Title: Differential geometry and algebraic topology of biomolecules
Speaker: Guowei Wei (Michigan State University)
Abstract: A major feature of biological sciences in the 21st Century is their transition from phenomenological and descriptive disciplines to quantitative and predictive ones. However, the emergence of complexity in self-organizing biological systems poses fabulous challenges to their quantitative description because of the excessively high dimensionality. A crucial question is how to reduce the number of degrees of freedom, while preserving the fundamental physics in complex biological systems. We discuss a differential geometry based multiscale and multiphysics paradigm for biomolecular systems. We describe macromolecular systems by a number of approaches, including macroscopic electrostatics and elasticity and/or microscopic molecular mechanics and quantum mechanics; while treating the aqueous environment as a dielectric continuum or electrolytic fluids. We use differential geometry theory of surfaces to couple various microscopic and macroscopic domains on an equal footing. Based on the variational principle, we derive the coupled Poisson-Boltzmann, Nernst-Planck, Kohn-Sham, Laplace-Beltrami, Newton, elasticity and/or Navier-Stokes equations for the structure, function, dynamics and transport of protein, protein-ligand binding and ion-channel systems. Finally, we briefly discuss the topological modeling and analysis of complex biomolecular data. We propose new multidimensional persistence to dramatically reduce the dimensionality of excessively large virus data. We also introduce topological fingerprints as an efficient means to resolve ill-posed inverse problems in cryo-EM structure determination.