PROBING BIOLOGICAL CELL NETWORKS USING MATHEMATICAL MODELS1

Mathematical methods that we have used to analyze and help to identify the Planar Cell Polarity (PCP) signaling mechanism in fly wings are described. Often, in modeling biological signaling circuits such as this, only incomplete abstracted hypotheses exist to explain observed complex patterning. Thus, the development of mathematical models usually proceeds in iterative fashion, in which the structure of the model is chosen to represent certain hypotheses about how the system operates, and then parameters for this model are selected. In protein regulatory networks, the number of states to model is typically large and depends on the number of proteins of interest, the parameter spaces are large, and the most appropriate models are nonlinear. Therefore it is becoming increasingly important to develop fast, efficient, scalable methods for modeling in systems biology. In this paper, we present an overview of the biological questions being asked about PCP, a review of our earlier results in building models for PCP, as well as an algorithm for performing automatic parameter identification on differential equation models of biological systems. In the conference talk, we will additionally present new biological results and we will show how this model can be used to test a developmental hypothesis about the relationship between cell geometry and polarity.