Homeostasis occurs when an output variable remains approximately constant as an input parameter varies over an interval. Housekeeping genes are required for the maintenance of basic cellular function, and are expressed in all cells of an organism. Some housekeeping genes are expressed at relatively constant rates in most non-pathological situations.

We formulate homeostasis in the context of singularity theory by replacing ‘approximately constant over an interval’ with ‘zero derivative of the output with respect to the inputs at a point’. Unfolding theory makes the concept structurally stable. In particular, in one input systems the ‘chair’ singularity (fold catastrophe) of Best, Nijhout, & Reed is especially important in applications. We discuss a use in gene regulatory network motifs. We also show that the hyperbolic umbilic can organize evolution to homeostasis in two input systems. This work is joint with Fernando Antoneli, Ian Stewart, and Yangyang Wang. Speaker(s): Marty Golubitsky (Ohio State Univ)