Non-monotonic Response to Monotonic Stimulus: Regulation of Glyoxylate Shunt Gene-Expression Dynamics in Mycobacterium tuberculosis

Understanding how dynamical responses of biological networks are constrained by underlying network topology is one of the fundamental goals of systems biology. Here we employ monotone systems theory to formulate a theorem stating necessary conditions for non-monotonic time-response of a biochemical network to a monotonic stimulus. We apply this theorem to analyze the non-monotonic dynamics of the σB-regulated glyoxylate shunt gene expression in Mycobacterium tuberculosis cells exposed to hypoxia. We first demonstrate that the known network structure is inconsistent with observed dynamics. To resolve this inconsistency we employ the formulated theorem, modeling simulations and optimization along with follow-up dynamic experimental measurements. We show a requirement for post-translational modulation of σB activity in order to reconcile the network dynamics with its topology. The results of this analysis make testable experimental predictions and demonstrate wider applicability of the developed methodology to a wide class of biological systems.Author Summary: Over the last several years mathematical modeling has become widely used to understand how biochemical systems respond to perturbations. In particular, dynamics of the response, i.e. the precise nature of how the responses changes with time, has become the focus of multiple studies. However, to this date only a few general rules that relate the dynamical responses with the structure of the underlying networks have been formulated. To this end, we ask which properties of the network allow systems to have a non-monotonic time-response (first increasing and then decreasing) to a monotonically increasing signal. We show that the networks displaying such responses must include indirect negative feedback or incoherent feedforward loop. Applying this result to the measured non-monotonic expression for glyoxylate shunt genes in Mycobacterium tuberculosis, a network known to be important to mycobacterial virulence, we show that the currently postulated network structure does not match the predictions of the theorem. Using a combination of mathematical modeling and follow-up experimental test we predict a novel incoherent loop in the network. This methodology has wide applications outside the specific network studied in this work—the theorem may potentially simplify the analysis of many biological systems.