Feedback Effects On Signal Dynamics In A Mitogen-Activated Protein Kinase (MAPK) Cascade
Catherine
Lloyd
Bioengineering Institute, University of Auckland
Model Status
This model has been recoded in CellML without the use of the reaction element. The parameters and differential equations described in the original publication were used. This CellML model is known to read in both COR and PCEnv although currently it is unable to recreate the published results from the original model.
ValidateCellML detects widespread unit inconsistency within this model.
Model Structure
In 2001, Anand Asthagiri and Douglas Lauffenburger published a mathematical model which examined the mechanisms that govern MAPK pathway dynamics (see the figure below). Their model builds upon the MAPK cascade model of Chi-Ying Huang and James Ferrell (1996). This earlier model focused on the steady-state effects of signaling, whereas more recently, it has been discovered that a signal's information content partly resides in its dynamics.
In their model, Anand Asthagiri and Douglas Lauffenburger concentrate on the role of negative feedback mechanisms in the generation of signal adaptation - a term referring to the reset of a signal to prestimulation levels. They assess how different modes of feedback affect the properties of MAPK signalling dynamics.
The complete original paper reference is cited below:
A Computational Study of Feedback Effects on Signal Dynamics in a Mitogen-Activated Protein Kinase (MAPK) Pathway Model
, Anand R. Asthagiri and Douglas A. Lauffenburger, 2001,
Biotechnol. Prog
, 17, 227-239. (
Full text
and PDF versions are available to subscribers on the ACS Publications website.
PubMed ID: 11312698
the conventional rendering of the MAPK cascade with feedback effects
A rendering of the MAPK cascade with feedback effects. Species are represented by rounded rectangles, and reactions by arrows. The action of a catalyst on a reaction is represented by dashed lines.
In CellML, models are thought of as connected networks of discrete components. These components may correspond to physiologically separated regions or chemically distinct objects, or may be useful modelling abstractions. This model has 71 components representing chemically distinct objects (41 chemical species and 30 reactions) and one component defined for modelling convenience which stores the universal variable time. Because this model has so many components, its CellML rendering would be complex. For an example of a CellML rendering of a reaction pathway see The Bhalla Iyengar EGF Pathway Model, 1999.
$\frac{d \mathrm{a2\_minus}}{d \mathrm{time}}=\frac{\mathrm{kcat\_x}}{\mathrm{kr}}\frac{\mathrm{E4\_T}}{\mathrm{A2\_T}}\mathrm{e0\_star\_e4\_star}$
$\frac{d \mathrm{e5\_star\_p5}}{d \mathrm{time}}=\frac{\mathrm{kP5\_plus}\mathrm{E5\_T}}{\mathrm{kr}}\mathrm{e5\_star}\mathrm{p5}-(\frac{\mathrm{kP5\_minus}}{\mathrm{kr}}+\frac{\mathrm{kcat\_P5}}{\mathrm{kr}})\mathrm{e5\_star\_p5}$
$\frac{d \mathrm{e3\_star}}{d \mathrm{time}}=\frac{\mathrm{kcat\_3}}{\mathrm{kr}}\mathrm{e3\_e2\_star}+\frac{\mathrm{k4\_minus}+\mathrm{kcat\_4}}{\mathrm{kr}}\frac{\mathrm{E4\_T}}{\mathrm{E3\_T}}\mathrm{e4\_e3\_star}+\frac{\mathrm{kP3\_minus}}{\mathrm{kr}}\frac{\mathrm{P3\_T}}{\mathrm{E3\_T}}\mathrm{e3\_star\_p3}-\frac{\mathrm{k4\_plus}\mathrm{E4\_T}}{\mathrm{kr}}\mathrm{e3\_star}\mathrm{e4}+\frac{\mathrm{kP3\_plus}\mathrm{P3\_T}}{\mathrm{kr}}\mathrm{e3\_star}\mathrm{p3}$
