Bennett's acceptance ratio and histogram analysis methods enhanced by umbrella sampling along a reaction coordinate in configurational space

2012 ◽  
Vol 136 (16) ◽  
pp. 164103 ◽  
Author(s):  
Ilsoo Kim ◽  
Toby W. Allen
Keyword(s):  
Umbrella Sampling ◽  
Reaction Coordinate ◽  
Histogram Analysis ◽  
Acceptance Ratio ◽  
Configurational Space ◽  
Analysis Methods ◽  
Bennett’S Acceptance Ratio

scholarly journals BAR-based Optimum Adaptive Steered MD for Configurational Sampling

2018 ◽  
Author(s):  
Xiaohui Wang ◽  
Xingzhao Tu ◽  
Boming Deng ◽  
John Z. H. Zhang ◽  
Zhaoxi Sun
Keyword(s):  
Free Energy ◽  
Adaptive Sampling ◽  
Sampling Method ◽  
Time Derivative ◽  
Selection Criterion ◽  
Equal Time ◽  
Acceptance Ratio ◽  
Configurational Space ◽  
State Discrimination ◽  
Bennett’S Acceptance Ratio

<p>Previously we proposed the equilibrium and nonequilibrium adaptive alchemical free energy simulation methods Optimum Bennett’s Acceptance Ratio (OBAR) and Optimum Crooks’ Equation (OCE). They are based on the statistically optimal bidirectional reweighting estimator named Bennett’s Acceptance Ratio (BAR) or Crooks’ Equation (CE). They perform initial sampling in the staging alchemical transformation and then determine the importance rank of different states via the time-derivative of the variance (TDV). The method is proven to give speedups compared with the equal time rule. In the current work, we extended the time derivative of variance guided adaptive sampling method to the configurational space, falling in the term of Steered MD (SMD). The SMD approach biasing physically meaningful collective variable (CV) such as one dihedral or one distance to pulling the system from one conformational state to another. By minimizing the variance of the free energy differences along the pathway in an optimized way, a new type of adaptive SMD (ASMD) is introduced. As exhibits in the alchemical case, this adaptive sampling method outperforms the traditional equal-time SMD in nonequilibrium stratification. Also, the method gives much more efficient calculation of potential of mean force than the selection criterion based ASMD scheme, which is proven to be more efficient than traditional SMD. The variance-linearly-dependent minus time derivative of overall variance proposed for OBAR and OCE criterion is extended to determine the importance rank of the nonequilibrium pulling in the configurational space. It is shown that the importance rank given by the standard deviation of the free energy difference is wrong, but by correcting it with the simulation time we obtain the true importance rank in nonequilibrium stratification. The OCE workflow is periodicity-of-CV dependent while ASMD is not. In the non-periodic CV case, the end-state discrimination in the SD rank is eliminated in the TDV rank, while in the periodic CV case the correction introduced in the TDV rank is not that significant. The performance is demonstrated in a dihedral flipping case and two distance pulling cases, accounting for periodic and non-periodic CVs, respectively. </p>

BAR-based Optimum Adaptive Steered MD for Configurational Sampling

2019 ◽  
Author(s):  
Xiaohui Wang ◽  
Xingzhao Tu ◽  
Boming Deng ◽  
John Z. H. Zhang ◽  
Zhaoxi Sun
Keyword(s):  
Free Energy ◽  
Adaptive Sampling ◽  
Sampling Method ◽  
Time Derivative ◽  
Selection Criterion ◽  
Equal Time ◽  
Acceptance Ratio ◽  
Configurational Space ◽  
State Discrimination ◽  
Bennett’S Acceptance Ratio

