Change in Heat Capacity for Enzyme Catalysis Determines

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The Change in Heat Capacity for Enzyme Catalysis Determines the Temperature Dependence of Enzyme Catalysed Rates Joanne K Hobbs, Wanting Jiao, Ashley D Easter, Emily J. Parker, Louis A. Schipper, and Vickery L. Arcus ACS Chem. Biol., Just Accepted Manuscript • DOI: 10.1021/cb4005029 • Publication Date (Web): 09 Sep 2013 Downloaded from http://pubs.acs.org on September 10, 2013

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ACS Chemical Biology

The Change in Heat Capacity for Enzyme Catalysis Determines the Temperature Dependence of Enzyme Catalysed Rates Joanne K. Hobbs†, Wanting Jiao‡, Ashley D. Easter†, Emily J. Parker‡, Louis A. Schipper§ and Vickery L. Arcus*,†

†

Department of Biological Sciences, Faculty of Science and Engineering, University of

Waikato, Hamilton 3240, New Zealand ‡

Biomolecular Interaction Centre and Department of Chemistry, University of Canterbury,

Christchurch, New Zealand §

Department of Earth and Ocean Sciences, Faculty of Science and Engineering, University of

Waikato, Hamilton 3240, New Zealand

*Corresponding author Prof Vickery L. Arcus Mailing address: Department of Biological Sciences, Faculty of Science and Engineering, University of Waikato, Private Bag 3105, Hamilton 3240, New Zealand Email: [email protected] Telephone: +64 7 838 4679

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ABSTRACT: The increase in enzymatic rates with temperature up to an optimum temperature (Topt) is widely attributed to classical Arrhenius behaviour, with the decrease in enzymatic rates above Topt ascribed to protein denaturation and/or aggregation. This account persists despite many investigators noting that denaturation is insufficient to explain the decline in enzymatic rates above Topt. Here we show that it is the change in heat capacity associated with enzyme catalysis (∆C‡p), and its effect on the temperature dependence of ∆G‡, that determines the temperature dependence of enzyme activity. Through mutagenesis, we demonstrate that the Topt of an enzyme is correlated with ∆C‡p, and that changes to ∆C‡p are sufficient to change Topt without affecting the catalytic rate. Furthermore, using X-ray crystallography and molecular dynamics simulations we reveal the molecular details underpinning these changes in ∆C‡p. The influence of ∆C‡p on enzymatic rates has implications for the temperature dependence of biological rates from enzymes to ecosystems.

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The relationship between temperature and the rate of a chemical reaction is most simply described by the 19th century Arrhenius equation: k = Ae-EA/RT, where k is the rate constant, A is a pre-exponential factor, EA is the activation energy for the reaction, R is the universal gas constant and T is the temperature. Early in the 20th century Eyring and Polanyi developed Transition State Theory, expanding the Arrhenius equation and expressing k in terms of Boltzmann and Planck’s constants (kB, h), the transmission coefficient (κ, for simplicity assumed to be 1 here), and the difference in Gibbs free energy between the ground state and the transition state (∆G‡, equations 1 and 2). In turn, ∆C‡p (the difference in heat capacity between the ground state and the transition state at constant pressure) quantifies the temperature dependence of ∆G‡ and thus, describes the temperature dependence of the reaction rate according to equation (3):

k BT −∆G k= e RT h

‡

(1)

 k BT  [∆G ‡ ] ln(k) = ln −  h  RT

(2)

‡ ‡ ‡ ‡  k BT  [∆H T0 + ∆C p (T − T0 )] [∆ST0 + ∆C p ln(T /T0 )] ln(k) = ln + −  h  RT R

(3)

where T0 is a reference temperature, and ∆H‡T0 and ∆S‡T0 are the difference in enthalpy and entropy between the ground state and the transition state, respectively, at T0.1 If ∆G‡ is simply linearly dependent on temperature according to ∆G‡ = ∆H‡-T∆S‡, then ∆C‡p = 0 and equation (3) collapses to an Arrhenius function. However, if ∆H‡ and ∆S‡ are temperature dependent then ∆C‡p ≠ 0 and the relationship between rate and temperature will show curvature in an ln(k) versus T plot (Figure 1a). Negative curvature is well documented for the temperature dependence of enzymatic rates, giving rise to temperature optima (Topt) for enzymes.2,3 Previously, this negative 3



