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Sun Z, He Q. Seeding the multi-dimensional nonequilibrium pulling for Hamiltonian variation: indirect nonequilibrium free energy simulations at QM levels. Phys Chem Chem Phys 2022; 24:8800-8819. [PMID: 35352744 DOI: 10.1039/d2cp00355d] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
The combination of free energy simulations in the alchemical and configurational spaces provides a feasible route to access the thermodynamic profiles under a computationally demanding target Hamiltonian. Normally, due to the significant differences between the computational cost of ab initio quantum mechanics (QM) calculations and those of semi-empirical quantum mechanics (SQM) and molecular mechanics (MM), this indirect method could be used to obtain the QM thermodynamics by combining the SQM or MM results and the SQM-to-QM or MM-to-QM corrections. In our previous work, a multi-dimensional nonequilibrium pulling framework for Hamiltonian variations was introduced based on bidirectional pulling and bidirectional reweighting. The method performs nonequilibrium free energy simulations in the configurational space to obtain the thermodynamic profile along the conformational change pathway under a selected computationally efficient Hamiltonian, and uses the nonequilibrium alchemical method to correct or perturb the thermodynamic profile to that under the target Hamiltonian. The BAR-based method is designed to achieve the best generality and transferability and thus leads to modest (∼20 fold) speedup. In this work, we explore the possibility of further accelerating the nonequilibrium free energy simulation by employing unidirectional pulling and using the selection criterion to obtain the initial configurations used to initiate nonequilibrium trajectories following the idea of adaptive steered molecular dynamics (ASMD). A single initial condition is used to seed the whole multi-dimensional nonequilibrium free energy simulation and the sampling is performed fully in the nonequilibrium ensemble. Introducing very short ps-length equilibrium sampling to grab more initial seeds could also be helpful. The ASMD scheme estimates the free energy difference with the unidirectional exponential average (EXP), but it does not follow exactly the requirements of the EXP estimator. Another deficiency of the seeding simulation is the inherently sequential or serial pulling due to the inter-segment dependency, which triggers some problems in the parallelizability of the simulation. Numerical tests are performed to grasp some insights and guidelines for using this selection-criterion-based ASMD scheme. The presented selection-criterion-based multi-dimensional ASMD scheme follows the same perturbation network of the BAR-based method, and thus could be used in various Hamiltonian-variation cases.
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Affiliation(s)
- Zhaoxi Sun
- Beijing National Laboratory for Molecular Sciences, College of Chemistry and Molecular Engineering, Institute of Theoretical and Computational Chemistry, Peking University, Beijing 100871, China.
| | - Qiaole He
- AI Department of Enzymaster (Ningbo) Bio-Engineering Co., Ltd, North Century Avenue 333, 315100 Ningbo, China
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Sun Z, Liu Z. BAR‐Based Multi‐Dimensional Nonequilibrium Pulling for Indirect Construction of QM/MM Free Energy Landscapes: Varying the QM Region. ADVANCED THEORY AND SIMULATIONS 2021. [DOI: 10.1002/adts.202100185] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Affiliation(s)
- Zhaoxi Sun
- Beijing National Laboratory for Molecular Sciences, College of Chemistry and Molecular Engineering Peking University Beijing 100871 China
| | - Zhirong Liu
- Beijing National Laboratory for Molecular Sciences, College of Chemistry and Molecular Engineering Peking University Beijing 100871 China
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Sun Z. BAR-based multi-dimensional nonequilibrium pulling for indirect construction of QM/MM free energy landscapes: from semi-empirical to ab initio. Phys Chem Chem Phys 2019; 21:21942-21959. [PMID: 31552953 DOI: 10.1039/c9cp04113c] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
Abstract
The indirect method for the construction of quantum mechanics (QM)/molecular mechanics (MM) free energy landscapes provides a cheaper alternative for free energy simulations at the QM level. The indirect method features a direct calculation of the free energy profile with a computationally efficient but less accurate Hamiltonian (i.e. low-level Hamiltonian) and a low-level-to-high-level correction. In the thermodynamic cycle, the direct low-level calculation along the physically meaningful reaction coordinate is corrected via the alchemical method, which is often achieved with perturbation-based techniques. In our previous work, a multi-dimensional nonequilibrium pulling framework is proposed for the indirect construction of QM/MM free energy landscapes. Previously, we focused on obtaining semi-empirical QM (SQM) results indirectly from direct MM simulations and MM to SQM corrections. In this work, we apply this method to obtain results under ab initio QM Hamiltonians by combining direct SQM results and SQM to QM corrections. A series of SQM and QM Hamiltonians are benchmarked. It is observed that PM6 achieves the best performance among the low-level Hamiltonians. Therefore, we recommend using PM6 as the low-level theory in the indirect free energy simulation. Considering its higher similarity to the high-level Hamiltonians, PM6 corrected with the bond charge correction could be more accurate than the existing AM1-BCC model. Another central result in the current work is a basic protocol of choosing the strength of restraints and an appropriate time step in nonequilibrium free energy simulation at the stiff spring limit. We provide theoretical derivations to emphasize the importance of using a sufficiently large force constant and choosing an appropriate time step. It is worth noting that a general rule of thumb for choosing the time step, according to our derivation, is that a time step of 1 fs or smaller should be used, as long as the stiff spring approximation is employed, even in simulations with constraints on bonds involving hydrogen atoms.
