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Efficient Determination of Free Energy Landscapes in Multiple Dimensions from Biased Umbrella Sampling Simulations Using Linear Regression.

ABSTRACT: The weighted histogram analysis method (WHAM) is a standard protocol for postprocessing the information from biased umbrella sampling simulations to construct the potential of mean force with respect to a set of order parameters. By virtue of the WHAM equations, the unbiased density of state is determined by satisfying a self-consistent condition through an iterative procedure. While the method works very effectively when the number of order parameters is small, its computational cost grows rapidly in higher dimension. Here, we present a simple and efficient alternative strategy, which avoids solving the self-consistent WHAM equations iteratively. An efficient multivariate linear regression framework is utilized to link the biased probability densities of individual umbrella windows and yield an unbiased global free energy landscape in the space of order parameters. It is demonstrated with practical examples that free energy landscapes that are comparable in accuracy to WHAM can be generated at a small fraction of the cost.

SUBMITTER: Meng Y

PROVIDER: S-EPMC4894281 | biostudies-literature | 2015 Aug

REPOSITORIES: biostudies-literature

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Efficient Determination of Free Energy Landscapes in Multiple Dimensions from Biased Umbrella Sampling Simulations Using Linear Regression.

Meng Yilin Y Roux Benoît B

Journal of chemical theory and computation 20150707 8

The weighted histogram analysis method (WHAM) is a standard protocol for postprocessing the information from biased umbrella sampling simulations to construct the potential of mean force with respect to a set of order parameters. By virtue of the WHAM equations, the unbiased density of state is determined by satisfying a self-consistent condition through an iterative procedure. While the method works very effectively when the number of order parameters is small, its computational cost grows rapi ...[more]

PMID: 26574437

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Project description:IntroductionRiboswitches are cis-acting regulatory RNA elements prevalently located in the leader sequences of bacterial mRNA. An adenine sensing riboswitch cis-regulates adeninosine deaminase gene (add) in Vibrio vulnificus. The structural mechanism regulating its conformational changes upon ligand binding mostly remains to be elucidated. In this open framework it has been suggested that the ligand stabilizes the interaction of the distal "kissing loop" complex. Using accurate full-atom molecular dynamics with explicit solvent in combination with enhanced sampling techniques and advanced analysis methods it could be possible to provide a more detailed perspective on the formation of these tertiary contacts.MethodsIn this work, we used umbrella sampling simulations to study the thermodynamics of the kissing loop complex in the presence and in the absence of the cognate ligand. We enforced the breaking/formation of the loop-loop interaction restraining the distance between the two loops. We also assessed the convergence of the results by using two alternative initialization protocols. A structural analysis was performed using a novel approach to analyze base contacts.ResultsContacts between the two loops were progressively lost when larger inter-loop distances were enforced. Inter-loop Watson-Crick contacts survived at larger separation when compared with non-canonical pairing and stacking interactions. Intra-loop stacking contacts remained formed upon loop undocking. Our simulations qualitatively indicated that the ligand could stabilize the kissing loop complex. We also compared with previously published simulation studies.Discussion and conclusionsKissing complex stabilization given by the ligand was compatible with available experimental data. However, the dependence of its value on the initialization protocol of the umbrella sampling simulations posed some questions on the quantitative interpretation of the results and called for better converged enhanced sampling simulations.

Project description:Changes in free energy provide valuable information for molecular recognition, including both ligand-receptor binding thermodynamics and kinetics. Umbrella sampling (US), a widely used free energy calculation method, has long been used to explore the dissociation process of ligand-receptor systems and compute binding free energy. In existing publications, the binding free energy computed from the potential of mean force (PMF) with US simulation mostly yielded "ball park" values with experimental data. However, the computed PMF values are highly influenced by factors such as initial conformations and/or trajectories provided, the reaction coordinate, and sampling of conformational space in each US window. These critical factors have rarely been carefully studied. Here we used US to study the guest aspirin and 1-butanol dissociation processes of β-cyclodextrin (β-CD) and an inhibitor SB2 dissociation from a p38α mitogen-activated protein kinase (MAPK) complex. For β-CD, we used three different β-CD conformations to generate the dissociation path with US windows. For p38α, we generated the dissociation pathway by using accelerated molecular dynamics followed by conformational relaxing with short conventional MD, steered MD, and manual pulling. We found that, even for small β-CD complexes, different β-CD conformations altered the height of the PMF, but the pattern of PMF was not affected if the MD sampling in each US window was well-converged. Because changing the macrocyclic ring conformation needs to rotate dihedral angles in the ring, a bound ligand largely restrains the motion of cyclodextrin. Therefore, once a guest is in the binding site, cyclodextrin cannot freely change its initial conformation, resulting in different absolute heights of the PMF, which cannot be overcome by running excessively long MD simulations for each US window. Moreover, if the US simulations were not converged, the important barrier and minimum were missed. For ligand-protein systems, our studies also suggest that the dissociation trajectories modeled by an enhanced sampling method must maintain a natural molecular movement to avoid biased PMF plots when using US simulations.

Dataset Information

Efficient Determination of Free Energy Landscapes in Multiple Dimensions from Biased Umbrella Sampling Simulations Using Linear Regression.

Publications

Efficient Determination of Free Energy Landscapes in Multiple Dimensions from Biased Umbrella Sampling Simulations Using Linear Regression.

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