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curvature has been attributed to Arrhenius-like behaviour for temperatures below Topt, combined with enzyme denaturation and/or aggregation for temperatures >Topt. A similar model incorporating protein denaturation is also used to explain the temperature dependence of microorganism growth rates.4,5 Explanations based on denaturation are inadequate as several studies have noted that denaturation alone is insufficient to explain the decrease in enzyme rates above Topt.2,6,7 Furthermore, an enigmatic characteristic of psychrophilic enzymes is their loss of activity at temperatures well below their denaturation temperature.3 Recently, an alternative model has been proposed which postulates (ad hoc) an inactive, folded intermediate, in rapid equilibrium with the active enzyme to account for the negative curvature of the temperature dependence of enzyme rates.2 Curvature is a natural consequence of equation (3) (Figure 1a) and here we show that the temperature dependence of enzymatic rates is attributable to negative values of ∆C‡p for enzyme catalysis. ∆C‡p is a critical parameter in statistical thermodynamics that has not previously been considered for enzyme catalysis. We have measured ∆C‡p for a number of enzymes, and we find that equation (3) can fully account for the observed downward curvature in enzymatic rates above Topt independent of denaturation. Furthermore, we present a physical explanation for the magnitude and sign of ∆C‡p, and show that Topt and ∆C‡p are correlated, as theory predicts. We initially investigated the temperature-rate relationship for enzymes using the wellstudied enzyme barnase (ribonuclease; E.C. 3.1.27.3) and its stabilized double mutant A43C/S80C, whose Michaelis-Menten kinetics and unfolding rates with temperature have been well documented1,8,9 (Figure 1b). The curvature seen in an ln(kcat) versus T plot for wildtype barnase could be rationalized as a combination of Arrhenius-like behaviour at temperatures below 312 K (Topt) and denaturation above 312 K (the temperature midpoint of thermal unfolding, Tm, for barnase is 326 K)8. However, this cannot account for the curvature 4


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of A43C/S80C which contains a stabilizing disulphide bond and has an increased Tm (331 K).8 Although this mutant has been stabilized, the curvature in ln(kcat) versus temperature remains and there is no increase in Topt (Figure 1b). The failure of the textbook model (Arrhenius + denaturation) to explain the Topt of A43C/S80C can be simply resolved by considering a negative value for ∆C‡p for catalysis. Fitting equation (3) to the temperaturerate data for wildtype barnase and A43C/S80C gives similar, large and negative ∆C‡p values of -4.6±0.8 and -5.3±0.4 kJ mol-1 K-1, respectively (Figure 1b). Although ∆C‡p has not previously been considered with respect to enzyme catalysis, these values are commensurate with those previously determined for an enzyme binding to a transition state analogue at equilibrium.10 We note that these large, negative values for ∆C‡p pertain to the reaction system as a whole which includes both the reactants and the enzyme. One would not expect to see such large values for simple organic reactions alone. We used a second enzyme, MalL (α-glucosidase; E.C. 3.2.1.10), to test the generality of our description and probe the relationship between ∆C‡p and Topt. By screening a library of 268 single amino acid substitution mutants of MalL, we identified four point mutations that conferred increases in Topt: V200A, V200S, V200T and G202P. The temperature-rate data for these enzymes were fitted to equation (3) to determine ∆C‡p (Figure 2a). In each case, the enzymatic rates at each temperature tested were determined using the first 10 s of rate data to ensure that they were not confounded by denaturation. The mutants V200T and V200A showed modest increases in Topt compared with wildtype MalL (∆Topt = 2.3 and 5.7 K, respectively). These mutations also resulted in modest increases in ∆C‡p (∆∆C‡p = 0.7 and 1.2 kJ mol-1 K-1, respectively). In the case of V200A, significant changes were observed in both the enzyme’s affinity for the substrate (KM) and its turnover rate (kcat; Figure 2b). The mutants V200S and G202P exhibited greater increases in Topt when compared with wildtype 5