$r=1.0-c+2.0(\mathrm{c2}+\mathrm{c\_star}+\frac{\mathrm{A1\_T}}{\mathrm{R0}}\mathrm{c\_star\_a1}+\frac{\mathrm{A2\_T}}{\mathrm{R0}}\mathrm{e0\_star}+\frac{\mathrm{E4\_T}}{\mathrm{R0}}\mathrm{e0\_star\_e4\_star}+\frac{\mathrm{E1\_T}}{\mathrm{R0}}\mathrm{e1\_e0\_star})$
$\frac{d \mathrm{e0\_star}}{d \mathrm{time}}=\frac{\mathrm{kf\_2}\mathrm{A1\_T}}{\mathrm{kr}}\mathrm{c\_star\_a1}\mathrm{a2}+\frac{\mathrm{kf\_12}\mathrm{A1\_T}}{\mathrm{kr}}\mathrm{c\_star}\mathrm{a1a2}+\frac{\mathrm{k1\_minus}+\mathrm{kcat\_1}}{\mathrm{kr}}\frac{\mathrm{E1\_T}}{\mathrm{A2\_T}}\mathrm{e1\_e0\_star}+\frac{\mathrm{kx\_minus}}{\mathrm{kr}}\frac{\mathrm{E4\_T}}{\mathrm{A2\_T}}\mathrm{e0\_star\_e4\_star}-\frac{\mathrm{kr\_2}}{\mathrm{kr}}\mathrm{e0\_star}+\frac{\mathrm{kr\_12}}{\mathrm{kr}}\mathrm{e0\_star}+\frac{\mathrm{k1\_plus}\mathrm{E1\_T}}{\mathrm{kr}}\mathrm{e0\_star}\mathrm{e1}+\frac{\mathrm{kx\_plus}\mathrm{E4\_T}}{\mathrm{kr}}\mathrm{e0\_star}\mathrm{e4\_star}$
$\frac{d \mathrm{e3\_star\_p3}}{d \mathrm{time}}=\frac{\mathrm{kP3\_plus}\mathrm{E3\_T}}{\mathrm{kr}}\mathrm{e3\_star}\mathrm{p3}-(\frac{\mathrm{kP3\_minus}}{\mathrm{kr}}+\frac{\mathrm{kcat\_P3}}{\mathrm{kr}})\mathrm{e3\_star\_p3}$
$\frac{d \mathrm{a1a2}}{d \mathrm{time}}=\frac{\mathrm{kr\_12}}{\mathrm{kr}}\frac{\mathrm{A2\_T}}{\mathrm{A1\_T}}\mathrm{e0\_star}+\frac{\mathrm{kc\_12}\mathrm{A2\_T}}{\mathrm{kr}}\mathrm{a1}\mathrm{a2}-\frac{\mathrm{kd\_12}}{\mathrm{kr}}\mathrm{a1a2}+\frac{\mathrm{kf\_12}\mathrm{R0}}{\mathrm{kr}}\mathrm{c\_star}\mathrm{a1a2}$
$\frac{d \mathrm{e2\_star\_p2}}{d \mathrm{time}}=\frac{\mathrm{kP2\_plus}\mathrm{E2\_T}}{\mathrm{kr}}\mathrm{e2\_star}\mathrm{p2}-(\frac{\mathrm{kP2\_minus}}{\mathrm{kr}}+\frac{\mathrm{kcat\_P2}}{\mathrm{kr}})\mathrm{e2\_star\_p2}$
$\frac{d \mathrm{e1\_star\_p1}}{d \mathrm{time}}=\frac{\mathrm{kP1\_plus}\mathrm{E1\_T}}{\mathrm{kr}}\mathrm{e1\_star}\mathrm{p1}-(\frac{\mathrm{kP1\_minus}}{\mathrm{kr}}+\frac{\mathrm{kcat\_P1}}{\mathrm{kr}})\mathrm{e1\_star\_p1}$
$\frac{d \mathrm{e5\_e4\_star}}{d \mathrm{time}}=\frac{\mathrm{k5\_plus}\mathrm{E4\_T}}{\mathrm{kr}}\mathrm{e5}\mathrm{e4\_star}-(\frac{\mathrm{k5\_minus}}{\mathrm{kr}}+\frac{\mathrm{kcat\_5}}{\mathrm{kr}})\mathrm{e5\_e4\_star}$
$\mathrm{a2}=1.0-\frac{\mathrm{A1\_T}}{\mathrm{A2\_T}}\mathrm{a1a2}+\mathrm{e0\_star}+\frac{\mathrm{E4\_T}}{\mathrm{A2\_T}}\mathrm{e0\_star\_e4\_star}+\frac{\mathrm{E1\_T}}{\mathrm{A2\_T}}\mathrm{e1\_e0\_star}+\mathrm{a2\_minus}$
$\frac{d \mathrm{c\_star\_a1}}{d \mathrm{time}}=\frac{\mathrm{kf\_1}\mathrm{R0}}{\mathrm{kr}}\mathrm{c\_star}\mathrm{a1}+\frac{\mathrm{kr\_2}}{\mathrm{kr}}\frac{\mathrm{A2\_T}}{\mathrm{A1\_T}}\mathrm{e0\_star}+\frac{\mathrm{kcat\_x}}{\mathrm{kr}}\frac{\mathrm{E4\_T}}{\mathrm{A1\_T}}\mathrm{e0\_star\_e4\_star}-\frac{\mathrm{kr\_1}}{\mathrm{kr}}\mathrm{c\_star\_a1}+\frac{\mathrm{kf\_2}\mathrm{A2\_T}}{\mathrm{kr}}\mathrm{c\_star\_a1}\mathrm{a2}$
$\frac{d \mathrm{c\_star}}{d \mathrm{time}}=\frac{\mathrm{kc\_plus}}{\mathrm{kr}}\mathrm{c2}+\frac{\mathrm{kr\_1}}{\mathrm{kr}}\frac{\mathrm{A1\_T}}{\mathrm{R0}}\mathrm{c\_star\_a1}+\frac{\mathrm{kr\_12}}{\mathrm{kr}}\frac{\mathrm{A2\_T}}{\mathrm{R0}}\mathrm{e0\_star}-\frac{\mathrm{kc\_minus}}{\mathrm{kr}}\mathrm{c\_star}+\frac{\mathrm{kf\_1}\mathrm{A1\_T}}{\mathrm{kr}}\mathrm{c\_star}\mathrm{a1}+\frac{\mathrm{kf\_12}\mathrm{A1\_T}}{\mathrm{kr}}\mathrm{c\_star}\mathrm{a1a2}$
$\frac{d \mathrm{e3\_e2\_star}}{d \mathrm{time}}=\frac{\mathrm{k3\_plus}\mathrm{E2\_T}}{\mathrm{kr}}\mathrm{e3}\mathrm{e2\_star}-(\frac{\mathrm{k3\_minus}}{\mathrm{kr}}+\frac{\mathrm{kcat\_3}}{\mathrm{kr}})\mathrm{e3\_e2\_star}$
$\mathrm{p5}=1.0-\mathrm{e5\_star\_p5}$
