Ligand Binding Energy and Enzyme Efficiency from Reductions in Protein Dynamics

Tetrameric rabbit muscle glyceraldehyde 3-phosphate dehydrogenase (GAPDH; EC 1.2.1.12) binds successively four molecules of its cofactor (NAD + ) with affinities of ca 10 11 M −1 , 10 9 M −1 , 10 7 M −1 , and 10 5 M −1 . The reduction in the dynamics of the protein is greatest upon binding the first NAD + molecule. Smaller reductions then occur upon binding the second and third NAD + molecules, and the fourth NAD + molecule binds without dynamic change. Reduction of the GAPDH dynamics, with consequent improvements in its internal bonding, can account for the increase in NAD + binding affinity from 10 5 M −1 to 10 11 M −1 . Evidence is provided that comparable fractions of the binding energy of other ligands, and of the catalytic efficiency of enzymes, may be derived in the same way. Keywords enzyme catalysis cooperativity non-covalent interactions binding energy Abbreviations used GAPDH glyceraldehyde 3-phosphate dehydrogenase ESI-MS electrospray ionization mass spectrometry H/D exchange hydrogen/deuterium exchange Introduction It has long been considered that enzymes commonly modify their structures when they bind to their substrates and to transition state analogs. 1 In a classic overview of enzyme catalysis as it existed in the 1970s, Jencks constructed a thermodynamic cycle containing the free enzyme in its thermodynamically most stable state (E) and its active form (E′) found in the presence of substrate S ( Figure 1 ). 2 According to this cycle ( Figure 1 ), it is argued that in the overall free energy change in passing from E to the complex E'S, there is a cost in forcing a change in the structure of the enzyme from E to E′ (both as it exists in its isolated state E′, and when part of the complex E'S). However, although there must be a cost in free energy in passing from E to E′, it cannot be concluded that there must be a cost in free energy to make E′ as it exists within the complex E'S. The complex E'S is a new thermodynamic entity, and it cannot be considered that a species with a free energy that can be defined as that of E′ exists within E'S. We demonstrate the above point by noting that the extension of the system E to E'S can be compared with the extension of a truncated protein structure (P) to the complete structure (P′p). In both cases, organized systems (E and P) are extended by addition of a further entity (S and p). With regard to the conversion P→P′p, the complete protein structure P′p is typically more compact and less dynamic, and is a more stable organized system than is the partial structure P (assembled from less than 100% of the parts). 3–6 For example, the form of an α-helix, 4 or a β-hairpin, 5 that is dynamic and loose when made as an isolated entity, becomes less dynamic and more stable as an organized structure when it is a part of the complete protein. The helix or β-hairpin structures that exist in isolation are contracted spontaneously with a benefit in free energy to the whole upon the addition of the other units in a positively cooperative manner. Therefore, the extension of these systems, through the making of additional non-covalent bonds to them, stabilizes the whole in cases where the extension leads to reduced dynamics. Although the benefits in free energy may be accompanied by conformational change, they require only subtle contractions of protein structures. We show here that when the co-factor NAD + is bound to an enzyme (rabbit muscle glyceraldehyde 3-phosphate dehydrogenase (GAPDH), EC 1.2.1.12), the reduced dynamic behavior of (and consequent improved bonding within) the co-factor/receptor system is correlated excellently with a stepwise increase in the co-factor binding energy over the range 10 5 M −1 to 10 11 M −1 . Thus, the reduced dynamics that can occur within protein structures upon binding cognate small molecules can provide a large source of favorable binding energy. Additionally, we cite evidence that comparable fractions of the catalytic efficiency of enzymes may be derived in the same way. Results and Discussion Rabbit muscle GAPDH functions as a tetramer that successively binds four molecules of its cofactor (NAD + ), respectively with affinities of ca 10 11 M −1 , 10 9 M −1 , 10 7 M −1 , and 10 5 M −1 . 