced 1/2 w seconds apart. Thus, in order to analytically reproduce a set of Fhkl in the case pC = 00, the conditions NX : 2Nh, Ny 1 2 Nk and NZ 1 2N, must be satisfied, where Nh’ Nk and N2 refer to the maximum value observed for the associated indices. The sampling requirements associated with non-trivial modifications of 80 increase with the degree of the modi- fication. For example, when pc = oi, the sampling require- ment doubles in each direction with respect to Shannon's criterion (119). In the present study some sacrifice in computational efficiency was opted for in favor of maximum reliability and flexibility in the choice of trial modification adjustments. It was desired to eliminate as completely as practical any possible computational artifacts. Thus, even though a milder modification scheme than pc = pg was used, assignments of NX = 76, Ny = N2 = 100 were made, which are approximately five times the maximum index in the respective directions. Even with such a fine grid, the cost of the FFT calculation was about 1/3 to 1/2 that of conventional Fourier transformation using a coarser grid of size NX = 76, N = Nz = 60. y As a test of the programs, one cycle of difference 117 density modification was performed on ANS-a-CHT, pH 3.6, with the trivial modification Apc = A00. The calculated structure factors were identical to the set from which A00 was calculated, and the scale factor between the sets was 1.000. The structure factors calculated for reflec- tions not included in A00 were identically zero. C. Difference Electron Density Modification Applied to c-CHT Derivatives The difference electron density modification procedure (DDM) is an iterative sequence of alternating difference density modification and Fourier inversion calculations. The jth cycle consists of the following steps: AoéJ—l) = FIF§$'1) - FN}, (33) Aoéj'l) = MApéJ-l), <3“) AFéJ) = F'1IApé3‘1)>, <35) s§%) = tan-1 (:N : :%::>, (36) N D F§%) = IFNDIexp(ic§%)). (37) The difference electron density is calculated in 118 Equation (33), where F is the FFT. For cycle 1, Fég) = |FND|exp(i0N), where IFNDI is the measured protein deriva- tive structure amplitude. In Equation (3“), ApéJ-l) is modified by function M, and this is followed by FFT in- version (F'7l) in Equation (35). A new phase angle, (J) O‘ND ’ using Equation (36), and a new protein-derivative structure is obtained for the protein—derivative structure by factor, Fgg), is formed as in Equation (37). The native phase angles used to calculate A B and F are the 2.88 N’ N N resolution subset of the 1.88 resolution native a—CHT set obtained by EDM refinement—extension (78). The protein- derivative amplitudes, IFNDI’ are scaled to those of the native structure, |F as described in Chapter III, A. NI. The modification function is shown in Figure 16 and is based on the EDM function of Collins and coworkers (112, 113). The latter is shown in Figure 15 and is given by Equation (19). Since the difference density is of interest in the present case, the modification is performed on both positive and negative densities, and an additional back- ground cutoff level, 0, has been introduced. The X param- eter is calculated on a relative basis. Thus its value in absolute units may change from cycle to cycle even if X is unaltered. The 0 parameter is designed for setting to zero those features in the difference map which are at such a low level that they are judged to be almost cer- tainly random noise. However, its value must be assigned 119 _. ______ .1 LC Figure 16. Modification of A00 as applied to protein derivative phase refinement. 120 with care so that it does not produce too discontinuous of a modification. As pointed out by Collins and co- workers (113), it was Lanczos (120) who observed:"a func- tion which is jumpy and highly irregular will have a Four- ier series which is very slowly convergent". Thus, such a discontinuity may cause the need for higher frequency terms in the series, terms which are not provided for by the observed data, and this is tentamount to introducing series termination errors. However, when w is applied at low levels, it causes only a small discontinuity in the difference density, which is already close to zero. In practice, it was found that when X is near 0.5, 0 could be assigned at a level between one and two times 0(A0é0)) with apparent safety. In contrast to X, 0 was evaluated in absolute units so that it would remain constant from cycle to cycle in the absence of external intervention. The goal of this study was to refine the phases a§%). The manner in which they are formed (according to Equa- tion (36)) is shown geometrically in Figure 17. The vectors F and AFéJ) are fixed, as is the amplitude of F N ND’ Equation (36) gives an a§$> corresponding to the extrapola— so that to the "head" of AFéJ). It is essential to (J) 0 tion of IFND' form FND in this manner or subsequent A0 would merely echo the choice of modification function. As shown in Figure 17, Apéj-l) (Equation (33)) is the Fourier trans- form of the coefficients AFéJ). 