Conditions for the computation of the species’ time-integrals in terms of the Species-Reaction graph.

The conditions amount to the graph having a (possibly disjoint) subgraph containing every red R-node with all their adjacent red S-nodes not linked with any black R-nodes; in this subgraph, the number of red R-nodes and red S-nodes must be the same. (A) Networks with two nonlinear reactions () satisfying the conditions. The red subgraphs are marked with dashed boxes. (B) Networks that do not satisfy the conditions. (C) A generic complex-formation mechanism satisfying the conditions. A spatially-fixed molecule binds a diffusible ligand to form a complex . Species and are synthesized at a constant rate and linearly degraded. External stimuli of ligand can be modeled via a spatiotemporal influx . The Species-Reaction graph is shown in the inset. (D) Genetic regulation via protein sequestration [12] is an instance of the mechanism in C. A nondiffusive inhibitor sequesters a transcriptional activator to form an inactive complex , causing the downregulation of gene expression.