<p>Previously we proposed the equilibrium and nonequilibrium adaptive alchemical free energy simulation methods Optimum Bennett’s Acceptance Ratio (OBAR) and Optimum Crooks’ Equation (OCE). They are based on the statistically optimal bidirectional reweighting estimator named Bennett’s Acceptance Ratio (BAR) or Crooks’ Equation (CE). They perform initial sampling in the staging alchemical transformation and then determine the importance rank of different states via the time-derivative of the variance (TDV). The method is proven to give speedups compared with the equal time rule. In the current work, we extended the time derivative of variance guided adaptive sampling method to the configurational space, falling in the term of Steered MD (SMD). The SMD approach biasing physically meaningful collective variable (CV) such as one dihedral or one distance to pulling the system from one conformational state to another. By minimizing the variance of the free energy differences along the pathway in an optimized way, a new type of adaptive SMD (ASMD) is introduced. As exhibits in the alchemical case, this adaptive sampling method outperforms the traditional equal-time SMD in nonequilibrium stratification. Also, the method gives much more efficient calculation of potential of mean force than the selection criterion based ASMD scheme, which is proven to be more efficient than traditional SMD. The variance-linearly-dependent minus time derivative of overall variance proposed for OBAR and OCE criterion is extended to determine the importance rank of the nonequilibrium pulling in the configurational space. It is shown that the importance rank given by the standard deviation of the free energy difference is wrong, but by correcting it with the simulation time we obtain the true importance rank in nonequilibrium stratification. The OCE workflow is periodicity-of-CV dependent while ASMD is not. In the non-periodic CV case, the end-state discrimination in the SD rank is eliminated in the TDV rank, while in the periodic CV case the correction introduced in the TDV rank is not that significant. The performance is demonstrated in a dihedral flipping case and two distance pulling cases, accounting for periodic and non-periodic CVs, respectively. </p>

scholarly journals BAR-based Optimum Adaptive Steered MD for Configurational Sampling

2019 ◽  
Author(s):  
Xiaohui Wang ◽  
Xingzhao Tu ◽  
Boming Deng ◽  
John Z. H. Zhang ◽  
Zhaoxi Sun
Keyword(s):  
Free Energy ◽  
Adaptive Sampling ◽  
Sampling Method ◽  
Time Derivative ◽  
Selection Criterion ◽  
Equal Time ◽  
Acceptance Ratio ◽  
Configurational Space ◽  
State Discrimination ◽  
Bennett’S Acceptance Ratio

<p>Previously we proposed the equilibrium and nonequilibrium adaptive alchemical free energy simulation methods Optimum Bennett’s Acceptance Ratio (OBAR) and Optimum Crooks’ Equation (OCE). They are based on the statistically optimal bidirectional reweighting estimator named Bennett’s Acceptance Ratio (BAR) or Crooks’ Equation (CE). They perform initial sampling in the staging alchemical transformation and then determine the importance rank of different states via the time-derivative of the variance (TDV). The method is proven to give speedups compared with the equal time rule. In the current work, we extended the time derivative of variance guided adaptive sampling method to the configurational space, falling in the term of Steered MD (SMD). The SMD approach biasing physically meaningful collective variable (CV) such as one dihedral or one distance to pulling the system from one conformational state to another. By minimizing the variance of the free energy differences along the pathway in an optimized way, a new type of adaptive SMD (ASMD) is introduced. As exhibits in the alchemical case, this adaptive sampling method outperforms the traditional equal-time SMD in nonequilibrium stratification. Also, the method gives much more efficient calculation of potential of mean force than the selection criterion based ASMD scheme, which is proven to be more efficient than traditional SMD. The variance-linearly-dependent minus time derivative of overall variance proposed for OBAR and OCE criterion is extended to determine the importance rank of the nonequilibrium pulling in the configurational space. It is shown that the importance rank given by the standard deviation of the free energy difference is wrong, but by correcting it with the simulation time we obtain the true importance rank in nonequilibrium stratification. The OCE workflow is periodicity-of-CV dependent while ASMD is not. In the non-periodic CV case, the end-state discrimination in the SD rank is eliminated in the TDV rank, while in the periodic CV case the correction introduced in the TDV rank is not that significant. The performance is demonstrated in a dihedral flipping case and two distance pulling cases, accounting for periodic and non-periodic CVs, respectively. </p>

scholarly journals Multiensemble Markov models of molecular thermodynamics and kinetics

2016 ◽  
Vol 113 (23) ◽  
pp. E3221-E3230 ◽  
Author(s):  
Hao Wu ◽  
Fabian Paul ◽  
Christoph Wehmeyer ◽  
Frank Noé
Keyword(s):  
Detailed Balance ◽  
Rare Event ◽  
Umbrella Sampling ◽  
High Dimensional ◽  
Acceptance Ratio ◽  
Markov State ◽  
Markov State Models ◽  
Bennett Acceptance Ratio ◽  
Special Cases ◽  
State Models

