Multiple “time step” Monte Carlo

Hetényi, Balázs; Bernacki, Katarzyna; Berne, B. J.

doi:10.1063/1.1512645

Cited by 53 publications

(65 citation statements)

References 14 publications

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“…A second class of strategies attempts directly to enhance sampling of atomic-resolution models, including multiple time step methods [5,6], replica exchange [7]/parallel tempering [8,9,10], and other generalized ensemble techniques [11]. Parallel tempering (PT), which employs a ladder of replicas simulated at increasing temperatures, is widely used for state-of-the-art molecular dynamics simulations, but presently is limited to small proteins [12], as the resources required increase rapidly with the system size.…”

Section: Pacs Numbersmentioning

confidence: 99%

Resolution Exchange Simulation

2006

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We extend replica exchange simulation in two ways, and apply our approaches to biomolecules. The first generalization permits exchange simulation between models of differing resolutioni.e., between detailed and coarse-grained models. Such "resolution exchange" can be applied to molecular systems or spin systems. The second extension is to "pseudo-exchange" simulations, which require little CPU usage for most levels of the exchange ladder and also substantially reduces the need for overlap between levels. Pseudo exchanges can be used in either replica or resolution exchange simulations. We perform efficient, converged simulations of a 50-atom peptide to illustrate the new approaches.Accepted for publication in physical review letters. PACS numbers:The simulation of biomolecules with 10 4 − 10 5 degrees of freedom has become routine, thanks to the accessibility of powerful computing resources, the development of reliable simulation software, and standardized empirical potential energy functions. For many biological applications, such as binding free energy estimation, it is desirable to generate an equilibrated ensemble of conformations. In principle, standard Monte Carlo (MC) and molecular dynamics (MD) algorithms are perfectly ergodic, and therefore will eventually generate such ensembles. In practice, the µ sec − sec timescale, which describes biologically relevant fluctuations, is not within reach of computation even for small proteins.Two broad strategies have been developed to address this problem. In one approach, dating to the earliest computational studies of proteins[1, 2], coarse-grained protein representations are adopted. This strategy continues to be popular [3,4].A second class of strategies attempts directly to enhance sampling of atomic-resolution models, including multiple time step methods [5,6], replica exchange [7]/parallel tempering [8,9,10], and other generalized ensemble techniques [11]. Parallel tempering (PT), which employs a ladder of replicas simulated at increasing temperatures, is widely used for state-of-the-art molecular dynamics simulations, but presently is limited to small proteins [12], as the resources required increase rapidly with the system size.This Letter presents two new tools for biomolecular simulation, by extending the PT approach and exploiting the speed of coarse-grained models. The first extension is a "resolution exchange" (res-ex) algorithm whichinstead of using high-temperature simulation to increase sampling, as does PT -uses inexpensive coarse-grained * elyman@ccbb.pitt.edu † dmz@ccbb.pitt.edu models to cross barriers. Boltzmann-weighted ensembles are produced. The algorithm is implemented in close analogy to PT, and can also be applied to magnetic systems (e.g., the Ising model). The res-ex approach is natural for proteins, and indeed the kernel of the idea was suggested in the early days of protein simulation [1]. More recently, the approach has been implemented in an ad hoc way, without proper statistical weighting [3]. A rigorous method to calculate free en...

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Section: Pacs Numbersmentioning

confidence: 99%

Resolution Exchange Simulation

2006

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“…NpT, in a relatively straightforward manner. On the other hand, an efficient sampling of phase space in MC requires smart and system dependent trial moves [30][31][32][33][34] , making the application of the method more intricate than molecular dynamics where configurational sampling follows a general principle. Within the framework of MC, McGrath and coworkers 27 reported the first results from first-principles simulations of liquid water in the isobaric-isothermal ensemble at ambient pressure.…”

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Bulk Liquid Water at Ambient Temperature and Pressure from MP2 Theory

