About Me

I am 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.

Research Interests

The overarching goal of my research program is to develop conceptual models of molecular interactions that are simple enough to form intuitive explanations, yet flexible enough to implement in specific examples. They should explain a puzzling qualitative property of the system and retain this property in the face of broad parameter variations. The statements should ideally be understandable to non-mathematicians such as biology colleagues, even when the proofs of the results can involve considerable technical work under the hood.

Quantitative modeling methods are helpful in order to integrate different types of experimental data, as well as explaining global dynamical behavior using local interaction information. Molecular biology has provided scientists with the ultimate list of parts, since molecules lie at the bottom of the biological hierarchy. Our ability to intervene in biochemical processes to affect disease outcomes and our quality of life depends on our understanding how these molecules interact. A significant long-term challenge is to conceptualize and quantify the properties of complex gene and protein networks, including hidden phenomena driven by stochastic effects. Even after careful quantification, the most valuable insights are qualitative properties that do not depend on specific parameter values, since such values are often unknown or ill-defined in changing biological environments.

For the past few years I have been particularly interested in the mathematics behind chemical reaction networks, and phenomena such as absolute concentration robustness, which my colleagues and I have worked to extend to the stochastic case. In collaboration with experimentalists, I am also working on studying the behavior of Chlamydia infections inside of mammalian hosts, and the relation between chromatin structure and gene expression.