121 H3 Figure 17. Hypothetical arrangement of FN, IFNDI, (J) (J) “ND , and AFD in phase space. Once IFNDI’ a§%) and FN are specified, AF£J) follows as a geometrical consequence. 122 (J) D , according to sequential application of Equations (3“) When calculating a set of structure factors AF and (35), one must apply a scale factor in order to nor- malize AFéJ) relative to the observed data. A scale factor of the form z(lAFéJ)|IAFf(£) ) (38) (J) 2 z(IAFD | km was calculated for this purpose during each cycle. In (O) f IIFNDI — IFNII, so that changes in the difference maps some trials, 2 was set equal to zero, where IAF |= between cycles would be only due to changes in céj) (Fig— ure 17). With i=0, AFéJ) is placed on the same scale in each cycle. In other trials, an additional scale factor, kHA’ was subsequently applied to AFéJ) in order to compen- sate for the fact that IAF§0)|underestimates the true IAFDI. Values for kHA were derived from the observed peak height enhancement occurring with convergence of least squares refinement of heavy atom positions in MIR pro- tein structure determinations (59,121). A kHA was applied only at i=0 so that AFéJ) was again placed on the same scale in each cycle. Finally, in yet other trial cycles, 8 was set to J-l. This allowed the scaling to be respon- sive to increases of lAFéJ)| accompanying improved phasing of FND' 123 D. Data Processing All calculations were performed on aCHX36500 computer. A space group specific FFT program (122) was originally modified by Dr. N. V. Raghavan to perform the native a— CHT EDM extension of phases. The program was further modified as a part of the present study to perform the DDM refinement. Prior to refinement of an a-CHT deriva- tive, the observed derivative data were combined with the native data by use of an efficient SORTMERG program written by Dr. S. R. Ernst of this laboratory. The data files carried between cycles were divided into blocks of 100 binary records with a record counter as a separate record before each block. Each of the blocked records may be referred to generically as: h k A A0 AN AC BO BN BC FO FN FC IFM where the suffixes O, N and C refer to observed, native and calculated respectively; F refers to a structure amplitude; IFM is the figure of merit (not included in the other variables); and h, k, z, IFM are to be read as integers. "Observed" in the DDM study refers to Fég) "native" to FN, and "calculated" to AFéJ). The input file to cycle one (SORTMERG) had only 10 variables per binary record because AC, BC, and FC had to be determined. In cycle one, in the step indicated by Equation (35), 12“ F0 is converted to IIFNDI - IFNII,and so remains during subsequent cycles. This enables the user to compare ||F lel and IAFéJ)| directly in the outputs of NDl ' the FFT calculations and still retrieve |FND| from A0 and B0. At the user's option, FO can be updated to IAFéJ)| during each cycle. The FFT calculations do not seem. The scale factor in Equation (38) is calculated and applied at the same time as F-l. Several smaller programs have been created to apply an independent scale factor, to calculate refinement statistics, to reformat the data for further iterations (calculate F§%)) and also for input to the XRAY70 Fourier program. A more detailed description of this software is given in Appendix A. Reflections for which IAFEJ)|/IAF§£)| failed to reach a cut-off limit, usually 0.1 to 0.15, were discarded between cycles. This practice never resulted in the loss of more than 5% of the data in a given series of refinement cycles. D. Trial Refinements DDM refinements were performed with difference maps of ANS-q-CHT, pH 3.6, ANS-a-CHT, pH 6.6, and a-CHT, pH 5.“. The first is an excellent isomorphous substitution of a—CHT pH 3.6, while the second is a nearly isomorphous substitution of the third. With the first, the effects of DDM refinement could be observed in a derivative 125 with only small protein structural changes while the ef- fects of larger changes could be observed with the deriva- tives that possess complex but similar difference maps, and in which the starting phase model is much poorer. Several parameters were inspected from cycle to cycle. These were k(J); R A defined: XIIIFNDI - IFNII - IAFgJ>II RA = 3 (38) ZIIFNDI -| FNII RAS’ when an external scale factor, kHA was applied to aFéJ) as it appears in Equation (35): _ (J) a = X'kHAI'FND' 'FN'I " 'AFD "; (39) AS 2 kHAIIFNDI - IFNI RB defined: ZIIF I - IF + F'J'II RB = ND N D , (“0) ZIFNDl which is related to the average lack of closure, l.c.: ZIIF I — IF + AF(3)|| l.c. = ND N D , (“1) NR in which NR is the total number of reflections; and the average change in the magnitude of the phase angle = 126 (J) z - <|Ac|> = IaND aNI . (“2) NR The absolute values of these parameters are not neces— sarily meaningful in such a refinement (113), but con- vergence can be assessed by the manner in which they change. A chronological summary of the DDM refinements is given in Table XVII. Initially convergence was ex- pected to be achieved rapidly, similar to the manner of the native protein structure in EDM refinement at 2.83 resolu- tion (78). When this did not occur, the independent scale factor kHA was introduced. This was determined by comparing the relative structure amplitudes of heavy atom deriva- tives, in d-CHT (59) and in KDPG aldolase (121), before (as AFéO)) and after least squares refinement. A negli- gible scattering angle dependence was observed and the resultant average ratio in the a-CHT MIR study was 1.73 and that in aldolase was l.