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Affiliation(s)
- Zhaoxi Sun
- State Key Laboratory of Precision Spectroscopy, School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, China
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Wang X, He Q, Sun Z. BAR-based multi-dimensional nonequilibrium pulling for indirect construction of a QM/MM free energy landscape. Phys Chem Chem Phys 2019; 21:6672-6688. [PMID: 30855611 DOI: 10.1039/c8cp07012a] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
Construction of free energy landscapes at the quantum mechanics (QM) level is computationally demanding. As shown in previous studies, by employing an indirect scheme (i.e. constructing a thermodynamic cycle connecting QM states via an alchemical pathway), simulations are converged with much less computational burden. The indirect scheme makes QM/molecular mechanics (MM) free energy simulation orders of magnitude faster than the direct QM/MM schemes. However, the indirect QM/MM simulations were mostly equilibrium sampling based and the nonequilibrium methods were merely exploited in one-dimensional alchemical QM/MM end-state correction at two end states. In this work, we represent a multi-dimensional nonequilibrium pulling scheme for indirect QM/MM free energy simulations, where the whole free energy simulation is performed only with nonequilibrium methods. The collective variable (CV) space we explore is a combination of one alchemical CV and one physically meaningful CV. The current nonequilibrium indirect QM/MM simulation method can be seen as the generalization of equilibrium perturbation based indirect QM/MM methods. The test systems include one backbone dihedral case and one distance case. The two cases are significantly different in size, enabling us to investigate the dependence of the speedup of the indirect scheme on the size of the system. It is shown that the speedup becomes larger when the size of the system becomes larger, which is consistent with the scaling behavior of QM Hamiltonians.
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Affiliation(s)
- Xiaohui Wang
- State Key Laboratory of Precision Spectroscopy, School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, China
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Radak BK, Roux B. Efficiency in nonequilibrium molecular dynamics Monte Carlo simulations. J Chem Phys 2017; 145:134109. [PMID: 27782441 DOI: 10.1063/1.4964288] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Hybrid algorithms combining nonequilibrium molecular dynamics and Monte Carlo (neMD/MC) offer a powerful avenue for improving the sampling efficiency of computer simulations of complex systems. These neMD/MC algorithms are also increasingly finding use in applications where conventional approaches are impractical, such as constant-pH simulations with explicit solvent. However, selecting an optimal nonequilibrium protocol for maximum efficiency often represents a non-trivial challenge. This work evaluates the efficiency of a broad class of neMD/MC algorithms and protocols within the theoretical framework of linear response theory. The approximations are validated against constant pH-MD simulations and shown to provide accurate predictions of neMD/MC performance. An assessment of a large set of protocols confirms (both theoretically and empirically) that a linear work protocol gives the best neMD/MC performance. Finally, a well-defined criterion for optimizing the time parameters of the protocol is proposed and demonstrated with an adaptive algorithm that improves the performance on-the-fly with minimal cost.
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Affiliation(s)
- Brian K Radak
- Leadership Computing Facility, Argonne National Laboratory, Argonne, Illinois 60439-8643, USA
| | - Benoît Roux
- Department of Biochemistry and Molecular Biology, University of Chicago, Chicago, Illinois 60637-1454, USA
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Giovannelli E, Cardini G, Chelli R. Simulations in generalized ensembles through noninstantaneous switches. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:043310. [PMID: 26565367 DOI: 10.1103/physreve.92.043310] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2015] [Indexed: 06/05/2023]
Abstract
Generalized-ensemble simulations, such as replica exchange and serial generalized-ensemble methods, are powerful simulation tools to enhance sampling of free energy landscapes in systems with high energy barriers. In these methods, sampling is enhanced through instantaneous transitions of replicas, i.e., copies of the system, between different ensembles characterized by some control parameter associated with thermodynamical variables (e.g., temperature or pressure) or collective mechanical variables (e.g., interatomic distances or torsional angles). An interesting evolution of these methodologies has been proposed by replacing the conventional instantaneous (trial) switches of replicas with noninstantaneous switches, realized by varying the control parameter in a finite time and accepting the final replica configuration with a Metropolis-like criterion based on the Crooks nonequilibrium work (CNW) theorem. Here we revise these techniques focusing on their correlation with the CNW theorem in the framework of Markovian processes. An outcome of this report is the derivation of the acceptance probability for noninstantaneous switches in serial generalized-ensemble simulations, where we show that explicit knowledge of the time dependence of the weight factors entering such simulations is not necessary. A generalized relationship of the CNW theorem is also provided in terms of the underlying equilibrium probability distribution at a fixed control parameter. Illustrative calculations on a toy model are performed with serial generalized-ensemble simulations, especially focusing on the different behavior of instantaneous and noninstantaneous replica transition schemes.
