Asymptotic Robustness in Biochemical Systems

Abstract

Living systems maintain stable internal states despite environmental fluctuations. Absolute concentration robustness (ACR) is a striking homeostatic phenomenon in which the steady-state concentration of a species remains invariant despite changes in total supply. Although experimental studies have reported approximate-but not exact-robustness in steady-state concentrations, such behavior has often been attributed to exact ACR motifs perturbed by measurement noise or minor reactions, rather than recognized as a structural property of a network itself. Here, we introduce a previously underappreciated phenomenon, namely asymptotic ACR (aACR): approximate robustness can emerge solely from the network structure, without requiring exact ACR motifs or negligible parameters. We find that aACR is more pervasive than classical ACR, as demonstrated in systems such as the Escherichia coli EnvZ-OmpR osmoregulation system and a futile cycle. Furthermore, we prove that such ubiquity stems solely from network structure without fine-tuning of kinetic parameters. The notion of aACR provides a rigorous and practical tool to analyze robust responses in broad biochemical systems.