“0. Application of these factors (see Table XVII) resulted in faster convergence and a dramatic enhancement of dif- ference peaks. From a visual inspection of the ANS-a-CHT, pH 3.6 difference maps, it was not at all clear whether a genuine improvement was realized in signal-to—noise ratio or whether it remained unchanged. An independent method for determining peak significance was employed. One cycle of DDM was performed in which Table XVII. 127 Chronology of DDM Refinements. Series Designation Cycle HA A ANS-a-CHT, pH 3.6 B ANS-a-CHT, pH 3.6 c ANS-q-CHT, pH D ANS-a-CHT, pH E d-CHT, pH 5.“ F ANS-a—CHT, pH G ANS-a-CHT, pH H ANS-q-CHT, pH 3. 3. 3. 6. 6. 6 6 6 6 6 .II‘WI’UI—‘IZ'UUMF-‘JZ‘UUNHHNH NH l\)l—' UTI—‘UUMI-J .5 .5 (non—mod as test) U1 UTU'IU‘IWU'IUIWWU'IU'IU'I (Coor. WU‘IU'IU'IU'I U1 Zero) 10. 2.5 2.5 0000 1:12?le U‘IU'IU'IU‘I U'IU'IU'I NNNIUN OOOO OOOU‘I OO UTUTU'IU'IUI 1.00 .73 .73 .73 .73 .“0 .“0 .“0 .“0 .“0 .“0 .“0 .“0 .“O .“0 FJIJ FJI4 F’IA FJIA .00 .00 F’}4 F'I4 F'FJ FJIJ .00 .00 .00 .00 .00 FJIA FJI4 F' 128 Table XVII. Continued. Series Designation Cycle X 0 kHA 1* ANS—c-CHT, pH 3.6 l .5 2.5 1.00 2 .5 2.5 1.00 3 .5 2.5 1.00 “ .5 2.5 1.00 J** ANS-a-CHT, pH 3.6 l .5 0 1.00 ** Modified as by Figure 18. 129 the modification function was a coordinate dependent zeroing of Apéj'l) so that only the ANS substitution and its immediate environment were preserved. An independent scale factor, kHA = l.“0, was applied, as in the im- mediately preceeding cycles of DDM (Table XVII). A product difference map was formed via an element by element mul- tiplication of the zeroed DDM difference map with that of cycle 1 series D. Chemically significant features in the Apél) formed by the zeroing modification should recover a peak height above noise, as in the heavy atom method of structural solution (for example, see (123)). A cut-off was determined by calculating the ratio of ANS peak height increase over four cycles in series D, and multiplying that value times the noise level in Apéo) (ANS-a-CHT, pH 3.6). Peaks in the product map corresponding to peaks in the cycle “ map at or below the cut-off level varied unpredictably in height. It was therefore concluded that application of the scale factor, kHA’ produced too severe a modification, and this lead to an artifically "improved" difference map. This example, further experience in which X=0 and w z “0(A0) were examined (Table XVII)and.the results of Ito and Shibuya (111), in which five refinement cycles were necessary for reasonable convergence with a much more accurate starting phase set (but with a mild modifica- tion), have caused the philosophy of this study to evolve toward one of milder modification and more cycling. VI. RESULTS The statistics of the DDM refinements are summarized in Table XVIII. It is customary to judge convergence on the basis of an approach by such parameters to a constant and reasonable value. The criteria for reasonability are not always apparent prior to a refinement. For ex- ample, the RA parameter is a measure of the variation of IAFéj)| from its values at some reference point, in this case, cycle 0. Thus, although RA (or HAS) is expected to increase and level off during refinement, its final value depends both on the characteristics of the modifica— tion function, and on the manner in which these relate to the difference map features arizing from each data set, |F On the other hand, k(J) can be expected to approach NDI' unit with convergence as the modification exhausts itself by suppressing low—lying features to zero after many cycles. The average figure of merit for the data sets under study is 0.87, which corresponds to an average error of :30° in the 0N phase angles. Thus, an inspection of the progress of A0 in the series A refinement caused concern over whether a significant phase change was taking place. An additional scale factor of k = 1.73 was then applied HA in series C, and m was increased to about 20(A0) (Table XVII). The change in 0 had no effect on k(l). Apparent 130 131 00.0 H.m 0.0 0.00 0.0H H00.H000.H 0 02 0.0 0.0 0.00 0.0 H00.H00H.H 0 02 0.0 0.0 0.0H 00.0 H00.H00H.H m 02 0.0 00.H 0.0H 0.0 H00.vaH.H 0 00.0 0.0 0.H 0.HH 0.0 H00.H00H.H H 0.0 ms .000I0I020 .m 00.0 0.0H 0.HH 0.00 0.0H H00.H000.0 