Jianqiang Sun, Ming Yi*, Lijian Yang, Wenbin Wei，Yiming Ding, Ya Jia； Enhancement oftunability of MAPK cascade due to coexistence of processive and distributivephosphorylation mechanisms,

Biophysical journal, 106, 1215–1226,(2014).

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 mixeddual-site phosphorylation (MDP) mechanism in a single-layer phosphorylation cycle. Further, we build a degree model byapplying 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 switchbetween 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 ourfindings. 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 theMAPK cascade become a flexible signal module, and the coexistence of processive and distributive phosphorylation mechanismsenhances the tunability of the MAPK cascade.