Using correlated motions to determine sufficient sampling times for molecular dynamics

Abstract

Here we present a time-dependent correlation method that provides insight into how long a system takes to grow into its equal-time (Pearson) correlation. We also show a usage of an extant time-lagged correlation method that indicates the time for parts of a system to become decorrelated, relative to equal-time correlation. Given a completed simulation (or set of simulations), these tools estimate (i) how long of a simulation of the same system would be sufficient to observe the same correlated motions, (ii) if patterns of observed correlated motions indicate events beyond the timescale of the simulation, and (iii) how long of a simulation is needed to observe these longer timescale events. We view this method as a decision-support tool that will aid researchers in determining necessary sampling times. In principle, this tool is extendable to any multidimensional time series data with a notion of correlated fluctuations; however, here we limit our discussion to data from molecular-dynamics simulations.

FIG. 1.

Correlation coefficients of time-lagged correlation matrix at a series of τ values to the typical equal-time correlation matrix are presented for (a) and (b) therapeutic DNA strand F10 in physiological solvents [(a) potassium-heavy and (b) sodium-heavy], NEMO zinc finger with (c) and without (d) a bound zinc ion, Thrombin in (e) a stabilizing and (f) a destabilizing solvent, and MutSα with (g) cisplatinated DNA and (h) carboplatinated DNA. Bars indicate one standard error. Data are truncated at the minimum y-axis value.

FIG. 2.

Correlation coefficients of the correlation propagator at a series of τ values to the typical equal-time correlation matrix are presented for (a) and (b) therapeutic DNA strand F10 in physiological solvents [(a) potassium-heavy and (b) sodium-heavy], NEMO zinc finger with (c) and without (d) a bound zinc ion, Thrombin in (e) a stabilizing and (f) a destabilizing solvent, and MutSα with (g) cisplatinated DNA and (h) carboplatinated DNA. Bars are one standard error. Data are truncated at the maximum y-axis value.