Efficiently finding the minimum free energy path from steepest descent path

Chen, Changjun; Huang, Yanzhao; Ji, Xiaofeng; Xiao, Yi

doi:10.1063/1.4799236

Cited by 26 publications

(30 citation statements)

References 74 publications

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“…It is clear that the free energy function in Eq 6 has two terms, and so does its derivative. However, as we tested before [26, 27], the second term is much smaller than the first term. So in this work, only the first term, i.e., the ensemble average of the Lagrange multiplier < λ >, is used in the calculation of the free energy gradient in Eqs 2 and 5.…”

Section: Theoretical Methodsmentioning

confidence: 89%

“…Due to the determinant of the metric tensor in Eq 6, analytic derivation of the second term is very complicated. For simple molecules like ALA dipeptide in the low dimensional collective variable space, it can be approximately calculated by the numerical central difference method [27]. However, for large molecules with lots of constraints, like 10-ALA in this work, even the numerical method becomes impractical.…”

Section: Resultsmentioning

confidence: 99%

“…This is because the Hamiltonian of the system is modified by the biasing potentials. To make a comparison between the optimizations, we assume the metric tensor M to be diagonal [27] So it forces the free energy gradient ∇ F to be parallel to the tangent of the path (not M ·∇ F ). Actually, such kind of formula has been used by Ulitsky and Elber in 1990 [3].…”

Section: Theoretical Methodsmentioning

confidence: 99%

“…Besides, as two useful variants of the string method, the climbing string method is proposed for searching the transition states [15] and the freezing string method is proposed for decreasing the gradients calculations [16, 17]. Recently, we apply the constrained dynamics method [18–25] in the calculation of the free energy gradients of the snapshots on the path [26] and show that the constrained dynamics method [18–25] is also a useful technique for the path optimize problem [27]. …”

Section: Introductionmentioning

confidence: 99%

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Fast exploration of an optimal path on the multidimensional free energy surface

Chen

2017

PLoS ONE

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In a reaction, determination of an optimal path with a high reaction rate (or a low free energy barrier) is important for the study of the reaction mechanism. This is a complicated problem that involves lots of degrees of freedom. For simple models, one can build an initial path in the collective variable space by the interpolation method first and then update the whole path constantly in the optimization. However, such interpolation method could be risky in the high dimensional space for large molecules. On the path, steric clashes between neighboring atoms could cause extremely high energy barriers and thus fail the optimization. Moreover, performing simulations for all the snapshots on the path is also time-consuming. In this paper, we build and optimize the path by a growing method on the free energy surface. The method grows a path from the reactant and extends its length in the collective variable space step by step. The growing direction is determined by both the free energy gradient at the end of the path and the direction vector pointing at the product. With fewer snapshots on the path, this strategy can let the path avoid the high energy states in the growing process and save the precious simulation time at each iteration step. Applications show that the presented method is efficient enough to produce optimal paths on either the two-dimensional or the twelve-dimensional free energy surfaces of different small molecules.

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Section: Theoretical Methodsmentioning

confidence: 89%

Section: Resultsmentioning

confidence: 99%

Section: Theoretical Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fast exploration of an optimal path on the multidimensional free energy surface

Chen

2017

PLoS ONE

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“…In terms of efficiency, the mentioned WZ method is slower than popular optimization methods like gradient-based steepest descent [7], Newton-Raphson [12], Fletcher-Powell [17], or Broyden-FletcherGoldfarb-Shanno (BFGS) [59]. However, it finds a global minimum of the potential energy with higher probability and has a lower tendency to converge on and get stuck in the nearest local minimum, which is not necessarily the global minimum of the energy function [66].…”

Section: Methodsmentioning

confidence: 99%

Scaling Ab Initio Predictions of 3D Protein Structures in Microsoft Azure Cloud

2015

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Computational methods for protein structure prediction allow us to determine a three-dimensional structure of a protein based on its pure amino acid sequence. These methods are a very important alternative to costly and slow experimental methods, like X-ray crystallography or Nuclear Magnetic Resonance. However, conventional calculations of protein structure are time-consuming and require ample computational resources, especially when carried out with the use of ab initio methods that rely on physical forces and interactions between atoms in a protein.Fortunately, at the present stage of the development of computer science, such huge computational resources are available from public cloud providers on a payas-you-go basis. We have designed and developed a scalable and extensible system, called Cloud4PSP, which enables predictions of 3D protein structures in the Microsoft Azure commercial cloud. The system makes use of the Warecki-Znamirowski method as a sample procedure for protein structure prediction, and this prediction method was used to test the scalability of the system. The results of the efficiency tests performed proved good acceleration of predictions when scaling the system vertically and horizontally. In the paper, we show the system architecture that allowed us to achieve such good results, the Cloud4PSP processing model, and the results of the scalability tests. At the end of the paper, we try to answer which of the scaling techniques, scaling out or scaling up, is better for solving such computational problems with the use of Cloud computing.

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Walking freely in the energy and temperature space by the modified replica exchange molecular dynamics method

Chen

Huang

2016

J. Comput. Chem.

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Replica Exchange Molecular Dynamics (REMD) method is a powerful sampling tool in molecular simulations. Recently, we made a modification to the standard REMD method. It places some inactive replicas at different temperatures as well as the active replicas. The method completely decouples the number of the active replicas and the number of the temperature levels. In this article, we make a further modification to our previous method. It uses the inactive replicas in a different way. The inactive replicas first sample in their own knowledge-based energy databases and then participate in the replica exchange operations in the REMD simulation. In fact, this method is a hybrid between the standard REMD method and the simulated tempering method. Using different active replicas, one can freely control the calculation quantity and the convergence speed of the simulation. To illustrate the performance of the method, we apply it to some small models. The distribution functions of the replicas in the energy space and temperature space show that the modified REMD method in this work can let the replicas walk freely in both of the two spaces. With the same number of the active replicas, the free energy surface in the simulation converges faster than the standard REMD. © 2016 Wiley Periodicals, Inc.

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Efficiently finding the minimum free energy path from steepest descent path

Cited by 26 publications

References 74 publications

Fast exploration of an optimal path on the multidimensional free energy surface

Fast exploration of an optimal path on the multidimensional free energy surface

Scaling Ab Initio Predictions of 3D Protein Structures in Microsoft Azure Cloud

Walking freely in the energy and temperature space by the modified replica exchange molecular dynamics method

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