Markovian Promoter Models: A Mechanistic Alternative to Hill Functions in Gene Regulatory Networks

TL;DR

This paper introduces a hybrid Markovian-ODE model for gene regulation that explicitly captures promoter stochasticity, is parameterized with in vivo data, and offers a computationally efficient alternative to traditional stochastic simulations.

Contribution

It presents a novel mechanistic modeling framework combining Markov chains with ODEs, parameterized from chromatin data, to accurately and efficiently simulate gene regulatory networks.

Findings

Achieves similar accuracy to stochastic simulations

Runs 10-100 times faster than SSA

Validated on diverse gene regulatory systems

Abstract

Gene regulatory networks are typically modeled using ordinary differential equations (ODEs) with phenomenological Hill functions to represent transcriptional regulation. While computationally efficient, Hill functions lack mechanistic grounding and cannot capture stochastic promoter dynamics. We present a hybrid Markovian-ODE framework that explicitly models discrete promoter states while maintaining computational tractability. Uniquely, we parameterize this model using fractional dwell times derived from ChEC-seq data, enabling the inference of in vivo kinetic rates from steady-state chromatin profiling. Our approach tracks individual transcription factor binding events as a continuous-time Markov chain, linked to deterministic molecular dynamics. We validate this framework on seven gene regulatory systems spanning basic to advanced complexity: the GAL system, repressilator, Goodwin oscillator, toggle switch, incoherent feed-forward loop, p53-Mdm2 oscillator, and NF-$\kappa$B pathway. Comparison with stochastic simulation algorithm (SSA) ground truth demonstrates that Markovian promoter models achieve similar accuracy to full stochastic simulations while being 10-100$\times$ faster. Our framework provides a mechanistic foundation for gene regulation modeling and enables investigation of promoter-level stochasticity in complex regulatory networks.