Operating regimes in a single enzymatic cascade at ensemble-level.

Single enzymatic cascade, ubiquitously found in cellular signaling networks, is a phosphorylation-dephosphorylation reaction cycle causing a transition between inactive and active states of a protein catalysed by kinase and phosphatase, respectively. Steady-state information processing ability of such a cycle (e.g., MAPK cascade) has been classified into four qualitatively different operating regimes, viz., hyperbolic (H), signal-transducing (ST), threshold-hyperbolic (TH) and ultrasensitive (U). These four regimes represent qualitatively different dose-response curves, that is, relationship between concentrations of input kinase (e.g., pMEK) and response activated protein (e.g., pERK). Regimes were identified using a deterministic model accounting for population-averaged behavior only. Operating regimes can be strongly influenced by the inherently present cell-to-cell variability in an ensemble of cells which is captured in the form of pMEK and pERK distributions using reporter-based single-cell experimentation. In this study, we show that such experimentally acquired snapshot pMEK and pERK distribution data of a single MAPK cascade can be directly used to infer the underlying operating regime even in the absence of a dose-response curve. This deduction is possible primarily due to the presence of a monotonic relationship between experimental observables RIQR, ratio of the inter-quartile range of the pERK and pMEK distribution pairs and RM, ratio of the medians of the distribution pair. We demonstrate this relationship by systematic analysis of a quasi-steady state approximated model superimposed with an input gamma distribution constrained by the stimulus strength specific pMEK distribution measured on Jurkat-T cells stimulated with PMA. As a first, we show that introduction of cell-to-cell variability only in the upstream kinase achieved by superimposition of an appropriate input pMEK distribution on the dose-response curve can predict bimodal response pERK distribution in ST regime. Implementation of the proposed method on the input-response distribution pair obtained in stimulated Jurkat-T cells revealed that while low-dosage PMA stimulation preserves the H regime observed in resting cells, high-dosage causes H to ST regime transition.