Modeling and simulation of Lac-Operon using reaction-diffusion master equation on heterogeneous parallel platforms

Abstract

The Lac-Operon is a pivotal molecular mechanism controlling gene expression in response to presence or absence of lactose. Mastering its dynamics aids cellular comprehension and gene circuit design. Employing the multi-particle diffusion reaction-diffusion master equation (MPD-RDME), we model gene expression kinetics. This couples with the Gillespie algorithm-driven Next sub-volume method for particle reactions and diffusion, enabling predictive time-course molecule concentration insights via RDME and Gillespie. Such insights inform experimentation and elucidate cellular operations. Particularly, inducible operon kinetics, like Lac-Operon, hold applications in recombinant protein production and gene therapy. Our work constructs a Lac-Operon gene expression model utilizing MPD-RDME and Next sub-volume on a Heterogeneous Parallel Platform (HPP). Implementation employs the combination of host and GPU, and host and homogeneous GPU pairs. Simulation speed, affected by external inducers, repressor count, and lattice spacing, is compared. Protein and mRNA count under various conditions were simulated on host, GPU, and GPU pairs. Results display 75 %–80 % speed enhancement on the HPP compared to host and GPU combination. This adaptable method extends to explore diverse gene circuits, unraveling molecular-level biological system behaviors.