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Sampling of slow diffusive conformational transitions with accelerated molecular dynamics
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/content/aip/journal/jcp/127/15/10.1063/1.2789432
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Figures

Image of FIG. 1.

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FIG. 1.

(Color) Schematic representation of a 1D potential (solid line) and three modified potentials (dashed lines) with the same boost potential with three different values of . The larger becomes, the closer the modified potential gets to the original potential. The red dashed potential has the smallest value of , and the green dashed potential has the largest value of .

Image of FIG. 2.

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FIG. 2.

(Color) The phi/psi free energy plot in of alanine dipeptide in explicit water molecules sampled with normal MD simulation (a), accelerated MD simulation wherein the boost potential is applied only to the torsional terms (aMDt) (b), and accelerated MD simulation wherein the boost potential is applied to the total potential function (aMDT) (c).

Image of FIG. 3.

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FIG. 3.

Radial distribution functions between the oxygen atoms of the water molecules and all of the atoms of alanine dipeptide, including the hydrogen atoms (first column) and the hydrogen atoms of the water molecules and all of the atoms of alanine dipeptide, including the hydrogen atoms (second column) averaged over the entire normal MD simulation (upper row), accelerated MD simulation wherein the boost potential is applied only to the torsional term (aMDt) (middle row), and accelerated MD simulation wherein the boost potential is applied to the total potential function (aMDT) (lower row). The error bars, which are not visible, represent the standard error and were estimated by subdividing the whole trajectories into four equal parts.

Image of FIG. 4.

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FIG. 4.

(Color) The mean-square displacement of the water molecules around alanine-dipeptide (top) and rotational autocorrelation functions of alanine-dipeptide in water (bottom) during the normal MD simulation (black), the accelerated MD simulation wherein the boost potential is applied only to the torsional term (aMDt) (red), and the accelerated MD simulation wherein the boost potential is applied to the total potential function (aMDT) (green). The rotational autocorrelation function was estimated by calculating the autocorrelation function of the vector perpendicular to the plane formed by the backbone atoms C, CA, and N of alanine.

Image of FIG. 5.

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FIG. 5.

(Color) The phi/psi free energy plot in of alanine dipeptide in explicit water molecules sampled with the accelerated MD simulations wherein the boost potential is applied separately to the torsional terms and to the total potential energy function (aMDtT). aMDtT-I (a) and aMDtT-II (b) represent two different conditions of the boost potential applied to the total potential function. aMDtT-I and aMDtT-II have the same boost potential applied to the torsional terms.

Image of FIG. 6.

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FIG. 6.

Radial distribution functions between the oxygen atoms of the water molecules and all of the atoms of alanine dipeptide, including the hydrogen atoms (first column) and the hydrogen atoms of the water molecules and all of the atoms of alanine dipeptide, including the hydrogen atoms (second column) averaged over the entire dual boosting accelerated MD simulations wherein the boost potential is applied separately to the torsional terms and to the total potential energy function (aMDtT), aMDtT-I (upper row) and aMDtT-II (lower row). The error bars, which are not visible, represent the standard error and were estimated by subdividing the whole trajectories into four equal parts.

Image of FIG. 7.

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FIG. 7.

(Color) The mean-square displacement of the water molecules around alanine-dipeptide (top) and rotational autocorrelation functions of alanine-dipeptide in water (bottom) during the normal MD simulation (black) and in the dual boosting accelerated MD simulations wherein the boost potential is applied separately to the torsional terms and to the total potential energy function (aMDtT), aMDtT-I (blue), and aMDtT-II (violet).

Image of FIG. 8.

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FIG. 8.

(Color) Molecular model of . The Cys and Trp residues at the ends are shown with van der Waals spheres.

Image of FIG. 9.

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FIG. 9.

