By Karthika Swamy Cohen
Timothy Elston of
University of North Carolina at Chapel Hill gave an invited talk, “Mathematical
Models for Cell Polarization and Gradient Sensing” at the SIAM Conference on
the Life Sciences being held in Boston this week. Elston described mathematical
approaches to study polarized growth and gradient sensing, two processes
essential to cellular growth. Combining mathematical analysis with experimental
observations, Elston’s group studies the biochemical and molecular mechanisms
behind directed growth and gradient sensing.
In polarized growth, a
front is maintained, allowing migration and differentiation in multicellular
organisms.When cells polarize, they distribute protein in an asymmetric
"Symmetry breaking happens in the context of polarization,” explained Elston. “Here, each individual cell can break symmetry, and this happens through Turing instability.”
Using the example of the protein Cdc-45, and its movement in the cytoplasm, he explained how polarity is established in yeast cells. Not surprisingly, Cdc-45 is essential for cell division and mating in yeast. Quite simply, Elston explained a simple model of polarity, "There's always competition and the bigger people always win." Elston described a stochastic model, which tracks the position and chemical state of each molecule. The process is analyzed in more detail by switching to reaction diffusion equations.