How Enzymes Work: Analysis by Modern Rate Theory and Computer Simulations

Garcia‐Viloca, Mireia; Gao, Jiali; Karplus, Martin; Truhlar, Donald G.

doi:10.1126/science.1088172

Cited by 1,074 publications

(1,135 citation statements)

References 99 publications

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“…We derive below a PMF description of a reaction system within the QM/MM framework, although the theory is not dependent on the QM/MM method. The partition function of a QM/MM system is (5) in which E is the total energy of the system as a function of both r QM and r MM ; M and M′ represent the number of degree of freedom of the QM and MM subsystems, respectively. The free energy of the system is then (6) If we focus on the conformation of a selected subset of the system, e.g., the QM subsystem, we have a free energy expression of r QM which is also regarded as a potential of mean force of r QM , that is, (7) The integration of the potential of mean force in the r QM space recovers the complete free energy of the system: (8) With the MM contributions averaged out, the conformational space of the whole reaction system has been reduced to the potential of mean force surface of the QM subsystem.…”

Section: Potential Of Mean Force Of the Qm Coordinatesmentioning

confidence: 99%

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QM/MM Minimum Free-Energy Path: Methodology and Application to Triosephosphate Isomerase

Yang

2007

J. Chem. Theory Comput.

139

198

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Structural and energetic changes are two important characteristic properties of a chemical reaction process. In the condensed phase, studying these two properties is very challenging because of the great computational cost associated with the quantum mechanical calculations and phase space sampling. Although the combined quantum mechanics/molecular mechanics (QM/MM) approach significantly reduces the amount of the quantum mechanical calculations and facilitates the simulation of solution phase and enzyme catalyzed reactions, the required quantum mechanical calculations remain quite expensive and extensive sampling can be achieved routinely only with semiempirical quantum mechanical methods. QM/MM simulations with ab initio QM methods, therefore, are often restricted to narrow regions of the potential energy surface such as the reactant, product and transition state, or the minimum energy path. Such ab initio QM/MM calculations have previously been performed with the QM/MM-Free Energy (QM/MM-FE) method of Zhang et al. 1 to generate the free energy profile along the reaction coordinate using free energy perturbation calculations at fixed structures of the QM subsystems. Results obtained with the QM/MM-FE method depend on the determination of the minimum energy reaction path, which is based on local conformations of the protein/solvent environment and can be difficult to obtain in practice. To overcome the difficulties associated with the QM/MM-FE method and to further enhance the sampling of the MM environment conformations, we develop here a new method to determine the QM/MM minimum free energy path (QM/MM-MFEP) for chemical reaction processes in solution and in enzymes. Within the QM/MM framework, we express the free energy of the system as a function of the QM conformation, thus leading to a simplified potential of mean force (PMF) description for the thermodynamics of the system. The free energy difference between two QM conformations is evaluated by the QM/MM free energy perturbation method. The free energy gradients with respect to the QM degrees of freedom are calculated from molecular dynamics simulations at given QM conformations. With the free energy and free energy gradients in hand, we further implement chain-of-conformation optimization algorithms in the search for the reaction path on the free energy surface without specifying a reaction coordinate. This method thus efficiently provides a unique minimum free energy path for solution and enzyme reactions, with structural and energetic properties being determined simultaneously. To further incorporate the dynamic contributions of the QM subsystem into the simulations, we develop the reaction path potential of Lu, et al. 2 for the minimum free energy path. The combination of the methods developed here presents a comprehensive and accurate treatment for the simulation of reaction processes in solution and in enzymes with ab initio QM/MM methods. The method has been demonstrated on the first step of the reaction of the enzyme triosephosphate isome...

