Retroactivity induced operating regime transition in a phosphorylation- dephosphorylation cycle

Operating regimes characterizing the input-output behaviour of an activated phosphorylation-dephosphorylation reaction cycle (PdPC) such as a single MAPK cascade are dictated by the saturated/unsaturated state of the two underlying enzymatic reactions. Four combinations of the states of these two enzymatic reactions led to identification of distinct operating regimes, viz., Hyperbolic (H), Signal transducing (ST), Threshold-hyperbolic (TH) and Ultrasensitive (U). A single PdPC without an explicit feedback have been classically viewed as a module offering signal flow from upstream to downstream, that is, one-way communication. Recently it has been shown that load due to sequestration of the phosphorylated or unphosphorylated form of the substrate by corresponding downstream targets permits retroactive signalling that offers two-way communication. We systematically characterize the operating regimes of a single PdPC subject to retroactivity in either of the substrate forms. We identify five possible regime transitions that could be achieved by increasing the retroactivity strength on either of the two substrate forms. Remarkably, a retroactivity strength of 0.30 in the unphosphorylated form of the substrate is sufficient to induce a transition from ST to H regime indicating that the input-output behaviour of a PdPC is highly sensitive to the presence of a downstream load. Using sensitivity and rate-balance analysis, we show that modulation of the saturation levels of the two enzymatic reactions by increasing retroactivity is the fundamental mechanism governing operating regime transition. HighlightsO_LICharacterization of operating regimes in the presence of retroactivity. C_LIO_LIRetroactivity can induce a transition between different operating regimes. C_LIO_LISaturation levels of the two enzymatic reactions govern the regime transition. C_LIO_LISensitivity of the protein levels to retroactivity is dictated by saturation levels. C_LI