0 00.0 H.0H H.0 0.00 0.0H H00.H000.m H 0.0 ma .emousumza .0 00.H 0.0H 0.0H 0.00 0.0H H00.H000.H 0 0H.H m.0H 0.0H 0.00 0.0H H00.H000.m H 0.0 we .emousumze .0 00.0 0.0 0.0 0.00 0.mH H00.H0H0.H 0 00.0 0.0 0.0 0.00 0.HH H00.H00H.H m 00.0 0.0 0.0 0.H0 0.0 H00.H00H.H 0 00.0 0.0 0.0 0.0H 0.0 H00.H00H.H H 0.0 ms .emous .0 00.0 m.w 0.0 0.00 m.mH H00.HVmH.H 0 00.0 H.0 H.0 0.H0 0.0H 00.H000.H m 00.0 0.0 0.0 0.00 0.HH H00.H000.H 0 00.0 0.0 0.0 0.00 0.0 H00.H00m.H H 0.0 ms .emousnmze .0 0H.H 0.0 0.0 m0 0.0H H00.H000.0 0 00.H 0.0 m.0 00 H.0H Hm0.Hv00.H m 00.0 0.0 0.0 00 0.0H H00.H000.H 0 00.0 m.0H 0.0 00* 0.0 H00.H000.H H 0.0 ma .emoIsnmze .0 H0000 0 00 H0W00 u HHW000 H00.H000.H H 0.0 00 .emousnmza .m 00.0 0.0 0.0 H0 0.0 H00.H000.H 0 mIM600.0 00.0 00.0 00H 00.0 H00.H000.H H 0.0 ma .emousumze .0 XME Q< .O.H mm AmvHQ®Q wmfihmm .mecssmcH0cm 200 00 meHsmmm HmcHemHemem .HHH>x cHeme 132 .oopmHSOHmo poz u 02 $.20 m1.0.0000 u 00500 .0.0 me .000:0 m-«000.0 u 00500 .0.0 ms .emousnmze . me 0 0 0-0000 0 u 00 0.0 00 emoaanmze ”000 wcsHme 0 0H000 0* .m0 :oHpmsqm :0 A_0<_v ou stvm * 00.0 H.0 0.0 0.0 HH.0 H00.H000.0 H 0.0 00 .emoasnmze .0 00.0 w.m 0.m 0.0m 0.0H H00.vam.H 0 02 0.0 H.0 0.00 0.0 H00.H000.H m 02 0.0 0.0 0.00 0.0 H00.H000.H 0 02 00.0 00.0 00.0H 60.0 H00.H00m.H H 0.0 ma .emousnmza .H xmwQe .c.H mm H0000 000 H0000H000 00 .>Hsmo mcHsmm .0mscHecco .HHH>x mHhme 133 convergence resulted after four cycles, and a more sig— nificant A0 was observed along with an enhancement of the ANS substitution peak by a factor of 2.7 with respect to its Apéo) value. The Apéo) did not contain a figure of merit weighting scheme, and its ANS substitution peak height underwent only a 5% enhancement with respect to the "best" difference density. The resulting difference map calculated with the co- efficients IFNDleXp(iaN8)) also demonstrated a remarkable enhancement of features previously regarded as below the limit of significance. Their enhancement was most fre- quently on the order of a factor slightly greater than two. They were features lying Just above the w cut-off as they appeared in cycle 0. Either these peaks were real and their presence in the refined difference map indicated that the "isomorphous" ANS-d-CHT, pH 3.6 derivative in- volved much more complex and subtle protein structural changes than was supposed, or their enhancement was an artifact of an overly severe modification scheme which forced peak heights to increase without enhancing the sig- nal to noise ratio. Although the greater enhancement factor of 2.7 had been observed for the ANS substitution peak height, this was somewhat suspect as only a factor of 2.0 had been expected. Refinement series D and E were then performed with a smaller kHA = 1.“0. The a-CHT, pH 5.“ difference map had 13“ many more peaks at cycle 0 than that of ANS—c-CHT, pH 3.6. They were of more uniform height in the former, and distributed throughout the asymmetric unit. Although 0N is a more inferior initial phase model for a-CHT, pH 5.“ than for ANS-a—CHT, pH 3.6, the former derivative structure is somewhat more analogous in its density distribution to a native structure, of the kind for which EDM was successfully used previously. Thus, series E was calculated with a derivative containing more difference electron density in the asymmetric unit, in the hope that it might lead to more obvious results. Since the maximum (0) 0 that of the ANS-a-CHT, pH 3.6 substitution (Table XVIII), peak height in Ap of a—CHT, pH 5.“ was much lower than and because this leads to a corresponding lowering of the values in absolute units affected by a given X assignment, the value of 0 was initialized at a lower level in series E. The final difference map of series D resembled that of series C, although it appeared somewhat less complex, and that of series E was far more complex than either. A total of 107 difference peaks of magnitude greater than 0.30eA"3 were recorded for the final series D difference map. The level 0.30eA'3 is on the order of twice the significance level that was adopted in "best" difference map analysis. In order to establish the noise level in the refined difference map more definitively, the non-ANS 135 peaks in the cycle “ difference maps of series D were compared in detail with those of the product map (Chapter V, E) as well as with those resulting from cycle 2 series F, a follow up F"1 of the IFND'eXp(iGND)) map of non-ANS region zeroing. The ANS substitution peak height (Ap ) increased by a factor of 2.3 from cycle 0 to cycle max “ of series D (Table XVIII). This multiple of the sig— nificance level, 0.17eA-3, in the "best" difference map is approximately 0.“0eA-3. The coordinates and heights of peaks greater than or equal to 0.“0eA-3 in the cycle “ series D difference map are listed in Table XIX. Also listed are the heights of corresponding peaks in the product map, and the cycle 2 series F difference map. A similar listing for a number of randomly selected peaks of height less than |0.