Robust Parameter Identification with Adaptive Sparse Grid-based Optimization for Nonlinear Systems Biology Models

A major limiting step in the creation of systems biology models is the determination of appropriate parameter values that fit available experimental data. Parameter identification is hindered by the experimental difficulties in examining biological systems and the growing size and complexity of nonlinear models. In addition, the majority of systems biology models are 'sloppy,' allowing many parameter sets to fit the data. Typically, these sets are only distinguished by their quantitative fit, with the goal to minimize the least square error between simulation and data. Instead of this single-minded focus on error, parameter sets can also be distinguished by the model's relative robustness to parameter changes with that set. Robustness of a model in general has been explored, but choosing model parameters based on relative robustness is fairly new. This choice is reasonable both from the biological perspective, in that a system would be more resistant to mutations with robust parameters, and from the modeling prospective, in that robust parameters could allow easier re-fitting of the model to new data. A sparse grid-based parameter identification method has been recently developed for nonlinear models with large uncertain parameter spaces. Sparse grid parameter identification has the added benefit of storing information about the entire global parameter space, unlike commonly used stochastic methods and most deterministic algorithms. This information can be exploited for a robustness analysis that requires no additional model simulations or manipulation of the model equations. Herein, sparse grid-based identification is extended to include a novel parameter robustness analysis method that can be applied to any type of quantitative model.