Thermodynamically consistent, reduced models of gene regulatory networks.

Synthetic biology aims to engineer novel functionalities into biological systems. While the approach has been predominantly applied to single cells, a richer set of biological phenomena can be engineered by applying synthetic biology to cell populations. To rationally design cell populations, we require mathematical models that link between intracellular biochemistry and intercellular interactions. In this study, we develop a kinetic model of gene expression that is suitable for incorporation into agent-based models of cell populations. To be scalable to large cell populations, models of gene expression should be both computationally efficient and compliant with the laws of physics. We satisfy the first requirement by applying a model reduction scheme to translation and the second requirement by formulating models using bond graphs, a modelling approach that ensures thermodynamic consistency. Our reduced model is significantly faster to simulate than the full model and reproduces important behaviours of the full model. We couple separate models of gene expression to build models of the toggle switch and repressilator. With these models, we explore the effects of resource availability and cell-to-cell heterogeneity on circuit behaviour. The modelling approaches developed here are a bridge towards engineering collective cell behaviours such as synchronization and division of labour.