Bayesian estimation for stochastic gene expression using multifidelity models

Abstract

The finite state projection (FSP) approach to solving the chemical master equation has enabled successful inference of discrete stochastic models to predict single-cell gene regulation dynamics. Unfortunately, the FSP approach is highly computationally intensive for all but the simplest models, an issue that is highly problematic when parameter inference and uncertainty quantification takes enormous numbers of parameter evaluations. To address this issue, we propose two new computational methods for the Bayesian inference of stochastic gene expression parameters given single-cell experiments. We formulate and verify an Adaptive Delayed Acceptance Metropolis-Hastings (ADAMH) algorithm to utilize with reduced Krylov-basis projections of the FSP. We then introduce an extension of the ADAMH into a Hybrid scheme that consists of an initial phase to construct a reduced model and a faster second phase to sample from the approximate posterior distribution determined by the constructed model. We test and compare both algorithms to an adaptive Metropolis algorithm with full FSP-based likelihood evaluations on three example models and simulated data to show that the new ADAMH variants achieve substantial speedup in comparison to the full FSP approach. By reducing the computational costs of parameter estimation, we expect the ADAMH approach to enable efficient data-driven estimation for more complex gene regulation models.

The finite state projection based Fisher information matrix approach to estimate information and optimize single-cell experiments

“…Our initial investigations focused on intrinsic stochastic fluctuations of small biochemical processes, and we used simulated data to verify our new computational tools. For models with large molecular counts of four or more species or with the addition of mechanisms to account for extrinsic variability, existing methods to solve the FSP-FIM will remain intractable until more efficient probability density based CME analyses can be developed to address such problems [52–56]. Until higher dimension CME approaches are developed, approximate moment-based experiment design methods, such as the SM-FIM and LNA-FIM, may remain the only available options to design experiments for large biochemical pathways.…”

Bayesian inference of Stochastic reaction networks using Multifidelity Sequential Tempered Markov Chain Monte Carlo

“…These datasets consist of independent single-cell measurements, each of which measures the copy number of biochemical species at a single time point. The standard approach to sample from the posterior distribution implied by this data is to use Markov Chain Monte Carlo (MCMC) algorithms such as the random walk Metropolis-Hastings MCMC sampler [11,22]. With high-fidelity CME solutions enabled by the FSP, one can compute the likelihood of observing these single-cell data and then perform Bayesian inference for model parameters.…”

“…Similarly, approaches to multifidelity MCMC have been explored in the literature such as multifidelity delayed acceptance schemes, Multilevel Markov Chain Monte Carlo, and multifidelity approaches to SMC [33][34][35][36][37][38]. Multifidelity delayed acceptance schemes have been applied to Bayesian inference for the CME before [22,39,40]. Within these methods, a fast surrogate of the expensive likelihood function is used to pre-screen proposed samples within MCMC before they are accepted or rejected based on the expensive CME likelihood.…”