Operating regimes in a single enzymatic cascade at ensemble-level
Authors: Parundekar Akshay , Kalantre Girija , Khadpekar Akshada , Viswanathan Ganesh 
Published: March 2019

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 RIQR(=ratio of the inter-quartile range of the response and input distributions) and Rm(=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 constantsK1andK2, the two key parameters that dictate the operating regimes. We implement the proposed method on the stimulus strength dependent steady-state single-cell 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 summary

Single 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 non-plasmid 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 (pMEK) and response (pERK) protein levels in an ensemble of PMA stimulated immortalized cancer (Jurkat E6.1) cells, we superimpose pMEK data-guided upstream kinase distribution capturing cell-to-cell variability on the steady-state Michaelis-Menten (MM) kinetic model. Following extensive MM constants sampling and simulations, we systematically identify that monotonicity between RIQR, the ratio of the inter-quartile range of response and input distributions, and RM, the median ratio of the two distributions, enables regime identification of the measured pERK distribution. We further show qualitative assessment of the modality of the response distribution can constrain the parameter range within an operating regime. Both RIQRand RMbeing experimental observables makes the proposed method suitable for assessing signal modulation capability of an enzymatic cascade of interest.