An Adjoint-Based Parameter Identification Algorithm Applied to Planar Cell Polarity Signaling

Abstract

This paper presents an adjoint-based algorithm for performing automatic parameter identification on differential equation models of biological systems. The algorithm locally 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 are the governing parameterized equations. The tractability and the speed of convergence (to local minima) of the algorithm are strongly favorable to numerical parameter search algorithms which do not make use of the adjoint. Furthermore, initializing the algorithm with different instantiations of the parameters allows one to effectively search the parameter space. Results of the application of this algorithm to a previously presented mathematical model of planar cell polarity (PCP) signaling in the wings of Drosophila melanogaster are presented, and some new insights into the PCP mechanism that are enabled by the algorithm are described.