(Color) The end-to-end distance as a function of simulation time (first column), end-to-end distance distribution (second column), and survival probabilities of the loop-closure times (third column) of in explicit water in the normal MD simulation (black), the accelerated MD simulation wherein the boost potential is applied only to the torsional terms (aMDt) (red), and the dual boosting accelerated MD simulations wherein the boost potential is applied separately to the torsional terms and to the total potential energy function (aMDtT), aMDtT-I (blue), and aMDtT-II (violet). The normal MD was carried out for , and the aMD simulations were carried out for . Only the first of each simulation are shown. The error on the loop-closure time is one standard deviation from the mean and is estimated by subdividing the trajectory into five equal parts.

Image of FIG. 10.

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FIG. 10.

(Color) Convergence of the normal MD simulation and the aMD simulations in explicit water. The loop-closure time of calculated as the simulations progressed at time increments for the normal MD simulation (black), the accelerated MD simulation wherein the boost potential is applied only to the torsional terms (aMDt) (red), the dual boosting accelerated MD simulations wherein the boost potential is applied separately to the torsional terms and to the total potential energy function (aMDtT), aMDtT-I (blue), and aMDtT-II (violet).

Image of FIG. 11.

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FIG. 11.

(Color) Phi/psi angles sampled by the six central residues of in explicit water for the normal MD simulation (black), the accelerated MD simulation wherein the boost potential is applied only to the torsional terms (aMDt) (red), and the dual boosting accelerated MD simulations wherein the boost potential is applied separately to the torsional terms and to the total potential energy function (aMDtT), aMDtT-I (blue), and aMDtT-II (violet).

Image of FIG. 12.

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FIG. 12.

(Color) Convergence of the average end-to-end distance of the normal MD simulation and the aMD simulations in explicit water. The average end-to-end distance of calculated as the simulations progressed at time increments for the normal MD simulation (black), the accelerated MD simulation wherein the boost potential is applied only to the torsional terms (aMDt) (red), the dual boosting accelerated MD simulations wherein the boost potential is applied separately to the torsional terms and to the total potential energy function (aMDtT), aMDtT-I (blue), and aMDtT-II (violet).

Image of FIG. 13.

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FIG. 13.

The end-to-end distance as a function of simulation time (first column), end-to-end distance distribution (second column), and survival probabilities of the loop-closure times (third column) of simulated using the Langevin equation with a generalized Born solvation model without the apolar solvation (SA) term added to the potential function and a collision frequency of carried out for of normal MD (top), with the SA term added to the potential function and with a collision frequency of also carried out for of normal MD (middle), and with the SA term included in the potential function and with a collision frequency of carried out for of normal MD (bottom). Only the first of each simulation are shown. The error on the loop-closure time is one standard deviation from the mean and is estimated by subdividing the trajectory into five equal parts.

Image of FIG. 14.

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FIG. 14.

Convergence of the normal MD simulations with implicit solvation. The loop-closure time of calculated as the simulations progressed at time increments for the simulation with the SA term added to the potential function and with a collision frequency of (circles), and the simulation with the SA term included in the potential function and with a collision frequency of (triangles).

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/content/aip/journal/jcp/127/15/10.1063/1.2789432
2007-10-15
2014-04-18

Abstract

Slow diffusive conformational transitions play key functional roles in biomolecular systems. Our ability to sample these motions with molecular dynamics simulation in explicit solvent is limited by the slow diffusion of the solvent molecules around the biomolecules. Previously, we proposed an acceleratedmolecular dynamics method that has been shown to efficiently sample the torsional degrees of freedom of biomolecules beyond the millisecond timescale. However, in our previous approach, large-amplitude displacements of biomolecules are still slowed by the diffusion of the solvent. Here we present a unified approach of efficiently sampling both the torsional degrees of freedom and the diffusive motions concurrently. We show that this approach samples the configuration space more efficiently than normal molecular dynamics and that ensemble averages converge faster to the correct values.

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Scitation: Sampling of slow diffusive conformational transitions with accelerated molecular dynamics
http://aip.metastore.ingenta.com/content/aip/journal/jcp/127/15/10.1063/1.2789432
10.1063/1.2789432
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