^{1,a)}, Donald Hamelberg

^{1}and J. Andrew McCammon

^{1}

### Abstract

Molecular dynamics (MD) simulation is the standard computational technique used to obtain information on the time evolution of the conformations of proteins and many other molecular systems. However, for most biological systems of interest, the time scale for slow conformational transitions is still inaccessible to standard MD simulations. Several sampling methods have been proposed to address this issue, including the acceleratedmolecular dynamics method. In this work, we study the extent of sampling of the phi/psi space of alanine dipeptide in explicit water using acceleratedmolecular dynamics and present a framework to recover the correct kinetic rate constant for the helix to beta-strand transition. We show that the accelerated MD can drastically enhance the sampling of the phi/psi conformational phase space when compared to normal MD. In addition, the free energy density plots of the phi/psi space show that all minima regions are accurately sampled and the canonical distribution is recovered. Moreover, the kinetic rate constant for the helix to beta-strand transition is accurately estimated from these simulations by relating the diffusion coefficient to the local energetic roughness of the energy landscape. Surprisingly, even for such a low barrier transition, it is difficult to obtain enough transitions to accurately estimate the rate constant when one uses normal MD.

This work was supported in part by grants from NSF, NIH, the Center for Theoretical Biological Physics, the National Biomedical Computation Resource, San Diego Supercomputing Center, and Accelrys, Inc.

INTRODUCTION

COMPUTATIONAL DETAILS

RESULTS AND DISCUSSION

Enhanced sampling and correct canonical ensemble

Estimating kinetic rate constant

CONCLUSION

### Key Topics

- Molecular dynamics
- 41.0
- Potential energy surfaces
- 18.0
- Peptides
- 17.0
- Conformational dynamics
- 16.0
- Free energy
- 14.0

## Figures

Alanine dipeptide molecule.

Alanine dipeptide molecule.

Plot of psi (left) and phi (right) angles of the alanine dipeptide during the normal MD simulations at (a) and (b) .

Plot of psi (left) and phi (right) angles of the alanine dipeptide during the normal MD simulations at (a) and (b) .

Plot of psi (left) and phi (right) angles of the alanine dipeptide during the accelerated MD simulations: (a) , ; (b) , ; and (c) , .

Plot of psi (left) and phi (right) angles of the alanine dipeptide during the accelerated MD simulations: (a) , ; (b) , ; and (c) , .

Plot of psi (left) and phi (right) angles of the alanine dipeptide during the accelerated MD simulations: (a) , ; (b) , ; and (c) , .

(Color) Free energy plots for the transitions along the phi and psi angles of the alanine dipeptide: (left) contour density plot and (right) surface plot in units of .

(Color) Free energy plots for the transitions along the phi and psi angles of the alanine dipeptide: (left) contour density plot and (right) surface plot in units of .

(Color) Free energy plots for the transitions along the phi and psi angles of the alanine dipeptide: (left) contour density plot and (right) surface plot in units of .

Unweighted free energy profile of psi torsional angle obtained from accelerated MD at eight different values of . The lower the barrier, the smaller the .

Unweighted free energy profile of psi torsional angle obtained from accelerated MD at eight different values of . The lower the barrier, the smaller the .

(Color) Exponential decay of the probability distribution of the survival time in the free energy well defined by calculated from normal MD at and accelerated MD with eight different values of .

(Color) Exponential decay of the probability distribution of the survival time in the free energy well defined by calculated from normal MD at and accelerated MD with eight different values of .

Plot calculated from eight accelerated MD simulations relating the escaping rate , barrier height , and angular frequencies and with the boost potential .

Plot calculated from eight accelerated MD simulations relating the escaping rate , barrier height , and angular frequencies and with the boost potential .

## Tables

Summary of the data collected from the normal MD simulations (at 300 and ) and accelerated MD simulations at different values of ..

Summary of the data collected from the normal MD simulations (at 300 and ) and accelerated MD simulations at different values of ..

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