A theoretical modeling for frequency modulation of Ca2+ signal on activation of MAPK cascade Original Research Article

It is known that Ca2+ signal regulates mitogen-activated protein kinase (MAPK) cascade by a central Ras protein in GTPase-cycle. Therefore, we construct an integrated theoretical model comprising Ca2+ oscillations, GTPase-cycle and MAPK cascade modules sequentially. Meanwhile, based on multiple feedback regulations in MAPK cascade, three operation modes of this model are introduced. An extended version of this model is further built when spatial heterogeneity is involved. These models allow us to investigate the very interesting and broad question about the effects of Ca2+ oscillations on the activation of MAPK cascade in both the homogeneous and heterogeneous systems. When the Li–Rinzel model is adopted to simulate endogenous Ca2+ oscillations, our theoretical results illustrate that the appropriate operation mode of MAPK cascade is required for the negative correlation between a decreasing frequency of Ca2+ oscillations and activation of MAPK cascade, which was found in the experiment (S. Kupzig et al. PNAS 102 (2005) 7577–7582). While a piecewise function is used to generate Ca2+ signal to explore much larger range of periods of Ca2+ oscillations, it is found that the negative correlation feature is independent on the operation mode of MAPK cascade. In this case, different operation modes only influence the strength of negative correlation between activation of MAPK cascade and periods of Ca2+ oscillations. The quantitative results may be of great use in analyzing interaction of IP3 − Ca2+ and Ras–MAPK signaling pathways, and motivate the further experimental research.