Inference and Uncertainty Quantification of Stochastic Gene Expression via Synthetic Models

Abstract

Estimating uncertainty in model predictions is a central task in quantitative biology. Biological models at the single-cell level are intrinsically stochastic and nonlinear, creating formidable challenges for their statistical estimation which inevitably has to rely on approximations that trade accuracy for tractability. Despite intensive interest, a sweet spot in this trade off has not been found yet. We propose a flexible procedure for uncertainty quantification in a wide class of reaction networks describing stochastic gene expression including those with feedback. The method is based on creating a tractable coarse-graining of the model that is learned from simulations, a synthetic model, to approximate the likelihood function. We demonstrate that synthetic models can substantially outperform state-of-the-art approaches on a number of nontrivial systems and datasets, yielding an accurate and computationally viable solution to uncertainty quantification in stochastic models of gene expression.

Approximating Solutions of the Chemical Master Equation using Neural Networks

“…3. Increasing the number of mixture components does not lead to overfitting, as observed in [26], but can increase the training time.…”

“…We approximate the marginal distribution of interest by a mixture of negative binomials, a flexible parametric class of distributions that has been shown to be very accurate for a large class of reaction networks [25,26]. Indeed, it is known that single-time marginal distributions predicted by the CME for many different reaction networks can be modeled as a mixture of negative binomials in the presence of timescale separation [25,[38][39][40][41].…”

“…Using only a moderate number of simulations of the specified reaction system at different parameter values, we train a neural network to learn the marginal probability distributions predicted by the CME over the whole parameter region of interest. We approximate the target distributions using mixtures of negative binomials, a flexible class of distributions particularly well-suited for this task [25, 26]. Once trained, Nessie becomes a surrogate for the CME that can efficiently and accurately predict the solution of the CME for a wide range of parameters, bypassing the need to use further simulations or expensive approximation techniques to analyze the reaction network in question.…”

“…The results indicate that Nessie can learn the dynamics of biochemical reaction networks for a wide range of parameters, allowing us to investigate physical properties of a given system such as multimodality and parameter identifiability. Furthermore, in Section 4.3, we demonstrate how Nessie enables us to build upon [26] and perform efficient parameter inference from population snapshot data, a challenging problem for CME-based models. We conclude by discussing our results in Section 5.…”

Single-cell Ca 2+ parameter inference reveals how transcriptional states inform dynamic cell responses

“…Inference methods have also been applied to single-cell data for the discovery of new properties of single-cell oscillations [29,30] and cell-cell variability [31][32][33], as well as to study cell-cell communication [34]. New methods to infer the parameters of models of stochastic gene expression provide means to study single-cell dynamics in greater depth [35,36].…”