7–10 We have determined, by electrospray mass spectrometry (ESI-MS), 11,12 the reduction in dynamic behavior of the enzyme as the four molecules of NAD + are bound successively ( Figure 2 ). The maximum degree of exchange of the backbone amide protons of the protein is near to 160 ( Figure 2 ), out of a total of 320. Therefore, under the conditions of our experiment, complete unfolding of the protein is a very improbable event, and the hydrogen/deuterium (H/D) exchange that occurs must do so very preponderantly via either local unfolding or through channel “breathing” of the folded state (“opening events”). The large binding constants for the first three NAD + s to bind, and the excess of NAD + at a relatively high concentration for the binding of the fourth NAD + , ensure that when NAD + is present, it is the ligand-bound protein that undergoes exchange. Under these circumstances, the exchange data can be interpreted in the terms that are summarized in Figure 3 . Reduced H/D exchange occurs upon positively cooperative binding of a molecule to the protein because the opening event to generate the species L.P pu then becomes less probable, although species with smaller opened segments ( L . P pu ′ ) can still be generated more probably than can L.P pu . Due to the positively cooperative binding of the ligand, the structure of the protein is tighter in L.P f than it is in P f . Since partial unfolding of the protein reduces the extent of the positive cooperativity of ligand binding, the free energy cost of this partial unfolding is greater in the presence of the ligand (Δ G 2 >Δ G 1 ). The reduction in the dynamics of the protein is greatest upon binding the first NAD + molecule. The binding of the second NAD + reduces the dynamics of the enzyme to a smaller degree, and of the third NAD + to an even smaller degree. The fourth NAD + to bind does not change the dynamic behavior of the enzyme to a measurable extent ( Figure 2 ). The improvements in local packing of the protein that are implicit in the reduced dynamic behavior of the GAPDH derive support from decreases in volume (on the order of 1%) that occur when N -acetyl- d -glucosamine (GlcNAc) oligomers bind to lysozyme. 13 Importantly, the largest decreases in volume are observed for the GlcNAc oligomer that exhibits the highest affinity. Such small decreases in volume require that the reductions in non-covalent bond lengths (with their consequent strengthening) will be very small, but they are clearly detectable by H/D exchange. Therefore, the binding of NAD + to the GAPDH tetramer is, using the term “positively cooperative” in the sense as it is used in the folding of proteins, and crystallization, highly positively cooperative in the first step, and decreasingly positively cooperative in the second and third steps. There is no distinguishable change in the dynamic behavior of the protein upon binding the fourth ligand ( K ∼10 5 M −1 ), since the number of backbone amide protons of the protein that undergo exchange is the same within experimental error ( Figure 2 ; data reproducible to within ±1 NH). Therefore, the fourth binding event is not cooperative. This finding indicates also that the ligand does not provide detectable protection of any backbone amide protons of the protein that could, in principle, be involved directly in binding the NAD + . This is consistent with an X-ray crystal study on human GAPDH that identifies only one such hydrogen bond (Ile13 amide NH of the enzyme, which corresponds to Ile11 in rabbit muscle GAPDH, to NAD + ). 