BIOMD0000000009 - Huang1996_MAPK_ultrasens

This a model from the article:
Ultrasensitivity in the mitogen-activated protein kinase cascade.
Huang CY, Ferrell JE Jr Proc. Natl. Acad. Sci. U.S.A. [1996:93(19):10078-83; PMID: 8816754,
Abstract:
The mitogen-activated protein kinase (MAPK) cascade is a highly conserved series of three protein kinases implicated in diverse biological processes. Here we demonstrate that the cascade arrangement has unexpected consequences for the dynamics of MAPK signaling. We solved the rate equations for the cascade numerically and found that MAPK is predicted to behave like a highly cooperative enzyme, even though it was not assumed that any of the enzymes in the cascade were regulated cooperatively. Measurements of MAPK activation in Xenopus oocyte extracts confirmed this prediction. The stimulus/response curve of the MAPK was found to be as steep as that of a cooperative enzyme with a Hill coefficient of 4-5, well in excess of that of the classical allosteric protein hemoglobin. The shape of the MAPK stimulus/ response curve may make the cascade particularly appropriate for mediating processes like mitogenesis, cell fate induction, and oocyte maturation, where a cell switches from one discrete state to another.

The species K_PP_norm, KKK_P_norm and KK_PP_norm are the relative concentrations of the active MAPK, MAPKK and MAPKKK, that is the double, or single resp. phophorylated forms divided by the total concentrations of each kinase. For MAPK additionally the also active MAPK divided by the maximal concentration of active MAPK is given by rel_K_PP_max. The parameter K_PP_norm_max, the maximal ratio of active MapK, has to be calculated for each change of parameters.

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