Free energy calculation from steered molecular dynamics simulations using Jarzynski’s equality

Park, Sang‐Hyun; Khalili‐Araghi, Fatemeh; Tajkhorshid, Emad; Schulten, Klaus

doi:10.1063/1.1590311

Cited by 753 publications

(1,017 citation statements)

References 33 publications

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“…The free energy calculation was based on Jarzynski's equality and the stiff-spring approximation described by Park and Schulten. 29 The free energy was calculated based on the first order cumulant expansion formula, the second order cumulant expansion formula, and the full exponential formula. The convergence of the free energy curves derived from the second order cumulant and the full exponential formula was used as an indication that the work distribution is Gaussian.…”

Section: Simulation Detailsmentioning

confidence: 99%

Self-Assembling Cyclic Peptides: Molecular Dynamics Studies of Dimers in Polar and Nonpolar Solvents

et al. 2006

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The self-assembly of cyclic D,L-R-peptides into hollow nanotubes is a crucial mechanistic step in their application as antibacterial and drug-delivery agents. To understand this process, molecular dynamics (MD) simulations were performed on dimers of cyclic peptides formed from cyclo [(-L-Trp-D-N-MeLeu-) 4 -] 2 and cyclo [(-L-Trp-D-Leu-) 4 -] 2 subunits in nonpolar (nonane) and polar (water) solvent. The dimers were observed to be stable only in nonpolar solvent over the full 10 ns length of the MD trajectory. The behavior of the dimers in different solvents is rationalized in terms of the intersubunit hydrogen bonding, hydrogen bonding with the solvent, and planarity of the rings. It is shown that the and ψ dihedral angles of a single uncapped ring in nonane lie in the -sheet region of the Ramachandran plot, and the ring stays in a flat conformation. Steered MD (SMD) simulations based on Jarzynski's equality were performed to obtain the potential of mean force as a function of the distance between the two rings of the capped dimer in nonane. It is also shown that a single peptide subunit prefers to reside close to the nonane/water interface rather than in bulk solvent because of the amphiphilic character of the peptide ring. The present MD results build the foundation for using MD simulations to study the mechanism of the formation of cyclic peptide nanotubes in lipid bilayers.

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Section: Simulation Detailsmentioning

confidence: 99%

Self-Assembling Cyclic Peptides: Molecular Dynamics Studies of Dimers in Polar and Nonpolar Solvents

et al. 2006

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“…Figure 5 plots the gradient of the estimated PMF using the various work paths and directly using the relation given in Equation 14 (the inset plots the raw PMF). The dashed lines in the plots correspond to the PMF estimated from 100 copies estimated along a single (estimated) diffusion model; the solid black line corresponds to that of pooling the work paths from all synthetic trajectories together and then estimating the resulting PMF through evaluating the empirical exponential average and the solid red line plots the "exact" results [3]. We could easily increase the number of synthetic paths in an attempt to (at a relatively cheap computational cost) to create a larger number of synthetic trajectories in an attempt to get the large sample sizes needed to safely calculate an exponential average; however, a major point of this paper is that it more important to characterize the distribution of SDE coefficient functions than it is to sample the work paths that come from a small set of estimated SDEs.…”

Section: B Synthetic Work and Approximating The Pmfmentioning

confidence: 99%

“…The goal is to obtain a stochastic differential equation (SDE), with nonlinear coefficient functions, that accurately describes the dynamics of a single trajectory associated with the time series output of a steered molecular dynamics (SMD) simulation. The system used to illustrate the approach is the well-studied example of using constant velocity SMD to simulate the unravelling (in vacuum) of deca-alanine at constant temperature (extensive simulation results exist for this system because it is a "fast-folder" [3]). …”

