Stochastic Processes in Biophysics

Course goals

1. Acquire a fundamental understanding of various stochastic processes and their relevance in biophysics.
2. Master analytical techniques such as generating functions, master equations, and stochastic differential equations for analyzing biophysical systems.
3. Develop the ability to apply concepts like moments, cumulants, and temporal correlations to biophysical contexts.
4. Gain insights into the role of stochasticity in biological phenomena such as population growth, gene expression/regulation, and concentration sensing.

Content

This course explores the interplay between stochastic processes and biophysical phenomena. Students will learn about discrete Markov processes, jump processes, branching processes, and continuous stochastic processes and their applications in biophysics. The course employs techniques such as generating functions, master equations, the Fokker-Planck equation, and stochastic differential equations to analyze various biophysical systems. Biological examples, including population dynamics, population genetics, intrinsic and extrinsic noise in gene expression and regulation, and chemotaxis and concentration sensing will be examined through the lens of stochastic processes. Time permitting, additional topics may encompass biological homochirality, information theory, and stochastic thermodynamics.