Automatic Parameter Identification via the Adjoint Method, with Application to Understanding Planar Cell Polarity

A key focus of systems biology has been the development of models, at the appropriate level of abstraction, to help understand different biological processes. This development usually proceeds in iterative fashion, in which the structure of the model is chosen to represent certain hypotheses about how the system operates and parameters for this structured model are chosen. Often, the first experiment is to ask if a robust set of parameters exists so that the model reproduces all or most of the observed biological data. The model is tested against this actual data and for its predictive capabilities. As new data and/or new understanding arises, the structure of the model may be altered, and new parameters 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 functions of the states. Thus it is becoming increasingly important to develop fast, efficient, scalable methods for large scale parameter identification. This paper presents an adjoint-based algorithm for performing automatic parameter identification on differential equation based models of biological systems. 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. Preliminary results of the application of this algorithm to a previously presented mathematical model of planar cell polarity signaling in the wings of Drosophila melanogaster are presented