Constructing diffusive models using Bayesian inference. Applications to conduction in synthetic membrane channels and permeability of lipid bilayers
Methods for calculation of free energies have become essential tools to theoreticians in the field of molecular simulation; however, free energies alone are not sufficient to characterize many important features of biomolecular systems, including transition rates, conductances, permeabilities, and mean first-passage times. Complete diffusive models require knowledge of not only the free energy as a function the collective variable of interest, but also the diffusivity, which normally exhibits significant dependence on this variable for heterogeneous systems. To complicate matters further, many approaches for determining diffusivities are incompatible with importance-sampling methods for free-energy calculation, notably those that involve time-dependent biases (e.g. adaptive biasing force, metadynamics). This incompatibility explains why, up until now, free energies and diffusivities often had to be computed independently. In this seminar, after reviewing basic methods for computing diffusivity, I will present a Bayesian inference scheme that consistently determines free-energy landscapes and coordinate-dependent diffusivities. The advantages of this scheme include compatibility with several importance-sampling algorithms used in free-energy calculation, as well as the ability to assume a variety diffusive models (e.g., Brownian dynamics, underdamped Langevin dynamics). As concrete examples, I will illustrate the use of the Bayesian inference scheme in studying water transport through a peptide nanotube and the passive permeation of small molecules through lipid bilayers.