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. 2009 Dec 7;131(21):214105.
doi: 10.1063/1.3267549.

Introducing sampling entropy in repository based adaptive umbrella sampling

Han Zheng  1 , Yingkai Zhang
Affiliations

Introducing sampling entropy in repository based adaptive umbrella sampling

Han Zheng et al. J Chem Phys. .

Abstract

Determining free energy surfaces along chosen reaction coordinates is a common and important task in simulating complex systems. Due to the complexity of energy landscapes and the existence of high barriers, one widely pursued objective to develop efficient simulation methods is to achieve uniform sampling among thermodynamic states of interest. In this work, we have demonstrated sampling entropy (SE) as an excellent indicator for uniform sampling as well as for the convergence of free energy simulations. By introducing SE and the concentration theorem into the biasing-potential-updating scheme, we have further improved the adaptivity, robustness, and applicability of our recently developed repository based adaptive umbrella sampling (RBAUS) approach [H. Zheng and Y. Zhang, J. Chem. Phys. 128, 204106 (2008)]. Besides simulations of one dimensional free energy profiles for various systems, the generality and efficiency of this new RBAUS-SE approach have been further demonstrated by determining two dimensional free energy surfaces for the alanine dipeptide in gas phase as well as in water.

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Figures

Figure 1
Figure 1
The flow chart for the RBAUS approach.
Figure 2
Figure 2
Schematic of the alanine dipeptide showing the ϕ and ψ angles.
Figure 3
Figure 3
The RMSD, NSE, and NECT factor curves for the double well model system with a barrier of 24 kcal/mol. The circle symbols represent the biasing-potential-updating points.
Figure 4
Figure 4
The RMSD, NSE, and NECT factor curves for the dissociation of a sodium chloride ion pair in aqueous solution. The circle symbols represent the biasing-potential-updating points.
Figure 5
Figure 5
Free energy surfaces of the alanine dipeptide system as a function of ϕ and ψ torsional angles in gas phase with 1 kcal/mol contour interval calculated by RBAUS-SE with 24 replica. Upper left: the free energy surface obtained after 10 ps simulation; upper right: the free energy surface obtained after 50 ps simulation; lower left: the free energy surface obtained after 100 ps simulation; lower right: the free energy surface obtained after 500 ps simulation.
Figure 6
Figure 6
Free energy surfaces of the alanine dipeptide system as a function of ϕ and ψ torsional angles in aqueous phase with 1 kcal/mol contour interval calculated by RBAUS-SE with 24 replica. Upper left: the free energy surface obtained after 10 ps simulation; upper right: the free energy surface obtained after 50 ps simulation; lower left: the free energy surface obtained after 100 ps simulation; lower right: the free energy surface obtained after 500 ps simulation.
Figure 7
Figure 7
The reference free energy surfaces of the alanine dipeptide system as a function of ϕ and ψ torsional angles in gas phase (left graph) and in aqueous phase (right graph) by biasing equilibrium umbrella sampling for 1 ns with 24 replica.
Figure 8
Figure 8
The RMSD, NSE, and NECT factor curves for the alanine dipeptide in gas phase. The circle symbols represent the biasing-potential-updating points.
Figure 9
Figure 9
The RMSD, NSE, and NECT factor curves for the alanine dipeptide in aqueous phase. The circle symbols represent the biasing-potential-updating points.
Figure 10
Figure 10
The RMSD curves for the alanine dipeptide in gas phase with both the original RBAUS-HHR approach and the current RBAUS-SE. The faster updating refers that the repository is updated every 1200 data points, which is similar to the repository updating frequency in previous studies (Ref. 27). The slower updating means that repository is updated every 12 000 data points.
Figure 11
Figure 11
The RMSD curves for the alanine dipeptide in aqueous phase with both the original RBAUS-HHR approach and the current RBAUS-SE. The faster updating refers that the repository is updated every 1200 data points, which is similar to the repository updating frequency in previous studies (Ref. 27). The slower updating means that repository is updated every 12 000 data points.
Figure 12
Figure 12
The correlation between the RMSD in simulated free energies and the NSE for all test systems based on RBAUS-SE simulations
Figure 13
Figure 13
The correlation between the RMSD in simulated free energies and the NSE for all test systems using equilibrium MD calculations with the inverse of the reference free energy surface as the biasing potential.
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