Constrained reaction coordinate dynamics for the simulation of rare events

Carter, E.A.; Ciccotti, Giovanni; Hynes, James T.; Kapral, Raymond

doi:10.1016/s0009-2614(89)87314-2

Cited by 898 publications

(919 citation statements)

References 23 publications

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“…The freezing of the QM subsystem makes the current method resemble some other methods such as the "blue moon sampling" which was developed with the constrained dynamics sampling approach. [82][83][84] It is clear that all these methods share the same origin as from thermodynamic integration. 76, 85 Interestingly however, the use of Cartesian coordinates of the QM subsystem as the reaction coordinate of the QM/MM-MFEP method again leads to the difference in the ways of carrying out simulation and analyzing the results.…”

Section: Connection To Previous Studies Of Sampling the Free Energy Smentioning

confidence: 99%

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

Yang

2007

J. Chem. Theory Comput.

140

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: Connection To Previous Studies Of Sampling the Free Energy Smentioning

confidence: 99%

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

Yang

2007

J. Chem. Theory Comput.

140

198

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“…Namely, in the limit of very large M , s is approximately fixed and is dynamically averaged over the electronic and ionic degrees of freedom. Hence, s efficaciously evolves with the force h i that is the derivative of the free energy with respect to s as in standard umbrella sampling and constrained dynamics [16,17]. V t; s is constructed to fill the free energy wells and drive the system towards the lowest saddle points.…”

mentioning

confidence: 99%

Efficient Exploration of Reactive Potential Energy Surfaces Using Car-Parrinello Molecular Dynamics

Iannuzzi¹,

Laio²,

Parrinello³

2003

Phys. Rev. Lett.

770

942

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The possibility of observing chemical reactions in ab initio molecular dynamics runs is severely hindered by the short simulation time accessible. We propose a new method for accelerating the reaction process, based on the ideas of the extended Lagrangian and coarse-grained non-Markovian metadynamics. We demonstrate that by this method it is possible to simulate reactions involving complex atomic rearrangements and very large energy barriers in runs of a few picoseconds.

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“…This was first noted by Carter, Ciccotti, Hynes, and Kapral in [CCHK89] (see also [SC98]) where the blue-moon sampling technique was introduced. The idea is to use ergodicity and evaluate the conditional average in (43) for F (q) by time-averaging over a trajectory whose dynamics is constrained such that q(x) = q and has as its equilibrium density Z −1 e −βV (x) restricted in this surface.…”

Section: Blue-moon Sampling Techniquementioning

confidence: 83%

“…F can then be estimated by integration of F -a step referred to as thermodynamic integration [FS01]. In [CCHK89], it was proposed to compute the expectation in (43) via Hamiltonian dynamics simulations subject to proper constraint. Another possibility is to usė…”

Section: Blue-moon Sampling Techniquementioning

confidence: 99%

Metastability, conformation dynamics, and transition pathways in complex systems

Weinan

Vanden‐Eijnden

2004

Multiscale Modelling and Simulation

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Summary. We present a systematic introduction to the basic concepts and techniques for determining transition pathways and transition rates in systems with multiple metastable states. After discussing the classical transition state theory and its limitations, we derive a new set of equations for the optimal dividing surfaces. We then discuss transition path sampling, which is the most general technique currently available for determining transition regions and rates. This is followed by a discussion on minimal energy path for systems with smooth energy landscapes. For systems with rough energy landscapes, our presentation is centered around the notion of reaction coordinates. We discuss the two related notions of free energies associated with a reaction coordinate, and show that at least in the high friction limit, there does exist an optimal reaction coordinate that gives asymptotically the correct prediction for the transition rates. Variational principles associated with the optimal reaction coordinates are exploited under the assumption that the transition paths are restricted to tubes, and this provides a theoretical justification for the finite temperature string method. Blue moon sampling techniques, metadynamics and a new form of accelerated dynamics are also discussed.

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Constrained reaction coordinate dynamics for the simulation of rare events

Cited by 898 publications

References 23 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

Efficient Exploration of Reactive Potential Energy Surfaces Using Car-Parrinello Molecular Dynamics

Metastability, conformation dynamics, and transition pathways in complex systems

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