We present our results in developing a partial and ordinary differential equation model for planar cell polarity signaling in fly wings. An adjoint-based algorithm for performing automatic parameter identification on differential equation based models of biological systems is presented. The algorithm solves an optimization problem, in which the cost reflects the deviation between the observed data and the output of the parameterized mathematical model, and the constraints reflect the governing parameterized equations themselves. We explicitly demonstrate that the model can explain the complex behaviors of the system, and can be used to test developmental hypotheses, such as the function of certain protein alleles, and the relationship between cell geometry and polarity.
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