SBML models of the MAP kinase pathway

Important Notes

1.) WARNING: The SBML models presented here are `wrong' in the following biological sense:
The models have a volume of size 1, which avoids conversion of the usual literature rate laws in units [concentration/time] to SBML's kinetic laws in units [substance/time] (default [µmol/sec]).

2.) NEW / BETTER VERSIONS: Some of the models below have been or are currently being adopted by the curated SBML model repository at biomodels. Please see the there for corrected and curated models. This repository is NOT MAINTAINED anymore.

3.) Several models were handwritten, and initially had severe syntactic erros. Thanks to Nicolas Le Novère for reporting. Hand-writing SBML is NOT recommended!

Models and Simulation Results

`oS results' lead you to websites displaying simulation results for the SBML versions of some published models of the MAP kinase pathway. The websites were generated with a Perl wrapper around the SBML_odeSolver (oS), a C command line tool, based on CVode and libSBML, the SBML C/C++ library.

Huang and Ferrel 1996:

oS results (ultrasensitivity) PubMed
The model was constructed by hand, from instructions in the original paper.
First published ODE model of the MAP kinase pathway! It was used to analyze the intrinsic ultrasensitivity of the cascade, that can (in part) account for a switch-like or all-or-none response to a progesterone signal of the Mos/MEK1/ERK2 pathway in Xenopus oocytes. Importantly the ultrasensitive behaviour depends on a two-step dual phosphorylation mechanism. Ferrell later showed that actual ultrasensitive behaviour additionally depends on a positive feedback via expression (translation) of the upstream kinase Mos, and is possibly further supported by co-translocation of MEK and ERK to the nucleus (where concentration increases due to smaller volume).

Kholodenko 2000:

oS results (oscillations) PubMed
The model was obtained from the official SBML model repository.
Potential for oscillatory behaviour of the MAP kinase pathway through a negative feedback form MAP kinase to MAPKK kinase, which however is unlikely/unknown to cause oscillations in in vitro or in vivo MAP kinase activation. The MAP kinase pathways are however, integrated - as a driving input - into many oscillatory systems, such as the cell cycle, the somitogenesis clock, or Dictyostelium cAMP signaling.

Markevich NI, Hoek JB, Kholodenko BN. 2004:

oS results (enyzme, and) oS results (mass action kinetics of Figure 1) PubMed
Above oS results were derived from (hand written) SBML versions of elementary step and mass action kinetics models of the reaction scheme in Figure 1.
Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades. J Cell Biol. 2004 Feb 2;164(3):353-9.
A model of the dual protein phosphorylation/dephosphorylation cycle of the MAP kinase. The model shows bistability in the absence of `real' positive feedback, contradictory to Thomas' conjecture ( Thomas 1976). This depends on an `apparent feedback' of the dual specificity converter enzymes: substrate saturation of the kinase (or the phosphatase, or both) leads to competitive inhibition of the second step by the product of the first step (= substrate of the second step). The parameter space domain for bistability is restricted by product inhibition, which was modelled in detail for the phosphatase reactions.
The work also analyses differences arising between models of elementary steps of catalysis, vs. Michaelis-Menten like descriptions of enzyme kinetics, that don't explicitly account for enyzme-substrate or enzyme-product complexes.

Schoeberl 2002:

oS results PubMed
The model was obtained from SigPath and intensively modified by hand. It is still not complete!!! The original Mathematica model compared complex formation on activated receptors (with the same reaction parameters) for both membrane-bound and internalized receptors. In this version of the model, only receptor activation at the membrane is included and internalization is thus treated as a sink for receptors. Reaction names, eg. v18_65, indicate that this reaction was modelled two times in the original model. Reaction names generally correspond to the figure in the original paper.
Thanks to Martin Ginkel for clarification! A full model will be available as soon as possible.
The incorrect model, that illegally coupled reaction v14 of an internalized species to membrane bound species, is still available at schoeberl_02 incorrect!.
Model of the effects of EGF receptor activation/internalization dynamics on SHC/GRB2/SOS adaptor complexes and Ras mediated activation of the Raf/MEK/ERK pathway. Quote: "It shows that EGF-induced responses are remarkably stable over a 100-fold range of ligand concentration and that the critical parameter in determining signal efficacy is the initial velocity of receptor activation." The model's dynamics were well supported and documented by an experimental system in HeLa cell culture.
The initial velocity of EGF receptor activation in fibroblasts was shown to depend on a positive (double negative) feedback cycle in lateral signal propagation, see Reynolds 2003 below.
Differential dynamics of receptor internalization also account for the differential response of PC12 cells to EGF (proliferation induced by a transient ERK signal via Ras/c-Raf-1) and NGF (differentiation into a neuronal phenotype through sustained ERK activation via Rap1/B-Raf). The elucidation of differential activation profiles and fine tuning of ERK activity by Ras/c-Raf-1 and Rap1/B-Raf cooperation, and an important crosslink to the ancient cAMP signaling system, are only recent fascinating insights in the complex immediate upstream events of MAPK function.