We introduce the general transition-based reweighting analysis method (TRAM), a statistically optimal approach to integrate both unbiased and biased molecular dynamics simulations, such as umbrella sampling or replica exchange. TRAM estimates a multiensemble Markov model (MEMM) with full thermodynamic and kinetic information at all ensembles. The approach combines the benefits of Markov state models—clustering of high-dimensional spaces and modeling of complex many-state systems—with those of the multistate Bennett acceptance ratio of exploiting biased or high-temperature ensembles to accelerate rare-event sampling. TRAM does not depend on any rate model in addition to the widely used Markov state model approximation, but uses only fundamental relations such as detailed balance and binless reweighting of configurations between ensembles. Previous methods, including the multistate Bennett acceptance ratio, discrete TRAM, and Markov state models are special cases and can be derived from the TRAM equations. TRAM is demonstrated by efficiently computing MEMMs in cases where other estimators break down, including the full thermodynamics and rare-event kinetics from high-dimensional simulation data of an all-atom protein–ligand binding model.

scholarly journals Chemically Accurate Relative Folding Stability of RNA Hairpins from Molecular Simulations

2018 ◽  
Author(s):  
Louis G. Smith ◽  
Zhen Tan ◽  
Aleksandar Spasic ◽  
Debapratim Dutta ◽  
Leslie A. Salas-Estrada ◽  
...  
Keyword(s):  
Free Energy ◽  
Molecular Simulations ◽  
Umbrella Sampling ◽  
Reaction Coordinate ◽  
Free Energy Change ◽  
Energy Change ◽  
Random Coil ◽  
Free Energies ◽  
Rna Hairpins ◽  
Rna Hairpin

AbstractThis study describes a comparison between melts and simulated stabilities of the same RNAs that could be used to benchmark RNA force fields, and potentially to determine future melt-ing experiments. Using umbrella sampling molecular simulations of three 12-nucleotide RNA hairpin stem loops, for which there are experimentally determined free energies of unfold-ing, we projected unfolding onto the reaction coordinate of end to end (5′ to 3′ hydroxyl oxygen) distance. We estimate the free energy change of the transition from the native con-formation to a fully extended conformation—the stretched state—with no hydrogen bonds between non-neighboring bases. Each simulation was performed four times using the AM-BER FF99+bsc0+χOL3 force field and each window, spaced at 1 Å intervals, was sampled for 1 μs, for a total of 552 μs of simulation. We compared differences in the simulated free energy changes to analogous differences in free energies from optical melting experiments using ther-modynamic cycles where the free energy change between stretched and random coil sequences is assumed to be sequence independent. The differences between experimental and simulated ΔΔG° are on average 1.00 ± 0.66 kcal/mol, which is chemically accurate and suggests analo-gous simulations could be used predictively. We also report a novel method to identify where replica free energies diverge along the reaction coordinate, thus indicating where additional sampling would most improve convergence. We conclude by discussing methods to more economically perform such simulations.

Unorthodox uses of Bennett's acceptance ratio method

2009 ◽  
Vol 30 (11) ◽  
pp. 1712-1718 ◽  
Author(s):  
Gerhard König ◽  
Stefan Bruckner ◽  
Stefan Boresch
Keyword(s):  
Ratio Method ◽  
Acceptance Ratio ◽  
Bennett’S Acceptance Ratio

scholarly journals Hydrophobicity of small alkane molecules (propane dimer) in solvents: a classical molecular dynamics study

BIBECHANA ◽  
2020 ◽  
Vol 17 ◽  
pp. 1-12
Author(s):  
Bikash Panthi ◽  
Nurapati Pantha
Keyword(s):  
Molecular Dynamics ◽  
Md Simulations ◽  
Umbrella Sampling ◽  
Potential Of Mean Force ◽  
Histogram Analysis ◽  
Analysis Method ◽  
Classical Molecular Dynamics ◽  
Solvent Environment ◽  
Weighted Histogram ◽  
Weighted Histogram Analysis

Molecular Dynamics (MD) simulations of propane dimer in different solvents (water, acetonitrile and methanol) were performed by using CHARMM platform for modeling the solute and solvents. A series of Umbrella sampling MD simulations were carried out in each solvent separately and potential of mean force (PMFs) were calculated by using Weighted Histogram Analysis Method. Results show that two minima (contact minima and solvent separated minima) characterize the PMF of propane dimer in all three solvent environments. The contact minima are deeper and less sensitive to solvent environment for its position. However, significant effect in the position of second minima, solvent separated minima, was observed. Our study reveals that the interaction between propane dimer is softer in methanol and acetonitrile than in water. BIBECHANA 17 (2020) 1-12  

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