$\frac{d \mathrm{e2\_minus}}{d \mathrm{time}}=\frac{\mathrm{kcat\_z}}{\mathrm{kr}}\frac{\mathrm{E4\_T}}{\mathrm{E2\_T}}\mathrm{e2\_star\_e4\_star}$
$\mathrm{p2}=1.0-\mathrm{e2\_star\_p2}$
$\frac{d \mathrm{e4\_star\_p4}}{d \mathrm{time}}=\frac{\mathrm{kP4\_plus}\mathrm{E4\_T}}{\mathrm{kr}}\mathrm{e4\_star}\mathrm{p4}-(\frac{\mathrm{kP4\_minus}}{\mathrm{kr}}+\frac{\mathrm{kcat\_P4}}{\mathrm{kr}})\mathrm{e4\_star\_p4}$
$\mathrm{p1}=1.0-\mathrm{e1\_star\_p1}$
$\mathrm{p4}=1.0-\mathrm{e4\_star\_p4}$
$\mathrm{p3}=1.0-\mathrm{e3\_star\_p3}$
$\mathrm{L0}=\frac{\mathrm{kr}}{\mathrm{kf}}\mathrm{kr\_1}=\mathrm{kf\_1}\times 1E-7\mathrm{kr\_2}=\mathrm{kf\_2}\times 1E-7\mathrm{kr\_12}=\mathrm{kf\_12}\times 1E-7\mathrm{kd\_12}=\mathrm{kc\_12}\times 1E-7$
$\frac{d \mathrm{e1\_e0\_star}}{d \mathrm{time}}=\frac{\mathrm{k1\_plus}\mathrm{A2\_T}}{\mathrm{kr}}\mathrm{e1}\mathrm{e0\_star}-(\frac{\mathrm{k1\_minus}}{\mathrm{kr}}+\frac{\mathrm{kcat\_1}}{\mathrm{kr}})\mathrm{e1\_e0\_star}$
$\frac{d \mathrm{e5\_star}}{d \mathrm{time}}=\frac{\mathrm{kcat\_5}}{\mathrm{kr}}\mathrm{e5\_e4\_star}+\frac{\mathrm{kP5\_minus}}{\mathrm{kr}}\frac{\mathrm{P5\_T}}{\mathrm{E5\_T}}\mathrm{e5\_star\_p5}-\frac{\mathrm{kP5\_plus}\mathrm{P5\_T}}{\mathrm{kr}}\mathrm{e5\_star}\mathrm{p5}$
$\frac{d \mathrm{e2\_star}}{d \mathrm{time}}=\frac{\mathrm{kcat\_2}}{\mathrm{kr}}\mathrm{e2\_e1\_star}+\frac{\mathrm{k3\_minus}+\mathrm{kcat\_3}}{\mathrm{kr}}\frac{\mathrm{E3\_T}}{\mathrm{E2\_T}}\mathrm{e3\_e2\_star}+\frac{\mathrm{kP2\_minus}}{\mathrm{kr}}\frac{\mathrm{P2\_T}}{\mathrm{E2\_T}}\mathrm{e2\_star\_p2}+\frac{\mathrm{kz\_minus}}{\mathrm{kr}}\frac{\mathrm{E4\_T}}{\mathrm{E2\_T}}\mathrm{e2\_star\_e4\_star}-\frac{\mathrm{k3\_plus}\mathrm{E3\_T}}{\mathrm{kr}}\mathrm{e2\_star}\mathrm{e3}+\frac{\mathrm{kP2\_plus}\mathrm{P2\_T}}{\mathrm{kr}}\mathrm{e2\_star}\mathrm{p2}+\frac{\mathrm{kz\_plus}\mathrm{E4\_T}}{\mathrm{kr}}\mathrm{e2\_star}\mathrm{e4\_star}$
$\frac{d \mathrm{e1\_star}}{d \mathrm{time}}=\frac{\mathrm{kcat\_1}}{\mathrm{kr}}\mathrm{e1\_e0\_star}+\frac{\mathrm{k2\_minus}+\mathrm{kcat\_2}}{\mathrm{kr}}\frac{\mathrm{E2\_T}}{\mathrm{E1\_T}}\mathrm{e2\_e1\_star}+\frac{\mathrm{kP1\_minus}}{\mathrm{kr}}\frac{\mathrm{P1\_T}}{\mathrm{E1\_T}}\mathrm{e1\_star\_p1}-\frac{\mathrm{k2\_plus}\mathrm{E2\_T}}{\mathrm{kr}}\mathrm{e1\_star}\mathrm{e2}+\frac{\mathrm{kP1\_plus}\mathrm{P1\_T}}{\mathrm{kr}}\mathrm{e1\_star}\mathrm{p1}$
$\mathrm{e3}=1.0-\mathrm{e3\_e2\_star}+\mathrm{e3\_star}+\frac{\mathrm{E4\_T}}{\mathrm{E3\_T}}\mathrm{e4\_e3\_star}+\frac{\mathrm{P3\_T}}{\mathrm{E3\_T}}\mathrm{e3\_star\_p3}$
$\mathrm{e2}=1.0-\mathrm{e3\_e2\_star}+\mathrm{e3\_star}+\frac{\mathrm{E3\_T}}{\mathrm{E2\_T}}\mathrm{e3\_e2\_star}+\frac{\mathrm{E4\_T}}{\mathrm{E2\_T}}\mathrm{e2\_star\_e4\_star}+\frac{\mathrm{P2\_T}}{\mathrm{E2\_T}}\mathrm{e2\_star\_p2}$
$\mathrm{a1}=1.0-\mathrm{c\_star\_a1}+\mathrm{a1a2}+\frac{\mathrm{A2\_T}}{\mathrm{A1\_T}}\mathrm{e0\_star}+\frac{\mathrm{E4\_T}}{\mathrm{A1\_T}}\mathrm{e0\_star\_e4\_star}+\frac{\mathrm{E1\_T}}{\mathrm{A1\_T}}\mathrm{e1\_e0\_star}$
$\frac{d c}{d \mathrm{time}}=\frac{\mathrm{L0}}{\frac{\mathrm{kr}}{\mathrm{kf}}}r+2.0\frac{\mathrm{ku}}{\mathrm{kr}}\mathrm{c2}-c+2.0\frac{\mathrm{R0}}{\frac{\mathrm{kr}}{\mathrm{kc}}}c^{2.0}$
$\frac{d \mathrm{e4\_e3\_star}}{d \mathrm{time}}=\frac{\mathrm{k4\_plus}\mathrm{E3\_T}}{\mathrm{kr}}\mathrm{e4}\mathrm{e3\_star}-(\frac{\mathrm{k4\_minus}}{\mathrm{kr}}+\frac{\mathrm{kcat\_4}}{\mathrm{kr}})\mathrm{e4\_e3\_star}$
$\mathrm{e5}=1.0-\mathrm{e5\_e4\_star}+\mathrm{e5\_star}+\frac{\mathrm{P5\_T}}{\mathrm{E5\_T}}\mathrm{e5\_star\_p5}$
