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Efficiently finding the minimum free energy path from steepest descent path
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10.1063/1.4799236
/content/aip/journal/jcp/138/16/10.1063/1.4799236
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/16/10.1063/1.4799236
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Two model peptides in our work. (a) ALA dipeptide, from C7eq to C7ax. (b) 10-ALA peptide, from α-helix to β-hairpin. The figure is produced by VMD. 74

Image of FIG. 2.
FIG. 2.

Free energy landscape for ALA dipeptide in vacuum (obtained by Adaptively Biased Molecular Dynamics (ABMD), 13,14 in kcal/mol). The backbone angles, Φ and Ψ, are chosen as the degrees of freedom. Two minima on the surface, C7eq and C7ax, are marked by labels. The solid lines on the surface represent the optimized path after 0, 100, 200 and 300 iterations, respectively, from straight line to the most bending curve. The path is optimized by Eq. (2) .

Image of FIG. 3.
FIG. 3.

(a) Potential energy profiles for ALA dipeptide in vacuum from state C7eq to C7ax. The lines from top to bottom are the paths after 0, 100, 200 and 300 iterations (unit: kcal/mol). (b) The gradient of the path during the reaction path optimization (unit: kcal/mol). (c) The determinant of the generalized inverse of transformation matrix from Cartesian coordinate to collective variables.

Image of FIG. 4.
FIG. 4.

The free energy gradients in the constrained dynamics, obtained from Eq. (6) . (a) The gradient of the first term. (b) The gradient of the second term. See the details of the computation in the main text.

Image of FIG. 5.
FIG. 5.

The movement of the path on the free energy landscape during the MFEP optimization. The solid lines represent the path after 0, 100, 200 and 300 iterations from SDP (see SDP in Fig. 2 ), and the dashed lines represent the path after 0, 100, 200 and 300 iterations from the initial straight path.

Image of FIG. 6.
FIG. 6.

(a) Free energy profiles for ALA dipeptide in vacuum from state C7eq to C7ax. The lines from top to bottom are the data of the initial straight path, SDP, MFEP from initial path and MFEP from SDP, respectively. (b) The gradient of the path during the MFEP optimization from the initial straight path (dotted line) or SDP (solid line).

Image of FIG. 7.
FIG. 7.

Optimization of 10-ALA peptide from α-helix to β-hairpin by three typical methods: Conjugate Gradient (CG, 51,52 dotted line), Limited Broyden-Fletcher-Goldfarb-Shanno (LBFGS, 50 dashed line), and Truncated Newton (TN, 53 solid line). (a) Energy variance during the optimization (unit: kcal/mol). (b) Gradient variance during the optimization (unit: kcal/mol). (c) Structural RMSD during the optimization (unit: Å).

Image of FIG. 8.
FIG. 8.

(a) Potential energy profiles for 10-ALA peptide in solvent from α-helix to β-hairpin. The lines from top to bottom indicate the paths after 0, 50, 100, 200, 300, and 500 iterations (unit: kcal/mol). (b) The gradient of the path during the reaction path optimization (unit: kcal/mol). (c) The determinant of the generalized inverse of transformation matrix from Cartesian coordinate to collective variables.

Image of FIG. 9.
FIG. 9.

(a) Free energy profiles for 10-ALA peptide in solvent from α-helix to β-hairpin. The lines from top to bottom are the data of the initial straight path, SDP, MFEP from initial path and MFEP from SDP, respectively. (b) The gradient of the path during the MFEP optimization from the initial path (dotted line) or SDP (solid line).

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/content/aip/journal/jcp/138/16/10.1063/1.4799236
2013-04-26
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Efficiently finding the minimum free energy path from steepest descent path
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/16/10.1063/1.4799236
10.1063/1.4799236
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