SBML models of the MAP kinase pathway
1.) WARNING: The SBML models presented here are `wrong' in the following
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
(oS), a C command line tool, based on CVode and
libSBML, the SBML
Huang and Ferrel 1996:
The model was constructed by hand, from instructions in the
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
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
Markevich NI, Hoek JB, Kholodenko BN. 2004:
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
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 et.al. 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 et.al. 2002:
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 et.al. 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 et.al. 2003:
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
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
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
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
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 tbi.univie.ac.at) for
questions and suggestions.
Last modified: 2006-08-31 13:06:20 raim