We propose two step-by-step approaches to the analysis of robustness in biochemical networks. Our aim is to measure the ability of the network to exhibit step-by-step limited variations on the concentration of a species of interest at varying of the initial concentration of other species. The first approach we propose is reaction-by-reaction, i.e. we compare the states reached by nominal and perturbed networks after they have performed the same number of reactions. We provide a statistical technique allowing for estimating robustness, we implement it in a tool called spebnr ( a Simple Python Environment for statistical estimation of Biochemical Network Robustness ) and showcase it on three case studies: the EnvZ/OmpR osmoregulatory signaling system of Escherichia Coli, the mechanism of bacterial chemotaxis of Escherichia Coli, and enzyme activity at saturation. Then, we consider a time-by-time approach, in which networks are compared on the basis of the states they reached at the same time point, regardless of how many reactions occurred. This approach is implemented in Stark , and we apply it to the study the robustness of the EnvZ/OmpR osmoregulatory signaling system and the Lotka-Volterra equations.

In this paper, we recall the basic features of the CospanSpan(Graph) algebra for the compositional description of reconfigurable hierarchical networks. In particular, we focus on compositionality and on the possibility of describing the interactions among physical/biological systems, using a parall el with communication operation not considered in the usual Kleene’s algebra. As a novel application, we give a complete compositional description in Span(Graph) of a simplified version of the heart system.