Nonlinear RANSAC Optimization for Parameter Estimation with Applications to Phagocyte Transmigration

Developing vigorous mathematical models and estimating accurate parameters within feasible computational time are two indispensable parts to build reliable system models for representing biological properties of the system and for producing reliable simulation. For a complex biological system with limited observations, one of the daunting tasks is the large number of unknown parameters in the mathematical modeling whose values directly determine the performance of computational modeling. To tackle this problem, we have developed a data-driven global optimization method, nonlinear RANSAC, based on Random Sample Consensus (a.k.a. RANSAC) method, for parameter estimation of nonlinear system models. Conventional RANSAC method is sound and simple, but it is oriented for linear system models. We not only adopt the strengths of RANSAC, but also extend the method for nonlinear systems with outstanding performance. As a specific application example, we have targeted understanding phagocyte transmigration which is involved in the fibrosis process for biomedical device implantation. With well-defined mathematical nonlinear equations of the system, nonlinear RANSAC is performed for the parameter estimation. Moreover, simulations of the system for propagation prediction over the time are conducted under both normal conditions and knock-out conditions. In order to evaluate the general performance of the method, we also applied the method to signalling pathways where mathematical equations which are representing interaction of proteins are generated using ordinary differential equations as a general format, and public data sets for nonlinear regression evaluation are used to assess its performance.