The Langevin Equation (LE) formalism for the dynamics of biological macromolecules is an extension of models applied to synthetic homopolymers, and begins by projecting the solvent and all atomic degrees of freedom onto one (for amino acids) or two (for nucleic acids) sites per residue (base). We utilize a multi-scale approach where molecular dynamic (MD) simulations are performed to obtain quantitative structural averages used as input to a coarse-grained Langevin dynamical description which can be solved analytically. The normal mode analytical solution provides a minimal basis set in which important differences between synthetic and biological polymers can be accounted for, such as the anisotropic global structure, dynamical renormalization due to internal motion on a complex free-energy surface, and intrinsic sequence specificity as a heteropolymer. This multi-scale modeling method predicts the dynamics of both global rotational diffusion and constrained internal motion from the picosecond to the nanosecond regime, and is quantitative when compared to both simulation trajectory and NMR relaxation times. A conformational jump model can be seamlessly integrated into the formalism to elucidate biologically important active states exchanging in the microsecond regime and their kinetic conversion rates; applications include large-scale DNA/RNA breathing important in many biological processes.

Langevin equation approach to the dynamics of biological macromolecules: Anisotropic tumbling and internal motion on rough free energy surfaces

246th National Meeting (2013)

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