Genetics, Geometry and Evolution

Cornell University, Ithaca NY

Investigators

Abstract

In this project the PI develops arguments for convergent evolution in gene networks based on simulation and bifurcation theory (or the geometric theory of differential equations). This requires defining a measure of fitness that the network optimizes and showing that mutation rates (which are unknown) to not bias the result. Darwin understood that complex organs such as the eye could evolve by continual small changes if all the intermediate steps increased the fitness. The same question will be posed for networks and answered computationally: what networks can be learned by gradient ascent (ie hill climbing). When evolution proceeds by hill climbing, the same local maxima are found irrespective of mutation rates. Generic fitness measures for embryonic patterning and the input-output response of signaling systems are suggested that may capture the phyla-wide properties of developmental networks. In situations where the network produces a static pattern, bifurcation theory enumerates the types of patterns that occur as parameters change continuously. Near the bifurcation point there are simple polynomial equations that collapse many physical variables into a few, and thus provide a description of the system with as few parameters as mathematics allows. Geometric models with fixed points, saddle points and sources may be an effective way to quantitatively model biological networks, and possibly evolution itself. A complementary experimental program will time cell divisions and other markers during embryonic development in the worm C.elegans to see if their fluctuations conform to geometric models. To see whether the structure of developmental signaling pathways can be understood from their input-output response, TGF-beta pathway in Xenopus will be probed with time and space dependent stimuli and time-lapsed imaged in sheets of embryonic cells. Students and postdocs will be engaged in research projects related to this proposal.