$\frac{d \mathrm{c2}}{d \mathrm{time}}=\frac{\mathrm{R0}}{\frac{\mathrm{kr}}{\mathrm{kc}}}c^{2.0}+\frac{\mathrm{kc\_minus}}{\mathrm{kr}}\mathrm{c\_star}-\frac{\mathrm{ku}}{\mathrm{kr}}c+\frac{\mathrm{kc\_plus}}{\mathrm{kr}}\mathrm{c2}$
$\mathrm{e4}=1.0-\mathrm{e4\_e3\_star}+\mathrm{e4\_star}+\frac{\mathrm{E5\_T}}{\mathrm{E4\_T}}\mathrm{e5\_e4\_star}+\frac{\mathrm{P4\_T}}{\mathrm{E4\_T}}\mathrm{e4\_star\_p4}+\mathrm{e0\_star\_e4\_star}+\mathrm{e2\_star\_e4\_star}$
$\mathrm{e1}=1.0-\mathrm{e1\_e0\_star}+\mathrm{e1\_star}+\frac{\mathrm{E2\_T}}{\mathrm{E1\_T}}\mathrm{e2\_e1\_star}+\frac{\mathrm{P1\_T}}{\mathrm{E1\_T}}\mathrm{e1\_star\_p1}$
$\frac{d \mathrm{e4\_star}}{d \mathrm{time}}=\frac{\mathrm{kcat\_4}}{\mathrm{kr}}\mathrm{e4\_e3\_star}+\frac{\mathrm{k5\_minus}+\mathrm{kcat\_5}}{\mathrm{kr}}\frac{\mathrm{E5\_T}}{\mathrm{E4\_T}}\mathrm{e5\_e4\_star}+\frac{\mathrm{kP4\_minus}}{\mathrm{kr}}\frac{\mathrm{P4\_T}}{\mathrm{E4\_T}}\mathrm{e4\_star\_p4}+(\frac{\mathrm{kx\_minus}}{\mathrm{kr}}+\frac{\mathrm{kcat\_x}}{\mathrm{kr}})\mathrm{e0\_star\_e4\_star}+(\frac{\mathrm{kz\_minus}}{\mathrm{kr}}+\frac{\mathrm{kcat\_z}}{\mathrm{kr}})\mathrm{e2\_star\_e4\_star}-\frac{\mathrm{k5\_plus}\mathrm{E5\_T}}{\mathrm{kr}}\mathrm{e4\_star}\mathrm{e5}+\frac{\mathrm{kP4\_plus}\mathrm{P4\_T}}{\mathrm{kr}}\mathrm{e4\_star}\mathrm{p4}+\frac{\mathrm{kx\_plus}\mathrm{A2\_T}}{\mathrm{kr}}\mathrm{e0\_star}\mathrm{e4\_star}+\frac{\mathrm{kz\_plus}\mathrm{E2\_T}}{\mathrm{kr}}\mathrm{e2\_star}\mathrm{e4\_star}$
$\frac{d \mathrm{e2\_star\_e4\_star}}{d \mathrm{time}}=\frac{\mathrm{kz\_plus}\mathrm{E2\_T}}{\mathrm{kr}}\mathrm{e4\_star}\mathrm{e2\_star}-(\frac{\mathrm{kz\_minus}}{\mathrm{kr}}+\frac{\mathrm{kcat\_z}}{\mathrm{kr}})\mathrm{e2\_star\_e4\_star}$
$\frac{d \mathrm{e0\_star\_e4\_star}}{d \mathrm{time}}=\frac{\mathrm{kx\_plus}\mathrm{A2\_T}}{\mathrm{kr}}\mathrm{e4\_star}\mathrm{e0\_star}-(\frac{\mathrm{kx\_minus}}{\mathrm{kr}}+\frac{\mathrm{kcat\_x}}{\mathrm{kr}})\mathrm{e0\_star\_e4\_star}$
$\frac{d \mathrm{e2\_e1\_star}}{d \mathrm{time}}=\frac{\mathrm{k2\_plus}\mathrm{E1\_T}}{\mathrm{kr}}\mathrm{e2}\mathrm{e1\_star}-(\frac{\mathrm{k2\_minus}}{\mathrm{kr}}+\frac{\mathrm{kcat\_2}}{\mathrm{kr}})\mathrm{e2\_e1\_star}$
Total number of adaptor protein A2 molecules
Concentration of dimerized and activated receptor
Concentration of the transition complex between inactive substrate E1 and its activator E0*
Concentration of the transition complex between inactive substrate E1 and its activator E0*
Rate constant for activation of dimerized receptor-ligand complexes
Concentration of active signaling enzyme 3
Concentration of E2* and E4* transition complex in feedback mediated by enzyme E4*
Initial number of free receptors
Rate constant for dimerization of ligand-bound receptors
Concentration of active signaling enzyme 5
transition complex between an inactive substate and its activator (5)
Rate constant for dissociation of dimers
Concentration of inactive signaling enzyme 4
Total number of activating enzymes at stage 4
activated signalling enzyme 1
dimerised and activated receptor
Total number of activating enzymes at stage 1
Total number of activating enzymes at stage 1
adaptor heterodimer
Concentration of nonfunctional second enzyme
Concentration of adaptor heterodimer
Concentration of deactivating enzyme P3
Concentration of E0* and E4* transition complex in feedback mediated by enzyme E4*
Total number of activating enzymes at stage 4
Receptor-ligand dissociation rate constant
Receptor-ligand association rate constant
