Developing a computational tool for multiscale simulations of chemically coupled cell populations

Many biological systems are spatially organised, from animals and plants to microbial communities. Mathematical modelling can help us improve our understanding of, and design better-informed experiments to probe, the dynamics of such systems. The development of computational tools for modelling spatially organised biological systems has largely focused on either so-called agent-based models or on physico-chemical models based on partial differential equations (PDEs) Agent-based models can readily incorporate cell-specific properties such as speciation, cell cycle dynamics, and replication. However, these models typically allow limited spatial resolution for chemical dynamics, have a high computational cost, and can be affected from user-implementation choices, such as the chosen sequence of simulation updating rules. In contrast, PDE-based models allow a much finer grained simulation based on densities of state variables and are well suited to simulations based on physical properties, geometry, mechanical motion, and chemical reactions; however, cell-specific attributes cannot be readily incorporated in these models. Here, we combine the benefits of agent-based and PDE models, by extending an existing software library, Chaste, to allow coupling between agent-based and PDE models. Chaste is a modular, open-source PDE solver platform that is widely used by the systems biology community already. It utilises finite element solvers to simulate individual reaction-diffusion equations, coupled to a mesh-based layer that defines structures acting as chemical sources or sinks. These PDE solvers may be solved across a mutable mesh embedded with a wide range of cell-based modelling paradigms with easily customisable modular cell behaviours, aspects enhanced when compared to similar softwares. Here, we expand this CHASTE functionality to allow the simulation of complex reaction-diffusion dynamics with multiple PDE variables and multiple cell structures. The resulting system will allows us to model and simulate multicellular systems coupled through any number of shared or communicated chemicals. As such, the new system will be suitable to study the dynamics of biological systems such as bacterial biofilms. In our own work, we aim to use this extended CHASTE platform to simulate early evolution of protocellular metabolic systems, in particular, reaction systems that are separated across cell-like phase separations in an otherwise homogenous primordial soup. Spatial dynamics in such early metabolic systems have not been considered to date and it will be interesting to characterise what kind of system dynamics can emerge under different parameter regimes of metabolite diffusion, phase dynamics, and reaction kinetics.