“0|eA-3 is presented in Table XX. From Tables XIX and XX, it appears that those peaks corresponding to cycle four series D peaks which are at a level of about l0.“0|eA-3 or lower possess a much greater degree of peak height variability - and some of these decreasetx>what is clearly background. These observa- tions do not support an assertion that the series D refinement produced an enhancement of the signal-to-noise ratio in the difference map, and suggest that kHA = l.“0 type of scaling is also too severe. However, they are consistent with the choice of significance level assigned for the "best" difference maps. 136 Table XIX. Non-Substitution A0 Peaks, ANS—a-CHT, pH 3.6. Peak Heights 32:22:33: (.101 Series X Y Z Segle: D 5;:T2;]%) Cy 2 geries 0.72“ 0.217 0.933 -0.68ex-3 -1.22eA'—3 -0.72eA-3** 0.658 0.383 0.017 0.58 1.08 0.60** 0.026 0.267 0.750 -0.52 -0.58 -0.3“ 0.6“5 0.383 0.967 -0.52 -0.72 -0.60** 0.6“5 0.233 0.017 -0.50 -0.““ -0.“2 0.316 0.317 0.733 -0.50 -0.26 -0.20 0.618 0.167 0.067 0.“6 —0.26 0.22 0.93“ 0.“67 0.“50 -0.““ -0.20 -0.18 0.671 0.167 0.“l7 0.“2 0.28 0.28 0.658 0.217 0.933 0.“2 0.72 0.56** 0.526 0.283 0.733 -0.“2 -0.22 -0.22 0.“61 0.“17 0.933 -0.“2 0.1“ <|0.16|**** 0.0“0 0.100 0.750 -0.“0 -0.1u was observed relative to IIF IFNII and the large scale factor which resulted ND| ' from this procedure did not decrease. 1“2 Extension of series H and I by additional cycles of refinement to achieve convergence was terminated in the light of observations which implied that the modification function which was being employed may not be optimally suited for DDM. In the EDM refinements reported to date (78,79), the scale factor, k(J), has never been larger than 1.20 and is typically 1.10 in the early cycles. In the present study, a consistently large k(J) has been related to over-modifying and its associated liabilities. Thus, the relatively large k(J) in the majority of the refinements has been a matter of constant concern. It had been noted, for example, by comparison of series 0 and H, that a dramatic sensitivity in k(J) resulted when w exceeded a value such that its effect was independent of the portion of the modification curve (given in Fig- urelfiU which is nearest zero. Further, even with 0 at 0.05eA-3, the scale factors in the ANS-a-CHT, pH 3.6 series were consistently larger than those involving a-CHT derivatives in the pH 5.“-6.6 range.* A simple empirical test of the origin of the larger scale factors was devised based on the analytical nature of the FFT.1 calculation. This was in the form of a modification which enhanced ApéJ-l) everywhere, and which * In series including kHA > 1.00, or for which R = J-l, no additional effect on k(J) is induced in cycle 1. l“3 is represented in Figure 18. It was constructed by deleting the suppression domains (Figure 16) and substi- tuting a second tangent, from the origin to x. The modifi- cation in Figure 18 corresponds to a x value of 0.5. One cycle with this modification yielded a value for k(1) of 0.89. In the d-CHT derivatives under study, the ratio 0(A0)/A0max ranged from approximately 0.125 to 0.21. Thus, oin contrast to the EDM studies, the great majority of sampling grid points in the difference electron density are subject to the most severe suppression effects of the modification function (Figure 16). A reduction in X: which would help alleviate the excessively high scale fac— tors, would slow convergence to an extent which would make the procedure impractical. The function plotted in Figure 18 was designed only for the purpose of testing a pure en- hancement that would be mild near zero. Interestingly, although this function was elsewhere comparable to that in Figure 16 for x = 0.5, it gave rise to a negligible A0. These results suggest that the A0 possesses different modification requirements than does the protein electron density itself. Figure 18. 1““ \ x ——————————_ £5 Modification function (tangential line seg- ments) used to provide an exclusively en— hancing modification. IV. DISCUSSION In principle, electron density modification techniques lead to a correct result because structural information is present in both intensity and phase data. Even if the modified phases were initially to arize in a somewhat arbitrary way, they would ultimately lead to preferential survival or enhancement of correct features by their com- bination with the measured structure amplitudes. This will favor phase changes which take place in the right directions in subsequent cycles. Thus arises the flex- ibility in choice of modification function. Judging by the results of Barrett and Zwick (108), it is possible to obtain an essentially accurate result in phase extension of protein structures even when the extended phases appear to be somewhat random. In their work with myoglobin (108), a comparison of the final extended phase set with an MIR set for identical diffraction data gave = 78°, where 90° is expected