Introduction

The highly conserved MAP kinase cascade module is composed by three kinases, MAPK kinase kinase (MAPKKK), MAPK kinase (MAPKK) and MAPK [11]. Either a small GTP-binding protein or another kinase (e.g. PKC) serves as input for the cascade and activate MAPKKK. The activated MAPKKK phosphorylates MAPKK at two serine residues. Dual phosphorylated MAPKK works as threonine/tyrosine kinase and phosphorylates MAPK at two conserved loci. MAPK acts mainly as a kinase for transcription factors, but it can also phosphorylate protein kinases and phospholipases. This three step cascade is present in all eukaryotes and has a wide range of functions in signal transductions, such as stress-response, cell-cycle-control, cell-wall-construction, osmosensing, growth and differentiation.

Figure 1: A schematic view of the MAPK cascade

But why does the module have three steps? It is obvious, that one possible function is to generate high amplification [6]. Another role of the three steps might be to generate switch-like output. This seems reasonable, since the MAPK module is used for many important decisions in cells. On the other hand Asthagiri and Laufenburger argue that the integral of activated MAPK over time may serve as a reasonable metric for the output [3] rather than the steady state of the system. In this case, MAPK cascade can work as a feedback controller capable to adapt to different stimuli. Such a robust adaptation has been demonstrated in bacterial chemotaxis [12]. Moreover, the three steps might be used to integrate many inputs, like as it is known in osmosensors.

The aim of this paper is the analysis fo switch-like behavior, amplification and feedback in previously published models of the MAPK cascade. Three models of MAPK can be found in the literature. Huang and Ferrell [9] developed a model to describe MAPK activation in Xenopus oocyte, they focused on the role of MAPK in all-or-none decisions [8]. Within a model large model of second messenger cascades in neurons, Bhalla and Iyengar [4] also model the MAPK module. They focus rather on properties of the whole network like bistability and oscillations than on features of small modules. Another module version is described by Asthagiri/Laufenburger [3,2], where they illustrate how the MAPK cascade shows adaptation.

In the following we compare module versions of Refs. [7] and [4] using the kinetic parameters of these papers as a default setting.

Figure 2: These plots show the steady-state activation of the three kinases involved in the MAPK cascade module for the models according to Bhalla/Iyengar [4] (left) and Huang/Ferrell [9] (right). The Huang/Ferrell model shows increasing switch-like behavior going downstream in the cascade. For the Bhalla/Iyengar model the sigmoidality increases only slightly from the the first to the next step.