Departments of Statistic, Ecology and Evolution, Molecular Genetics & Cell Biology, and the College
Institute of Genomics & Systems Biology
Committee on Computational and Applied Mathematics (CCAM)
My laboratory is engaged in a long term project to understand how DNA sequence specifies biological form. We use systems of nonlinear ODEs to understand how an animal generates the blueprint for its own body. Underlying this dynamical activity is the control of transcription. Here we seek to understand the cis-regulatory code, by which DNA sequence controls gene expression by interactions with proteins called transcription factors. In the past we have explored these questions using our own experimental data from the fruit fly Drosophila melanogaster, obtained from both fixed and live embryos, and we are now widening our efforts to include other flies as well as mice and humans.
These biological questions have in turn involved us in a variety of areas in computer science, mathematics, and statistics. With respect to computer science, we are interested in large scale optimization by simulated annealing and stochastic gradient descent, as well as the application of machine learning techniques to fundamental problems in genetics. With respect to math and statistics, transcription is itself a stochastic process characterized by random bursts, which we monitor in the lab and model computationally. This problem has led us to consider both exact and numerical solutions of the chemical master equation in the context of both abstract symmetries and the use of Bayesian statistical techniques. On a deterministic level, the astonishing error correction capabilities of the embryo have led us to the use of dynamical systems techniques to understand error correction in terms of attracting sets and their basins.