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# Applied Mathematics Colloquium – Anna C. Nelson (Duke)

## April 17 @ 3:30 pm - 4:30 pm

**Mathematical modeling of polymerization processes in physiology**

**Abstract: **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 this talk, I will discuss efforts I have made towards understanding polymerization processes in physiology, as well as new research directions. In the first part, I will discuss a mathematical model that represents the formation of a fibrin polymer mesh with interactions with its precursor molecule, fibrinogen. We investigate how these interactions can impact gel structure and gel time. In the second part, I will briefly introduce a stochastic mathematical model of microtubule growth 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.