Parameter uncertainty quantification using surrogate models applied to a spatial model of yeast mating polarization

A common challenge in systems biology is quantifying the effects of unknown parameters and estimating parameter values from data. For many systems, this task is computationally intractable due to expensive model evaluations and large numbers of parameters. In this work, we investigate a new method for performing sensitivity analysis and parameter estimation of complex biological models using techniques from uncertainty quantification. The primary advance is a significant improvement in computational efficiency from the replacement of model simulation by evaluation of a polynomial surrogate model. We demonstrate the method on two models of mating in budding yeast: a smaller ODE model of the heterotrimeric G-protein cycle, and a larger spatial model of pheromone-induced cell polarization. A small number of model simulations are used to fit the polynomial surrogates, which are then used to calculate global parameter sensitivities. The surrogate models also allow rapid Bayesian inference of the parameters via Markov chain Monte Carlo (MCMC) by eliminating model simulations at each step. Application to the ODE model shows results consistent with published single-point estimates for the model and data, with the added benefit of calculating the correlations between pairs of parameters. On the larger PDE model, the surrogate models allowed convergence for the distribution of 15 parameters, which otherwise would have been computationally prohibitive using simulations at each MCMC step. We inferred parameter distributions that in certain cases peaked at values different from published values, and showed that a wide range of parameters would permit polarization in the model. Strikingly our results suggested different diffusion constants for active versus inactive Cdc42 to achieve good polarization, which is consistent with experimental observations in another yeast species S. pombe.Author summary: Mathematical models in systems biology often have many parameters, such as biochemical reaction rates, whose true values are unknown. When the number of parameters is large, it becomes computationally difficult to analyze their effects and to estimate parameter values from experimental data. This is especially challenging when the model is expensive to evaluate, which is the case for large spatial models. In this paper, we introduce a methodology for using surrogate models to drastically reduce the cost of parameter analysis in such models. By using a polynomial approximation to the full mathematical model, parameter sensitivity analysis and parameter estimation can be performed without the need for a large number of model evaluations. We explore the application of this methodology to two models for yeast mating polarization. A simpler non-spatial model is used to demonstrate the techniques and compare with published results, and a larger spatial model is used to demonstrate the computational savings offered by this method.