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

Abstract

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.

NNVA: Neural Network Assisted Visual Analysis of Yeast Cell Polarization Simulation

“…Fig. 7: (a) Comparative evaluation of the simulation results using parameter configurations discovered by our system (black) and previous analysis work (red) [48]. Comparison curves of Cdc42 concentration for (b) a highly uncertain prediction and (c) a good prediction instance.…”

“…Previous Simulation Model Analysis: Previous efforts into analyzing this simulation model involved creating a polynomial surrogate model [48]. The surrogate model was created by uniformly sampling the parameter space and fitting a polynomial function to the polarization factor (PF) values (Equation 1).…”

“…We use this neural network-based surrogate model to create a visual analysis system for the simulation model. We utilize some of the important findings in the previous work [48] to extensively evaluate and validate the results produced by our proposed system.…”

“…In this section, we perform two case studies using our visual analysis system and evaluate the results by comparing against the original simulation outcomes as well as the findings from a previous polynomial surrogate model based analysis of the simulation [48].…”

“…We also allow the experts to validate the surrogate model itself, by analyzing the various weight matrices and extracting the knowledge learned by the surrogate during the training process. We performed extensive evaluations of the proposed framework by comparing with the original simulation model and the results of a previous analysis effort which used polynomial surrogate models [48].…”