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 non-trivial 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

“…We approximate the marginal distribution of interest by a mixture of negative binomials, a flexible parametric class of distributions that have been shown to be very accurate for a large class of reaction networks ( Öcal et al., 2022 ; Perez-Carrasco et al., 2020 ). 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 ( Friedman et al., 2006 ; Shahrezaei and Swain, 2008 ; Z.…”

“…Although adding extra components does not lead to overfitting, as observed by Öcal et al. (2022) it increases the training time and can also make the network more prone to mistakenly predicting too many modes in the solution for certain parameter regimes, which can be regarded as an unphysical artifact.…”

“…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 ( Perez-Carrasco et al., 2020 ; Öcal et al., 2022 ). Once trained, Nessie becomes a surrogate for the CME that can efficiently and accurately predict the solution of the CME at different times 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 the physical properties of a given system such as multimodality and parameter identifiability. Furthermore, we demonstrate how Nessie enables us to build on Öcal et al. (2022) and perform efficient parameter inference from population snapshot data, a challenging problem for CME-based models.…”

Genome-wide inference reveals that feedback regulations constrain promoter-dependent transcriptional burst kinetics

“…Third, our hierarchical model only considered self-regulatory feedback ( 117 ), the simplest feedback form. More complex regulatory forms may exist in gene-expression systems ( 118 ). However, since they reflect high-level structure regulation ( 10 ), more complex yet reasonable mathematical models and more powerful inference methods need to be developed for better studying transcriptional burst kinetics.…”