Minimal oscillating subnetwork in the Huang-Ferrell model of the MAPK cascade

Abstract

Prompted by the recent growing evidence of oscillatory behavior involving MAPK cascades we present a systematic approach of analyzing models and elucidating the nature of biochemical oscillations based on reaction network theory. In particular, we formulate a minimal biochemically consistent mass action subnetwork of the Huang-Ferrell model of the MAPK signalling that provides an oscillatory response when a parameter controlling the activation of the top-tier kinase is varied. Such dynamics are either intertwined with or separated from the earlier found bistable/hysteretic behavior in this model. Using the theory of stability of stoichiometric networks, we reduce the original MAPK model, convert kinetic to convex parameters and examine those properties of the minimal subnetwork that underlie the oscillatory dynamics. We also use the methods of classification of chemical oscillatory networks to explain the rhythmic behavior in physicochemical terms, i.e., we identify of the role of individual biochemical species in positive and negative feedback loops and describe their coordinated action leading to oscillations. Our approach provides an insight into dynamics without the necessity of knowing rate coefficients and thus is useful prior the statistical evaluation of parameters.

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

“…The other region is characterized by the coexistence of the off‐state, two unstable steady states, and one stable periodic regime. The origin of both these regions comes from the dynamics of the MAPK cascade as it was reported previously ,. Particularly, analytical expressions for boundaries of the bistability region in the parameter space of the MAPK cascade itself (here it corresponds to the region with three stable steady states) have been found .…”

“…Either the unphosphorylated form B or double phosphorylated form B2 dominates in these steady states, which is the result of the competition of B and B1 forms for the binding sites of A*. Stable periodic regimes in MAPK cascade emerge when A* can be reversibly produced from A . A detailed explanation of the mechanisms leading to bistability and oscillations is given in Ref …”

“…Stable periodic regimes in MAPK cascade emerge when A* can be reversibly produced from A . A detailed explanation of the mechanisms leading to bistability and oscillations is given in Ref …”

“…The reaction network schematically drawn in Figure is still quite complex. Recently, we have identified a minimal subnetwork in the MAPK cascade that allows for the emergence of bistable and oscillatory regimes . The subnetwork exhibits qualitatively the same behavior as the original cascade.…”

“…Briefly, (i) the last stage of MAPK cascade does not qualitatively contribute to the complexity of MAPK dynamics, i. e. the components C, C1, and C2 were removed, (ii) the enzymes phosphatases were considered in pool conditions, (iii) the reverse dissociation steps of enzyme‐substrate complexes were removed as they do not contribute to the emergence of instabilities, (iv) the quasi‐steady state approximation was used for all enzyme‐substrate complexes except the MAPKKK‐MAPKK complex (A*B). Detailed justification of these simplification steps is provided in Refs . Further, we assume that the activation of A to A* is described by the first order kinetics with respect to the ligand‐receptor complex concentration K and to the concentration of inactive form A.…”