Conditions for the computation of the species’ time-integrals in terms of the Species-Reaction graph. A. OyarzúnDiego López-CaamalFernando R. GarcíaMíriam H. MiddletonRichard Y. WeißeAndrea 2013 <p>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. (<b>A</b>) Networks with two nonlinear reactions () satisfying the conditions. The red subgraphs are marked with dashed boxes. (<b>B</b>) Networks that do not satisfy the conditions. (<b>C</b>) 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. (<b>D</b>) Genetic regulation via protein sequestration <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0062834#pone.0062834-Buchler1" target="_blank">[12]</a> is an instance of the mechanism in <b>C</b>. A nondiffusive inhibitor sequesters a transcriptional activator to form an inactive complex , causing the downregulation of gene expression.</p>