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Aristoff D, Copperman J, Simpson G, Webber RJ, Zuckerman DM. Weighted ensemble: Recent mathematical developments. J Chem Phys 2023; 158:014108. [PMID: 36610976 PMCID: PMC9822651 DOI: 10.1063/5.0110873] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2022] [Accepted: 12/04/2022] [Indexed: 12/12/2022] Open
Abstract
Weighted ensemble (WE) is an enhanced sampling method based on periodically replicating and pruning trajectories generated in parallel. WE has grown increasingly popular for computational biochemistry problems due, in part, to improved hardware and accessible software implementations. Algorithmic and analytical improvements have played an important role, and progress has accelerated in recent years. Here, we discuss and elaborate on the WE method from a mathematical perspective, highlighting recent results that enhance the computational efficiency. The mathematical theory reveals a new strategy for optimizing trajectory management that approaches the best possible variance while generalizing to systems of arbitrary dimension.
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Affiliation(s)
- D. Aristoff
- Mathematics, Colorado State University, Fort Collins, CO 80521 USA
| | - J. Copperman
- Biomedical Engineering, Oregon Health and Science University, Portland, OR 97239 USA
| | - G. Simpson
- Mathematics, Drexel University, Philadelphia, Pennsylvania 19104 USA
| | - R. J. Webber
- Computing and Mathematical Sciences, California Institute of Technology, Pasadena, California 91125 USA
| | - D. M. Zuckerman
- Biomedical Engineering, Oregon Health and Science University, Portland, OR 97239 USA
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Bogetti AT, Leung JMG, Russo JD, Zhang S, Thompson JP, Saglam AS, Ray D, Mostofian B, Pratt AJ, Abraham RC, Harrison PO, Dudek M, Torrillo PA, DeGrave AJ, Adhikari U, Faeder JR, Andricioaei I, Adelman JL, Zwier MC, LeBard DN, Zuckerman DM, Chong LT. A Suite of Tutorials for the WESTPA 2.0 Rare-Events Sampling Software [Article v2.0]. LIVING JOURNAL OF COMPUTATIONAL MOLECULAR SCIENCE 2023; 5:1655. [PMID: 37200895 PMCID: PMC10191340 DOI: 10.33011/livecoms.5.1.1655] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
The weighted ensemble (WE) strategy has been demonstrated to be highly efficient in generating pathways and rate constants for rare events such as protein folding and protein binding using atomistic molecular dynamics simulations. Here we present two sets of tutorials instructing users in the best practices for preparing, carrying out, and analyzing WE simulations for various applications using the WESTPA software. The first set of more basic tutorials describes a range of simulation types, from a molecular association process in explicit solvent to more complex processes such as host-guest association, peptide conformational sampling, and protein folding. The second set ecompasses six advanced tutorials instructing users in the best practices of using key new features and plugins/extensions of the WESTPA 2.0 software package, which consists of major upgrades for larger systems and/or slower processes. The advanced tutorials demonstrate the use of the following key features: (i) a generalized resampler module for the creation of "binless" schemes, (ii) a minimal adaptive binning scheme for more efficient surmounting of free energy barriers, (iii) streamlined handling of large simulation datasets using an HDF5 framework, (iv) two different schemes for more efficient rate-constant estimation, (v) a Python API for simplified analysis of WE simulations, and (vi) plugins/extensions for Markovian Weighted Ensemble Milestoning and WE rule-based modeling for systems biology models. Applications of the advanced tutorials include atomistic and non-spatial models, and consist of complex processes such as protein folding and the membrane permeability of a drug-like molecule. Users are expected to already have significant experience with running conventional molecular dynamics or systems biology simulations.