Ben

Schönherr

Hutter

et al. 2013

J. Phys. Chem. Lett.

138

112

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MP2 provides a good description of hydrogen bonding in water clusters and includes longrange dispersion interactions without the need to introduce empirical elements in the description of the interatomic potential. To assess its performance for bulk liquid water under ambient conditions, an isobaric-isothermal (NpT) Monte Carlo simulation at the second-order Moller-Plesset perturbation theory level (MP2) has been performed. The obtained value of the water density is excellent (1.02 g/mL), and the calculated radial distribution functions are in fair agreement with experimental data. The MP2 results are compared to a few density functional approximations, including semilocal functionals, hybrid functionals, and functionals including empirical dispersion corrections. These results demonstrate the feasibility of directly sampling the potential energy surface of condensed-phase systems using correlated wave function theory, and their quality paves the way for further applications. Understanding the structural and electronic properties of liquid water at ambient conditions is a major challenge in condensed matter simulations. Water is a crucial ingredient for a large variety of systems of prime importance in basic chemistry, biology, and physics, as well as in the applied fields of catalysis and energy production. The water molecule has a large dipole moment and polarizability, is a multiple hydrogen donor and acceptor and can easily build network structures.The total cohesive energy in the condensed phase is, as a consequence of these properties, a sum of many weak interactions. Theoretical models face therefore the challenge to describe many different effects and their subtle interplay at a high precision. The development of sophisticated empirical potentials for water 1-10 , allowed to gain insights into water's behavior and its thermodynamic properties [11][12][13] , such as, density maxima, heat capacity and effects of supercooling. However, empirical models lack transferability and might fail if used under conditions away from their fitting range. Most importantly, as soon as water takes an active role in a chemical process, either as a strongly interacting solvent, or for example as a source of protons, the electronic properties of the water molecule need to be taken into account. In this respect, first-principles methods offer the possibility to describe all the underlying physics on the same footing, simplifying the treatment of intra-and inter-molecular interactions. The capability to reproduce properties of complex systems such as liquid water can therefore be used to judge the sophistication and predictive power of a given quantum mechanical model. Density functional theory (DFT) is the most used quantum mechanical method employed for studying physical and chemical properties of condensed phase systems. Many DFT based simulation of bulk water have been reported in the literature, and in this context three main methods of sampling the phase space can be recognized 14 : the Car-Parrinello molecula...

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“…Expanding this expression gives: (32) where α(j|i) and acc L (j|i) are the selection and acceptance probabilities of outer state j from state i. Following the MTS-MC derivation, 35 the probability of selecting state j from state i is given by the following: (33) where the above transition probability is the product of the individual transition probabilities of the inner loop (34) In the short-range, or inner loop of sampling, neither the switching function nor the Born radii are updated, so that each step obeys the following detailed balance relation: (35) The transition between outer states j and i obeys the following detailed balance relation: (36) Combining eqs 32-35 and solving for the ratio of acceptance probabilities gives the following: (37) Protocols A and B follow the same updating scheme for the switching functions. The acceptance probability for protocol A is expressed in eq 17 as follows: (38) The ratio of eqs 37 and 38 is unity (39) and therefore, the sampling scheme described by eqs 37 and 38 rigorously obeys detailed balance.…”

Section: Discussionmentioning

confidence: 99%

Multiscale Monte Carlo Sampling of Protein Sidechains: Application to Binding Pocket Flexibility

Nilmeier

Jacobson

2008

J. Chem. Theory Comput.

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We present a Monte Carlo sidechain sampling procedure and apply it to assessing the flexibility of protein binding pockets. We implemented a multiple "time step" Monte Carlo algorithm to optimize sidechain sampling with a surface generalized Born implicit solvent model. In this approach, certain forces (those due to long-range electrostatics and the implicit solvent model) are updated infrequently, in "outer steps", while short-range forces (covalent, local nonbonded interactions) are updated at every "inner step". Two multistep protocols were studied. The first protocol rigorously obeys detailed balance, and the second protocol introduces an approximation to the solvation term that increases the acceptance ratio. The first protocol gives a 10-fold improvement over a protocol that does not use multiple time steps, while the second protocol generates comparable ensembles and gives a 15-fold improvement. A range of 50-200 inner steps per outer step was found to give optimal performance for both protocols. The resultant method is a practical means to assess sidechain flexibility in ligand binding pockets, as we illustrate with proof-of-principle calculations on six proteins: DB3 antibody, thermolysin, estrogen receptor, PPAR-γ, PI3 kinase, and CDK2. The resulting sidechain ensembles of the apo binding sites correlate well with known induced fit conformational changes and provide insights into binding pocket flexibility.

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Multiple “time step” Monte Carlo

Cited by 53 publications

References 14 publications

Resolution Exchange Simulation

Resolution Exchange Simulation

Bulk Liquid Water at Ambient Temperature and Pressure from MP2 Theory

Multiscale Monte Carlo Sampling of Protein Sidechains: Application to Binding Pocket Flexibility

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