for random results. Even so, the refined electron density compared very favorably with the MIR map (108). This suggests that for a DDM refine- ment, where the native protein phase model is a good approximation to 0ND, but differs from it randomly, noticeable improvement might be obtained by changes in aé$> which are merely in the right direction, if not completely accurate in magnitude. l“5 l“6 Phase refinement within a fixed resolution data set should produce markedly improved electron densities as a result of relatively small phase corrections. In this kind of experiment the phases are of greater importance in Fourier synthesis than the structure amplitudes. This was shown by Srinivasan (12“), who found an impressive agreement between the Fourier transform of the structure factors of L-tyrosine and that calculated by replacing the L-tyrosine structure amplitudes with those derived from an unrelated, arbitrary atomic configuration. Unlike the EDM procedure, the DDM experiment begins with a data set in which both the phases and structure amplitudes are deficient. Thus, peak height enhancement in the protein derivative difference map occurs not only from phasing, but from the development of IAF§3)I as well. Also in contrast with EDM is the fact that the phases which are calculated from the modified difference map are not directly those quantities which are the desired result of refinement. Further, geometrical considerations (Figure 17) dictate an interdependence between the refined phases, a§%), and amplitudes |AF§J)|, which to- gether influence subsequent aéJ). In DDM refinement a geometrical limit is imposed on A0, and this is why a larger A0 was observed at convergence in series C than in series D, the latter of which had the smaller kHA' With application of kHA’ all of the IAFéJ)I are scaled 1“7 uniformly regardless of the difference between 0N and aND' A parallel effect follows in IAFéJ)| and A0. Al- though the kHA may somewhat incorrectly exaggerate A0 from cycle to cycle, the starting “N are random with respect to 9D in the first place, so that this does not result in a trend toward suppression due to inferior phasing. On the other hand, any improvement of 0§%) has been diminished. It appears that this may be the origin of the ambiguities reported in the results of series C, D, and E. An identical effect will be produced when k(J) becomes excessively large. The value of k(J) was shown to be very sensitive to the manner in which the modifica- tion function suppressed the difference map features nearest zero, due to the overwhelming preponderance of the latter. Thus, those |AFéJ)| which were heavily in- fluenced by features of a level that escaped suppression became unrepresentatively scaled by k(J), and this led to a significant peak-height enhancement, independent of phase refinement. The influence which is exercised on k(J) by kHA’ when applied, or by setting £=j-l, is less straight forward. Frequently, the closer the external scaling is to 1.00, the more persistent or extreme are values of k<3> that are apparently excessive. It seems that this behavior results from reciprocating cycles of suppression and restoration of the low lying features — restoration 1“8 by the large cumulative scale on IAFéj)| — each capable of undoing the other. It should be noted that k(j) values which appear excessively large are not automatically damaging provided they result in response to the overall modification rather than primarily to its action on only one kind of peak. Such a response that is originating from back- ground peaks in the difference map probably represents a worst case. No significant phase change was observed in ANS-0- CHT, pH 3.6, series J, after one cycle of the enhance- ment-on1y modification. This was true regardless of the fact that the extent of modification exercised on peaks above the significance level was comparable to that in previous series, and that the procedure generated a k(j) = 0.89. The value of RA’ 0.6%, indicated a negligible average variability in the magnitudes of lAFél)| with respect to |AFéO)|. It appears that the results of the modification were partitioned only into IAFél)|. This is probably due to the mildness of the modification near zero, and the relative paucity of grid points near X z 0.5. It means that a relatively mild modification which is all positive or all negative may have an overall effect similar to scaling the difference map. It also indicates that there are not enough features above the significance level in the ANS—a-CHT, pH 3.6 difference map to produce 1“9 an effective perturbation of the native protein phases under a modification procedure which uses a function similar to that given in Figure 16. The difference map produced as a result of the enhancement-only modification was nearly identical to that of cycle 0. In contrast to series J, the modification used in several other series was found to produce significant