Enhancement of tunability of MAPK cascade due to coexistence of processive and distributive phosphorylation mechanisms

Abstract

The processive phosphorylation mechanism becomes important when there is macromolecular crowding in the cytoplasm. Integrating the processive phosphorylation mechanism with the traditional distributive one, we propose a mixed dual-site phosphorylation (MDP) mechanism in a single-layer phosphorylation cycle. Further, we build a degree model by applying the MDP mechanism to a three-layer mitogen-activated protein kinase (MAPK) cascade. By bifurcation analysis, our study suggests that the crowded-environment-induced pseudoprocessive mechanism can qualitatively change the response of this biological network. By adjusting the degree of processivity in our model, we find that the MAPK cascade is able to switch between the ultrasensitivity, bistability, and oscillatory dynamical states. Sensitivity analysis shows that the theoretical results remain unchanged within a reasonably chosen variation of parameter perturbation. By scaling the reaction rates and also introducing new connections into the kinetic scheme, we further construct a proportion model of the MAPK cascade to validate our findings. Finally, it is illustrated that the spatial propagation of the activated MAPK signal can be improved (or attenuated) by increasing the degree of processivity of kinase (or phosphatase). Our research implies that the MDP mechanism makes the MAPK cascade become a flexible signal module, and the coexistence of processive and distributive phosphorylation mechanisms enhances the tunability of the MAPK cascade.

Figure 1

Schematic of processive and distributive mechanisms of the two-site phosphorylation and dephosphorylation cycle. Reactions 3 and 6 represent the corresponding processive mechanisms of kinase and phosphatase, respectively, in this single-layer cycle.

Figure 2

Scheme A. Elementary reactions for the MDP mechanism of kinase phosphorylation in the degree model. The substrate $S_0$ binds reversibly to the kinase, E, forming the enzyme-substrate complex $E{S}_0$. By catalysis reactions, the phosphorylation products of $S_1$ and $S_2$ are released from the intermediate complex with a distributive reaction and a processive reaction, respectively.

Figure 3

Scheme B. Elementary reactions for the MDP mechanism of phosphatase dephosphorylation in the degree model. The substrate $S_2$ binds reversibly to the phosphatase, F, forming the enzyme-substrate complex $F{S}_2$. By catalysis reactions, the dephosphorylation products of $S_1$ and $S_0$ are released from the intermediate complex with a distributive reaction and a processive reaction, respectively.

Figure 4

Schematic of the MDP model of three-layer MAPK cascade. The processive mechanisms of kinase (reactions 12 and 11) and phosphatase (reactions 14 and 13) are integrated into the traditional distribution mechanism in the MAP2K and MAPK layers, respectively. The dash-dotted line indicates the potential feedback of ppMAPK on MAP3K layer. To see this figure in color, go online.

Figure 5

Dose-response curves of the degree model for nonfeedback mode with different degree of kinase processivity, k (a) and phosphatase processivity, p (b).

Figure 6

Dose-response curves of the degree model for positive feedback mode with different degrees of kinase processivity, k (a) and phosphatase processivity, p (b).

Figure 7

Dose-response curves of the degree model for negative feedback mode with different degrees of kinase processivity, k (a) and phosphatase processivity, p (b). To see this figure in color, go online.

Figure 8

Spatial distributions of ppMAPK from cell membrane (left) to nucleus (right) for nonfeedback (a), positive-feedback (b), and negative-feedback (c) modes in the degree model. The distribution curves gradually converge (or diverge) in the direction of propagation when modulating kinase processivity, k (or phosphatase processivity, p) independently.