Paper detail

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

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-$κ$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.