An efficient timer and sizer of biomacromolecular motions

Life ticks as fast as how efficiently proteins perform their functional dynamics. Well-folded/structured biomacromolecules perform functions via large-scale intrinsic motions across multiple conformational states, which occur at timescales of nano- to milliseconds. Computationally expensive molecular dynamics (MD) 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 proteins and ribosome. Quasi-harmonic analysis, fluctuation-profile matching (FPM) and the Wiener-Khintchine theorem (WKT) are used to define the "time-periods", t , for anharmonic principal components (PCs) which are validated by 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) = 86.9λ ENM -1.9 and σ 2 (A 2 ) = 46.1λ ENM -2.5 are established allowing the characterization of the time scales of NMR-resolved conformers, crystallographic anisotropic displacement parameters, and important ribosomal motions, as well as motional sizes of the latter.