I am interested in pattern formation and communication in living systems. I believe we can achieve a better understanding of these processes by searching for the underlying mathematical principles which govern these phenomena. The construction of such models is a interdisciplinary and collaborative enterprise, requiring new quantitative experimental techniques and innovative mathematical problem solving.
Research Interests
At cellular and organismal scales, I have been interested in understanding how the pigmentation patterns and intricate shape of aquatic mollusks arise. Shell growth is controlled by a neurosecretory system of cells in the mollusk’s mantle -- a tongue like protrusion that wraps around the shell edge during shell growth. By modeling the neural interactions within this layer, we have been able to reproduce a vast variety of shell shapes and patterns. Of a few of my favourite are shown, right. This work is a collaboration with Prof. George Oster at UC Berkeley and Prof. Bard Ermentrout at the University of Pittsburgh. We recently published this work in PNAS. The work was also featured on ScienceDaily.com, labspaces.net, physorg.com, sciencecentric.com, bio-medicine.org, Atlas Geographic Magazine, and Seed Magazine.
On the population scale, I have been studying tools to discover new patterns between the vast remote sensing databases of land use and animal behavior. This work is a collaboration with Prof. Wayne Getz at UC Berkeley and Prof. Wittemyer at Colorado State University.
At the molecular scale, I am interested in how cells perform reliable computations through stochastic chemical interactions. Like any living system, a cell makes numerous measurements about its environment and then determines some appropriate behavior. This process is most evident and accessible during embryonic development, where an incredible network of signals are reliably encoded and decoded by different cells who migrate, differentiate, or die in highly controlled responses. I want to understand the molecular mechanisms that make this system reliable.
I am currently studying the effect of different mechanisms of transcriptional regulation on the control of the timing of gene expression. In Drosophila, many of the central patterning genes are regulated at the transcriptional elongation step, not at transcriptional initiation. The discovery of a high frequency of `paused polymerase’ stably loaded on the upstream regions of many developmental genes prior to their normal expression, surprised the transcriptional community in 2007. My research shows that many of these `paused genes’ are subsequently activated in a much more synchronous manner than comparable non-paused genes. This suggests an evolutionary role for pausing in coordinating synchronous gene expression. Some summary results are shown here.
Comparison of initiation regulated and elongation regulated genes. Each green dot marks an actively transcribing nucleus. Embryos exhibiting temporary asynchronous (patchy) expression are much more frequent for initiation regulated genes.
Comparison of real mollusk shells (left or top) with the corresponding mathematical models of the species.
My CV
