Professor Tom Chou
University of California at Los Angeles
Structured population models for cell size, proofreading reactions, and kinetic theory
Location: 1080 Physics Research Building
Faculty Host: Ralf Bundschuh
Abstract: I will briefly review classic structured population models
(based mainly on the classical deterministic age-structured McKendrick
model) and show how these PDEs can be used to describe problems in
physical biology. Two applications are evolving populations of cells
stratified by size, added size, and/or age, and waiting times in
kinetic proofreading reactions. These applications not only highlight
the utility of classical PDE models, but also motivate the development
of new theoretical extensions. Here, I will present a stochastic
framework of structured population models that can developed using
ideas from gas kinetic theory. The high-dimensional kinetic equations
can be marginalized in different ways to define PDEs for different
moments and correlations, which can be closed under certain conditions
on individual parameters such as birth and death rates. The kinetic
theory is shown to unify Markovian birth-death type master equations
with deterministic age-dependent birth/death rate models. The new
kinetic theory can be further extended to track multiple attributes
(such as a whole panel of gene expression levels) and generational
subpopulations.