Mathematics

Stochastic Modeling

Biological systems are inherently noisy. Stochastic models capture this randomness mathematically, describing everything from ion channel flickering to pharmacokinetic drug distribution. Markov chains model the probabilistic transitions between cardiac rhythm states — from normal sinus rhythm to atrial fibrillation to ventricular tachycardia. The Gillespie algorithm simulates the stochastic biochemistry inside individual cells, revealing that gene expression is not deterministic but fundamentally random, with consequences that ripple up to organism-level phenotypes.