Biopolymers (flexible rods), biomembranes (fluid sheets like soap bubbles), and force-sensitive biomolecular bonds are the Lego blocks of cells, used repeatedly inside cells to build a variety of nanometer-sized machines that help perform functions, like allowing cells to divide, crawl, organize their interiors, sense their environment and communicate with other cells.

Actin asters

Simulation of formin-myosin-actin asters in the cytoplasm of cancer cells. The vertical axis is time (moving downwards).

The physical properties of these components are more and more (although incompletely) understood. But a major open question is how these components are combined inside cells into their specific architectures and how these machines perform their function (crawling, communicating, etc.). And, as in the study of all biological systems, there is an underlying question of why evolution selected the architecture that it did, and whether human engineering can benefit from the problem-solving strategies invented by cells.

Our group develops physically-based mathematical models of subcellular machines, with the aim of connecting nanoscale architecture to specific cellular function. Analysis of our models involves mathematical methods from nonlinear partial differential equations, stochastic dynamics, Bayesian statistics and high-performance computing. Mathematical models are particularly powerful when addressing questions about mechanics: models based on physics can transform measurable quantities such as displacements and velocities into information about forces, which are notoriously difficult to measure exprimentally. Mathematical models can also highlight physical similarities between biologically disparate systems. We work on bacterial cells, plant cells, human immune cells, cancer cells, among others.