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Affiliation(s)
- Edoardo Giovannelli
- Dipartimento di Chimica, Università di Firenze, Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy
| | - Gianni Cardini
- Dipartimento di Chimica, Università di Firenze, Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy
| | - Riccardo Chelli
- Dipartimento di Chimica, Università di Firenze, Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy
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Somani S, Okamoto Y, Ballard AJ, Wales DJ. Equilibrium molecular thermodynamics from Kirkwood sampling. J Phys Chem B 2015; 119:6155-69. [PMID: 25915525 PMCID: PMC4500650 DOI: 10.1021/acs.jpcb.5b01800] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
![]()
We
present two methods for barrierless equilibrium sampling of
molecular systems based on the recently proposed Kirkwood method (J. Chem. Phys.2009, 130,
134102). Kirkwood sampling employs low-order correlations among internal
coordinates of a molecule for random (or non-Markovian) sampling of
the high dimensional conformational space. This is a geometrical sampling
method independent of the potential energy surface. The first method
is a variant of biased Monte Carlo, where Kirkwood sampling is used
for generating trial Monte Carlo moves. Using this method, equilibrium
distributions corresponding to different temperatures and potential
energy functions can be generated from a given set of low-order correlations.
Since Kirkwood samples are generated independently, this method is
ideally suited for massively parallel distributed computing. The second
approach is a variant of reservoir replica exchange, where Kirkwood
sampling is used to construct a reservoir of conformations, which
exchanges conformations with the replicas performing equilibrium sampling
corresponding to different thermodynamic states. Coupling with the
Kirkwood reservoir enhances sampling by facilitating global jumps
in the conformational space. The efficiency of both methods depends
on the overlap of the Kirkwood distribution with the target equilibrium
distribution. We present proof-of-concept results for a model nine-atom
linear molecule and alanine dipeptide.
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Affiliation(s)
- Sandeep Somani
- †University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Yuko Okamoto
- ‡Department of Physics, Graduate School of Science, Nagoya University, Nagoya, Aichi 464-8602, Japan.,§Structural Biology Research Center, Graduate School of Science, Nagoya University, Nagoya, Aichi 464-8602, Japan.,∥Center for Computational Science, Graduate School of Engineering, Nagoya University, Nagoya, Aichi 464-8603, Japan.,⊥Information Technology Center, Nagoya University, Nagoya, Aichi 464-8601, Japan
| | - Andrew J Ballard
- †University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - David J Wales
- †University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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Bonança MVS, Deffner S. Optimal driving of isothermal processes close to equilibrium. J Chem Phys 2014; 140:244119. [DOI: 10.1063/1.4885277] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Marcus V. S. Bonança
- Instituto de Física “Gleb Wataghin,” Universidade Estadual de Campinas, 13083-859, Campinas, São Paulo, Brazil
- Department of Chemistry and Biochemistry and Institute of Physical Sciences and Technology, University of Maryland, College Park, Maryland 20742, USA
| | - Sebastian Deffner
- Department of Chemistry and Biochemistry and Institute of Physical Sciences and Technology, University of Maryland, College Park, Maryland 20742, USA
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Computing Equilibrium Free Energies Using Non-Equilibrium Molecular Dynamics. ENTROPY 2013. [DOI: 10.3390/e16010041] [Citation(s) in RCA: 50] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Lee TS, Radak BK, Huang M, Wong KY, York DM. Roadmaps through free energy landscapes calculated using the multi-dimensional vFEP approach. J Chem Theory Comput 2013; 10:24-34. [PMID: 24505217 DOI: 10.1021/ct400691f] [Citation(s) in RCA: 55] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
The variational free energy profile (vFEP) method is extended to two dimensions and tested with molecular simulation applications. The proposed 2D-vFEP approach effectively addresses the two major obstacles to constructing free energy profiles from simulation data using traditional methods: the need for overlap in the re-weighting procedure and the problem of data representation. This is especially evident as these problems are shown to be more severe in two dimensions. The vFEP method is demonstrated to be highly robust and able to provide stable, analytic free energy profiles with only a paucity of sampled data. The analytic profiles can be analyzed with conventional search methods to easily identify stationary points (e.g. minima and first-order saddle points) as well as the pathways that connect these points. These "roadmaps" through the free energy surface are useful not only as a post-processing tool to characterize mechanisms, but can also serve as a basis from which to direct more focused "on-the-fly" sampling or adaptive force biasing. Test cases demonstrate that 2D-vFEP outperforms other methods in terms of the amount and sparsity of the data needed to construct stable, converged analytic free energy profiles. In a classic test case, the two dimensional free energy profile of the backbone torsion angles of alanine dipeptide, 2D-vFEP needs less than 1% of the original data set to reach a sampling accuracy of 0.5 kcal/mol in free energy shifts between windows. A new software tool for performing one and two dimensional vFEP calculations is herein described and made publicly available.
