Geometry and Genetics
The application of quantitative methods to biological problems faces the choice of how much detail to include and the generality of the conclusions. Both routine data analysis and airy pronouncements that have almost nothing to say about almost everything are to be avoided. The middle ground entails some use phenomenology, a well-regarded approach in physics. A sampling of examples will be presented from my work in the area of developmental biology, to give a flavor of what is possible. The phenomenon of canalization is a license to develop models that are quantitative and dynamic yet do not begin from an enumeration of the relevant genes. Modern mathematics (ie post 1960) has many similarities to experimental embryology and allows the enumeration of categories of dynamical behaviors. Applications to stem cell differentiation will be given as illustrations. Theory can also use computational evolution, in analogy to a screen, to suggest dynamical systems that generate the desired pattern from plausible boundary conditions. Phenomenology of the sort envisioned is essential to bridge the scales from the cell, to tissue to embryo, by breaking the system into blocks that can be separately parameterized.
Place: Hybrid: Math, 501 and