Forward rate constant for association of activated receptor complex (C*) with adaptor protein 1 (A1)
free first adaptor
Time domain for simulation
Concentration of E0* and E4* transition complex in feedback mediated by enzyme E4*
Total number of activating enzymes at stage 3
Total number of activating enzymes at stage 1
Receptor-ligand dissociation rate constant
Total number of adaptor protein A1 molecules
Concentration of transition complex between active substrate E3* and deactivating enzyme P3
Forward rate constant for association of heteroadaptor complex (A1A2) with activated receptor complex (C*)
Concentration of active signaling enzyme 1
Concentration of receptor-ligand dimer bound to adaptors 1 and 2
Time domain for simulation
Receptor-ligand dissociation rate constant
Concentration of nonfunctional second enzyme
First order rate constant for dissociation of E0*E4* complex into C*A1, A2- and E4*
Receptor-ligand dissociation rate constant
Total number of activating enzymes at stage 3
free second adaptor
Total number of activating enzymes at stage 1
Concentration of transition complex between inactive substrate E4 and its activator E3*
Concentration of transition complex between inactive substrate E4 and its activator E3*
Time domain for simulation
Time domain for simulation
Backward rate constant for association of inactive signaling enzyme 1 (E1) with receptor-ligand dimer bound to adaptors 1 and 2 (E0*)
Concentration of transition complex between inactive substrate E3 and its activator E2*
Total number of activating enzymes at stage 1
Concentration of deactivating enzyme P5
Concentration of active receptor-ligand dimer bound to adaptor 1 complex
Rate constant for deactivation of active receptor-ligand dimers
inactive signalling enzyme 3
Concentration of E2* and E4* transition complex in feedback mediated by enzyme E4*
Time domain for simulation
Total number of activating enzymes at stage 2
Total number of adaptor protein A2 molecules
Concentration of E0* and E4* transition complex in feedback mediated by enzyme E4*
Total number of activating enzymes at stage 4
Concentration of E2* and E4* transition complex in feedback mediated by enzyme E4*
Concentration of deactivating enzyme P3
Concentration of transition complex between inactive substrate E5 and its activator E4*
activated signalling enzyme 4
inactive signalling enzyme 4
Concentration of transition complex between active substrate E1* and deactivating enzyme P1
Total number of activating enzymes at stage 4
Concentration of transition complex between active substrate E5* and deactivating enzyme P5
Time domain for simulation
Total number of activating enzymes at stage 2
Concentration of transition complex between active substrate E1* and deactivating enzyme P1
Concentration of inactive signaling enzyme 2
nonfunctional second adaptor
Backward rate constant for association of activated receptor complex bound to adaptor protein 1 (C*A1) and adaptor protein 2 (A2)
Rate constant for dissociation of dimers
Concentration of transition complex between active substrate E5* and deactivating enzyme P5
Backward rate constant for association of heteroadaptor complex (A1A2) with activated receptor complex (C*)
Time domain for simulation
inactive signalling enzyme 5
The mitogen-activated protein kinase (MAPK) cascade, 2001
Catherine Lloyd
This is the CellML description of Asthagiri and Lauffenburger's mathematical model of the mitogen-activated protein kinase (MAPK) cascade (2001). They examine MAPK pathway dynamics, especially the role of negative feedback mechanisms in generating signal adaptation.
