Mathematical models of polymerization processes in physiology

Anna Nelson
Department of Mathematics
Duke University

Polymerization, or aggregation, is essential for many physiological systems. For example, the emergence of a fibrin polymer mesh during the formation of a blood clot is required for a stable clot and long-term, sustained intracellular transport in neurons rely on persistent yet dynamic polymers that comprise the microtubule cytoskeleton. In the first part of the talk, I will discuss a kinetic polymerization model that represents the formation of a fibrin polymer mesh with interactions with its precursor molecule, fibrinogen. With this model, we investigate how fibrin-fibrinogen interactions can impact gel structure (such as concentration of branch points) and gel time. In the second part, I will introduce a stochastic mathematical model of individual microtubule growth and catastrophe in the dendrite of a neuron. Using parameters informed by experimental data, we explore what mechanisms could control the equilibrium microtubule length and validate these mechanisms using fluorescence microscopy data.