Organizations in reaction-diffusion systems: Effects of diffusion and boundary conditions

Abstract

Chemical Organization Theory (COT) has been successfully applied to analyze complex reaction networks where species interact and new species can emerge. The COT has been well studied, but is yet to analyze high dimensional systems dynamics over time equivalent to ordinary differential equations. Moreover, spatial effects, such as diffusion and boundary conditions have also not been considered yet. Here, we extend the COT to cope with reaction-diffusion systems. Thereby we focus on the effects of diffusion and various boundary conditions. In order to demonstrate the effectiveness of our approach, we analyze two models based on partial differential equations, one of which is on HIV virus dynamics.The analysis shows interesting organizational structures when using different ranges of diffusion rates, as well as for Dirichlet and positive Neumann boundary conditions. The advantage of this novel approach is that it is based solely on the model structure (reaction rules) but is independent of kinetic details, such as rate constants. Hence, it copes with high-dimensional systems without the need of numerical simulations, and it can be applied without detailed mathematical knowledge. Our tool is available, without restriction at https://github.com/stephanpeter/orgs-rds.