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BIOMD0000000009 - Huang1996 - Ultrasensitivity in MAPK cascade

 

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Reference Publication
Publication ID: 8816754
Huang CY, Ferrell JE Jr.
Ultrasensitivity in the mitogen-activated protein kinase cascade.
Proc. Natl. Acad. Sci. U.S.A. 1996 Sep; 93(19): 10078-10083
Department of Molecular Pharmacology, Stanford University School of Medicine, CA 94305-5332, USA.  [more]
Model
Original Model: BIOMD0000000009.xml.origin
Submitter: Nicolas Le Novère
Submission ID: MODEL6615048798
Submission Date: 13 Sep 2005 20:37:52 UTC
Last Modification Date: 16 Jul 2013 18:02:42 UTC
Creation Date: 11 Feb 2005 07:39:30 UTC
Encoders:  Rainer Machne
set #1
bqbiol:isVersionOf Gene Ontology MAPK cascade
bqbiol:isHomologTo Reactome REACT_634
set #2
bqbiol:occursIn Taxonomy Xenopus laevis
Notes
Huang1996 - Ultrasensitivity in MAPK cascade

The temporal sequence of kinase activation, from MAPKKK (activated RAF) to the final effector MAPK (activated ERK), is described here. It is observed from the model that there is an increase in sensitivity along the levels of the cascade, where the activity of MAPK reaches its maximal before MAPKKK.

This model is described in the article:

Huang CY, Ferrell JE Jr
Proc. Natl. Acad. Sci. U.S.A. 1996:93(19):10078-83

Abstract:

The mitogen-activated protein kinase (MAPK) cascade is a highly conserved series of three protein kinases implicated in diverse biological processes. Here we demonstrate that the cascade arrangement has unexpected consequences for the dynamics of MAPK signaling. We solved the rate equations for the cascade numerically and found that MAPK is predicted to behave like a highly cooperative enzyme, even though it was not assumed that any of the enzymes in the cascade were regulated cooperatively. Measurements of MAPK activation in Xenopus oocyte extracts confirmed this prediction. The stimulus/response curve of the MAPK was found to be as steep as that of a cooperative enzyme with a Hill coefficient of 4-5, well in excess of that of the classical allosteric protein hemoglobin. The shape of the MAPK stimulus/ response curve may make the cascade particularly appropriate for mediating processes like mitogenesis, cell fate induction, and oocyte maturation, where a cell switches from one discrete state to another.

The species K_PP_norm, KKK_P_norm and KK_PP_norm are the relative concentrations of the active MAPK, MAPKK and MAPKKK, that is the double, or single resp. phophorylated forms divided by the total concentrations of each kinase. For MAPK additionally the also active MAPK divided by the maximal concentration of active MAPK is given by rel_K_PP_max. The parameter K_PP_norm_max, the maximal ratio of active MapK, has to be calculated for each change of parameters.

To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. Please refer to CC0 Public Domain Dedication for more information.

Model
Publication ID: 8816754 Submission Date: 13 Sep 2005 20:37:52 UTC Last Modification Date: 16 Jul 2013 18:02:42 UTC Creation Date: 11 Feb 2005 07:39:30 UTC
Mathematical expressions
Reactions
binding of MAPKKK activator MAPKKK activation binding of MAPKKK inactivator MAPKKK inactivation
binding P-MAPKKK and MAPKK phosphorylation of MAPKK binding MAPKK-Pase and P-MAPKK dephosphorylation of P-MAPKK
binding P-MAPKKK and P-MAPKK phosphorylation of P-MAPKK binding MAPKK-Pase and PP-MAPKK dephosphorylation of PP-MAPKK
binding MAPK and PP-MAPKK phosphorylation of MAPK binding MAPK-Pase and P-MAPK dephosphorylation of P-MAPK
binding PP-MAPKK and P-MAPK phosphorylation of P-MAPK binding MAPK-Pase and PP-MAPK dephosphorylation of PP-MAPK
Rules
Assignment Rule (variable: K_PP_norm) Assignment Rule (variable: relative maximal K_PP) Assignment Rule (variable: KK_PP_norm) Assignment Rule (variable: KKK_P_norm)
Physical entities
Compartments Species
compartment MAPKKK activator (Ras) MAPKKK inactivator Mos
Mos-P Mek1 Mek1-P
Mek1-PP Erk2 Erk2-P
Erk2-PP MAPK-Pase MAPKK-Pase
E1_Mos E2_Mos-P P-Mos_Mek1
P-Mos_P-Mek1 PP-Mek1_Erk2 PP-Mek1_P-Erk2
MAPKK-Pase_PP-Mek1 MAPKK-Pase_P-Mek1 MAPK-Pase_PP-Erk2
MAPK-Pase_P-Erk2 K_PP_norm KK_PP_norm
KKK_P_norm relative maximal K_PP  
Global parameters
K_PP_norm_max      
Reactions (20)
 
 binding of MAPKKK activator [Mos] + [MAPKKK activator (Ras)] ↔ [E1_Mos];  
 
