A divide-and-conquer method for analyzing high-dimensional noisy gene expression networks

Intracellular gene expression systems are inevitably random due to low molecular counts. Consequently, mechanistic models for gene expression should be stochastic, and central to the analysis and inference of such models is solving the Chemical Master Equation (CME), which characterizes the probability evolution of the randomly evolving copy-numbers of the reacting species. While conventional methods such as Monte-Carlo simulations and finite state projections exist for estimating CME solutions, they suffer from the curse of dimensionality, significantly decreasing their efficacy for high-dimensional systems. Here, we propose a new computational method that resolves this issue through a novel divide-and-conquer approach. Our method divides the system into a leader system and several conditionally independent follower subsystems. The solution of the CME is then constructed by combining Monte Carlo estimation for the leader system with stochastic filtering procedures for the follower subsystems. We develop an optimized system decomposition, which ensures the low-dimensionality of the sub-problems, thereby allowing for improved scalability with increasing system dimension. The efficiency and accuracy of the method are demonstrated through several biologically relevant examples in high-dimensional estimation and inference problems. We demonstrate that our method can successfully identify a yeast transcription system at the single-cell resolution, leveraging mRNA time-course microscopy data, allowing us to rigorously examine the heterogeneity in rate parameters among isogenic cells cultured under identical conditions. Furthermore, we validate this finding using a novel noise decomposition technique introduced in this study. This technique exploits experimental time-course data to quantify intrinsic and extrinsic noise components, without requiring supplementary components, such as dual-reporter systems.