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MalL (∆Topt = 9.3 and 7.5 K, respectively) which were accompanied by large increases in ∆C‡p (∆∆C‡p = 5.7 and 5.9 kJ mol-1 K-1, respectively). These changes had no effect on the Michaelis-Menten kinetics for V200S however the G202P mutation resulted in significant impairment of kcat (Figure 2b). The MalL mutants suggest a correlation between ∆C‡p and Topt, and this is supported by theory. Provided ∆C‡p ≠ 0, Topt is defined by equation (3) when δk/δT = 0 and hence:

− ∆C = ‡ p

∆H T‡0 + RTopt

(4)

Topt − T0

Thus, changing ∆C‡p is sufficient to change Topt without compromising MichaelisMenten parameters (i.e. no change in ∆H‡ and hence no impact on ∆G‡). This is clearly the case for wildtype MalL, V200T and V200S, whose kcat values are nearly identical at 313 K but where the temperature dependence of the catalyzed rate differs (Figure 2a). We combined data for MalL and barnase mutants with data obtained for variants of a third enzyme, LeuB,11 and found that the correlation predicted by equation (4) holds for all three enzymes over a wide temperature range (Figure 3). This emphasises that changes in Topt (without affecting enzyme kinetics) are possible via changes to ∆C‡p. This finding has important implications for biotechnology, where manipulation of an enzyme’s Topt without compromising catalytic kinetics is an ongoing challenge. If ∆C‡p ≠ 0, equation (3) provides further constraints on the thermodynamics of enzyme catalysis by fixing ∆H‡ at the Topt for an enzyme. At Topt, ∆H‡ = -RTopt provided ∆C‡p ≠ 0. This implies that the enthalpic contributions to enzyme catalysis are very similar for all enzymes (provided enzyme kinetics are measured at the Topt for the enzyme). Fixing ∆H‡ at Topt also implies a central role of ∆S‡ in determining enzyme rates as this is the only parameter that can vary at Topt. This is illustrated here for MalL where an increase in rate is 6


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the result of an increase in ∆S‡ near the active site upon the mutation V200A, although this is accompanied by a weaker KM for catalysis and thus a comparatively poorer kcat/KM value overall (Figure 2b). The V200S and G202P mutants exhibit large increases in ∆C‡p and Topt compared with wildtype MalL. What underlies these increases in ∆C‡p? The greatest contribution to the heat capacity of a folded protein is the number of available vibrational and rotational modes associated with covalent bonds (i.e. protein dynamics). These modes contribute an estimated 85% of the Cp term for globular proteins.12,13 The hydration term is thought to contribute the remaining ~15% to the Cp for globular proteins. In contrast, the hydration term contributes up to 40% of the Cp for unfolded proteins and this change in hydration is the dominant factor affecting ∆Cp for protein folding.1 If large numbers of vibrational and rotational modes are available to a protein, this will give rise to a high value for Cp whereas a reduction in these modes will lead to a lower value of Cp for the same protein. To effect a change in Cp for an enzyme-catalyzed reaction, either there needs to be a change to the number of conformational modes available to the “reactants” (i.e. free enzyme + enzyme-substrate complex) or a change to these modes at the “transition state” (i.e. enzyme-transition state complex). We determined high resolution crystal structures for wildtype MalL, V200S and G202P (Supplementary Table 1), and combined these with molecular dynamics (MD) simulations to compare the conformational dynamics of these enzymes. The structures of the three proteins are very similar, with RMS deviations between wildtype MalL and V200S of 0.18 Å, and between wildtype MalL and G202P of 0.20 Å. In contrast, the dynamics simulations of the apo-enzymes show marked differences and the number of conformational states available to the V200S mutant is substantially reduced when compared with wildtype MalL (Figure 4a and b). This, combined with the lack of change in kcat (Figure 2b), indicates that the basis for the change in ∆C‡p for V200S is the rigidification of the ground state 7



