The pseudo-compartment method for coupling partial differential equation and compartment-based models of diffusion

摘要: Spatial reaction–diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted the literature implements systems of partial differential equations (PDEs), which assumes there are sufficient densities particles that a continuum approximation is valid. However, owing recent advances computational power, simulation and therefore postulation, computationally intensive individual-based has become popular way investigate effects noise regions low copy numbers exist. specific stochastic with we shall be concerned this manuscript referred as ‘compartment-based’ or ‘on-lattice’. These characterized by discretization domain into grid/lattice ‘compartments’. Within each compartment, assumed well mixed permitted react other within their compartment transfer between neighbouring compartments. Stochastic provide accuracy, but at cost significant resources. For both high concentrations, it often desirable, for reasons efficiency, employ coupled multi-scale paradigms. In work, develop two hybrid algorithms PDE one region compartment-based model other. Rather than attempting balance average fluxes, our answer more fundamental question: ‘how individual transported vastly different descriptions?’ First, present an algorithm derived carefully redefining continuous concentration probability distribution. While first shows very strong convergence analytical solutions test problems, can cumbersome simulate. Our second simplified efficient implementation first, limit over alone. We methods functionality accuracy variety scenarios comparing averaged simulations PDEs mean concentrations.