Effects of Nonlinear Responses of the Huang-Ferrell Model of MAPK Cascades on the Character of Autocrine Communication

Autocrine communication in cellular systems is mediated by the interaction between extracellular ligands and membrane-bound receptors. In our previous works, we have studied the effects of ligand-receptor kinetics, transport parameters, and interstitial flow on the propagation velocity of autocrine signaling. However, the process of signal transmission strongly depends on the dynamics of intracellular processes. Signal coming from a ligand-receptor complex into the intracellular space is typically amplified in MAPK phosphorylation/dephosphorylation cascade. It was recently shown that the widely accepted Huang-Ferrell model of MAPK signaling offers bistable (switch-like) and oscillatory behavior. These nonlinearities can strongly alter the release of new ligand molecules into intracellular matrix as the MAPK output modifies various transcription factors or activates protease precursors. Here we developed a mathematical model of autocrine communication that considers important reaction-transport processes in the intracellular and extracellular domains together. By the method of stoichiometric network analysis, we have found the minimal subnetwork of MAPK cascade that offers oscillatory behavior and steady state multiplicities. This subnetwork was then incorporated into the model of autocrine signaling, where it plays a role of positive or negative feedback for the process of ligand release. By numerical simulation of the model equation, we study transient behavior of the developed model at the interface between cells with and without high MAPK activity. We identify and classify possible responses of cellular systems to specific regimes of MAPK cascades in parametric space.