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A virtual-system coupled multicanonical molecular dynamics simulation: Principles and applications to free-energy landscape of protein–protein interaction with an all-atom model in explicit solvent
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Figures

Image of FIG. 1.

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FIG. 1.

Virtual-state transition from to . Two virtual states are shown in this figure, whereas more virtual states exist in actual simulations (see Fig. 2 ). The x-, y-, and z-axes, respectively, represent virtual energy ( ), real energy ( ), and multicanonical probability . Thick lines represent non-zero probability regions ( ≠ 0) for virtual states and . See main text for details of symbols or notations appearing in this figure.

Image of FIG. 2.

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FIG. 2.

System with five virtual states. Panel (a) presents the system in the same way as presented in Fig. 1 . Five segmental energy distributions ( = 1, …, 5) are shown. The broken line shows the energy distribution constructed from the five segments (see Eq. (27) ). Panel (b) is a projection of the system to [ , ] plane. Thick lines represent non-zero probability regions ( ≠ 0) for virtual states. Thin lines are index lines. Black and gray thick lines, respectively, show overlapping and non-overlapping regions. See main text for details of symbols appearing in this figure.

Image of FIG. 3.

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FIG. 3.

Initial conformation of simulation. Two KR-CSH-ET1 molecules are mutually distant. This conformation was used to initiate high-temperature (1000 K) canonical MD runs. Pre-V-McMD runs were followed.

Image of FIG. 4.

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FIG. 4.

(a) Energy distributions ( , ) from pre-V-McMD runs conducted at 13 temperatures: 800 K, 719 K, 629 K, 559 K, 503 K, 457 K, 419 K, 387 K, 359 K, 335 K, 315 K, 296 K, and 287 K. Energy distributions ( , ) from the first (b), fifth (c), and tenth (d) V-McMD runs. The tenth V-McMD is the production run. Table I shows information for virtual states [ , , ...]. Canonical distributions ln[ ( , 300 K)] and ln[ ( , 800 K)] are shown in panel (d), which was calculated from Eq. (1) .

Image of FIG. 5.

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FIG. 5.

Number of intermolecular atomic contacts ( ) as a function of real energy ( ) for ten iterative simulations. Panel (a) is from V-McMD; panel (b) is from McMD. The red circles represent calculated from the native complex, the x coordinates of which correspond to at 300 K.

Image of FIG. 6.

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FIG. 6.

Energy distributions ( ) from the first (a), fifth (b), and tenth (c) McMD simulations. The tenth McMD is the production run. Panel (c) also plots ( ) from the tenth V-McMD simulations.

Image of FIG. 7.

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FIG. 7.

Relation between and from the first (a), fifth (b), and tenth (c) V-McMD. Broken red lines represent the energy levels corresponding to 300 K.

Image of FIG. 8.

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FIG. 8.

Sampled complex structure probable at 300 K. = 1.001 Å, , and . Residues in stick models are Arg and Glu forming intermolecular salt bridges. Residues in CPK model are Phe forming intermolecular stacking. The yellow ribbon model shows that the intermolecular β-sheet is formed behind the Phe residues.

Image of FIG. 9.

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FIG. 9.

Relation between and from the first (a), fifth (b), and tenth (c) McMD. Broken red lines show the energy level corresponding to 300 K.

Image of FIG. 10.

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FIG. 10.

(a) Native complex drawn to show two quantities: and . Red arrows are inter-Cα atomic vectors from Lys to Cys of the two molecules. Blue arrows are those from Arg to that of Ser for the two molecules. Two unit vectors and are parallel to one of red arrows, respectively. Two unit vectors and are parallel to one of blue arrows, respectively. Character “N” denotes the N-terminal of each molecule. Panels (b) and (c) are two-dimensional free-energy landscapes (potential of mean force) at 300 K projected on the plane of and , respectively, from the tenth V-McMD and the tenth McMD. Scale bars on the right show the relation between contrast and free energy. The lowest free energy is set to zero. Red circles show the native complex position.

Image of FIG. 11.

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FIG. 11.

One-dimensional free-energy (potential of mean force) profile as a function of at 300 K and 400 K from the tenth V-McMD (a) and McMD (b). The lowest free energy is set to zero.

Tables

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Table I.

Virtual state setting and simulation length.

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Table II.

Real-energy range for virtual states for V-McMD.

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/content/aip/journal/jcp/138/18/10.1063/1.4803468
2013-05-10
2014-04-20

Abstract

We propose a novel generalized ensemble method, a virtual-system coupled multicanonical molecular dynamics (V-McMD), to enhance conformational sampling of biomolecules expressed by an all-atom model in an explicit solvent. In this method, a virtual system, of which physical quantities can be set arbitrarily, is coupled with the biomolecular system, which is the target to be studied. This method was applied to a system of an Endothelin-1 derivative, KR-CSH-ET1, known to form an antisymmetric homodimer at room temperature. V-McMD was performed starting from a configuration in which two KR-CSH-ET1 molecules were mutually distant in an explicit solvent. The lowest free-energy state (the most thermally stable state) at room temperature coincides with the experimentally determined native complex structure. This state was separated to other non-native minor clusters by a free-energy barrier, although the barrier disappeared with elevated temperature. V-McMD produced a canonical ensemble faster than a conventional McMD method.

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Scitation: A virtual-system coupled multicanonical molecular dynamics simulation: Principles and applications to free-energy landscape of protein–protein interaction with an all-atom model in explicit solvent
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/18/10.1063/1.4803468
10.1063/1.4803468
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