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(E+S⇌ES) without an impact on the transition state, and thus no impact on the rate (Figure 4b). The crystal structure of V200S also shows that the mutation introduces two new hydrogen bonds that form part of a network of short- and long-range interactions (Supplementary Figure 1). This network of interactions in the apo-enzyme provides an explanation for the reduced number of available conformational states. In contrast, the G202P mutation has not affected the conformational dynamics for the apo-enzyme when compared with the wildtype (Figure 4b and c), but has compromised the transition state as evidenced by its impaired kcat (Figure 2b). In this case, the increase in ∆C‡p has been achieved by increasing the flexibility of the transition state, but this has come at the cost of kcat (i.e. the increased flexibility of the transition state has caused an increase in ∆G‡ for the reaction and therefore a reduction in the enzyme-catalyzed rate). These MD simulations clearly illustrate the two mechanisms through which the ∆C‡p of an enzyme-catalyzed reaction, and therefore the Topt, can change. The Topt–∆C‡p correlation provides an explanation for the rigidity of thermophilic enzymes.14 To increase Topt without compromising rate requires increases in the ∆C‡p for catalysis, and thus increases in enzyme rigidity (irrespective of the requirements for stability at high temperatures). It also provides an explanation for the anomalous temperature dependence of reaction rates for psychrophilic enzymes.3 The Topt–∆C‡p relationship implies that increased flexibility in the ground state is required to achieve lower ∆C‡p values, and hence lower Topt values. Further, equation (3) implies that increases in ∆S‡ are required to enhance rates at low temperatures given that ∆H‡ is fixed and linearly dependent on Topt. Intriguingly, the relationship between ∆C‡p and the temperature dependence of catalysed rates may also suggest a role for ∆C‡p in allostery and oligomerization, and this warrants further investigation. 8


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Our results point towards changes in protein dynamics as the source of the changes to ∆C‡p for enzyme catalysis, however the role of water and desolvation of the active site should also be considered. The significant difference in ∆C‡p for V200S compared with V200T, and the lack of difference in their kcat values at 313 K, suggests that the dominant contributor to ∆C‡p is conformational dynamics and the contribution of water is small. However, we do not discount the role of water and this is the subject of ongoing experiments in our laboratory. Understanding precisely how enzymes work has been the subject of renewed debate recently, in particular the role of protein dynamics in catalysis.15,16 Arguments have been presented based on statistical thermodynamics,17 MD,15 transition state barrier crossing18 and Marcus theory and preorganization,16 amongst others. The size and magnitude of ∆C‡p for enzyme catalysis is consistent with each of these descriptions. In terms of statistical thermodynamics, a large negative ∆C‡p is the result of the very tight binding of the transition state, and the reduction in the number of conformational states available to the system at the transition state compared with the ground state. In terms of transition state barrier crossing, a large negative ∆C‡p is the result of the instantaneous reduction in the vibrational and rotational modes of the enzyme at the transition state barrier. We anticipate that measuring ∆C‡p for a wide range of enzymes and their mutants, combined with sophisticated simulations, will provide experimental access to the nature of the transition state for enzyme catalysis. Enzymes are a fundamental component of biological systems and the drivers of cellular metabolism. As such, we speculate that curvature in the temperature dependence of enzymatic rates will make a significant contribution to the temperature dependence of metabolic processes inside cells. In general, enzyme Topt values are well correlated with the optimum growth temperature of the parent organism.11 Thus, we would expect to see an observed ∆C‡p signature (∆C‡p,obs) in the temperature dependence of microorganism growth 9



