Competing docking interactions can bring about bistability in the MAPK cascade

Abstract

Mitogen-activated protein kinases are crucial regulators of various cell fate decisions including proliferation, differentiation, and apoptosis. Depending on the cellular context, the Raf-Mek-Erk mitogen-activated protein kinase cascade responds to extracellular stimuli in an all-or-none manner, most likely due to bistable behavior. Here, we describe a previously unrecognized positive-feedback mechanism that emerges from experimentally observed sequestration effects in the core Raf-Mek-Erk cascade. Unphosphorylated/monophosphorylated Erk sequesters Mek into Raf-inaccessible complexes upon weak stimulation, and thereby inhibits cascade activation. Mek, once phosphorylated by Raf, triggers Erk phosphorylation, which in turn induces dissociation of Raf-inaccessible Mek-Erk heterodimers, and thus further amplifies Mek phosphorylation. We show that this positive circuit can bring about bistability for parameter values measured experimentally in living cells. Previous studies revealed that bistability can also arise from enzyme depletion effects in the Erk double (de)phosphorylation cycle. We demonstrate that the feedback mechanism proposed in this article synergizes with such enzyme depletion effects to bring about a much larger bistable range than either mechanism alone. Our results show that stable docking interactions and competition effects, which are common in protein kinase cascades, can result in sequestration-based feedback, and thus can have profound effects on the qualitative behavior of signaling pathways.

FIGURE 1

Proposed bistability mechanism and model structure. (A–C) Schematic representation of the proposed bistability mechanism. Upon weak stimulation (i.e., at low pRaf levels), Erk and Mek are mostly unphosphorylated/monophosphorylated (indicated by white boxes), and pathway activation is suppressed by Mek sequestration into Raf-inaccessible (p)Mek-(p)Erk heterodimers (A). Stronger stimulation increases the amount of double phosphorylated ppMek, which then triggers Erk double phosphorylation (B). Erk double phosphorylation in turn induces dissociation of Raf-inaccessible Mek-Erk heterodimers (relief from inhibition), and thus amplifies Mek phosphorylation in a positive-feedback circuit (B), so that finally the pathway is completely activated (C). (D) Schematic representation of model topology (see Supplementary Material for differential equations). The black arrows indicate the previously described “basic model” that includes Raf-mediated Mek phosphorylation, Mek-mediated Erk phosphorylation, and the antagonizing phosphatase reactions (27). The “sequestration model” analyzed in this article additionally includes association of various Mek species with unphosphorylated/monophosphorylated Erk (gray arrows), and the resulting Mek sequestration complexes (i.e., Mek-Erk, Mek-pErk, pMek-Erk, and pMek-pErk).

FIGURE 2

Bistability due to Mek sequestration. (A) Bistable stimulus response of the core MAPK cascade. Extracellular stimulation was simulated by varying the total concentration of active Raf (pRaf_tot = pRaf + pRaf-Mek + pRaf-pMek), and bisphosphorylated Erk (ppErk) was taken as the response. The black curve corresponds to the previously analyzed basic model (Fig. 1 D, black arrows), whereas the gray stimulus-response was obtained for the sequestration model, which additionally takes Mek sequestration by Erk into account (Fig. 1 D, black and gray arrows). Kinetic parameters are given in Table 1. (B) Mek release from inactive sequestration complexes upon cascade activation. The amount of sequestered Mek (i.e., Mek-Erk + Mek-pErk + pMek-Erk + pMek-pErk) and the total amount of bisphosphorylated Mek (i.e., ppMek + ppMek-Erk + ppMek-pErk) is shown as a function of total active Raf for the kinetic parameters given in Table 1.

FIGURE 3

Kinetic requirements for bistability. (A) Bifurcation diagram for alterations in kinase expression. The stimulus-response curves of the sequestration model were calculated for varying total Mek and Erk concentrations, and were then classified into monostable (white area) and bistable (gray area). The dashed line corresponds to equal Mek and Erk expression. Default indicates the parameter set given in Table 1. Point I indicates the situation where the Mek concentration is low relative to that of the Erk phosphatase, so that Erk activation is completely abolished. Point II corresponds to a cell that expresses high levels of Mek relative to Erk phosphatase. This provokes strong Erk activation before the Mek cycle is switched on, and therefore excludes coordinated activation of both kinases in a positive-feedback circuit. (B) Bifurcation diagram for alterations in phosphatase expression. Similar to A, but bistable behavior was analyzed for varying maximal velocities (i.e., varying expression) of the phosphatases that dephosphorylate Mek and Erk. See A legend above for explanation of points I and II. Point III indicates the situation where strong Mek-phosphatase expression necessitates high levels of active Raf to elicit Mek phosphorylation. Under these conditions, Mek is strongly sequestered by active Raf, and this abolishes hysteresis.

FIGURE 4

Structural requirements for bistability. The sequestration model depicted in Fig. 1 D was extended to study the topological constraints for bistability. More specifically, Raf-mediated phosphorylation of Erk-bound Mek (i.e., noncompetitive binding of Raf and Erk to Mek) was taken into account. Additionally, we considered ppErk binding to Mek, pMek, and ppMek (i.e., by product inhibition in Erk phosphorylation). The stimulus-response curves of the resulting “extended sequestration model” (see Supplementary Material for differential equations) were classified as monostable and bistable for varying degrees of competition and product inhibition. The competition factor, c, equals the fold change in Raf's affinity for Mek brought about by Erk binding to Mek (and vice versa). Likewise, the product inhibition factor, p, quantifies how the affinity between Erk and Mek is altered by Erk double phosphorylation (relative to unphosphorylated/monophosphorylated Erk). The gray bistability range was calculated using the default parameters given in Table 1. The dashed black line indicates the bistable-to-monostable transition for a 10-fold lower Michaelis-Menten constant of the Mek phosphatase (K_M,Mek-PPase = 0.01 μM).

FIGURE 5

Synergism of bistability mechanisms. A broad range of bistability is observed in the stimulus-response (curve 2) of the sequestration model (Fig. 1 D, black and gray arrows) if the second step of Mek-mediated Erk phosphorylation proceeds faster than the first (“positive cooperativity”). Such pronounced hysteresis can be explained by synergism of the feedback mechanism discussed in this article with that described by Markevich et al. (22), which arises from enzyme depletion effects in the Erk cycle. The gray lines correspond to the stimulus-response curves of reduced models, where one of the two feedback mechanisms was eliminated, and thereby directly demonstrate such synergism. Curve 1 depicts the stimulus response of the basic model (Fig. 1 D, black arrows), which is devoid of Mek sequestration into Raf-inaccessible complexes. Curve 3 corresponds to a sequestration model (Fig. 1 D, black and gray arrows), where positive cooperativity and enzyme-depletion effects in the Erk cycle are eliminated. See Supplementary Material for differential equations and kinetic parameters.