14 In summary, the binding of the first NAD + restricts the dynamics of the enzyme to the greatest degree, and there are further reductions in the dynamics as the second and third molecules bind. The simplest reference point is the binding of the last NAD + , because this binding event is not cooperative. Given this reference point ( K ∼10 5 M −1 ), we propose that the increased affinities found for the first (increase of ca 10 11 /10 5 =10 6 ), second (increase of ca 10 9 /10 5 =10 4 ), and third (increase of ca 10 7 /10 5 =10 2 ) NAD + molecules arise because these NADs + reduce the dynamics of the enzyme. This proposal is supported strongly by the established increased affinities of peptide ligands to their receptors where ligand binding reduces the exchange rate of backbone amide protons of their receptors, with tightening of the receptor structure. 15–18 Since motion opposes bonding, the reductions in motion are accompanied by improvement in bonding within the enzyme. Additionally, since the last binding of NAD + ( K ∼10 5 M −1 ) occurs without cooperativity, and the first binding ( K ∼10 11 M −1 ) occurs with the greatest positive cooperativity, then greater than 50% of the total binding energy of the first NAD + to bind can be provided by ligand-induced “tightening” of the protein structure. Promotion of ligand binding is correlated excellently with the reduction in dynamics of (improved bonding within) the protein ( Figure 4 ). Comparison of a recent crystal structure (2.4 Å resolution) of the GAPDH tetramer in which only the two high-affinity sites of the GAPDH tetramer are occupied by NAD + , 19 with that of the free enzyme is informative. The largest specified difference is an inter-residue distance reduction of 0.4 Å upon binding NAD + . However, for the vast majority of residues, the NAD + -induced movements are negligible. 19 Thus, the positive cooperativity exercised in the binding of the more strongly binding NAD + molecules does not demand conformational change. Although structural reorganization is not required to utilize the favorable free energy of binding discussed here, such structural reorganization may occur in the general case (as evidenced by X-ray crystallographic structures in other systems). Other manifestations of NAD + binding carry the hallmarks of binding that is positively cooperative, in the sense of reduced dynamics with associated subtle contractions of the protein structure. 20 First, NAD + binding causes decreased susceptibility of the enzyme to proteolysis. 21 Controlled digestion of rabbit muscle GADPH with chymotrypsin, trypsin, subtilisin or pronase results in a substantial loss of enzymatic activity of the apo-enzyme (>70% to 95%), but not of the holo-enzyme. For all four proteases, binding of the first NAD + produces the greatest portion of resistance to proteolytic inactivation (more than 50%), and further NAD + bindings produce increasingly smaller effects, with negligible change in protection against proteolysis on the binding of the last NAD + . This behavior accords perfectly with the NH/N 2 H exchange data, and with our conclusions regarding the relation of reduced protein dynamics to increase the binding energy of the cofactor, through delocalized stabilization of the enzyme system when it is extended by binding of the cofactor. Second, the enthalpy (Δ H ) of thermal unfolding of the fully NAD + -bound enzyme is larger than for apo-GADPH. 22 For the enzyme from Bacillus stearothermophilus , Δ H =6780 kJ mol −1 (holo-enzyme) and 4415 kJ mol −1 (apo-enzyme); for the enzyme from rabbit muscle, Δ H =4800 kJ mol −1 (holo-enzyme) and 4300 kJ mol −1 (apo-enzyme). It is of course true that in the melting of the holo-enzyme, greater exothermicity might be anticipated than for the apo-enzyme, since the non-covalent interactions that the NAD + makes to the enzyme will be broken. However, the observed increases are approximately 2300 kJ mol −1 in the former case, and 500 kJ mol −1 in the latter case. These values are remarkably large if two points are borne in mind. First, that the making of the ligand/protein hydrogen bonds can be, at most, only very weakly exothermic overall, since the breaking of corresponding hydrogen bonds to water occurs. Second, the addition of NAD + increases the mass of the entity by only about 2%, whereas the exothermicity of the thermal unfolding is increased by about 53% and 11%, respectively. Additionally, upon full NAD + binding, an increase in thermal stability of the organized system is observed, and melting temperatures increase from 78.3 °C to 91.9 °C for GADPH from B. stearothermophilus , and from 58.4 °C to 64.5 °C for GADPH from rabbit muscle. 