This is a fun and challenging area of research, for which we have broad experience (Stites EC et al, Science, 2007; Stites EC et al, Cell Reports, 2012; Stites EC et al, Biophysical Journal, 2012; Hu J et al, Cell, 2013; McFall T et al, Science Signaling, 2019; McFall T et al, Cell Reports, 2021, Mendiratta et al, eLife, 2023; Trogdon et al, accepted), and where talented mathematicians can find fascinating, enjoyable, and illuminating research pursuits.

Mathematics has been a natural language for many sciences.   Although the past two decades have seen biology become increasingly quantitative, in part due to new methods that generate large data sets, mathematical models that can accurately describe and predict system behavior of the type commonly encountered in fields like physics and engineering are rarely encountered in biology.  This is likely because biology presents many distinctive challenges that complicate mathematical analysis.

Our work in mathematical modeling has focused on the complex details of biochemical regulation modulate and investigating how these features modulate biologically important phenotypes.  Quite often, we find that the details of biology that are commonly ignored by the field actually play critical roles in explaining biological behaviors.

We are particularly interested in mathematical models where we can study networks that exist in multiple states, such as healthy and diseased, and where the differences between the states can be understood in terms of aspects of the model (i.e., different parameters, different interactions, different attractors) and where these differences can be mapped back in a meaningful manner to the physical biological system.

Much of our work in this area involves RAS and the RAS pathway because there is extensive prior knowledge which includes reaction networks being well mapped, many reactions having been biophysically characterized to the level of reaction rate constants, reaction mechanisms being well-suited for mathematical modeling without the simplifications required for many other biologically important proteins, and because there are abundant and well-validated experimental reagents and resources that can be used to experimentally test model predictions.