Walking freely in the energy and temperature space by the modified replica exchange molecular dynamics method

Chen, Changjun; Huang, Yanzhao

doi:10.1002/jcc.24371

Cited by 4 publications

(5 citation statements)

References 56 publications

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“…This also highlights that converged free energy differences are not necessarily an indicator for sufficient sampling. However, this feature can be exploited in a more general fashion by adjusting the mixture of seed conformations with replica reservoirs − and frozen replica , methods.…”

Section: Discussionmentioning

confidence: 99%

Overcoming Orthogonal Barriers in Alchemical Free Energy Calculations: On the Relative Merits of λ-Variations, λ-Extrapolations, and Biasing

Hahn

König

Hünenberger

2020

J. Chem. Theory Comput.

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Alchemical free energy calculations using conventional molecular dynamics and thermodynamic integration rely on simulations performed at fixed values of the coupling parameter λ. When multiple conformers in equilibrium are separated by high barriers in the space orthogonal to λ, proper convergence may require extremely long simulations. Four main strategies can be employed to address this orthogonal-sampling problem: (a) λ-variations, where λ can change along the simulations to circumvent barriers; (b) λ-extrapolations, where statistical information is transferred between λ-points; (c) specific biasing, where orthogonal barriers are reduced using a biasing potential designed specifically for the system; and (d) generic biasing, where orthogonal barriers are reduced using a generic approach. Here, we investigate the relative merits of the first three strategies considering two benchmark systems. The KXK system involves a mutation of the central residue in a tripeptide to a glycine and the XTP system involves a hydrogen-to-bromine mutation in the base of a nucleotide. Three sampling methods are compared, the latter two involving λ-variations: molecular dynamics simulations with fixed λ-points, Hamiltonian replica exchange, and the recently introduced conveyor belt method. Two free energy estimators are applied, the second one involving λ-extrapolations: thermodynamic integration with Simpson quadrature and the multistate Bennett acceptance ratio. Finally, three different seeding schemes are considered for the generation of the initial configurations. For both benchmark systems, λ-extrapolations are found to provide little gain, whereas λ-variations can significantly enhance the convergence. They are sufficient on their own if the orthogonal barriers are low in at least one state (e.g., the glycine state in KXK). However, if the orthogonal barriers are high over the entire λ-range (e.g., the XTP system), λ-variations are only effective when applied together with a specific biasing for introducing such a low-barrier state.

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Section: Discussionmentioning

confidence: 99%

Overcoming Orthogonal Barriers in Alchemical Free Energy Calculations: On the Relative Merits of λ-Variations, λ-Extrapolations, and Biasing

Hahn

König

Hünenberger

2020

J. Chem. Theory Comput.

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“…Mixing REMD is implemented by Fortran90 language. Its REMD code and ABMD code have been written separately to work with the Tinker software in our previous papers . Now they are integrated together as a module and inserted into the AMBER software .…”

Section: Methodsmentioning

confidence: 99%

“…Its REMD code and ABMD code have been written separately to work with the Tinker software [75] in our previous papers. [76,77] Now they are integrated together as a module and inserted into the AMBER software. [71] For more discussions on the present method, please see the support information (Appendix S1)…”

Section: Methodsmentioning

confidence: 99%

Combining the biased and unbiased sampling strategy into one convenient free energy calculation method

et al. 2019

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Constructing a free energy landscape for a large molecule is difficult. One has to use either a high temperature or a strong driving force to enhance the sampling on the free energy barriers. In this work, we propose a mixed method that combines these two kinds of acceleration strategies into one simulation. First, it applies an adaptive biasing potential to some replicas of the molecule. These replicas are particularly accelerated in a collective variable space. Second, it places some unbiased and exchangeable replicas at various temperature levels. These replicas generate unbiased sampling data in the canonical ensemble. To improve the sampling efficiency, biased replicas transfer their state variables to the unbiased replicas after equilibrium by Monte Carlo trial moves. In comparison to previous integrated methods, it is more convenient for users. It does not need an initial reference biasing potential to guide the sampling of the molecule. And it is also unnecessary to insert many replicas for the requirement of passing the free energy barriers. The free energy calculation is accomplished in a single stage. It samples the data as fast as a biased simulation and it processes the data as simple as an unbiased simulation. The method provides a minimalist approach to the construction of the free energy landscape. © 2019 Wiley Periodicals, Inc.