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Section: Potential Of Mean Force Of the Qm Coordinatesmentioning

confidence: 99%

“…[3][4][5] Complementary to experimental studies, simulation methods can provide information that is often not easily accessed by conventional experimental approaches. For example, simulations can determine the transition state structure of a reaction process, which is difficult to obtain from experimental methods.…”

Section: Introductionmentioning

confidence: 99%

QM/MM Minimum Free-Energy Path: Methodology and Application to Triosephosphate Isomerase

Yang

2007

J. Chem. Theory Comput.

139

198

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“…Many efforts have been devoted during the last years to improve the understanding of the mechanism of action of natural enzymes [1][2][3][4][5] and apply this knowledge to the development of new biocatalysts. 6,7 Scientists began to use evolutionary strategies (Directed Evolution) 8 to tailor the properties of individual molecules.…”

Section: Introductionmentioning

confidence: 99%

Enzyme Promiscuity in Enolase Superfamily. Theoretical Study of o-Succinylbenzoate Synthase Using QM/MM Methods

et al. 2015

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The promiscuous activity of the enzyme o-Succinylbenzoate Synthase (OSBS) from the actinobacteria Amycolatopsis is investigated by means of QM/MM methods, using both Density Functional Theory and Semiempirical Hamiltonians. This enzyme catalyzes not only the dehydration of 2-succinyl-6R-hydroxy-2,4-cyclohexadiene-1R-carboxylate but also catalyzes racemization of different acylaminoacids, being N-succinyl-Rphenylglycine the best substrate. We investigated the molecular mechanisms for both reactions exploring the Potential Energy Surface. Then, Molecular Dynamics simulations were performed to obtain the free energy profiles and the averaged interaction energies of enzymatic residues with the reacting system. Our results confirm the plausibility of the reaction mechanisms proposed in the literature, with a good agreement between theoretical and experimentally-derived activation free energies. Our simulations unravel the role played by the different residues in each of the two possible reactions. The presence of flexible loops in the active site and the selection of structural modifications in the substrate seem to be key elements to promote the promiscuity of this enzyme.

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“…[3][4][5][6] However, the detailed relationship between conformational fluctuation and chemical kinetics is still not well understood at the theoretical level, partly because of the broad range of time scales of enzyme conformational dynamics, ranging from a few tens of femtoseconds to 100 s. The fast conformational dynamics on the time scale of femtoseconds to microseconds can be probed by molecule dynamics simulations. 5,7 However, most enzymatic reactions occur at much † Part of the "James T. (Casey) Hynes Festschrift". * Authors to whom correspondence should be addressed.…”

Section: Introductionmentioning

confidence: 99%

Two-Dimensional Reaction Free Energy Surfaces of Catalytic Reaction: Effects of Protein Conformational Dynamics on Enzyme Catalysis

2007

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We introduce a two-dimensional (2D) multisurface reaction free energy description of the catalytic cycle that explicitly connects the recently observed multi-time-scale conformational dynamics as well as dispersed enzymatic kinetics to the classical Michaelis-Menten equation. A slow conformational motion on a collective enzyme coordinate Q facilitates the catalytic reaction along the intrinsic reaction coordinate X, providing a dynamic realization of Pauling's well-known idea of transition-state stabilization. The catalytic cycle is modeled as transitions between multiple displaced harmonic wells in the XQ space representing different states of the cycle, which is constructed according to the free energy driving force of the cycle. Subsequent to substrate association with the enzyme, the enzyme-substrate complex under strain exhibits a nonequilibrium relaxation toward a new conformation that lowers the activation energy of the reaction, as first proposed by Haldane. The chemical reaction in X is thus enslaved to the down hill slow motion on the Q surface. One consequence of the present theory is that, in spite of the existence of dispersive kinetics, the Michaelis-Menten expression of the catalysis rate remains valid under certain conditions, as observed in recent single-molecule experiments. This dynamic theory builds the relationship between the protein conformational dynamics and the enzymatic reaction kinetics and offers a unified description of enzyme fluctuation-assisted catalysis.

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How Enzymes Work: Analysis by Modern Rate Theory and Computer Simulations

Cited by 1,074 publications

References 99 publications

QM/MM Minimum Free-Energy Path: Methodology and Application to Triosephosphate Isomerase

QM/MM Minimum Free-Energy Path: Methodology and Application to Triosephosphate Isomerase

Enzyme Promiscuity in Enolase Superfamily. Theoretical Study of o-Succinylbenzoate Synthase Using QM/MM Methods

Two-Dimensional Reaction Free Energy Surfaces of Catalytic Reaction: Effects of Protein Conformational Dynamics on Enzyme Catalysis

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