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Affiliation(s)
- Tai-Sung Lee
- Center for Integrative Proteomics Research and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA, Department of Chemistry, University of Minnesota, Minneapolis, MN 55455, USA, Scientific Computation Program, University of Minnesota, Minneapolis, MN 55455, USA, and Department of Physics, High Performance Cluster Computing Centre, and Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon Tong, Hong Kong
| | - Brian K Radak
- Center for Integrative Proteomics Research and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA, Department of Chemistry, University of Minnesota, Minneapolis, MN 55455, USA, Scientific Computation Program, University of Minnesota, Minneapolis, MN 55455, USA, and Department of Physics, High Performance Cluster Computing Centre, and Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon Tong, Hong Kong
| | - Ming Huang
- Center for Integrative Proteomics Research and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA, Department of Chemistry, University of Minnesota, Minneapolis, MN 55455, USA, Scientific Computation Program, University of Minnesota, Minneapolis, MN 55455, USA, and Department of Physics, High Performance Cluster Computing Centre, and Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon Tong, Hong Kong
| | - Kin-Yiu Wong
- Center for Integrative Proteomics Research and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA, Department of Chemistry, University of Minnesota, Minneapolis, MN 55455, USA, Scientific Computation Program, University of Minnesota, Minneapolis, MN 55455, USA, and Department of Physics, High Performance Cluster Computing Centre, and Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon Tong, Hong Kong
| | - Darrin M York
- Center for Integrative Proteomics Research and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA, Department of Chemistry, University of Minnesota, Minneapolis, MN 55455, USA, Scientific Computation Program, University of Minnesota, Minneapolis, MN 55455, USA, and Department of Physics, High Performance Cluster Computing Centre, and Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon Tong, Hong Kong
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Wright LB, Walsh TR. Efficient conformational sampling of peptides adsorbed onto inorganic surfaces: insights from a quartz binding peptide. Phys Chem Chem Phys 2013; 15:4715-26. [DOI: 10.1039/c3cp42921k] [Citation(s) in RCA: 71] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
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Lee TS, Radak BK, Pabis A, York DM. A New Maximum Likelihood Approach for Free Energy Profile Construction from Molecular Simulations. J Chem Theory Comput 2012; 9:153-164. [PMID: 23457427 DOI: 10.1021/ct300703z] [Citation(s) in RCA: 68] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
A novel variational method for construction of free energy profiles from molecular simulation data is presented. The variational free energy profile (VFEP) method uses the maximum likelihood principle applied to the global free energy profile based on the entire set of simulation data (e.g from multiple biased simulations) that spans the free energy surface. The new method addresses common obstacles in two major problems usually observed in traditional methods for estimating free energy surfaces: the need for overlap in the re-weighting procedure and the problem of data representation. Test cases demonstrate that VFEP outperforms other methods in terms of the amount and sparsity of the data needed to construct the overall free energy profiles. For typical chemical reactions, only ~5 windows and ~20-35 independent data points per window are sufficient to obtain an overall qualitatively correct free energy profile with sampling errors an order of magnitude smaller than the free energy barrier. The proposed approach thus provides a feasible mechanism to quickly construct the global free energy profile and identify free energy barriers and basins in free energy simulations via a robust, variational procedure that determines an analytic representation of the free energy profile without the requirement of numerically unstable histograms or binning procedures. It can serve as a new framework for biased simulations and is suitable to be used together with other methods to tackle with the free energy estimation problem.
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Affiliation(s)
- Tai-Sung Lee
- BioMaPS Institute for Quantitative Biology and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
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