Thermodynamically-consistent, reduced models of gene regulatory networks

Abstract

AbstractSynthetic biology aims to engineer novel functionalities into biological systems. While the approach has been widely applied to single cells, the scale of synthetic circuits designed in this way is limited by factors such as resource competition and retroactivity. Synthetic biology of cell populations has the potential to overcome some of these limitations by physically isolating synthetic genes from each other. To rationally design cell populations, we require mathematical models that link between intracellular biochemistry and intercellular interactions. The interfacing of agent-based models with systems biology models is particularly important in understanding the effects of cell heterogeneity and cell-to-cell interactions. In this study, we develop a 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. We show that the reduced model of translation faithfully reproduces the behaviour of the full model at steady state. The reduced model is benchmarked against the full model, and we find a sub-stantial speedup at realistic protein lengths. Using the modularity of the bond graph approach, 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 in this study are a bridge towards rationally designing collective cell behaviours such as synchronisation and division of labour.