Simulating the dynamics of gene regulatory systems at cellular scale

Abstract

The temporal nature of eukaryotic gene expression is the result of a complex, non-linear, dynamical system of regulatory processes. So far, models of such systems trade realism for tractability by using strict simplifying assumptions. These simplified models are often unfaithful to our biological understanding; however, without such simplifications, analytical solutions become more challenging and these dynamical systems must then be studied through simulation. Here, we explore the question of how this complex web of gene regulatory connections can be faithfully simulated for all tens of thousands of genes that usually define a eukaryotic organism. We present a proof-of-principle model and simulator, GeneRegulatorySystems.jl which is based on a biophysical chemical master equation that overcomes three key restrictions. First, it allows an exact stochastic simulation of fully non-linear gene expression dynamics, including feedback control, to parsimoniously capture cause and effect relationships of gene regulation. Further, it includes a general framework for implementing diverse mechanisms of gene control such as protein mediated degradation, RNAi, and protein complex formation. Finally, it scales realistically to tens of thousands of genes. We achieve this by introducing a domain-specific programming language to aid the design of experimental protocols from small-scale, well-studied, scenarios of gene regulation inspired by dynamical systems biology up to large-scale, single cell omics experiments with interventions. In this way, our framework provides a grammar of in silico experimental design that can capture single-cell gene expression dynamics for entire genomes.