Section: Introductionmentioning

confidence: 99%

“…This type of multiscale modeling approach often requires one to compute the potential of mean force (PMF) associated with the system. One technique for calculating the PMF associated with a set of well selected reaction coordinates [3] is to appeal to the Jarzynski work theorem [7] using the path dependent work (measured from the SMD simulations) in order to reconstruct the PMF associated with the selected reaction coordinate(s) of the system. To do this, one typically needs to assume variety of things about the system a priori [7,8]; even if all of the assumptions hold true for the selected reaction coordinate(s) of the system, calculating the PMF can be difficult in practice due in part to the number of sample paths needed in order to accurately approximate the PMF from atomistic simulation trajectories [6,9].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the use of local diffusion models for path ensemble averaging in potential of mean force computations

Calderon

2007

The Journal of Chemical Physics

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We use a constant velocity steered molecular dynamics (SMD) simulation of the stretching of deca-alanine in vacuum to demonstrate a technique that can be used to create surrogate stochastic processes using the time series that come out of SMD simulations. The surrogate processes are constructed by first estimating a sequence of local parametric models along a SMD trajectory and then a single global model is constructed by piecing the local models together through smoothing splines (estimation is made computationally feasible by likelihood function approximations). The calibrated surrogate models are then "bootstrapped" in order to simulate the large number of work paths typically needed to construct a potential of mean force (PMF) by appealing to Jarzynski's work theorem. When this procedure is repeated for a small number of SMD paths, it is shown that the global models appear to come from a single family of closely related diffusion processes. Possible techniques for exploiting this observation are also briefly discussed. The findings of this paper have potential relevance to computationally expensive computer simulations and experimental works involving optical tweezers where it difficult to collect a large number of samples, but possible to sample accurately and frequently in time.

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“…This could be alleviated by pulling at a slower speed that approaches the fully reversible regime, but the optimal speed is estimated to be about 0.0001 Å/ps. 39 Such a simulation would require more than 500 ns of total simulation time. Given the availability of a reaction path from the forward SMD runs, it is possible to apply umbrella sampling techniques to extract the PMF without multiple SMD pulls.…”

Section: Umbrella Samplingmentioning

confidence: 99%

Computational Modeling of Poly(alkylthiophene) Conductive Polymer Insertion into Phospholipid Bilayers

2007

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We have previously demonstrated that some poly(alkylthiophenes) (PATs) are able to increase the electrical conductance of unsupported phospholipid bilayers and have hypothesized that this effect is due to the ability of some PAT side chains to permit stable insertion into the bilayer. We have further proposed the development of long-term intracellular electrodes based on that phenomenon. In this article, we apply molecular dynamics techniques to study the insertion of two model PATs into a patch of a lipid bilayer. Steered molecular dynamics is used to obtain potential trajectories of insertion, followed by umbrella sampling to determine the free-energy change upon insertion. Our results indicate that both branched-side-chain poly(3-(2-ethylhexyl)thiophene) (EHPT) and straightside-chain poly(3-hexylthiophene) (HPT) are able to enter the bilayer but only EHPT can cross the center of the membrane and establish an electrical bridge. HPT penetrates the head groups but is not able to enter the alkyl tail phase. These findings support the feasibility of our electrode concept and raise questions regarding the mechanisms by which branched side chains grant PATs greater solubility in a lipid bilayer environment. The parameters and methods used in this study establish a novel framework for studying these and similar systems, and the results hold promise for the use of EHPT in biosensing and neural interfacing.

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Free energy calculation from steered molecular dynamics simulations using Jarzynski’s equality

Cited by 753 publications

References 33 publications

Self-Assembling Cyclic Peptides: Molecular Dynamics Studies of Dimers in Polar and Nonpolar Solvents

Self-Assembling Cyclic Peptides: Molecular Dynamics Studies of Dimers in Polar and Nonpolar Solvents

On the use of local diffusion models for path ensemble averaging in potential of mean force computations

Computational Modeling of Poly(alkylthiophene) Conductive Polymer Insertion into Phospholipid Bilayers

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