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“…Although the trajectories at each λ-point become discontinuous, the TI-like statistics is preserved, and the data can be analyzed in the same way as for TI. Recent extensions of the method involve in particular the consideration of more advanced exchange schemes, − of replica reservoirs, − of frozen replicas, , of heating-quenching steps between the sampling periods, ,− of the infinite-swapping limit, ,− and of generalized-ensemble distributions. − They also include the implementation of λ-moves that go beyond pairwise swaps with a selection based on a Suwa-Todo criterion, − as implemented in the HRP method. − In the latter case, enabling arbitrary permutations and abandoning the detailed-balance constraint lead to a significant increase in the probability of exchange acceptance.…”

Section: Introductionmentioning

confidence: 99%

Alchemical Free-Energy Calculations by Multiple-Replica λ-Dynamics: The Conveyor Belt Thermodynamic Integration Scheme

Hahn

Hünenberger

2019

J. Chem. Theory Comput.

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A new method is proposed to calculate alchemical free-energy differences based on molecular dynamics (MD) simulations, called the conveyor belt thermodynamic integration (CBTI) scheme. As in thermodynamic integration (TI), K replicas of the system are simulated at different values of the alchemical coupling parameter λ. The number K is taken to be even, and the replicas are equally spaced on a forward-turnbackward-turn path, akin to a conveyor belt (CB) between the two physical end-states; and as in λ-dynamics (λD), the λ-values associated with the individual systems evolve in time along the simulation. However, they do so in a concerted fashion, determined by the evolution of a single dynamical variable Λ of period 2π controlling the advance of the entire CB. Thus, a change of Λ is always associated with K/2 equispaced replicas moving forward and K/2 equispaced replicas moving backward along λ. As a result, the effective free-energy profile of the replica system along Λ is periodic of period 2πK −1 , and the magnitude of its variations decreases rapidly upon increasing K, at least as K −1 in the limit of large K. When a sufficient number of replicas is used, these variations become small, which enables a complete and quasi-homogeneous coverage of the λ-range by the replica system, without application of any biasing potential. If desired, a memory-based biasing potential can still be added to further homogenize the sampling, the preoptimization of which is computationally inexpensive. The final free-energy profile along λ is calculated similarly to TI, by binning of the Hamiltonian λ-derivative as a function of λ considering all replicas simultaneously, followed by quadrature integration. The associated quadrature error can be kept very low owing to the continuous and quasihomogeneous λ-sampling. The CBTI scheme can be viewed as a continuous/deterministic/dynamical analog of the Hamiltonian replica-exchange/permutation (HRE/HRP) schemes or as a correlated multiple-replica analog of the λD or λ-local elevation umbrella sampling (λ-LEUS) schemes. Compared to TI, it shares the advantage of the latter schemes in terms of enhanced orthogonal sampling, i.e. the availability of variable-λ paths to circumvent conformational barriers present at specific λ-values. Compared to HRE/HRP, it permits a deterministic and continuous sampling of the λ-range, is expected to be less sensitive to possible artifacts of the thermo-and barostating schemes, and bypasses the need to carefully preselect a λ-ladder and a swapping-attempt frequency. Compared to λ-LEUS, it eliminates (or drastically reduces) the dead time associated with the preoptimization of a biasing potential. The goal of this article is to provide the mathematical/physical formulation of the proposed CBTI scheme, along with an initial application of the method to the calculation of the hydration free energy of methanol.

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Walking freely in the energy and temperature space by the modified replica exchange molecular dynamics method

Cited by 4 publications

References 56 publications

Overcoming Orthogonal Barriers in Alchemical Free Energy Calculations: On the Relative Merits of λ-Variations, λ-Extrapolations, and Biasing

Overcoming Orthogonal Barriers in Alchemical Free Energy Calculations: On the Relative Merits of λ-Variations, λ-Extrapolations, and Biasing

Combining the biased and unbiased sampling strategy into one convenient free energy calculation method

Alchemical Free-Energy Calculations by Multiple-Replica λ-Dynamics: The Conveyor Belt Thermodynamic Integration Scheme

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