Overdamped Brownian dynamics in piecewise-defined energy landscapes

Out-of-Equilibrium Biophysical Chemistry: The Case for Multidimensional, Integrated Single-Molecule Approaches

Out-of-equilibrium processes are ubiquitous across living organisms and all structural hierarchies of life. At the molecular scale, out-of-equilibrium processes (for example, enzyme catalysis, gene regulation, and motor protein functions) cause biological macromolecules to sample an ensemble of conformations over a wide range of time scales. Quantifying and conceptualizing the structure–dynamics to function relationship is challenging because continuously evolving multidimensional energy landscapes are necessary to describe nonequilibrium biological processes in biological macromolecules. In this perspective, we explore the challenges associated with state-of-the-art experimental techniques to understanding biological macromolecular function. We argue that it is time to revisit how we probe and model functional out-of-equilibrium biomolecular dynamics. We suggest that developing integrated single-molecule multiparametric force–fluorescence instruments and using advanced molecular dynamics simulations to study out-of-equilibrium biomolecules will provide a path towards understanding the principles of and mechanisms behind the structure–dynamics to function paradigm in biological macromolecules.

Effective diffusion in one-dimensional rough potential-energy landscapes

Diffusion in spatially rough, confining, one-dimensional continuous energy landscapes is treated using Zwanzig's proposal, which is based on the Smoluchowski equation. We show that Zwanzig's conjecture agrees with Brownian dynamics simulations only in the regime of small roughness. Our correction of Zwanzig's framework corroborates well with numerical results. A numerical simulation scheme based on our coarse-grained Langevin dynamics offers significant reductions in computational time. The mean first-passage time problem in the case of random roughness is treated. Finally, we address the validity of the separation of length scales assumption for the case of polynomial backgrounds and cosine-based roughness. Our results are applicable to hierarchical energy landscapes such as that of a protein's folding and transport processes in disordered media, where there is clear separation of length scale between smooth underlying potential and its rough perturbation.