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Enzyme Catalysis and Flexibility

Flexibility is one of the most intriguing characteristics of enzymes and is in many cases required in order to undergo conformational changes as a requisite for substrate binding and release. However, enzymes must be stable enough to retain their 3D structure, but flexible enough to permit the evolution of the protein among the different conformations relevant at each step for the catalytic process (1,2). A rather controversial question is the impact of this flexibility on the rate constants (3-13): $$k_r = \frac{k_BT}{h}e^{\frac{\Delta G^\ddagger}{RT}} =\frac{k_BT}{h}e^{\frac{\Delta H^\ddagger - T\Delta S^\ddagger}{RT}} $$ where $h$, $k_B$ and $R$ are the Planck, Boltzman and gas constants. By only considering $$\Delta G^\ddagger = \Delta H^\ddagger - T\Delta S^\ddagger $$ it is clear that increased ground state flexibility will lead to a decrease in $\Delta S^\ddagger$ as the system goes to the transition state (TS). A more negative $\Delta S^\ddagger$ will increase the activation free energy, and consequently counteract the catalysis along the reaction coordinate (reduce $k_r$). It is however a rather common understanding that proteins need a certain degree of reorganization to attain TS (13). The idea is that the coordinates describing the transformation from reactants to products is a collective coordinate that involves degrees of freedom for both the solute/substrate and the surrounding environment.

In an uncatalyzed reaction where only water surrounds the reacting fragments, it is clear that the surroundings need to reorganize their dipoles and electrostatic interactions in acoordance with the reaction coordinate for the reaction to proceed. Obviously, enzymes do not have randomly distributed dipoles as they are preorganized in some way from the folding process. It is becoming a more established undestanding that enzymes are preorganized in accordance with the reaction coordinate of the catalytic mechanism, and it was reported by Adamczyk et. al. that enzyme catalysis arises from electrostatic preorganization and not from conformational motions (11). If we do not take into account the actual binding and release of the substrate, this implies that, since the flexibility counteracts the activation free energies, a frozen enzyme reaction should result in lowering the activation free energies. A recent publication from Garcia-Meseguer et al. reported that the $S_N2$ enzyme catalyzed reaction would be significantly more difficult in a frozen protein environment in which the solvent coordinate remain unchanged from the reactant state (RS) to TS (14). This means that protein flexibility plays a role in catalysis and that the environment needs to be rearranged when going from RS to TS to reach maximum reduction in the activation free energy.

Enzyme flexibility is necessary for binding and release of substrates, but wetter or not this flexibility actually is required for optimal catalysis along the reaciton coordinate is still controversial. If enzymes are preorganized towards TS it is logical to think that flexibility has an unfavorable effect on $\Delta G^\ddagger$. Nevertheless, if some degree of reorganization is required for optimal reaction rates, it is clear from the above mentioned references, that this reorganization energy is significantly lower in enzymes compared to the uncatalyzed reaction in water. If enzymes are completely preorganized or if some degree of reorganization is required for optimal catalysis thus seem to be two fronting edges within this research field these days.

If you have any thoughts on this subject you are more than welcome to discuss it in the forum.

References

1. Hammes, G. G., Benkovic, S. J. & Hammes-Schiffer, S. Flexibility, diversity, and cooperativity: pillars of enzyme catalysis. Biochemistry 50, 10422–10430 (2011).

2. Henzler-Wildman, K. A. et al. A hierarchy of timescales in protein dynamics is linked to enzyme catalysis. Nature 450, 913–916 (2007).

3. Garcia-Viloca, M., Gao, J., Karplus, M. & Truhlar, D. G. How enzymes work: analysis by modern rate theory and computer simulations. Science 303, 186–195 (2004).

4. Gao, J. et al. Mechanisms and free energies of enzymatic reactions. Chem. Rev. 106, 3188–3209 (2006).

5. Olsson, M. H. M., Parson, W. W. & Warshel, A. Dynamical contributions to enzyme catalysis: critical tests of a popular hypothesis. Chem. Rev. 106, 1737–1756 (2006).

6. Antoniou, D., Basner, J., Nu´n˜ez, S. & Schwartz, S. D. Computational and theoretical methods to explore the relation between enzyme dynamics and catalysis. Chem. Rev. 106, 3170–3187 (2006).

7. Nashine, V. C., Hammes-Schiffer, S. & Benkovic, S. J. Coupled motions in enzyme catalysis. Curr. Opin. Chem. Biol. 14, 644–651 (2010).

8. Ramanathan, A. & Agarwal, P. K. Evolutionarily conserved linkage between enzyme fold, flexibility, and catalysis. PLoS Biol 9, e1001193 (2011).

9. Zhang, J. & Klinman, J. P. Enzymatic methyl transfer: role of an active site residue in generating active site compaction that correlates with catalytic efficiency. J. Am. Chem. Soc. 133, 17134–17137 (2011).

10. Bhabha, G. et al. A dynamic knockout reveals that conformational fluctuations influence the chemical step of enzyme catalysis. Science 332, 234–238 (2011).

11. Adamczyk, A. J., Cao, J., Kamerlin, S. C. L. & Warshel, A. Catalysis by dihydrofolate reductase and other enzymes arises from electrostatic preorganization, not conformational motions. Proc. Natl Acad. Sci. USA 108,14115–14120 (2011).

12. Glowacki, D. R., Harvey, J. N. & Mulholland, A. J. Taking Ockham’s razor to enzyme dynamics and catalysis. Nature Chem. 4, 169–176 (2012).

13. Kamerlin, S. C. L. & Warshel, A. At the dawn of the 21st century: is dynamics the missing link for understanding enzyme catalysis? Proteins 78, 1339–1375 (2010).

14. Garcia-Meseguer, R., Marti, S. , Ruiz-Pernıa, J. J., Moliner, V. & Tunon, V. Studying the role of protein dynamics in an $S_N2$ enzyme catalyzed reaction using free-energy surfaces and solvent coordinates. Nature Chem. 1-6 (may 26, 2013).

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