No abstract

In vivo variations in the concentrations of biomolecular species are inevitable. These variations in turn propagate along networks of chemical reactions and modify the concentrations of still other species, which influence biological activity. Because excessive variations in the amounts of certain active species might hamper cell function, regulation systems have evolved that act to maintain concentrations within tight bounds. We identify simple yet subtle structural attributes that impart concentration robustness to any mass-action network possessing them. We thereby describe a large class of robustness-inducing networks that already embraces two quite different biochemical modules for which concentration robustness has been observed experimentally: the Escherichia coli osmoregulation system EnvZ-OmpR and the glyoxylate bypass control system isocitrate dehydrogenase kinase-phosphatase-isocitrate dehydrogenase. The structural attributes identified here might confer robustness far more broadly.

No abstract

No abstract

Abstract. For mass action kinetics, the capacity for multiple equilibria in an isothermal homogeneous continuous flow stirred tank reactor is determined by the structure of the underlying network of chemical reactions. We suggest a new graph-theoretical method for discriminating between complex reaction networks that can admit multiple equilibria and those that cannot. In particular, we associate with each network a species-reaction graph, which is similar to reaction network representations drawn by biochemists, and we show that, if the graph satisfies certain weak conditions, the differential equations corresponding to the network cannot admit multiple equilibria no matter what values the rate constants take. Because these conditions are very mild, they amount to powerful (and quite delicate) necessary conditions that a network must satisfy if it is to have the capacity to engender multiple equilibria. Broad qualitative results of this kind are especially apt, for individual reaction rate constants are rarely known fully for complex reaction networks (if they are known at all). Some concluding remarks address connections to biology. 1]). Models in cell biology sometimes invoke pictures and mathematics reminiscent of CFSTRs [9,12,17,14], so it not unreasonable to expect that theory presented here might ultimately provide insight that is useful in biological applications. Indeed, in biology one rarely has detailed knowledge of reaction rate constants; at the outset, then, it is especially appropriate to seek a qualitative understanding of the relationship between reaction network structure and the capacity for various kinds of behavior (e.g., bistability). As we indicated in the first article of this series [4], the connection between the two is quite delicate. The theory offered here is intended to render the relationship between reaction network structure and behavior more concrete.Our principal results will serve to describe very large classes of networks, including highly complex ones, that cannot give rise to multiple steady states regardless of parameter values. These results provide very strong necessary conditions that a network must satisfy if it is to have the capacity to give rise, for example, to bistable behavior.