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Error and efficiency of replica exchange molecular dynamics simulations
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10.1063/1.3249608
/content/aip/journal/jcp/131/16/10.1063/1.3249608
http://aip.metastore.ingenta.com/content/aip/journal/jcp/131/16/10.1063/1.3249608
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Temperature dependence of folding (, red) and unfolding (, blue) rates and of the relaxation rates (, black) of the -repressor fragment (Ref. 20). The temperature dependent rate constants were calculated based on Table II of Ref. 20 and the temperature dependence of the water viscosity.

Image of FIG. 2.
FIG. 2.

Kinetic model of replica exchange. Connectivity of all states is illustrated for (a) and (b) replicas. Black arrows represent folding and unfolding processes, while red arrows show replica exchange processes. The corresponding reduced linear kinetic schemes, obtained in the limit of fast replica exchange, are shown below the full kinetic diagrams.

Image of FIG. 3.
FIG. 3.

Efficiency gain of REMD over MD as a function of the highest replica temperature . The reference temperature is . Plotted is the efficiency in the limit of a large number of replicas, which is independent of , as obtained from Eq. (26). Note that for temperatures above 350 K, we used extrapolated rates.

Image of FIG. 4.
FIG. 4.

Convergence of the relaxation rate and the efficiency of REMD for the -repressor fragment (Ref. 20). (a) The exchange rate dependence of the rate limiting eigenvalue is shown for the full kinetic problem (blue line), for the exact fast replica exchange limit (black line), and for the approximate Eq. (18) (red line). The eigenvalues corresponding to MD (no replica exchange coupling), and are marked with arrows. (b) REMD efficiency [Eq. (7)] vs the target temperature. The fast-exchange limit is shown as black line with circles, the results using Eq. (25) are shown as red dashed line, the MD simulations correspond to efficiency of 1, shown in blue. The arrow indicates the variation in the efficiency for increasing replica exchange rate. The inset shows the REMD variance for different target temperatures.

Image of FIG. 5.
FIG. 5.

Convergence of the relaxation rate and the efficiency of REMD for the Arrhenius folding/unfolding rates of . (a) The exchange rate dependence of the rate limiting eigenvalue is shown for the full kinetic problem (blue line), for the exact fast replica exchange limit (black line), and for the approximate Eq. (18) (red line). The eigenvalues corresponding to MD (no replica exchange coupling), and are marked with arrows. (b) REMD efficiency [Eq. (7)] vs the target temperature. The fast-exchange limit is shown as black line with circles, the results using Eq. (25) are shown as red dashed line, the MD simulations correspond to an efficiency of 1, shown in blue. The arrow indicates the variation in the efficiency for increasing replica exchange rate. The inset shows the variance of the fraction folded as a function of the target temperature, scaled for reference and readability to a simulation length of .

Image of FIG. 6.
FIG. 6.

Autocorrelation function of the folding state at different temperatures obtained from REMD simulations of . Also shown are the corresponding for regular MD simulations at (blue) and (green), and the autocorrelation function of the number of folded states (red). The dashed black lines show exponential decays with the slowest relaxation rate obtained from Eq. (18).

Image of FIG. 7.
FIG. 7.

Variance in the fraction folded calculated from REMD simulations of for different target temperatures. For reference and readability, all results have been scaled to a simulation time of . The red symbols show data obtained from 11 independent 150-ns-long REMD simulations. The solid lines are obtained for the reduced kinetic model (blue) in the fast-exchange limit from the exact solution of the coarse grained kinetic model and in the continuum limit (black symbols) using the formula of Eq. (24). The green line corresponds to the variance for times longer MD simulations.

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/content/aip/journal/jcp/131/16/10.1063/1.3249608
2009-10-27
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Error and efficiency of replica exchange molecular dynamics simulations
http://aip.metastore.ingenta.com/content/aip/journal/jcp/131/16/10.1063/1.3249608
10.1063/1.3249608
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