Brownian Dynamics of Folded DNA and Protein Assemblies

Abstract

Molecular simulation of long time-scale dynamical motions of proteins and DNA/RNA assemblies is currently impossible using all-atom approaches. In order to partly overcome this limitation, Normal Mode Analysis (NMA) is commonly applied in vacuum to molecular assemblies to enable the calculation of large length-scale molecular motions, albeit with no feedback on their functionally crucial relaxation time-scales in solvent. Moreover, vacuum Normal Modes may differ substantially from Brownian Modes because linearized molecular motions in solvent are typically over-damped, whereas vacuum NMA assumes purely harmonic, inertia-dominated motion. To overcome the limitations associated with vacuum NMA, we introduce here a linearized Brownian Dynamics framework that enables the simulation of the over-damped motion of high molecular weight protein, DNA, and RNA assemblies based on the finite element method. We apply the procedure to simulate microsecond over-damped dynamics of Taq polymerase and programmed DNA nanostructures, and compare quantitatively Brownian Mode shapes with corresponding vacuum Normal Mode shapes, as well as analyze their respective relaxation time-scales. The present computational framework enables the simulation of long time-scale conformational dynamics of high molecular protein, DNA, and RNA assemblies in solvent that are inaccessible to all-atom approaches even on super-computers.