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rates even before the effects of the complex regulatory responses associated with temperature are considered. Indeed, negative curvature in microorganism growth rates has long been known.5 As with enzymes, the curvature in microorganism growth rates is usually attributed to denaturation above Topt.4,5 We note here that equation (3) models the temperature dependence of growth rates for diverse microorganisms with R2 values consistently >0.9 (Supplementary Table 2 and Supplementary Figure 2), including the curvature below Topt (a particular failure of the growth rate models that invoke denaturation19). The derived ∆C‡p,obs values are also consistent with those measured for enzyme catalysis (Figure 3), and much greater (and therefore more influential) than the ∆C‡p associated with denaturation and incorporated into the Ratkowsky growth rate model.4 In conclusion, we have demonstrated that the ∆C‡p associated with enzyme catalysis explains the temperature dependence of enzymatic rates and there is a clear molecular mechanism underpinning enzymatic ∆C‡p. The influence of ∆C‡p on allostery, oligomerization and biological rates at the whole cell level requires further investigation. Nevertheless it is likely that enzymatic ∆C‡p values contribute to the temperature dependence of biological rates at larger scales. METHODS Mutagenesis, protein expression and protein purification. Mutagenesis was performed using the Quikchange® Site-Directed Mutagenesis kit and either the barnase expression construct pMT100220 or malL from Bacillus subtilis 168 in pPROEX HTb as template. Barnase and A43C/S80C were expressed and purified as described elsewhere.20 MalL and its mutants were expressed at 18 °C overnight and purified as previously described,21 with further purification by size-exclusion chromatography.

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Enzyme assays. The activities of barnase and MalL enzymes on a fluorogenic nucleotide substrate and p-nitrophenol-α-D-glucopyranoside, respectively, were determined as previously described.21,22 Temperature profiles were determined by measuring activity at 2-3 °C intervals using substrate at either 2 × KM (barnase) or 10 × KM (MalL). Barnase and A43C/S80C data were corrected for Vmax based on KM determinations at two temperatures. Fits to equation (3) were performed in GraphPad Prism 6.0 with the reference temperature set to Topt - 4. Crystallization and structure determination. Crystallization of MalL proteins was performed using the sitting drop method at 18 °C. Crystals of wildtype MalL were obtained in 100 mM Bis-Tris pH 6.5, 200 mM LiSO4, 20% (w/v) PEG 3350. V200S and G202P were crystallized in 100 mM Tris pH 7.5 containing 22% and 24% (w/v) PEG 4000, respectively. Data collection was performed on flash-cooled crystals at the Australian synchrotron. The crystallization condition plus 15% glycerol was used as cryoprotectant. All data were indexed and integrated with MOSFLM23 and scaled using Aimless.24 The wildtype structure was solved by molecular replacement using Phaser25 and the structure of MalL from B. cereus (1UOK) as the search model. This was followed by iterative cycles of manual model building with Coot,26 and further refinement using Refmac.27 The structures of V200S and G202P were determined using the same protocol but using the structure of wildtype MalL as the search model. MD simulations. MD simulations using the crystal structure of wildtype MalL were conducted with NAMD28 running on the BlueFern supercomputer at the University of Canterbury. Crystallographic water and ligands were deleted, and missing residues were built in with Coot26 in accordance with the electron density map so that the dynamic properties of the disordered loops could be examined. For V200S and G202P, starting structures were 11



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generated by in silico mutation of the wildtype structure. Starting structures were solvated with explicit TIP3 water molecules in a box in VMD, and ionized by adding Na+ and Cl- ions to balance the net charge. Ions were added with a minimum distance of 5 Å from the molecule and each other. MD simulations were conducted with the CHARMM22 all-hydrogen parameter file for proteins at 322.15 K and 1 atm. The cut-off distance for van der Waals interactions was set to 12 Å. In each simulation, the system was first minimized for 5000 steps followed by 270 ns of dynamics simulations conducted with 2 fs time steps. The trajectory was written out at 100 ps time intervals, and a total of 2700 frames were obtained from each simulation. Supporting Information Available: This material is available free of charge via the Internet at http://pubs.acs.org. ACCESSION CODES The refined crystal structures for wildtype MalL, V200S and G202P have been deposited in the Protein Data Bank under accession numbers 4M56, 4MAZ and 4MB1, respectively. REFERENCES (1) Oliveberg, M., and Fersht, A. R. (1996) Thermodynamics of transient conformations in the folding pathway of barnase: reorganization of the folding intermediate at low pH, Biochemistry 35, 2738-2749. (2) Daniel, R. M., and Danson, M. J. (2010) A new understanding of how temperature affects the catalytic activity of enzyme, Trends Biochem. Sci. 35, 584-591. (3) Feller, G., and Gerday, C. (2003) Psychrophilic enzymes: hot topics in cold adaptation, Nat. Rev. Microbiol. 1, 200-208. (4) Corkrey, R., Olley, J., Ratkowsky, D., McMeekin, T., and Ross, T. (2012) Universality of thermodynamic constants governing biological growth rates, PLoS One 7, e32003. 12


