An Efficient Timer and Sizer of Biomacromolecular Motions.

Life ticks as fast as how proteins move. Computationally expensive molecular dynamics simulation has been the only theoretical tool to gauge the time and sizes of these motions, though barely to their slowest ends. Here, we convert a computationally cheap elastic network model (ENM) into a molecular timer and sizer to gauge the slowest functional motions of structured biomolecules. Quasi-harmonic analysis, fluctuation profile matching, and the Wiener-Khintchine theorem are used to define the "time periods," t , for anharmonic principal components (PCs), which are validated by nuclear magnetic resonance (NMR) order parameters. The PCs with their respective "time periods" are mapped to the eigenvalues (λ ENM) of the corresponding ENM modes. Thus, the power laws t (ns) = 56.1λ ENM −1.6 and σ2(Å2) = 32.7λ ENM −3.0 can be established allowing the characterization of the timescales of NMR-resolved conformers, crystallographic anisotropic displacement parameters, and important ribosomal motions, as well as motional sizes of the latter. • Defined timescales for modes of protein motions observed in a long MD simulation • Providing a timescale to experimentally observed protein fluctuation data • Mapping timescales and variances obtained from MD to a simple elastic network model • Establish two power laws relating the absolute timescale/variance with ENM modes Biological processes are often governed by protein functional dynamics that correspond to the large conformational transition and long timescales that cannot be practically studied using current simulation methodologies. We instead use the elastic network model (ENM), an efficient spring-bead model, and calibrate its predicted timescale and size of protein conformational changes with all-atom simulation data, resulting in time and space power laws with the only input being the ENM eigenvalues. [ABSTRACT FROM AUTHOR]