Title: A Concentrated Capacity Model for Diffusion-Advection: Advection Localized to a Moving Curve
Abstract: Proteins are chains of amino acids linked together in sequence along a polypeptide bond and are the molecular machines that drive many dynamics inside biological cells. In molecular dynamics simulations, resolving the motion of explicit solvent is a great computational expense. However, the localized interaction of solvent at different sites along the protein can strongly influence the conformation a protein takes. The implications for this extend to the molecular basis for disease as well as drug-design. In this talk, I will present a novel partial differential equations framework for considering the protein solvent interaction. Beginning with a simple diffusion-advection equation but then weakly passing to the limit so that chemical bonds (accordingly advection) are modeled as intrinsically 1d, we will discover a novel, coupled system between a 3d diffusion of solvent in the volume and a 1d diffusion of solvent along the protein. This is technically accomplished through the partial differential equations technique of concentrating capacity which is shown to make precise a parabolic pde whose equation coefficients are highly singular, time varying measures. Concentrating capacity is a tool which, like homogenization, is meant to accommodate the presence of multiple physical scales. However, unlike homogenization which averages the small scales into the larger, concentrating capacity resolves the small scale dynamics onto their intrinsic lower dimension.
Zoom information: To join the seminar by zoom, please use the following link:
Videos: Talk - https://osu.box.com/s/zqotc6asij2azrfajpet0simqxms2r98
Extended Q&A: - https://osu.box.com/s/7vtaxu6yn6ux55fgyc13t0ua5l7kux4p