MONDAY, March 17, 2008
Time: 1:30 - 2:30 PM
OCNPS 204

Title: A Perspective on the Interface Between Numerical Analysis and Developmental Neurobiology

Hugh MacMillan
Clemson University

I will begin with a brief introduction to first-order system least-squares (FOSLS) finite element methods, to give some flavor for my background and interest in the numerical analysis of PDEs and inverse problems. Then, for the bulk of the talk, I will turn to several questions fundamental to understanding developmental neurobiology. Briefly, the operation of neuronal circuitry within human brain involves ~10^14 synaptic connections between ~10^11 neurons. Genetic variability at the single neuron level enhances the information capacity of this circuitry and "individualizes" human brain [Muotri et al., Nat Rev Neuro, 2006]. Much of this variability is generated during development by random, isolated, and heritable genome rearrangements within neural progenitor cells (NPCs); i.e, from a single genome, development furnishes each individual brain with a unique genetic mosaic of neurons. Improved understanding of the mechanisms driving normal neuronal genetic mosaicism will impact therapeutic approaches to neurological diseases. As a complement to on-going experimental studies, mathematical modeling provides a means of testing hypotheses about the underlying interplay of developmental factors, integrating multiple levels of biological organization. I will present a family of models, increasing in complexity "from the top down" with respect to biological scale. The most elaborate mathematical models consist of single-cell level gene-regulatory network "modules" for DNA damage response signaling, embedded within a branching process, to explore putative links between physiologically-noisy DNA damage, NPC fate decision making, and the generation of neuronal genetic variability. Models within this family are placed within a common validation framework by appealing to biological robustness. I will discuss the mathematical and computational challenges that have arisen in this work, as well as outline future directions of my research.