changes between 0N and aND' One such series is represented by cycle 5 series H, and a comparison of the differences bEtWEGU 0N and 0D is presented in Appendix B for this cycle and cycle 1 series J. Two possible changes in approach have been indicated for DDM from this study: 1) Devise a new function which more severely modifies the significant features of the difference map (above m3o(Ap)) and modifies the lowest lying features to a much lesser extent or not at all, and 2) Refine derivatives with more significant'scatter- ing matter'in the difference map than has ANS-a-CHT, pH 3.6. It might be advantageous to employ a modification which suppresses part of the map in order to avoid the scaler effect noted in series J. For this purpose, Hoppe and Gassmann's Taylor series-like function, Equation (18), may be found to fit the conditions of approach (1) above, with the threshold for 00 suppression, T (109), set between 0 and %0(A0). In such a function, with T > 0, 150 suppression is still much milder than that shown in Figure 16. The linear function suggested by Hoppe, Gassmann and Zechmeister (110) would probably create an over-modification in the lowest lying features of the dif- ference map if set in such a way to adequately modify the significant features. A double linear function such as that shown in Figure 18, may be of value for work with difference maps that are richer in features than that of ANS-a-CHT, pH 3.6. The severity of this function can be altered by adjusting the nominal value of X- If the lower placed slope is re-oriented to cut the line described by the function A0O = A00, a mild suppression can be achieved, but this would also entail zeroing those values of Apo between the intersection of the lower slope with the po axis and zero. The refinement procedure is flexible enough to accommodate a very wide variety of modification functions. With an appropriate M, an 2=j~l scaling may still be of interest. One measure of the relative amount of Scattering matter'in a given difference map is the number of inde- pendent significant difference peaks. Where eight such peaks other than the ANS substitution were found in ANS— a-CHT, pH 3.6, there were 29 found in ANS-a-CHT, pH 6.6. 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APPENDICES APPENDIX A COMPUTATIONAL DETAILS OF DDM REFINEMENT AT MSU General Each refinement begins with scaling of the derivative data, and normalizing its average apparent isotropic temperature factor with the native data set of 1977 (2.8A resolution sub-set of 1.8A resolution refinement-exten— sion subset). Such a procedure was described in Chapter III,A. The data are then merged with the native structure amplitudes and phases by use of the program SORTMERG. The source listing of SORTMERG is located on CDC APLIB tape 1261, and contains a data card description. The native data are file FORMJ on CDC APLIB tape 73“5. It is best to merge the derivative data reduction file as this avoids complications involving the figure of merit, which is not to be included. In the step indicated by Equation (33), MAPTYP=“ is specified for calculation of the first difference map. An additional code, MAPTYP=7, was added for use in this step during subsequent cycles. Additional data parameters, BCOF and IDFR, have also been added. BCOF specifies the 0 parameters in "mini-map" units (50 mini-map units per 1.0eA-3); IDFR=0 specifies EDM; IDFR=1 specifies DDM as 160 161 in Figure 16; IDFR=2 specifies that 0 will be applied as the only modification in DDM; IDFR # 0, l, or 2 specifies a coordinate dependent zeroing of the map, for which the non-zeroed region is determined in the x direction as possessing a coordinate greater than or equal to IXLOW but smaller than or equal to IXHI. This last criterion is applied analogously in the y (IYLOW, IYHI) and z (IZLOW, IZHI) directions. When IDFRfiO, l, or 2, diagnostic state- ments are printed to help the user confirm the correct choice of coordinate limits. In any case, the maximum electron density is taken as the largest absolute magni- tude. Dummy values should be provided for parameters not used in a given calculation. The derivative data file input to the F calculation should be retained because it is required in the F-1, along with the modified Fourier map. The data parameter IDENTL has been added to the 7’1 program. The user always specifies IDENTL=1 for cycle 1. This causes F0 to be replaced withllFNDI - IFNII. In sub- sequent cycles, when an i=0 scaling (Equation (38)) is desired, the user inputs IDENTL=2. With IDENTL=2, F0 is not altered. When an £=j-l scaling is desired, IDENTL=3 is input and F0 is set to FC (AF§J'1)). This version of the F-1 program is called DIFSF3 and is located on CDC APLIB tape 2“75. Also on this tape is DIFOUR7, the F program. Subsequent to F'1 calculations, the data are processed 162 by the following programs. A modular approach was chosen to economically facilitate changes in the DDM