Mathematics Colloquia and Seminars

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Mathematical modeling provides a powerful framework for dissecting complex biological systems, enabling the generation of new hypotheses and deeper insights into emergent behaviors. In this talk, I will illustrate how mathematical approaches have illuminated two distinct biological systems: the self-propagating dynamics of protein aggregates and the intricate cascade of blood coagulation.

 

I will first delve into the world of prions—infectious protein aggregates that drive fatal neurodegenerative diseases like Creutzfeldt-Jakob disease in humans and "mad cow" disease in cattle, while also producing benign phenotypes in yeast. To reconcile discrepancies between in vitro protein dynamics and in vivo cellular behavior, we developed a stochastic model that integrates prion amplification with yeast cell division. This approach uncovered a previously unrecognized structural distinction between prion variants, offering a novel explanation for their differing stabilities and bridging a critical gap in the field.  

 

Next, I will turn to hemophilia A, a bleeding disorder marked by unpredictable clinical variability. Using a mechanistic model of the coagulation cascade, we simulated a computational "synthetic clinical trial" to explore the effects of varying levels of clotting factors and inhibitors. This approach revealed new molecular interactions that influence clotting behavior, identifying promising targets for therapeutic intervention and improving our understanding of the condition’s underlying variability.  

 

These examples highlight how mathematical models act as engines of discovery, guiding us toward innovative solutions for some of biology’s most pressing challenges.