A Compuational Study of Feedback Effects on Signal Dynamics in a Mitogen-Activated Protein Kinase (MAPK) Pathway Model
Biotechnology Progress
signal transduction
MAPK
kinase
pathway
cascade
Concentration of receptor-ligand dimer bound to adaptors 1 and 2
Concentration of transition complex between inactive substrate E2 and its activator E1*
Concentration of deactivating enzyme P4
Total number of activating enzymes at stage 4
Concentration of inactive signaling enzyme 1
Concentration of transition complex between active substrate E2* and deactivating enzyme P2
Total number of activating enzymes at stage 2
Concentration of E0* and E4* transition complex in feedback mediated by enzyme E4*
Concentration of free second adaptor protein
ligand-bound and dimerised receptor
Forward rate constant for association of adaptor protein 1 (A1) with adaptor protein 2 (A2)
Receptor-ligand dissociation rate constant
Receptor-ligand dissociation rate constant
transition complex between an inactive substate and its activator (1)
Concentration of deactivating enzyme P4
Forward rate constant for association of inactive signaling enzyme 1 (E1) with receptor-ligand dimer bound to adaptors 1 and 2 (E0*)
Concentration of dimerized and activated receptor
Total number of adaptor protein A1 molecules
Concentration of E2* and E4* transition complex in feedback mediated by enzyme E4*
Backward rate constant for association of activated receptor complex (C*) with adaptor protein 1 (A1)
Concentration of transition complex between active substrate E5* and deactivating enzyme P5
Concentration of receptor-ligand dimer bound to adaptors 1 and 2
Receptor-ligand dissociation rate constant
Total number of activating enzymes at stage 5
Concentration of transition complex between active substrate E2* and deactivating enzyme P2
deactivating enzyme 5
Total number of activating enzymes at stage 5
Backward rate constant for association of activated receptor complex (C*) with adaptor protein 1 (A1)
Initial number of free receptors
Receptor-ligand dissociation rate constant
Time domain for simulation
Inactive signaling enzyme 5
Concentration of adaptor heterodimer
Total number of adaptor protein A2 molecules
Concentration of adaptor heterodimer
Forward rate constant for association of inactive signaling enzyme 1 (E2) with activated signaling enzyme 1 (E1*)
Total number of activating enzymes at stage 5
Number of free receptors in cell
Concentration of deactivating enzyme P2
Time domain for simulation
Backward rate constant for association of heteroadaptor complex (A1A2) with activated receptor complex (C*)
Total number of adaptor protein A2 molecules
Concentration of active receptor-ligand dimer bound to adaptor 1 complex
Concentration of transition complex between active substrate E4* and deactivating enzyme P4
Forward rate constant for association of activated receptor complex (C*) with adaptor protein 1 (A1)
Total number of activating enzymes at stage 3
Concentration of inactive signaling enzyme 4
Concentration of transition complex between inactive substrate E5 and its activator E4*
Time domain for simulation
Backward rate constant for association of activated receptor complex bound to adaptor protein 1 (C*A1) and adaptor protein 2 (A2)
Concentration of active signaling enzyme 4
free receptor
Total number of activating enzymes at stage 5
Total number of activating enzymes at stage 4
Total number of adaptor protein A1 molecules
Forward rate constant for association of activated receptor complex bound to adaptor protein 1 (C*A1) and adaptor protein 2 (A2)
Receptor-ligand dissociation rate constant
Concentration of active signaling enzyme 4
Time domain for simulation
First order rate constant for dissociation of E0*E4* complex into C*A1, A2- and E4*
Forward rate constant for association of activated receptor complex bound to adaptor protein 1 (C*A1) and adaptor protein 2 (A2)
Concentration of transition complex between active substrate E3* and deactivating enzyme P3
Total number of activating enzymes at stage 2
Backward rate constant for association of heteroadaptor complex (A1A2) with activated receptor complex (C*)
deactivating enzyme 1
Receptor-ligand dissociation rate constant
transition complex between an active substate and its deactivating enzyme (1)
Concentration of transition complex between active substrate E1* and deactivating enzyme P1
Total number of adaptor protein A1 molecules
First-order rate constant for conversion of the transition complex E1E0* into products E0* and E1*
Initial ligand concentration
Concentration of transition complex between active substrate E3* and deactivating enzyme P3
Total number of activating enzymes at stage 5
Total number of adaptor protein A2 molecules
Updated curation status
Altered connections after chacking the model with the validator.
Catherine Lloyd
This model has been recoded in CellML without the use of the reaction element. The parameters and differential equations described in the original publication were used. This CellML model is known to read in both COR and PCEnv although currently it is unable to recreate the published results from the original model.
Added more metadata.
Changed unit dimensions E1_ to make them consistent.
Recoded the model to remove the reaction element.
The University of Auckland
The Bioengineering Research Group
Updated metadata to conform to the 16/1/02 CellML Metadata 1.0
Specification.
Added publication date information.
The University of Auckland, Bioengineering Research Group
Completely re-wrote the model to remove the reaction element.
Corrected the initial value of variable 'k6_' in component
'adaptor_heterodimer_syn'.
Concentration of transition complex between inactive substrate E3 and its activator E2*
Receptor-ligand dissociation rate constant
First order rate constant for dissociation of E0*E4* complex into C*A1, A2- and E4*
Concentration of active signaling enzyme 1
Total number of activating enzymes at stage 4
Concentration of receptor-ligand dimer bound to adaptors 1 and 2
Rate constant for deactivation of active receptor-ligand dimers
Concentration of E2* and E4* transition complex in feedback mediated by enzyme E4*
Concentration of active signaling enzyme 3
Total number of adaptor protein A2 molecules
Concentration of transition complex between inactive substrate E2 and its activator E1*
Concentration of free first adaptor protein
deactivating enzyme 2
transition complex between an active substate and its deactivating enzyme (4)
transition complex between an active substate and its deactivating enzyme (5)
e5_star_p5
Initial ligand concentration
