1
|
Hédin F, Plattner N, Doll JD, Meuwly M. Spatial Averaging: Sampling Enhancement for Exploring Configurational Space of Atomic Clusters and Biomolecules. J Chem Theory Comput 2014; 10:4284-96. [DOI: 10.1021/ct500529w] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Affiliation(s)
- Florent Hédin
- Department
of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
| | - Nuria Plattner
- Department
of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, D-14195 Berlin, Germany
| | - J. D. Doll
- Department
of Chemistry, Brown University, Providence, Rhode Island 02912, United States
| | - Markus Meuwly
- Department
of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
- Department
of Chemistry, Brown University, Providence, Rhode Island 02912, United States
| |
Collapse
|
2
|
Kim J, Straub JE, Keyes T. Replica exchange statistical temperature molecular dynamics algorithm. J Phys Chem B 2012; 116:8646-53. [PMID: 22540354 PMCID: PMC11240102 DOI: 10.1021/jp300366j] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
The replica exchange statistical temperature molecular dynamics (RESTMD) algorithm is presented, designed to alleviate an extensive increase of the number of replicas required as system size increases in the conventional temperature replica exchange method (tREM), and to obtain improved sampling in individual replicas. RESTMD optimally integrates multiple STMD (Phys. Rev. Lett. 2006, 97, 050601) runs with replica exchanges, giving rise to a flat energy sampling in each replica with a self-adjusting weight determination. The expanded flat energy dynamic sampling range allows the use of significantly fewer STMD replicas while maintaining the desired acceptance probability for replica exchanges. The computational advantages of RESTMD over conventional REM and single-replica STMD are explicitly demonstrated with an application to a coarse-grained protein model. The effect of two different kinetic temperature control schemes on the sampling efficiency is explored for diverse simulation conditions.
Collapse
Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, United States.
| | | | | |
Collapse
|
3
|
Kim J, Keyes T, Straub JE. Communication: Iteration-free, weighted histogram analysis method in terms of intensive variables. J Chem Phys 2012; 135:061103. [PMID: 21842919 DOI: 10.1063/1.3626150] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present an iteration-free weighted histogram method in terms of intensive variables that directly determines the inverse statistical temperature, β(S) = ∂S/∂E, with S the microcanonical entropy. The method eliminates iterative evaluations of the partition functions intrinsic to the conventional approach and leads to a dramatic acceleration of the posterior analysis of combining statistically independent simulations with no loss in accuracy. The synergistic combination of the method with generalized ensemble weights provides insights into the nature of the underlying phase transitions via signatures in β(S) characteristic of finite size systems. The versatility and accuracy of the method is illustrated for the Ising and Potts models.
Collapse
Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA.
| | | | | |
Collapse
|
4
|
Kim J, Keyes T, Straub JE. Generalized replica exchange method. J Chem Phys 2010; 132:224107. [PMID: 20550390 PMCID: PMC2896417 DOI: 10.1063/1.3432176] [Citation(s) in RCA: 74] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2010] [Accepted: 04/30/2010] [Indexed: 01/28/2023] Open
Abstract
We present a powerful replica exchange method, particularly suited to first-order phase transitions associated with the backbending in the statistical temperature, by merging an optimally designed generalized ensemble sampling with replica exchanges. The key ingredients of our method are parametrized effective sampling weights, smoothly joining ordered and disordered phases with a succession of unimodal energy distributions by transforming unstable or metastable energy states of canonical ensembles into stable ones. The inverse mapping between the sampling weight and the effective temperature provides a systematic way to design the effective sampling weights and determine a dynamic range of relevant parameters. Illustrative simulations on Potts spins with varying system size and simulation conditions demonstrate a comprehensive sampling for phase-coexistent states with a dramatic acceleration of tunneling transitions. A significant improvement over the power-law slowing down of mean tunneling times with increasing system size is obtained, and the underlying mechanism for accelerated tunneling is discussed.
Collapse
Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA.
| | | | | |
Collapse
|
5
|
Kim J, Keyes T, Straub JE. Replica exchange statistical temperature Monte Carlo. J Chem Phys 2009; 130:124112. [PMID: 19334813 DOI: 10.1063/1.3095422] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
The replica exchange statistical temperature Monte Carlo algorithm (RESTMC) is presented, extending the single-replica STMC algorithm [J. Kim, J. E. Straub, and T. Keyes, Phys. Rev. Lett. 97, 050601 (2006)] to alleviate the slow convergence of the conventional temperature replica exchange method (t-REM) with increasing system size. In contrast to the Gibbs-Boltzmann sampling at a specific temperature characteristic of the standard t-REM, RESTMC samples a range of temperatures in each replica and achieves a flat energy sampling employing the generalized sampling weight, which is automatically determined via the dynamic modification of the replica-dependent statistical temperature. Faster weight determination, through the dynamic update of the statistical temperature, and the flat energy sampling, maximizing energy overlaps between neighboring replicas, lead to a considerable acceleration in the convergence of simulations even while employing significantly fewer replicas. The performance of RESTMC is demonstrated and quantitatively compared with that of the conventional t-REM under varying simulation conditions for Lennard-Jones 19, 31, and 55 atomic clusters, exhibiting single- and double-funneled energy landscapes.
