Reality's A Drag: Accounting For Friction In Simple Protein Models

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Elastic network models (ENMs) are widely used for studying the global equilibrium dynamics of proteins because they predict motions on timescales that are generally inaccessible to molecular dynamics (MD) simulations. Although the slowest motions predicted by in vacuo ENMs have repeatedly shown to correlate well with experiment, the timescales of these motions do not. Here we develop a simple algorithm for scaling the characteristic timescales of slow motions predicted by an ENM to reflect the true timescales of the molecular motions. Using MD trajectories on the order of tens of nanoseconds, we calculate ideal friction constants for Langevin models of three proteins. We then demonstrate that the difference between the slowest vibrational frequencies predicted by the Langevin model and those predicted by an in vacuo ENM can be explained through simple physical arguments. We provide an expression for scaling the normal mode frequencies of an in vacuo ENM to realistic values and discuss the utility of our results in combining ENMs with MD simulations to predict large-scale protein dynamics.