procedure during its deve10pmental stages. Ultimately, greater efficiency would result from combining these various func- tions as options in the existing FFT calculations. This would also conveniently enable calculation of two or more cycles of refinement without user intervention. The programs are written on CDC APLIB tape 2“75. Proggams to Process Data Between Cycles 1. Name: “SCL Data Processing Function: Apply a scale constant (kHA) to FC, AC, and BC. Re-write scaled data file on TAPE2. Calculate Statistics: , (scaled), and over all reflections for which AN, BN, AC, and BC are not zero; <0N - 0c>, and <|0N - 0 >. -1 c I Input Data: a. F output file, as TAPEl. b. One data Card: 1. SCL, INDIC (F10.5, I5). The SCL is a scale constant. For INDIC=1, all the data are printed. Only the statistics are printed when INDIC#1. 2. Name: APT21“ Data Processing Function: For reflections where A0, B0, AN, and BN are not zero, and for which (FC/FO)>0.15, 163 calculate a§%) and update FC, AC, and BC by forming (J) the coefficients ('FNDIaND - IFNIGN)’ Re-write revised data file to TAPE“ for next cycle of refine- ment. Write Miller indices and new FC, AC, and BC to TAPE8 for input to the XRAY70 system Fourier pro- gram under FORMAT (315,3F10.2). Calculate Statistics: RA, RAS’ RB, l.c. (see equa- tions (38) to (“1)) and <|oN - a§%)> . APT21“ is programmed to calculate RAS based on the scale factor written in cards 67 and 72. Input Data: F'l output file, or “SCL output file as TAPEl. Name: ALFDIF Data Processing Function: None. Calculate Statistics: See APT21“. In addition, 2)1/2 ALFDIF calculates a 0(A0) = $~(2(|F - IFN + FCI) NDI After Cruickshank (125,126). Input Data: See APT21“. Name: FFRS Data Processing Function: None Calculate Statistics: Relative and Absolute distribu- tions of F0 and FC. Programmed to list F0 and PC for which (FC/FO) > “.5. -1 Input Data: F , “SCL, or APT21“ output files. 16“ 5. Name: PRMAPS Data Processing Function: Calculate product of the Fourier maps, element by element, and output in F"1 format. Map grids must be the same. Product elements are divided by 10 and preserve the sign of elements of map read as TAPEl. Product map is written to output, and in binary to TAPE3. Input Data: a. Two 7‘1 output files (TAPE3 or TAPE“) as TAPEl and TAPE2. b. Two data cards 1. ITITLE (20A“) 2. NX, NY, NZ, MCT, NLINES, NCOL (615). The grid dimensions are given by NX, NY, and NZ. A back— ground suppression for the absolute value of positive and negative product map features is given in map units by MCT. The maximum number of lines and columns desired in printing are given by NLINES and NCOL respectively. APPENDIX B DETAILS OF CALCULATION OF PHASE CHANGE BETWEEN NATIVE PROTEIN (ON) AND DERIVATIVE (0D) Calculations of the parameter Aa' = (“N - aD> for cycle 1 series J, and cycle 5 series H, gave values of -0.6“° and l.l°, respectively. These data sets were chosen in order to exemplify the two extremes of negligible and substantial 8ND refinement. The values were expected to be near zero in both cases due to the random relationship between 0N and 0D. For the same two refinements, calcula- tions of a" = yielded 103° and 118°, respec- tively. The phase angles are processed in the computer programs as values ranging from 0° to 180° and 0° to -180°, according to crystallographic convention.* This is why a random change in phase yields A0" = 90°. The values of A0" which are reported above do not imply that 0N and 0D are correlated. If IFNDI is smaller than IFNI, the negative sign in AFgo) egg), by 180° with respect to 0N. If the modification is is stored by shifting the phases, not too severe, the shifted phases that go into the dif— ference map calculation are returned by the F"1 very nearly 180° away from 0N. Inspection of the individual * This convention arises because of Friedel's Law, one consequence of which is that 0(hkl) = -0(ERE). 165 166 (a — 0D) values in cycle 1 series J, revealed that the N great majority were within one degree of 0° or 180°. In calculations of 00' and Ad", if individual pairs of 0N & 0D are of Opposite sign, one of them must be cor- rected by 360° in order to yield accurate results. The phase differences so calculated will range from 0° to 180° and 0° to -180°, and can have an average magnitude > 90° while A0' = 0, and without implying that 0N and 0D are correlated. The effect of a phase change of 180° is the same as that of 0° in calculation of egg) for refine- ment. In a derivative such as ANS-a—CHT, pH 3.6, which has few structural changes, many of the IdN - 0D] values near 180° arise from negative differences (IFNDI - IFNI) which involve structure amplitudes that. are equal within the error. For ANS—d-CHT, pH 6.6, the number of significant negative (IFNDI - IFNI) was greater, and so Ad" was larger. The relative variation of A0" from 90° between derivatives may serve as an indirect measure of the amount of 'scatter- ing matter' in their difference maps.