Collapse
Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA.
| | | | | |
Collapse
|
6
|
Kim J, Straub JE. Optimal replica exchange method combined with Tsallis weight sampling. J Chem Phys 2009; 130:144114. [PMID: 19368436 PMCID: PMC2736612 DOI: 10.1063/1.3108523] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2009] [Accepted: 03/08/2009] [Indexed: 02/03/2023] Open
Abstract
A unified framework integrating the generalized ensemble sampling associated with the Tsallis weight [C. Tsallis, J. Stat. Phys. 52, 479 (1988)] and the replica exchange method (REM) has been proposed to accelerate the convergence of the conventional temperature REM (t-REM). Using the effective temperature formulation of the Tsallis weight sampling, it is shown that the average acceptance probability for configurational swaps between neighboring replicas in the combination of Tsallis weight sampling and REM (Tsallis-REM) is directly proportional to an overlap integral of the energy distributions of neighboring replicas as in the t-REM. Based on this observation, we suggest a robust method to select optimal Tsallis parameters in the conventional parametrization scheme and present new parametrization schemes for the Tsallis-REM, which significantly improves the acceptance of configurational swaps by systematically modulating energy overlaps between neighboring replicas. The distinguished feature of our method is that all relevant parameters in the Tsallis-REM are automatically determined from the equilibrium phase simulation using the t-REM. The overall performance of our method is explicitly demonstrated for various simulation conditions for the Lennard-Jones 31 atom clusters, exhibiting a double-funneled energy landscape.
Collapse
Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA.
| | | |
Collapse
|
7
|
Kim J, Keyes T. Influence of Go-Like Interactions on Global Shapes of Energy Landscapes in β-Barrel Forming Model Proteins: Inherent Structure Analysis and Statistical Temperature Molecular Dynamics Simulation. J Phys Chem B 2007; 112:954-66. [DOI: 10.1021/jp072872u] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215
| | - Thomas Keyes
- Department of Chemistry, Boston University, Boston, Massachusetts 02215
| |
Collapse
|
8
|
Kim J, Straub JE, Keyes T. Statistical temperature molecular dynamics: Application to coarse-grained β-barrel-forming protein models. J Chem Phys 2007; 126:135101. [PMID: 17430069 DOI: 10.1063/1.2711812] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Recently the authors proposed a novel sampling algorithm, "statistical temperature molecular dynamics" (STMD) [J. Kim et al., Phys. Rev. Lett. 97, 050601 (2006)], which combines ingredients of multicanonical molecular dynamics and Wang-Landau sampling. Exploiting the relation between the statistical temperature and the density of states, STMD generates a flat energy distribution and efficient sampling with a dynamic update of the statistical temperature, transforming an initial constant estimate to the true statistical temperature T(U), with U being the potential energy. Here, the performance of STMD is examined in the Lennard-Jones fluid with diverse simulation conditions, and in the coarse-grained, off-lattice BLN 46-mer and 69-mer protein models, exhibiting rugged potential energy landscapes with a high degree of frustration. STMD simulations combined with inherent structure (IS) analysis allow an accurate determination of protein thermodynamics down to very low temperatures, overcoming quasiergodicity, and illuminate the transitions occurring in folding in terms of the energy landscape. It is found that a thermodynamic signature of folding is significantly suppressed by accurate sampling, due to an incoherent contribution from low-lying non-native IS in multifunneled landscapes. It is also shown that preferred accessibility to such IS during the collapse transition is intimately related to misfolding or poor foldability.
Collapse
Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA.
| | | | | |
Collapse
|
9
|
Kim J, Straub JE, Keyes T. Statistical-temperature Monte Carlo and molecular dynamics algorithms. PHYSICAL REVIEW LETTERS 2006; 97:050601. [PMID: 17026089 DOI: 10.1103/physrevlett.97.050601] [Citation(s) in RCA: 70] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2006] [Indexed: 05/12/2023]
Abstract
A simulation method is presented that achieves a flat energy distribution by updating the statistical temperature instead of the density of states in Wang-Landau sampling. A novel molecular dynamics algorithm (STMD) applicable to complex systems and a Monte Carlo algorithm are developed from this point of view. Accelerated convergence for large energy bins, essential for large systems, is demonstrated in tests on the Ising model, the Lennard-Jones fluid, and bead models of proteins. STMD shows a superior ability to find local minima in proteins and new global minima are found for the 55 bead AB model in two and three dimensions. Calculations of the occupation probabilities of individual protein inherent structures provide new insights into folding and misfolding.
Collapse
Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, MA 02215, USA.
| | | | | |
Collapse
|
10
|
Kim JG, Fukunishi Y, Kidera A, Nakamura H. Generalized simulated tempering realized on expanded ensembles of non-Boltzmann weights. J Chem Phys 2004; 121:5590-601. [PMID: 15366981 DOI: 10.1063/1.1786578] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A generalized version of the simulated tempering operated in the expanded ensembles of non-Boltzmann weights has been proposed to mitigate a quasiergodicity problem occurring in simulations of rough energy landscapes. In contrast to conventional simulated tempering employing the Boltzmann weight, our method utilizes a parametrized, generalized distribution as a workhorse for stochastic exchanges of configurations and subensembles transitions, which allows a considerable enhancement for the rate of convergence of Monte Carlo and molecular dynamics simulations using delocalized weights. A feature of our method is that the exploration of the parameter space encouraging subensembles transitions is greatly accelerated using the dynamic update scheme for the weight via the average guide specific to the energy distribution. The performance and characteristic feature of our method have been validated in the liquid-solid transition of Lennard-Jones clusters and the conformational sampling of alanine dipeptide by taking two types of Tsallis [C. Tsallis, J. Stat. Phys. 52, 479 (1988)] expanded ensembles associated with different parametrization schemes.
Collapse
Affiliation(s)
- Jae Gil Kim
- Japan Biological Information Research Center, JBIC, Aomi 2-41-6, Koto-ku, Tokyo 135-0064, Japan.
| | | | | | | |
Collapse
|