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.

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.

Right now we have three areas of focus.

Cell-cell interfaces

In many biological situations, including the immune response, wound healing, tissue development and tumor growth, cells exploit tactile senses to establish and regulate a physical interface with other cells. Their nanometer size and inaccessible geometry make cell-cell interfaces challenging to explore experimentally. Our lab is working to develop models of dynamics at these nanoscale interfaces, which will allow determination of relative positions of molecules on sub-optical scales, whether particular surface molecules are under tension versus compression, and their impact on initial signal transduction.

One example is offered by the T cell, an immune cell that detects antigen molecules on the surfaces of other cells and, roughly speaking, must determine whether the antigen comes from “self,” or is foreign, and therefore requires an immune response. A fundamental question is how T cells achieve the sensitivity to discriminate between self and non-self with the required precision. Mechanics come into play when we consider that molecules on the cells’ surfaces have widely varying sizes, such that two cells’ membranes must bend for the receptors on one to reach the antigen on the other, thereby squeezing nearby surface molecules, an effect that modulates biochemical signals inside the T cell. Our preliminary mathematical models of this interaction identify when significant squeezing will occur and, surprisingly, naturally reveal an effect of squeezing on antigen sensitivity. Conceptually, this mechanically induced sensitivity arises from competing timescales of antigen chemistry and force-driven motion of surrounding molecules. Incorporating the mechanics of cell components into mathematical models provides a powerful way to elucidate unexpected cellular mechanisms.

Microtubules

Microtubules have three several key dynamic properties: They are continually assembled and disassembled through polymerization and depolymerization; they have elastic properties that allow them to push, bend, and combine into bundles, star-shaped asters and other networks; and they act as highways for molecular motors (dynein and kinesin), which transport cargo across the cell. Each of these properties is now understood to quantitative detail, and ongoing efforts are combining these into holistic, quantitative models that recapitulate microtubule dynamics in cells. However, microtubule structures are maintained by cells because they confer advantage by performing cellular tasks. Therefore, a crucial role of biophysical modelling is to connect our understanding of microtubules to their cellular function. Experimental evidence demonstrates they are required for the transport of cargo, the organization of cell appendages including axons in neurons, and the proper growth of plant cell walls.

Biopolymer gels

Biopolymer gels, the most famous being actin-myosin, are complex materials that exhibit viscoelasticity (the properties of both solid and liquid), activity (by consuming energy they violate physical principles obeyed by inactive, non-living material) and internal polarity (like liquid crystals). At a microscopic level, they are composed of semiflexible filaments and hundreds of regulatory molecules that control their assembly, disassembly, crosslinking, and active reorganization. Our physical understanding of these gels arises from models at both the molecular and continuum material level. Besides canonical examples such as actin, subcellular structures that were previously unresolved have been reported to exhibit surprising gel-like properties like symmetry-breaking and clumping. One example is the pericentriolar material (PCM), a protein cloud surround the centrioles, organelles that are involved in cell division, microtubule organization and cilia genesis.