Total number of activating enzymes at stage 4
Concentration of inactive signaling enzyme 1
Time domain for simulation
Total number of activating enzymes at stage 4
Concentration of E0* and E4* transition complex in feedback mediated by enzyme E4*
Backward rate constant for association of inactive signaling enzyme 1 (E1) with receptor-ligand dimer bound to adaptors 1 and 2 (E0*)
Concentration of transition complex between active substrate E5* and deactivating enzyme P5
Concentration of receptor-ligand dimer bound to adaptors 1 and 2
transition complex between an inactive substate and its activator (3)
Forward rate constant for association of inactive signaling enzyme 1 (E2) with activated signaling enzyme 1 (E1*)
deactivating enzyme 3
Receptor-ligand dissociation rate constant
transition complex in feedback mediated by enzyme E4*
Concentration of free second adaptor protein
Concentration of deactivating enzyme P1
Time domain for simulation
Total number of activating enzymes at stage 2
Concentration of ligand-bound and dimerized receptor
Forward rate constant for association of inactive signaling enzyme 1 (E2) with activated signaling enzyme 1 (E1*)
Concentration of active signaling enzyme 2
Concentration of deactivating enzyme P2
Concentration of dimerized and activated receptor
Total number of adaptor protein A2 molecules
Receptor-ligand dissociation rate constant
Initial number of free receptors
Concentration of active signaling enzyme 4
Forward rate constant for association of heteroadaptor complex (A1A2) with activated receptor complex (C*)
deactivating enzyme 4
Concentration of active signaling enzyme 2
Concentration of receptor-ligand dimer bound to adaptors 1 and 2
Concentration of transition complex between active substrate E4* and deactivating enzyme P4
Initial number of free receptors
Concentration of deactivating enzyme P5
transition complex in feedback mediated by enzyme E4*
Total number of activating enzymes at stage 1
Concentration of transition complex between active substrate E4* and deactivating enzyme P4
Receptor-ligand dissociation rate constant
Total number of activating enzymes at stage 4
Rate constant for dimerization of ligand-bound receptors
Time domain for simulation
Concentration of active receptor-ligand dimer bound to adaptor 1 complex
Concentration of active signaling enzyme 4
Concentration of E2* and E4* transition complex in feedback mediated by enzyme E4*
Concentration of free ligand-bound receptor
Concentration of transition complex between active substrate E4* and deactivating enzyme P4
Inactive signaling enzyme 2
Concentration of ligand-bound and dimerized receptor
Initial number of free receptors
Concentration of active signaling enzyme 2
Rate constant for dimerization of ligand-bound receptors
Concentration of ligand-bound and dimerized receptor
Concentration of inactive signaling enzyme 5
Receptor-ligand dissociation rate constant
Rate constant for activation of dimerized receptor-ligand complexes
Concentration of transition complex between inactive substrate E4 and its activator E3*
Total number of deactivating enzymes at stage 1
Rate constant for activation of dimerized receptor-ligand complexes
receptor-ligand dimer:adaptors 1 and 2 complex
First order rate constant for dissociation of E0*E4* complex into C*A1, A2- and E4*
Concentration of active signaling enzyme 4
Concentration of the transition complex between inactive substrate E1 and its activator E0*
Total number of deactivating enzymes at stage 1
Total number of activating enzymes at stage 2
Forward rate constant for association adaptor protein 1 (A1) with adaptor protein 2 (A2)
Concentration of active signaling enzyme 3
Concentration of transition complex between inactive substrate E2 and its activator E1*
Concentration of receptor-ligand dimer bound to adaptors 1 and 2
Concentration of deactivating enzyme P5
Total number of activating enzymes at stage 3
Forward rate constant for association of inactive signaling enzyme 1 (E1) with receptor-ligand dimer bound to adaptors 1 and 2 (E0*)
Time domain for simulation
Concentration of free first adaptor protein
Concentration of free first adaptor protein
Concentration of deactivating enzyme P1
Time domain for simulation
Forward rate constant for association of inactive signaling enzyme 1 (E1) with receptor-ligand dimer bound to adaptors 1 and 2 (E0*)
Receptor-ligand dissociation rate constant
Concentration of E0* and E4* transition complex in feedback mediated by enzyme E4*
Concentration of dimerized and activated receptor
Rate constant for dissociation of dimers
Concentration of free second adaptor protein
Backward rate constant for association of adaptor protein 1 (A1) with adaptor protein 2 (A2)
First-order rate constant for conversion of the transition complex E1E0* into products E0* and E1*
Concentration of the transition complex between inactive substrate E1 and its activator E0*
Total number of activating enzymes at stage 3
Time domain for simulation
Concentration of active signaling enzyme 2
transition complex between an active substate and its deactivating enzyme (2)
Concentration of receptor-ligand dimer bound to adaptors 1 and 2
Total number of adaptor protein A2 molecules
Concentration of active signaling enzyme 3
Concentration of transition complex between inactive substrate E3 and its activator E2*
Total number of activating enzymes at stage 5
Concentration of free ligand-bound receptor
Total number of activating enzymes at stage 2
Total number of adaptor protein A1 molecules
Concentration of receptor-ligand dimer bound to adaptors 1 and 2
Total number of activating enzymes at stage 1
First order rate constant for dissociation of E0*E4* complex into C*A1, A2- and E4*
Concentration of active signaling enzyme 5
Receptor-ligand dissociation rate constant
Backward rate constant for association of heteroadaptor complex (A1A2) with activated receptor complex (C*)
Concentration of transition complex between active substrate E2* and deactivating enzyme P2
Concentration of E0* and E4* transition complex in feedback mediated by enzyme E4*
Concentration of nonfunctional second adaptor protein
Total number of activating enzymes at stage 4
Receptor-ligand dissociation rate constant
active receptor-ligand dimer:adaptor 1 complex
transition complex between an active substate and its deactivating enzyme (3)
Time domain for simulation
Total number of activating enzymes at stage 4
Time domain for simulation
ligand-bound receptor
Total number of adaptor protein A1 molecules
Total number of activating enzymes at stage 4