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Affiliation(s)
| | | | - John D. Russo
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, OR
| | | | | | - Ali S. Saglam
- Department of Biological Sciences, University of Pittsburgh, Pittsburgh, PA
| | - Dhiman Ray
- Department of Chemistry, University of California Irvine, Irvine, CA
| | - Barmak Mostofian
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, OR
| | - AJ Pratt
- Department of Chemistry, University of Pittsburgh, Pittsburgh, PA
| | - Rhea C. Abraham
- Department of Chemistry, University of Pittsburgh, Pittsburgh, PA
| | - Page O. Harrison
- Department of Chemistry, University of Pittsburgh, Pittsburgh, PA
| | - Max Dudek
- Department of Chemistry, University of Pittsburgh, Pittsburgh, PA
| | - Paul A. Torrillo
- Department of Chemistry, University of Pittsburgh, Pittsburgh, PA
| | - Alex J. DeGrave
- Department of Chemistry, University of Pittsburgh, Pittsburgh, PA
| | - Upendra Adhikari
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, OR
| | - James R. Faeder
- Department of Biological Sciences, University of Pittsburgh, Pittsburgh, PA
| | - Ioan Andricioaei
- Department of Chemistry, University of California Irvine, Irvine, CA
| | - Joshua L. Adelman
- Department of Biological Sciences, University of Pittsburgh, Pittsburgh, PA
| | | | | | - Daniel M. Zuckerman
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, OR
| | - Lillian T. Chong
- Department of Chemistry, University of Pittsburgh, Pittsburgh, PA
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Baudel M, Guyader A, Lelièvre T. On the Hill relation and the mean reaction time for metastable processes. Stoch Process Their Appl 2022. [DOI: 10.1016/j.spa.2022.10.014] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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Chen X, He H, Huo L, Chen Z. Application of Cement-Based Composite Nanomaterials in Prefabricated Thin-Wall Light Steel Structure Composite Wall. Int J Anal Chem 2022; 2022:6015826. [PMID: 36118269 PMCID: PMC9477572 DOI: 10.1155/2022/6015826] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2022] [Revised: 08/17/2022] [Accepted: 08/23/2022] [Indexed: 11/17/2022] Open
Abstract
In order to solve the problem of seismic performance of prefabricated concrete shear walls connected with ultra-high performance cement-based composite (UHPC) after short lap of steel bars, the author proposes a cement-based composite nanomaterial in the prefabricated thin-walled lightweight application in steel structure composite wall. In order to explore the influence of the axial compression ratio on its seismic performance, 1 is a cast-in-place shear wall with a design axial compression ratio of 0.2, and 3 is a prefabricated shear wall with a design axial compression ratio of 0.2, 0.33, and 0.47, respectively, all the specimens were mainly damaged by shear compression. The test results show that the cracking loads of specimens PW2 and PW3 are increased by 17.04% and 38.81%, respectively, the yield load is increased by 27.74% and 50.28%, respectively, and the peak load is increased by 25.29% and 48.4%, respectively. Conclusion. With the increase of the axial compression ratio, the crack resistance and bearing capacity of the specimens are significantly improved.
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Affiliation(s)
- Xiaoxu Chen
- Faculty of Architectural Engineering, Guangdong Baiyun University, Guangzhou, Guangdong 510000, China
| | - Huatuo He
- Sichuan Zhongyu Environmental Governance Co., Ltd., CITCI Envirotech, Guangzhou Co., Ltd., Guangzhou, Guangdong 510000, China
| | - Lingzhao Huo
- Guangzhou Country Garden Real Estate Co., Ltd., Guangzhou, Guangdong 510000, China
| | - Zhaorong Chen
- China Construction Fifth Engineering Bureau the Third Construction Co., Ltd., Changsha, Hunan 410004, China
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Abstract
Abstract
We study weighted ensemble, an interacting particle method for sampling distributions of Markov chains that has been used in computational chemistry since the 1990s. Many important applications of weighted ensemble require the computation of long time averages. We establish the consistency of weighted ensemble in this setting by proving an ergodic theorem for time averages. As part of the proof, we derive explicit variance formulas that could be useful for optimizing the method.
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Ahn SH, Ojha AA, Amaro RE, McCammon JA. Gaussian-Accelerated Molecular Dynamics with the Weighted Ensemble Method: A Hybrid Method Improves Thermodynamic and Kinetic Sampling. J Chem Theory Comput 2021; 17:7938-7951. [PMID: 34844409 DOI: 10.1021/acs.jctc.1c00770] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Gaussian-accelerated molecular dynamics (GaMD) is a well-established enhanced sampling method for molecular dynamics simulations that effectively samples the potential energy landscape of the system by adding a boost potential, which smoothens the surface and lowers the energy barriers between states. GaMD is unable to give time-dependent properties such as kinetics directly. On the other hand, the weighted ensemble (WE) method can efficiently sample transitions between states with its many weighted trajectories, which directly yield rates and pathways. However, convergence to equilibrium conditions remains a challenge for the WE method. Hence, we have developed a hybrid method that combines the two methods, wherein GaMD is first used to sample the potential energy landscape of the system and WE is subsequently used to further sample the potential energy landscape and kinetic properties of interest. We show that the hybrid method can sample both thermodynamic and kinetic properties more accurately and quickly compared to using either method alone.
