I am an Associate Professor at the University of California, Irvine Mathematics Department, with a joint appointment in the Department of Developmental and Cell Biology, working in the area of systems biology at the interface between the mathematical and the biological sciences.
I am interested in discovering design principles of cell signaling at the molecular level. For instance, allostery, i.e. the ability for different sites of an individual protein to interact with each other, has been shown to produce all-or-none responses to a given input, through a well known mechanism proposed by Monod and colleagues in the 1960s. My colleagues and I have proposed alternative mechanisms for multisite systems to behave in an ultrasensitive way, without the standard restrictions imposed on allosteric systems. This can have applications in systems as varied as DNA packaging, yeast cell cycle checkpoints, and chemotaxis.
Understanding such signaling and regulatory mechanisms usually involves small-scale idealized models that are amenable to mathematical analysis, rather than large-scale systems with too many moving parts. However the ultimate goal of the work is to show that the proposed mechanisms are being used in actual biological systems, therefore relevant experimental data is very much valued and used in the context of more realistic models. It is essential to have a significant understanding of the underlying biological systems as well as the necessary mathematical background.
In the past I have collaborated with biologists to model information processing in the retina, signaling cascades involved in cell proliferation and cancer, and the regulation of cell cycle proteins. I also work on mathematical questions inspired by these systems, from the study of chemical reaction networks to the qualitative behavior of monotone dynamical systems and Boolean networks.