22 Thus, when the enzyme is converted to the enzyme/cofactor system, the new system is less dynamic and more stable, and probably better bonded internally. Third, an increase in the cooperativity of unfolding is observed for the holo-enzyme (relative to the apo-enzyme), since progressive addition of NAD + to rabbit muscle apo-GAPDH increases the temperature ( T ) of the thermal unfolding transition and sharpens it, in terms of its temperature-width ( W T ) at half-height. 22 The T / W T values for the apo-enzyme are 58.4/6.1 °C, and upon progressive addition of NAD + they become: one NAD + molecule, 59.0/5.1 °C; two NAD + molecules, 59.5/4.9 °C; three NAD + molecules, 60.8/3.7 °C, and four NAD + molecules, 64.5/2.5 °C. Thus, the reported changes in the T / W T values for thermal unfolding indicate increasing cooperativity, although these changes are not linearly related to the changes in the dynamics of the system as reported here. In particular, it is not clear why the reported T / W T ratio increases upon addition of the fourth NAD + , whereas no reduction of protein dynamics is observed for this step in the present work. We note that the changes in the properties of the protein/ligand systems are, relative to those of the isolated proteins, precisely analogous to those observed in the binding, in a positively cooperative manner, of increasing numbers of layers of N 2 atoms on a cooled surface. 23 In both systems, the addition of an extra entity (be it ligand, or additional layer of N 2 atoms) serves to produce a more stable whole. Packing forces within protein crystals reduce the dynamics of the protein relative to the dynamics in aqueous solution. Therefore, positively cooperative effects associated with the restriction of protein dynamics by ligands are almost certainly larger in solution than in the crystalline state. Even allowing for this fact, X-ray crystallographic studies on GAPDH show that the tetramer of the fully bound holo-enzyme has a smaller total solvent-accessible surface area (43,298 Å 2 ) than does the apo-enzyme (44,992 Å 2 ). 24 The tetramer shrinks upon NAD + binding. Additionally, the solvent-accessible surface area of the monomer that is buried within the sub-unit interfaces of the tetramer is greater for the fully bound holo-GAPDH (8.1%) than for apo-enzyme (7%). Thus, the sub-units have tightened into more intimate contact in the transition from apo-enzyme to holo-enzyme, in accord with the conclusion that positively cooperative binding of ligands leads to the formation of more stable liganded forms of oligomeric proteins through widespread improvements in packing. Thus, previous data support our current conclusion, that improving the bonding within the enzyme allows a large increase in the co-factor binding energy. The same reductions in receptor dynamics due to binding at each site where ligand binding is equally strong at those sites In previous work, we have provided evidence that the reduced dynamic behavior of tetrameric streptavidin (STV) upon binding biotin contributes to the remarkably large affinity ( K =10 13.4 M −1 ) of biotin for the tetramer. 20 Jones and Kurzban have provided convincing evidence that the binding affinity of biotin to each subunit in tetrameric streptavidin is essentially the same. 25 The hypothesis advanced here requires that the affinity at each site of an oligomeric receptor should be enhanced in proportion to the reduction in dynamics of the oligomer that accompanies each ligand binding ( Figure 4 ). Thus, the data reported by Jones and Kurzban require that, upon sequential addition of one, two, three, and four equivalents of biotin to tetrameric STV, the receptor system will improve its packing to the same extent at each step. To test this requirement, the