Influence networks and network emulation. (A-B) Each node represents an influence species. The ball-head represents an activation influence, the bar-head represents an inhibition influence, and a simple edge represents an outgoing influence to another node. Each species activates or inhibits other species catalytically. (A) MI network: y activates itself and inhibits z, and conversely z activates itself and inhibits y. (B) QI network: a more complex pattern. The colors represent mappings of species and reactions from QI to MI. (C) Each influence species is represented by three chemical species, yielding 6 traces for MI with arbitrarily chosen rates and initial conditions. The vertical axis is species concentrations, and the horizontal axis is time. (D) Via an appropriate network morphism, we can always fix rates and initial conditions for QI such that its 12 traces overlap in pairs, and exactly overlap the 6 traces of MI. Also, as a consequence, QI reaches the same steady state as MI. The rates and initial conditions for QI do not sum to, but rather copy, those of MI.