Forward rate constant for association of activated receptor complex bound to adaptor protein 1 (C*A1) and adaptor protein 2 (A2)
Total number of adaptor protein A2 molecules
Total number of activating enzymes at stage 5
Receptor-ligand dissociation rate constant
Concentration of inactive signaling enzyme 3
Backward rate constant for association of inactive signaling enzyme 1 (E1) with receptor-ligand dimer bound to adaptors 1 and 2 (E0*)
Time domain for simulation
Forward rate constant for association of activated receptor complex (C*) with adaptor protein 1 (A1)
Receptor-ligand association rate constant
activated signalling enzyme 5
Concentration of transition complex between inactive substrate E5 and its activator E4*
Concentration of nonfunctional second adaptor protein
Concentration of transition complex between inactive substrate E4 and its activator E3*
Initial number of free receptors
Receptor-ligand association rate constant
First-order rate constant for conversion of the transition complex E1E0* into products E0* and E1*
Total number of activating enzymes at stage 2
Total number of activating enzymes at stage 4
Backward rate constant for association of activated receptor complex bound to adaptor protein 1 (C*A1) and adaptor protein 2 (A2)
Rate constant for activation of dimerized receptor-ligand complexes
Concentration of inactive signaling enzyme 3
Receptor-ligand dissociation rate constant
transition complex between an inactive substate and its activator (4)
Total number of activating enzymes at stage 2
Concentration of inactive signaling enzyme 3
Concentration of the transition complex between inactive substrate E1 and its activator E0*
Concentration of the transition complex between inactive substrate E1 and its activator E0*
Receptor-ligand dissociation rate constant
Total number of activating enzymes at stage 3
activated signalling enzyme 3
Concentration of transition complex between inactive substrate E3 and its activator E2*
Time domain for simulation
Total number of activating enzymes at stage 1
Concentration of inactive signaling enzyme 1
Concentration of deactivating enzyme P3
Concentration of active signaling enzyme 2
Concentration of receptor-ligand dimer bound to adaptors 1 and 2
Total number of activating enzymes at stage 2
Receptor-ligand dissociation rate constant
Total number of activating enzymes at stage 5
Receptor-ligand dissociation rate constant
Concentration of active receptor-ligand dimer bound to adaptor 1 complex
Concentration of transition complex between inactive substrate E3 and its activator E2*
Concentration of free first adaptor protein
Concentration of active signaling enzyme 1
Concentration of free second adaptor protein
Concentration of deactivating enzyme P2
Total number of adaptor protein A2 molecules
Concentration of transition complex between inactive substrate E2 and its activator E1*
Concentration of active signaling enzyme 4
First-order rate constant for conversion of the transition complex E1E0* into products E0* and E1*
Backward rate constant for association of adaptor protein 1 (A1) with adaptor protein 2 (A2)
Total number of adaptor protein A2 molecules
Concentration of transition complex between inactive substrate E2 and its activator E1*
Time domain for simulation
Total number of activating enzymes at stage 3
Inactive signaling enzyme 2
inactive signalling enzyme 1
Total number of activating enzymes at stage 1
Concentration of active signaling enzyme 4
Total number of activating enzymes at stage 4
Total number of adaptor protein A2 molecules
Concentration of transition complex between active substrate E1* and deactivating enzyme P1
Concentration of active signaling enzyme 5
transition complex between an inactive substate and its activator (2)
Receptor-ligand dissociation rate constant
Rate constant for deactivation of active receptor-ligand dimers
Total number of adaptor protein A1 molecules
inactive signalling enzyme 2
activated signalling enzyme 2
Total number of activating enzymes at stage 3
Total number of activating enzymes at stage 3
Concentration of inactive signaling enzyme 4
Time domain for simulation
Total number of activating enzymes at stage 4
Concentration of dimerized and activated receptor
Total number of activating enzymes at stage 2
Forward rate constant for association of heteroadaptor complex (A1A2) with activated receptor complex (C*)
Concentration of E0* and E4* transition complex in feedback mediated by enzyme E4*
Forward rate constant for association of inactive signaling enzyme 1 (E2) with activated signaling enzyme 1 (E1*)
Concentration of active signaling enzyme 4
Total number of activating enzymes at stage 3
Total number of deactivating enzymes at stage 1
Initial number of free receptors
Time domain for simulation
Concentration of transition complex between inactive substrate E5 and its activator E4*
Forward rate constant for association of heteroadaptor complex (A1A2) with activated receptor complex (C*)
Time domain for simulation
Concentration of adaptor heterodimer
Rate constant for deactivation of active receptor-ligand dimers
Concentration of ligand-bound and dimerized receptor
Concentration of free ligand-bound receptor
Total number of activating enzymes at stage 4
Total number of activating enzymes at stage 5
Backward rate constant for association of activated receptor complex (C*) with adaptor protein 1 (A1)
Concentration of the transition complex between inactive substrate E1 and its activator E0*
Concentration of active receptor-ligand dimer bound to adaptor 1 complex
Number of free receptors in cell
Receptor-ligand dissociation rate constant
Concentration of transition complex between active substrate E2* and deactivating enzyme P2
Concentration of transition complex between inactive substrate E5 and its activator E4*
Time domain for simulation
Total number of activating enzymes at stage 2
Total number of activating enzymes at stage 4
Concentration of transition complex between active substrate E3* and deactivating enzyme P3
Concentration of dimerized and activated receptor
Receptor-ligand dissociation rate constant
Concentration of active signaling enzyme 3
Concentration of adaptor heterodimer
Total number of adaptor protein A1 molecules
Total number of activating enzymes at stage 4
Inactive signaling enzyme 5
Concentration of deactivating enzyme P4
nonfunctional second enzyme
Concentration of deactivating enzyme P1
Concentration of transition complex between inactive substrate E4 and its activator E3*
Concentration of active signaling enzyme 1
Total number of activating enzymes at stage 2
Concentration of E0* and E4* transition complex in feedback mediated by enzyme E4*