Biophysics and Stochastics Research Group
A major goal of our research is to understand the fundamental biophysical mechanisms underlying cellular function in health and disease. This includes both single cells and multicellular systems. Our work draws upon a wide variety of methods in applied mathematics and theoretical physics including stochastic processes, statistical physics, nonlinear PDEs, and dynamical systems theory. Applications range from molecular and cellular neuroscience to gene networks to bacterial cell polarization and quorum sensing. We are also developing new mathematical and numerical methods for analyzing complex and stochastic nonlinear systems. Current research topics include the following:
- Biological processes in switching environments: diffusion in domains with randomly switching boundaries; diffusion-limited reactions; stochastic gap junctions; volume neurotransmission; genetic switches; bacterial persistence in switching environments
- Intracellular transport: molecular motors; synaptic democracy and axonal transport; exclusion processes; aggregation models of intracellular transport; random intermittent search;
- Cell polarization: active transport in budding yeast; MT regulation in growth cones; symmetry unbreaking in fission yeast
- Intracellular pattern formation: Turing mechanism and active transport; synaptogenesis in C elegans
- Cellular length control: axonal length sensing, intraflagellar transport
- Stochastic hybrid systems: stochastic ion channels; large deviations and path-integrals; switching master equations
- Quorum sensing: coupled PDE-ODE systems; stochastic models and moment closure