dynamic behavior of STV in the presence of zero, one, two, three, and four molar equivalents of biotin (relative to one molar equivalent of tetrameric STV) was monitored by H/D exchange. For all ligand-binding experiments, the average deuterium incorporation of the STV monomer (residues 13–139, from Streptomyces avidinii ) was determined by ESI-MS. The data show that the addition of one molar equivalent of biotin to tetrameric STV increases the packing efficiency of the protein such that five fewer backbone amide protons per subunit undergo H/D exchange ( Figure 5 ). Addition of two and three molar equivalents of biotin to tetrameric STV gave protection of a ca ten and 15 amide protons/subunit, respectively. Finally, fully bound STV resulted in an overall protection of approximately 20 amide protons ( Figure 5 ). Of these, only one is involved in a direct interaction with biotin, and none is involved in inter-subunit interactions. 20 The average incremental decrease of five exchangeable backbone amide protons per liganded sub-unit indicates that each biotin molecule stabilizes and reduces the dynamics of the tetrameric protein to essentially the same extent. Thus, the requirements of our hypothesis for cases where ligand binding is equally enhanced in each site are met. Relevance to enzyme catalysis It appeared possible that our findings are relevant to the efficiency of enzyme catalysis, the origins of which still appear to be at least partly obscure. Current models of catalysis require that positive cooperativity in the binding of the substrate transition state should be greater than in the binding of the substrate or the product. Our model therefore requires reduced dynamics of the enzyme that are larger in the transition state for reaction than in the binding of substrate or product. Schramm and colleagues have reported experiments on two enzymes that establish precisely such changes upon binding transition state analogues. 26,27 In one case, the positively cooperative binding of the transition state analogue reduces the dynamics within the enzyme (trimer) system to such a degree that 81 backbone protons are protected from H/D exchange. The reduction in dynamic behavior occurs almost throughout the trimer, 26 and binding energy of the transition state analogue can therefore be derived in a highly delocalized manner. The smaller positive cooperativity exercised in binding of a substrate analogue and product leads to protection of only 30 backbone amide protons. In the case of a second enzyme, when the transition-state analogue is bound, the dynamic behavior of the enzyme tetramer is reduced to such a degree that 34 backbone amide protons per subunit are protected from H/D exchange, 27 but only 21 from the binding of an equilibrium mixture of substrate and product. Once more, such amide protons are not simply localized near the binding site, but are distributed widely in the protein structure. In both these enzymes, the bonding efficiency within the enzyme is increased when either substrate or product is bound, and thus binding energy for these entities is provided (although this does not have to be true in the general case). However, such changes occur to a much greater extent in the transition state, and therefore greater binding energy is provided for the transition-state analogue. Evolution appears to have selected for the greatest improvements in non-covalent bonding within these enzymes in the transition state, since this allows for an increase in catalytic efficiency. Since small improvements in the strengths of non-covalent bonds can give a larger benefit in binding energy if the number of such bonds is large, a possible reason why enzymes are relatively large structures (in comparison to model catalysts) is suggested. We note also that there is a benefit to enzyme catalysis (favorable entropy term) that is derived by ordering the catalytic groups on the enzyme template. However, the observed reductions in dynamics of the enzymes in the transition states for reaction require that this favorable entropy term will be offset by an adverse entropy term associated with the reduced dynamic behavior. Additionally, since it is motion that opposes bonding, the reduced dynamics of the enzyme in the transition state will be accompanied by a benefit in the enthalpy of catalysis. Strikingly, where investigated, catalysis is largely derived through improvements in bonding (favorable enthalpy term), rather than by favorable entropy terms. 