Efficient global sensitivity analysis of biochemical networks using Gaussian process regression

A key objective of systems biology is to understand how the uncertainty in parameter values affects the responses of biochemical networks. Variance-based sensitivity analysis is a powerful approach to address this question. However, commonly used implementations based on (Quasi-) Monte Carlo require a very large number of model evaluations, and are thus impractical for computationally expensive models. Here, we present an alternative method for variance-based sensitivity analysis that uses Gaussian process regression. Thanks to the appealing mathematical properties of Gaussian processes, we are able to derive exact analytic formulas for the required sensitivity indices. In this way our approach yields more accurate estimates with significantly less computational cost compared to conventional methods, as we demonstrate for a nonlinear model of a bacterial signaling system.