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Affiliation(s)
- Surl-Hee Ahn
- Department of Chemistry, University of California San Diego, La Jolla 92093, California, United States
| | - Anupam A Ojha
- Department of Chemistry, University of California San Diego, La Jolla 92093, California, United States
| | - Rommie E Amaro
- Department of Chemistry, University of California San Diego, La Jolla 92093, California, United States
| | - J Andrew McCammon
- Department of Chemistry, University of California San Diego, La Jolla 92093, California, United States.,Department of Pharmacology, University of California San Diego, La Jolla 92093, California, United States
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Zuckerman DM, Russo JD. A gentle introduction to the non-equilibrium physics of trajectories: Theory, algorithms, and biomolecular applications. AMERICAN JOURNAL OF PHYSICS 2021; 89:1048-1061. [PMID: 35530173 PMCID: PMC9075726 DOI: 10.1119/10.0005603] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2021] [Accepted: 06/25/2021] [Indexed: 06/14/2023]
Abstract
Despite the importance of non-equilibrium statistical mechanics in modern physics and related fields, the topic is often omitted from undergraduate and core-graduate curricula. Key aspects of non-equilibrium physics, however, can be understood with a minimum of formalism based on a rigorous trajectory picture. The fundamental object is the ensemble of trajectories, a set of independent time-evolving systems, which easily can be visualized or simulated (e.g., for protein folding) and which can be analyzed rigorously in analogy to an ensemble of static system configurations. The trajectory picture provides a straightforward basis for understanding first-passage times, "mechanisms" in complex systems, and fundamental constraints on the apparent reversibility of complex processes. Trajectories make concrete the physics underlying the diffusion and Fokker-Planck partial differential equations. Last but not least, trajectory ensembles underpin some of the most important algorithms that have provided significant advances in biomolecular studies of protein conformational and binding processes.
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Torrillo PA, Bogetti AT, Chong LT. A Minimal, Adaptive Binning Scheme for Weighted Ensemble Simulations. J Phys Chem A 2021; 125:1642-1649. [PMID: 33577732 PMCID: PMC8091492 DOI: 10.1021/acs.jpca.0c10724] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
A promising approach for simulating rare events with rigorous kinetics is the weighted ensemble path sampling strategy. One challenge of this strategy is the division of configurational space into bins for sampling. Here we present a minimal adaptive binning (MAB) scheme for the automated, adaptive placement of bins along a progress coordinate within the framework of the weighted ensemble strategy. Results reveal that the MAB binning scheme, despite its simplicity, is more efficient than a manual, fixed binning scheme in generating transitions over large free energy barriers, generating a diversity of pathways, estimating rate constants, and sampling conformations. The scheme is general and extensible to any rare-events sampling strategy that employs progress coordinates.
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Affiliation(s)
- Paul A Torrillo
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - Anthony T Bogetti
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - Lillian T Chong
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
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Roussey NM, Dickson A. Enhanced Jarzynski free energy calculations using weighted ensemble. J Chem Phys 2020; 153:134116. [PMID: 33032408 PMCID: PMC7544513 DOI: 10.1063/5.0020600] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2020] [Accepted: 09/16/2020] [Indexed: 02/07/2023] Open
Abstract
The free energy of transitions between stable states is the key thermodynamic quantity that governs the relative probabilities of the forward and reverse reactions and the ratio of state probabilities at equilibrium. The binding free energy of a drug and its receptor is of particular interest, as it serves as an optimization function for drug design. Over the years, many computational methods have been developed to calculate binding free energies, and while many of these methods have a long history, issues such as convergence of free energy estimates and the projection of a binding process onto order parameters remain. Over 20 years ago, the Jarzynski equality was derived with the promise to calculate equilibrium free energies by measuring the work applied to short nonequilibrium trajectories. However, these calculations were found to be dominated by trajectories with low applied work that occur with extremely low probability. Here, we examine the combination of weighted ensemble algorithms with the Jarzynski equality. In this combined method, an ensemble of nonequilibrium trajectories are run in parallel, and cloning and merging operations are used to preferentially sample low-work trajectories that dominate the free energy calculations. Two additional methods are also examined: (i) a novel weighted ensemble resampler that samples trajectories directly according to their importance to the work of work and (ii) the diffusion Monte Carlo method using the applied work as the selection potential. We thoroughly examine both the accuracy and efficiency of unbinding free energy calculations for a series of model Lennard-Jones atom pairs with interaction strengths ranging from 2 kcal/mol to 20 kcal/mol. We find that weighted ensemble calculations can more efficiently determine accurate binding free energies, especially for deeper Lennard-Jones well depths.
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Affiliation(s)
- Nicole M. Roussey
- Department of Biochemistry and Molecular Biology, Michigan State University, East Lansing, Michigan 48823, USA
| | - Alex Dickson
- Author to whom correspondence should be addressed:
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