My Research
My research interests are in applied probability and mathematical biology. In particular, I study stochastic
processes with applications to population genetics and molecular biology. My Ph.D. research focused on Markov chain
models of DNA regulatory sequence evolution in organisms of different population sizes. I've also worked in the area of gene duplication, examining the selection pressures acting on zinc finger genes. For more information, see my Research
Statement (pdf). - last updated 5/07
Last summer I directed a project in mathematical population genetics for the Mathematics Research Experience for Undergraduates (REU) at The University
of Akron. This project motivated me to look at the relationship between stochastic models and their corresponding
mean-field approximations, a new research interest I'd like to pursue.
At the IMA, I am collaborating with Timothy Newman who is a long term visitor from Arizona State University. McKane
and Newman (J. Stat. Phys. 2007) discovered a mechanism for noise-induced (stochastic) oscillations in mesoscopic
systems for which the deterministic descriptions failed to show oscillations for any parameter values. Based on this
technique, we are modeling a gene regulatory network derived from the lambda switch (bacteriophage lambda) and
looking for noise-induced oscillations. Together with an experimental biophysicist here at the U of M, we are working
on a genetically engineered Cro system to try to validate this mechanism.
I am also collaborating with Peter Bates (Michigan State University),
who was an IMA long term visitor during the fall of 2007, and Judith Berman (U of M) to investigate various models
of hypermutation/adaptive mutation in yeast cells.
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