Traveling‐wave Phenomena in a Model of Autocrine Signaling Coupled with Dynamics of the MAPK Cascade

Abstract

Recently we have revealed a minimal reaction subnetwork in the MAPK (mitogen‐activated protein kinase) cascade that is responsible for the emergence of bistable and oscillatory behavior. Here we examine a possible mechanism that provides for the propagation of increased MAPK activity in cell populations by interconnecting the intracellular MAPK subnetwork with the ligand‐receptor signaling machinery. Such approach allows for significant reduction of the dimensionality of the parameter space on one hand and the conservation of dynamical complexity of the system on the other hand. The coupled model predicts coexistence of one, two or three different stable steady states, or the coexistence of a stable steady state and periodic solution. We found two robust and physiologically relevant characteristics of the proposed model: (i) There is a very large region of coexistence of at least one stable steady state with non‐zero MAPK activity and one steady state with zero MAPK activity in the parameter space. (ii) Spontaneous traveling front waves always switching originally inactive cells into ligand releasing cells emerge in adjacent cell populations, e. g. in healthy and injured tissues. Moreover, the formation of composite traveling front waves and spatial oscillatory patterns of MAPK activity are predicted and discussed.