Operating regimes in a single enzymatic cascade at ensemble-level

Abstract

Operating regime of a single enzymatic cascade such as ubiquitously conserved MAPK building block provides insights into the nature of the sensitivity of the steady-state dose response that maps the upstream kinase and the downstream activated substrate concentrations. Steady-state response can be viewed either at a single-cell level in an ensemble of cells or at population-average level. Four operating regimes, viz., hyperbolic, threshold-hyperbolic, signal transducing and saturated, have been identified using the population-average level dose response curve. However, cell-to-cell variability exists in enzymatic cascades. This variability is captured using reporter based experimentation at ensemble level which permits detection of snapshot(s) of ensemble-level distribution of phosphorylated proteins. As a result, often the corresponding underlying steady-state dose response curve may not be available. We consider the question if the underyling operating regime can be directly inferred from ensemble level snapshot upstream kinase (input) and downstream phosphorylated substrates (response) distributions. In order to address this question, we use mathematical model of a single enzymatic cascade based on quasi-steady state approximation superimposed with an input distribution constrained by single-cell level experimental measurements of the MAPK cascade in Jurkat E6.1 cells stimulated with Phorbol Myristate Acetate (PMA). We prove that, under steady-state conditions, a monotonic relationship between the R IQR (=ratio of the inter-quartile range of the response and input distributions) and R m (=ratio of medians of the two distributions), both of which are experimental observables, can be used to identify the underlying operating regime. We also show that the identification of the unimodal vs bimodal nature of the response distributions can further lead to identification of the potential parameter range in the planes of Michaelis-Menten constants K 1 and K 2 , the two key parameters that dictate the operating regimes. We implement the proposed method on the stimulus strength dependent steady-state single-cell 3 level pMEK (input) and pERK (response) distributions in Jurkat E6.1 cells treated with PMA.While cells stimulated using low concentrations of PMA are likely to operate in hyperbolic regime, those exposed to higher concentrations may lie in signal-transducing regime. Author's summarySingle enzymatic cascade, a ubiquitously found key building block in biological signaling networks, exhibits different steady-state behaviour at population (ensemble) level compared to population-averaged response. Detection at ensemble level typically achieved by nonplasmid based reporter permits snapshot fluorescence distribution measurement. We ask if there are signatures of fluorescence distribution of input kinase and response activated protein that can help decipher the underlying dose-response belonging to four distinct operating regimes a single enzymatic cascade exhibits. Based on simultaneously measured snapshot input (pME...

Retroactivity induced operating regime transition in a phosphorylation-dephosphorylation cycle

“…Input-output behaviour of an activated phosphorylation-dephosphorylation cycle (PdPC) has been studied extensively due to its ability to orchestrate cell fate in direct and indirect contextdependent manner (Chang and Karin, 2001;Dhanasekaran and Johnson, 2007;Parundekar et al, 2019). Michealis-Menten constants (MM) dictated saturated/unsaturated state of the two enzymatic reactions facilitates placing steady-state dose-response curves of a PdPC into Signal transducing (ST), Hyperbolic (H), Threshold hyperbolic (TH) and Ultrasensitive (U) operating regimes (Gomez-Uribe et al, 2007).…”

“…As a reference, we employ the nominal profiles corresponding to the case wherein retroactivity is absent. This classification has been suggested by Gomez-Uribe (Gomez-Uribe et al, 2007) and adopted in several recent studies (Straube, 2017;Parundekar et al, 2019).…”

“…for all n=H, ST, TH, and U. This criterion is based on the metric suggested by Gomez-Uribe et al (Gomez-Uribe et al, 2007) and recently used in Parundekar et al (Parundekar et al, 2019).…”

“…Operating regimes of the MAPK cascades juxtaposed with patient-stratification data have recently been considered in disease prognostics (Fey et al, 2015). Recently, using a hybrid deterministic-stochastic approach for predicting and characterising the input-output behaviour of a single PdP MAPK cycle from ensemble data it was shown that a dose-strength dependent regime transition can occur between H and ST regimes (Parundekar et al, 2019). A quasi-steady-state approximation Michealis-Menten model (Michaelis and Menten, 1913) employed in the hybrid approach (Parundekar et al, 2019) could not explain the observed dosestrength dependent regime transition.…”

“…Recently, using a hybrid deterministic-stochastic approach for predicting and characterising the input-output behaviour of a single PdP MAPK cycle from ensemble data it was shown that a dose-strength dependent regime transition can occur between H and ST regimes (Parundekar et al, 2019). A quasi-steady-state approximation Michealis-Menten model (Michaelis and Menten, 1913) employed in the hybrid approach (Parundekar et al, 2019) could not explain the observed dosestrength dependent regime transition. A question thus arises as to what could be the mechanism that may govern the observed stimulus-strength dependent operating regime transition under steady-state conditions.…”