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(24) Evans, P. R. (2011) An introduction to data reduction: space-group determination, scaling and intensity statistics, Acta Crystallogr. D Biol. Crystallogr. 67, 282-292. (25) McCoy, A. J., Grosse-Kunstleve, R. W., Storoni, L. C., and Read, R. J. (2005) Likelihood-enhanced fast translation functions, Acta Crystallogr. D Biol. Crystallogr. 61, 458-464. (26) Emsley, P., and Cowtan, K. (2004) Coot: model-building tools for molecular graphics, Acta Crystallogr. D Biol. Crystallogr. 60, 2126-2132. (27) Murshudov, G. N., Vagin, A. A., and Dodson, E. J. (1997) Refinement of macromolecular structures by the maximum-likelihood method, Acta Crystallogr. D Biol. Crystallogr. 53, 240-255. (28) Phillips, J. C., Braun, R., Wang, W., Gumbart, J., Tajkhorshid, E., Villa, E., Chipot, C., Skeel, R. D., Kale, L., and Schulten, K. (2005) Scalable molecular dynamics with NAMD, J. Comput. Chem. 26, 1781-1802. (29) Bakk, A. (2002) Heat capacities of solid state proteins: implications for protein stability in solution, Physica A 313, 540-548. ACKNOWLEDGEMENTS We would like to thank N. Pace (Texas A&M University) for providing the plasmid pMT1002 and J. Steemson for X-ray data collection for wildtype MalL. We thank V. Schramm, J. Clarke, M. Steyn-Ross and A. Steyn-Ross for valuable discussions and critical reading of the manuscript. This work was supported by a research grant from the Marsden Fund of New Zealand. X-ray diffraction data were collected at the Australian synchrotron and we thank the NZ Synchrotron Group for funding.

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FIGURE LEGENDS Figure 1. Effect of ∆C‡p on the temperature dependence of reaction rates. (a) Schematic representation of the relationship between temperature and rate as modeled by equation (3) when different values of ∆C‡p are applied. (b) Fit of equation (3) to temperature-rate data for barnase (●) and A43C/S80C (●). Data shown are the initial rate of enzyme activity at different temperatures as a function of the enzyme concentration (kcat) and the mean of at least two replicates. Error bars, where visible, represent the SD. ∆C‡p values are in kJ mol-1 K-1 (± SE). Topt is defined as the highest temperature at which the maximum rate of activity was observed. Figure 2. Effect of mutation on the Topt, ∆C‡p and Michaelis-Menten parameters of the α-glucosidase MalL. (a) Fit of equation (3) to temperature-rate data for wildtype MalL and its mutants. Data shown are the initial rate of enzyme activity at different temperatures as a function of the enzyme concentration (kcat) and the mean of three replicates. Error bars, where visible, represent the SD. ∆C‡p values are in kJ mol-1 K-1 (± SE). Arrows indicate the Topt for each enzyme, which is defined as in Figure 1. (b) Michaelis-Menten parameters for MalL and its mutants determined at 318 K (± SE of fitting). Figure 3. Relationship between Topt and ∆C‡p for enzymes. The relationship between Topt and ∆C‡p for an enzyme as described by equation (4) is shown using data for variants of barnase, MalL and LeuB (Supplementary Table 3). When combining ∆C‡p values for different enzymes, it is necessary to change the units to J g-1 K-1 by dividing by the enzyme Mr (the number of vibrational modes contributing to ∆C‡p for proteins has been shown previously to be linearly correlated with Mr).29 The curve represents