28–30 We conclude that enzymes may, in the general case, gain large rate accelerations through widespread improvements in non-covalent interactions within them, coupled to reductions in their dynamics, in the transition state. It appears that in the cases of positively cooperative ligand binding cited here, evolutionary selection has exploited the omission, from the protein, of the final element of structure (the ligand) that produces the most positively cooperative entity (the ligand–protein complex). The promotion of binding and catalysis through the reduction in dynamics of proteins possibly gives a new paradigm for understanding the remarkable efficiency of these processes. 18 In closing, we emphasize that converse effects are observed. That is, ligand binding to a protein that is negatively cooperative (i.e. opposite in its structural effect to that observed in protein folding and in crystallization) is evidenced to (i) increase protein dynamics and (ii) decrease the thermal stability of the resulting entity. Consider the effect of adding, to lipid bilayers constituted from phosphatidylserine, increasing quantities of cholesterol. Successive additions of cholesterol (an “impurity” that disturbs cooperative interactions that exist in the pure bilayer) progressively reduce the temperature, enthalpy, and cooperativity of the gel-to-liquid-crystalline phase transition of the lipid bilayers. 31 This negatively cooperative behavior is analogous to the lower melting temperature ( T m ) observed when a receptor is converted to a ligand/receptor system with a concomitant increase in dynamics. 32 The increased dynamic behavior of hemoglobin upon binding O 2 is also in accord with this model. 20,33 This binding is positively cooperative in the Monod–Wyman–Changeux (MWC) sense (increased binding affinity at each successive binding step of O 2 to the hemoglobin tetramer). 34 However, the increased dynamic behavior of hemoglobin upon binding O 2 shows that the binding is negatively cooperative in the sense that the cooperativity is opposite to that observed in protein folding and crystallization. 18 The observation of positive cooperativity in the MWC sense is a consequence of reduced negative cooperativity (i.e. an effect opposite to that observed in protein folding and crystallization) for each successive O 2 binding event. Materials and Methods Experiments with GAPDH GAPDH from rabbit muscle and NAD + were purchased from Sigma. The apo-enzyme of GAPDH was prepared using ion-exchange chromatography on CM-Sepharose (Sigma) as described. 35,36 The protein was desalted using a Sephadex G-25 (Sigma) column (0.8 cm×0.8 cm×35 cm) and concentrated. The concentration of the apo-enzyme was determined by measuring the absorbance at 280 nm using a Cary spectrometer: [E t ] (mM tetramer)= A 280 /116×dilution ( A 280 1.16×10 5 for the apo-enzyme 37 ). The required GAPDH to NAD + ratios were obtained by mixing the appropriate amounts of NAD + with apo-enzyme, in 100 mM ammonium acetate buffer (pH 8.5). The mixing was followed by 2 h of equilibration at 0 °C. The NAD + to GAPDH tetramer ratios were 1[E t ]×, 2[E t ]×, 3×[E t ] and 4×[E t ]+2.6(mM) for generation of the 1NAD + , 2NAD + , 3NAD + bound GAPDH tetramer states, and the holo-enzyme, respectively. The concentration of the enzyme in the four solutions was 0.5 mM. A relatively high concentration, and excess, of NAD + was used to generate the fully bound holo-enzyme in view of the weaker binding constant (ca 10 5 M −1 ) for the fourth NAD + molecule. H/D exchange was initiated by dilution of 20 μl of GAPDH/NAD + solutions into 180 μl of buffered 2 H 2 O (100 mM ammonium