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Understanding free-energy perturbation calculations through a model of harmonic oscillators: Theory and implications to improve the sampling efficiency by molecular simulation
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10.1063/1.3511703
/content/aip/journal/jcp/133/24/10.1063/1.3511703
http://aip.metastore.ingenta.com/content/aip/journal/jcp/133/24/10.1063/1.3511703

Figures

Image of FIG. 1.
FIG. 1.

Analytical solutions of the reference and target energy-space distributions of the four harmonic cases. The red and blue contours in each case, obtained from the distributions p A (U A ,W) and p B (U B ,W), represent the reference energy spaces of system A and system B, respectively. The cyan and magenta contours (e.g., in cases B and D, they are located to the right of the blue and the red contours), obtained from p A (U A ,W) × e βW and p B (U B ,W) × e + βW , represent the target energy spaces of system A and system B, respectively. The two insets show the rescaled plots of cases A and D. U and W have units of kT.

Image of FIG. 2.
FIG. 2.

Comparison of p A (U A ,W) and p B (U B ,W) distributions obtained by the different methods for the harmonic case A. All the yellow distributions represent the analytical solutions. The red and blue distributions are obtained by conducting the sampling in the reference systems A and B, respectively. The method used for obtaining the distribution is labeled above each distribution. The contours in the figure have been described in Fig. 1, here the red and cyan contours are plotted together and the blue and magenta contours are plotted together. U and W have units of kT.

Image of FIG. 3.
FIG. 3.

Comparison of the free energies calculated by the different methods for the harmonic case A. All the symbols represent the average results of ten independent calculations with the error bars attached to them. The symbols colored red or blue represent the results calculated by the corresponding red or blue distributions plotted in Fig. 2.

Image of FIG. 4.
FIG. 4.

Comparison of p A (U A ,W) and p B (U B ,W) distributions obtained by the different methods for the harmonic case B. The symbol descriptions are the same as in Fig. 2.

Image of FIG. 5.
FIG. 5.

Comparison of the free energies calculated by the different methods for the harmonic case B. The symbol descriptions are the same as in Fig. 3 except that the symbols colored red or blue represent the results calculated by the corresponding red or blue distributions plotted in Fig. 4.

Image of FIG. 6.
FIG. 6.

Comparison of p A (U A ,W) and p B (U B ,W) distributions obtained by the different methods for the harmonic case C. The symbol descriptions are the same as in Fig. 2.

Image of FIG. 7.
FIG. 7.

Comparison of the free energies calculated by the different methods for the harmonic case C. The symbol descriptions are the same as in Fig. 3 except that the symbols colored red or blue represent the results calculated by the corresponding red or blue distributions plotted in Fig. 6.

Image of FIG. 8.
FIG. 8.

Comparison of p A (U A ,W) and p B (U B ,W) distributions obtained by the different methods for the harmonic case D. The symbol descriptions are the same as in Fig. 2.

Image of FIG. 9.
FIG. 9.

Comparison of the free energies calculated by the different methods for the harmonic case D. The symbol descriptions are the same as in Fig. 3 except that the symbols colored red or blue represent the results calculated by the corresponding red or blue distributions plotted in Fig. 8.

Image of FIG. 10.
FIG. 10.

Schematic plot of alanine dipeptide and the ϕ, ψ dihedral angles.

Image of FIG. 11.
FIG. 11.

The ϕψ free-energy surface of alanine dipeptide in gas phase calculated by the Metropolis-sampling method M1. Energy levels are in kcal/mol.

Image of FIG. 12.
FIG. 12.

The free-energy surface of alanine dipeptide in gas phase calculated by the distribution method M4. Energy levels are in kcal/mol.

Image of FIG. 13.
FIG. 13.

The free-energy surface of alanine dipeptide in gas phase calculated by the distribution method M3. Energy levels are in kcal/mol.

Image of FIG. 14.
FIG. 14.

The free-energy surface of alanine dipeptide in gas phase calculated by the distribution method M5. Energy levels are in kcal/mol.

Image of FIG. 15.
FIG. 15.

The free-energy surface of alanine dipeptide in aqueous phase calculated by the distribution method M4. Energy levels are in kcal/mol.

Image of FIG. 16.
FIG. 16.

The free-energy surface of alanine dipeptide in aqueous phase calculated by the distribution method M3. Energy levels are in kcal/mol.

Image of FIG. 17.
FIG. 17.

The free-energy surface of alanine dipeptide in aqueous phase calculated by the distribution method M5-a. The method is described in the text. Energy levels are in kcal/mol.

Image of FIG. 18.
FIG. 18.

The free-energy surface of alanine dipeptide in aqueous phase calculated by the distribution method M5-b. The method is described in the text. Energy levels are in kcal/mol.

Tables

Generic image for table
Table I.

Parameter sets for the four harmonic-model cases. In all cases, N = 10, ω A = 1, and β = 1. The W A , W B , UA, and U B energy ranges are utilized in the distribution methods M2 A , M2 B , M3 A , and M3 B , respectively. The subscript denotes the reference system A or B. U and W have units of kT.

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2010-12-30
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Understanding free-energy perturbation calculations through a model of harmonic oscillators: Theory and implications to improve the sampling efficiency by molecular simulation
http://aip.metastore.ingenta.com/content/aip/journal/jcp/133/24/10.1063/1.3511703
10.1063/1.3511703
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