Reynolds 2003:

oS results PubMed

The paper included a small reaction network model of the feedback cycle, that was used for interpretation of the results. The SBML was written by hand.
Experimental study in fibroblasts, showing that EGF receptor lateral signal propagation depends on a positive (double negative) feedback cycle, potentially via ROS (reactive oxygen species) mediated inactivation of PTP - protein tyrosine phosphatases that inactivate EGF receptors.

Bhalla, Ram, Iyengar 2002:

The model was constructed computationally by a quick and dirty Perl script, using Perl bindings for the SBML library, and a text file description of the Kinetikit/Genesis model to Figure 1b of the article, available from the Upinder Bhalla's supplemenetary material website.
Known Errors:
The original model assumed a cellular volume of 1e-12 liters, and a nuclear volume of 0.2*10^-12 liters for the transcriptional regulation. Here the model has a default compartment of 1, and no nuclear compartment is used! To use compartments, you have to multiply all(!) reaction parameters, with the volume of the reaction's compartment.
Detailed active PKC species:
The Genesis/Kinetikit export file was additionally edited by hand, because the `pool' construct in the original Kinetikit/Genesis model, comprehending several forms of PKC into an `active' pool, cannot be expressed in SBML, and needed detailed reactions for each of the different PKC forms. The left image below, shows results for this version of the model, please click below the image to obtain the model and view results. I am not sure what is wrong with the model, but it doesn't need any PDGF to activate the positive feedback cycle. PDGF has been set to zero to indicate this fact.
Active PKC Pool as an SBML assignment rule:
The right figure displays results obtained by a version that uses SBML assignment rules to comprehend all active PKC species into `PKC_a_pool', and uses this abstract species for PKC mediated phosphorylation of GEF, c-Raf-1 and GAP. This construct is not correct in the context of the model, as active PKC species are consumed by formation of enzyme-substrate complexes, which should not be available for dissociation of the active species. If the phosphorylation reactions would be modeled with Michaelis-Menten instead of elementary step mass action kinetics for substrate binding and product dissociation, the model would be correct for analysis at steady state, but couldn't account for possible competition between PKC complex dissociation and downstream enzyme-substrate complex formation.
However, this model needs a 300 seconds PDGF pulse to activate MAPK, and the active MAPK concentration time series, shown in the right figure, looks a lot more like the one in Figure 1b of the original article. The slope of MAPK activation seems somewhat less steep, though!

Multiple active PKC species in detailed reactions
SBML assignment rule for active PKC pool
PDGF for 300 seconds
bhalla_02.xml bhalla_02pool.xml
oS results oS results
A big model around the MAP kinase pathway, activated by PDGF receptor activation, showing bistable behaviour and hysteresis via positive feedback cycles between MAP kinase and PLA2/PKC activation. The bistable behaviour could constitute an autonomous cellular memory mechanism, where a transient signal leads to sustained activation of the pathway. This behaviour has also been analyzed - with a different kind of positive feedback - in Ferrell's work for the MAP kinase in Xenopus oocyte. In this paper, an additional negative feedback via expression of the MAP kinase phosphatase MKP1 was shown to `turn off' bistability.

Please email Rainer Machné (to raim for questions and suggestions.

Rainer Machné
Last modified: 2006-08-31 13:06:20 raim