acetate, pD 8.5). The solutions were maintained at 4 °C and allowed to exchange for the required times. At appropriate time-points, 10 μl aliquots were removed and adjusted to pH 2.7 by the addition of 40 μl of ice-cold quench solution (water/methanol/formic acid; 89:9:2 (by vol.)), and then cooled to 0 °C. Quenched samples were frozen immediately in liquid nitrogen, and stored at −80 °C. Mass spectrometry All GAPDH mass spectra were acquired using a Q-STAR mass spectrometer (Applied Biosystems/MDS Sciex). A Harvard model syringe pump was used to infuse a solution of water/methanol/formic acid (90/9/1, by vol.) to the ESI probe at a rate of 20 μl min −1 . Deuterated samples were thawed and introduced into the solution via a Rheodyne 7125 injection valve. The solvents and the Rheodyne injector were kept at 0 °C by using ice-baths to minimize back exchange. Experiments with streptavidin H/D exchange was initiated by dilution of 10 μl of 3 mM STV (from Streptomyces avidinii ; Pierce) in 100 mM ammonium acetate buffer (pH 8.0) into 90 μl of 2 H 2 O, to give a final concentration of 300 μM. Samples containing biotin/STV at different molar ratios were mixed and incubated at room temperature for at least 1 h before dilution in 2 H 2 O. Solutions were maintained at room temperature and allowed to exchange for the desired lengths of time. At appropriate time-points, 10 μl of the STV solution was quenched in 40 μl of acidic quench solution (water/methanol/formic acid 90:9:1 (by vol.)) and analyzed by ESI-MS as described. 20 Acknowledgements This work was supported by the EPSRC, BBSRC, and Churchill College, Cambridge, UK. References 1 D.E. Koshland Jr Application of a theory of enzyme specificity to protein synthesis Proc. Natl Acad. Sci. USA 44 1958 98 104 2 W.P. Jencks Binding energy, specificity, and enzymic catalysis: the circe effect Advan. Enzymol. Relat. Areas Mol. Biol. 43 1975 219 410 3 F.J. Blanco G. Rivas L. Serrano A short linear peptide that folds into a native stable beta-hairpin in aqueous-solution Nature Struct. Biol. 1 1994 584 590 4 A. Jasanoff A.R. Fersht Quantitative-determination of helical propensities from trifluoroethanol titration curves Biochemistry 33 1994 2129 2135 5 J.P.L. Cox P.A. Evans L.C. Packman D.H. Williams D.N. Woolfson Dissecting the structure of a partially folded protein: circular dichroism and nuclear magnetic resonance studies of peptides from ubiquitin J. Mol. Biol. 234 1993 483 492 6 P.E. Wright H.J. Dyson R.A. Lerner Conformation of peptide fragments of proteins in aqueous solution: implications for initiation of protein folding Biochemistry 27 1988 7167 7175 7 A. Conway D.E. Koshland Jr Negative cooperativity in enzyme action. The binding of diphosphopyridine nucleotide to glyceraldehyde 3-phosphate dehydrogenase Biochemistry 7 1968 4011 4022 8 K. Kirschner E. Gallego I. Schuster D. Goodall Co-operative binding of nicotinamide-adenine dinucleotide to yeast glyceraldehyde-3-phosphate dehydrogenase J. Mol. Biol. 58 1971 29 50 9 A.G.W. Leslie A.J. Wonacott Coenzyme binding in crystals of glyceraldehyde-3-phosphate dehydrogenase J. Mol. Biol. 165 1983 375 391 10 J. Schlessinger A. Levitzki Molecular basis of negative co-operativity in rabbit muscle glyceraldehyde-3-phosphate dehydrogenase J. Mol. Biol. 82 1974 547 561 11 A.N. Hoofnagle K.A. Resing N.G. Ahn Protein analysis by hydrogen exchange mass spectrometry Annu. Rev. Biophys. Biomol. Struct. 32 2003 1 25 12 V. Katta B.T. Chait Hydrogen-deuterium exchange electrospray-ionization mass-spectrometry—a method for probing protein conformational change in solution J. Am. Chem. Soc. 115 1993 6317 6321 13 K. Gekko K. Yamagami Compressibility and volume changes of lysozyme due to inhibitor binding Chem. Letters 1998 839 840 14 W.D. Mercer S.I. Winn H.C. Watson Twinning in crystals of human skeletal muscle d -glyceraldehyde-3-phosphate dehydrogenase J. Mol. Biol. 104 1976 277 283 15 J.P. Mackay U. Gerhard D.A. Beauregard R.A. Maplestone D.H. Williams Dissection of the contributions towards dimerization of glycopeptide antibiotics J. Am. Chem. Soc. 