Mathematical Biology Seminar

How receptor surface diffusion and cell rotation increase association rates

Sean Lawley Department of Mathematics University of Utah
Wednesday, September 12, 2018, at 3:05pm LCB 225

Many biological processes are initiated when diffusing extracellular reactants reach cell-surface receptors. Calculating this arrival rate has therefore attracted theoretical interest for decades. However, prior work has largely ignored the fact that receptors diffuse on the two-dimensional cell membrane in a process called surface or lateral diffusion. In this talk, we derive an analytical formula for this arrival rate that takes into account receptor surface diffusion and cell rotational diffusion. Our theory predicts that the impact of these diffusive processes can be quantitatively described in terms of the relative size of the cell and the reactant, and that the impact is most significant when they are comparable in size. As applications, we find that surface and rotational diffusion can greatly enhance rates of cell adhesion and other reactions where the extracellular reactant is anchored to another cell. We verify our theoretical results by matching to computer simulations and experimental data.

Mathematically, our model is a three-dimensional anisotropic diffusion equation coupled to boundary conditions that are described by stochastic differential equations. We apply matched asymptotic analysis to this stochastic partial differential equation and use probabilistic methods to show that the solution can be represented by a Brownian particle in a stochastic environment. This representation enables efficient computation of solution statistics and verification of our analytical results.

Mathematical Biology Seminar

Modeling mutualisms in plants and cancer

Fred Adler Department of Mathematics University of Utah
Wednesday, October 24, 2018, at 3:05pm LCB 225

Essentially every ecological interaction has a combination of positive and negative aspects, but capturing that in models proves surprisingly difficult. I will discuss two models of so-called mutualisms. Using the first, a resource-mediated interaction of plants with their soil microbiome, we'll look at whether mutualisms buffer the system against environmental perturbations. With the second, a model of how cancer cells coopt the behavior of promoters of cell growth, we'll try to understand why cancer is rare but possible.

Mathematical Biology Seminar

Competition for binding to elastic tethers drives transport through the nuclear pore

Ben Fogelson Department of Mathematics University of Utah
Wednesday, October 3, 2018, at 3:05pm LCB 225

Transport through nuclear pores is the sole mechanism by which material moves between the cytoplasm and the cell nucleus. These pores, which are on the order of 50 nanometers in diameter and 50-80 nanometers in length, achieve cargo transport that is both fast and specific. One of the central challenges in understanding nuclear transport is understanding how the pore can achieve both speed and specificity. In this talk, we propose a novel physical mechanism for enhanced flux of specific cargos through the pore based on competition for elastically-tethered binding sites in the pore interior.