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the fit of equation (4) to the data when T0 = 306 K. Error bars, where visible, represent the SE in ∆C‡p/Mr. Figure 4. Dynamics simulations for wildtype MalL, V200S and G202P. Depictions of the 3D structure of MalL summarizing its MD trajectories, colored blue through red for the most rigid to the most dynamic regions (from the trajectory) with accompanying increases in tube width. A graph of Cp versus reaction coordinate is shown below each structure. The locations of the V200S and G202P mutations are indicated by spheres. (a) MD trajectories for wildtype MalL. (b) Trajectories for V200S showing a significant reduction in the dynamics for the loops surrounding the active site. This has lowered the Cp for the ground state (E+S⇌ES). A slight increase in flexibility is also observed for the helix consisting of residues 259-275, which is not seen in the other two systems. (c) Trajectories for G202P showing no change in the dynamics of the free enzyme and implying that ∆C‡p has been reduced by increasing the Cp for the enzyme-transition state complex (E-TS) without affecting Cp for the ground state.

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Figure 1. Effect of ∆C‡p on the temperature dependence of reaction rates. a) Schematic representation of the relationship between temperature and rate as modeled by equation (3) when different values of ∆C‡p are applied. b) Fit of equation (3) to temperature rate data for barnase (black) and A43C/S80C (orange). Data shown are the initial rate of enzyme activity at different temperatures as a function of the enzyme concentration (kcat) and the mean of at least two replicates. Error bars, where visible, represent the SD. ∆C‡p values are in kJ mol-1 K-1 (± SE). Topt is defined as the highest temperature at which the maximum rate of activity was observed. 120x56mm (300 x 300 DPI)


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Figure 2. Effect of mutation on the Topt, ∆C‡p and Michaelis-Menten parameters of the α-glucosidase MalL. a) Fit of equation (3) to temperature-rate data for wildtype MalL and its mutants. Data shown are the initial rate of enzyme activity at different temperatures as a function of the enzyme concentration (kcat) and the mean of three replicates. Error bars, where visible, represent the SD. ∆C‡p values are in kJ mol-1 K-1 (± SE). Arrows indicate the Topt for each enzyme, which is defined as in Figure 1. b) Michaelis-Menten parameters for MalL and its mutants determined at 318 K (± SE of fitting). 65x91mm (300 x 300 DPI)



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Figure 3. Relationship between Topt and ∆C‡p for enzymes. The relationship between Topt and ∆C‡p for an enzyme as described by equation (4) is shown using data for variants of barnase, MalL and LeuB (Supplementary Table 3). When combining ∆C‡p values for different enzymes, it is necessary to change the units to J g-1 K-1 by dividing by the enzyme Mr (the number of vibrational modes contributing to ∆C‡p for proteins has been shown previously to be linearly correlated with Mr).29 The curve represents the fit of equation (4) to the data when T0 = 306 K. Error bars, where visible, represent the SE in ∆C‡p/Mr. 58x41mm (300 x 300 DPI)


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Figure 4. Dynamics simulations for wildtype MalL, V200S and G202P. Depictions of the 3D structure of MalL summarizing its MD trajectories, colored blue through red for the most rigid to the most dynamic regions (from the trajectory) with accompanying increases in tube width. A graph of Cp versus reaction coordinate is shown below each structure. The locations of the V200S and G202P mutations are indicated by spheres. (a) MD trajectories for wildtype MalL. (b) Trajectories for V200S showing a significant reduction in the dynamics for the loops surrounding the active site. This has lowered the Cp for the ground state (E+S⇌ES). A slight increase in flexibility is also observed for the helix consisting of residues 259-275, which is not seen in the other two systems. (c) Trajectories for G202P showing no change in the dynamics of the free enzyme and implying that ∆C‡p has been reduced by increasing the Cp for the enzyme-transition state complex (E-TS) without affecting Cp for the ground state.

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Graphical table of contents 39x42mm (300 x 300 DPI)


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Change in Heat Capacity for Enzyme Catalysis Determines

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