116 1994 4581 4590 16 J.P. Mackay U. Gerhard D.A. Beauregard M.S. Westwell M.S. Searle D.H. Williams Glycopeptide activity and the possible role of dimerization. A model for biological signaling J. Am. Chem. Soc. 116 1994 4581 4590 17 D.H. Williams A.J. Maguire W. Tsuzuki M.S. Westwell An analysis of the origins of a cooperative binding energy of dimerization Science 280 1998 711 714 18 D.H. Williams E. Stephens D.P. O'Brien M. Zhou Understanding noncovalent interactions: ligand binding energy and catalytic efficiency from ligand-induced reductions in motions within receptors and enzymes Angew. Chem. Int. Ed. 43 2004 6596 6616 19 S.W. Cowan-Jacob M. Kaufmann A.N. Anselmo W. Stark M.G. Grütter Structure of rabbit-muscle glyceraldehyde-3-phosphate dehydrogenase Acta Crystallog. sect. D 59 2003 2218 2227 20 D.H. Williams E. Stephens M. Zhou Ligand binding energy and catalytic efficiency from improved packing within receptors and enzymes J. Mol. Biol. 329 2003 389 399 21 A. Fenselau Structure–function studies on glyceraldehyde-3-phosphate dehydrogenase. III. Dependency of proteolysis on NAD + concentration Biochem. Biophys. Res. Commun. 40 1970 481 488 22 P. Levashov V. Orlov S. Boschi-Muller F. Talfournier R. Asryants I. Bulatnikov Thermal unfolding of phosphorylating d -glyceraldehyde-3-phosphate dehydrogenase studied by differential scanning calorimetry Biochim. Biophys. Acta 1433 1999 294 306 23 J.A. Morrison L.E. Drain J.S. Dugdale Phase transition in multimolecular layers of adsorbed nitrogen Can. J. Chem. 30 1952 890 903 24 T. Skarzynski A.J. Wonacott Coenzyme-induced conformational changes in glyceraldehyde-3-phosphate dehydrogenase from Bacillus stearothermophilus J. Mol. Biol. 203 1988 1097 1118 25 M.L. Jones G.P. Kurzban Non-cooperativity of biotin binding to tetrameric strepatividin Biochemistry 34 1995 11750 11756 26 F. Wang R.W. Miles G.E.N. Kicska V.L. Schramm R.H. Angeletti Immucillin-H binding to purine nucleoside phosphorylase reduces dynamic solvent exchange Protein Sci. 9 2000 1660 1668 27 F. Wang W. Shi E. Nieves R.H. Angeletti V.L. Schramm C. Grubmeyer A transition-state analogue reduces protein dynamics in hypoxanthine-guanine phosphoribosyltransferase Biochemistry 40 2001 8043 8054 28 A. Radzicka R. Wolfenden A proficient enzyme Science 267 1995 90 93 29 M.J. Snider S. Gaunitz C. Ridgway S.A. Short R. Wolfenden Temperature effects on the catalytic efficiency, rate enhancement, and transition state affinity of cytidine deaminase, and the thermodynamic consequences for catalysis of removing a substrate “anchor” Biochemistry 39 2000 9746 9753 30 R. Wolfenden M. Snider C. Ridgway B. Miller The temperature dependence of enzyme rate enhancements J. Am. Chem. Soc. 121 1999 7419 7420 31 T.P.W. McMullen R.N.A.H. Lewis R.N. McElahney Differential scanning calorimetric and Fourier transform infrared spectroscopic studies of the effects of cholesterol on the thermotropic phase behavior and organization of a homologous series of linear saturated phosphatidylserine bilayer membranes Biophys. J. 79 2000 2056 2065 32 M.S. Celej G.G. Montich G.D. Fidelio Protein stability induced by ligand binding correlates with changes in protein flexibility Protein Sci. 12 2003 1496 1506 33 J.J. Englander C. Del Mar W. Li S.W. Englander J.S. Kim D.D. Stranz Protein structure changes studied by hydrogen-deuterium exchange, functional labeling, and mass spectrometry Proc. Natl Acad. Sci. USA 100 2003 7062 7075 34 J. Monod J. Wyman J.-P. Changeaux On the nature of allosteric transitions: a plausible model J. Mol. Biol. 12 1965 88 118 35 W. Bloch R.A. MacQuarrie S.A. Bernhard The nucleotide and acyl group content of native rabbit muscle glyceraldehyde-3-phosphate dehydrogenase J. Biol. Chem. 246 1971 780 790 36 B.D. Peczon H.O. Spivey Catalytic sites in rabbit muscle glyceraldehyde-3-phosphate dehydrogenase. Their number and their kinetic and spectral properties Biochemistry 11 1972 2209 2217 37 J.B. Fox Jr W.B. Dandliker The coenzyme content of rabbit muscle d -glyceraldehyde-3-phosphate dehydrogenase J. Biol. Chem. 221 1956 1005 1017