 MAPKKK activation [E1_Mos] → [MAPKKK activator (Ras)] + [Mos-P];  
 
 binding of MAPKKK inactivator [Mos-P] + [MAPKKK inactivator] ↔ [E2_Mos-P];  
 
 MAPKKK inactivation [E2_Mos-P] → [MAPKKK inactivator] + [Mos];  
 
 binding P-MAPKKK and MAPKK [Mek1] + [Mos-P] ↔ [P-Mos_Mek1];  
 
 phosphorylation of MAPKK [P-Mos_Mek1] → [Mek1-P] + [Mos-P];  
 
 binding MAPKK-Pase and P-MAPKK [Mek1-P] + [MAPKK-Pase] ↔ [MAPKK-Pase_P-Mek1];  
 
 dephosphorylation of P-MAPKK [MAPKK-Pase_P-Mek1] → [Mek1] + [MAPKK-Pase];  
 
 binding P-MAPKKK and P-MAPKK [Mek1-P] + [Mos-P] ↔ [P-Mos_P-Mek1];  
 
 phosphorylation of P-MAPKK [P-Mos_P-Mek1] → [Mek1-PP] + [Mos-P];  
 
 binding MAPKK-Pase and PP-MAPKK [Mek1-PP] + [MAPKK-Pase] ↔ [MAPKK-Pase_PP-Mek1];  
 
 dephosphorylation of PP-MAPKK [MAPKK-Pase_PP-Mek1] → [Mek1-P] + [MAPKK-Pase];  
 
 binding MAPK and PP-MAPKK [Erk2] + [Mek1-PP] ↔ [PP-Mek1_Erk2];  
 
 phosphorylation of MAPK [PP-Mek1_Erk2] → [Erk2-P] + [Mek1-PP];  
 
 binding MAPK-Pase and P-MAPK [Erk2-P] + [MAPK-Pase] ↔ [MAPK-Pase_P-Erk2];  
 
 dephosphorylation of P-MAPK [MAPK-Pase_P-Erk2] → [Erk2] + [MAPK-Pase];  
 
 binding PP-MAPKK and P-MAPK [Erk2-P] + [Mek1-PP] ↔ [PP-Mek1_P-Erk2];  
 
 phosphorylation of P-MAPK [PP-Mek1_P-Erk2] → [Mek1-PP] + [Erk2-PP];  
 
 binding MAPK-Pase and PP-MAPK [Erk2-PP] + [MAPK-Pase] ↔ [MAPK-Pase_PP-Erk2];  
 
 dephosphorylation of PP-MAPK [MAPK-Pase_PP-Erk2] → [Erk2-P] + [MAPK-Pase];  
 
Rules (4)
 
 Assignment Rule (name: K_PP_norm) K_PP_norm = (PP_K+KPase_PP_K)/(PP_K+P_K+K+PP_KK_K+PP_KK_P_K+KPase_PP_K+KPase_P_K)
 
 Assignment Rule (name: rel_K_PP_max) relative maximal K_PP = K_PP_norm/K_PP_norm_max
 
 Assignment Rule (name: KK_PP_norm) KK_PP_norm = (PP_KK+PP_KK_K+PP_KK_P_K+KKPase_PP_KK)/(PP_KK+P_KK+KK+PP_KK_K+PP_KK_P_K+P_KKK_KK+P_KKK_P_KK+KKPase_PP_KK+KKPase_P_KK)
 
 Assignment Rule (name: KKK_P_norm) KKK_P_norm = (P_KKK+P_KKK_KK+P_KKK_P_KK)/(KKK+P_KKK+P_KKK_KK+P_KKK_P_KK)
 
   Spatial dimensions: 3.0  Compartment size: 4.0E-12
 
 MAPKKK activator (Ras)
Compartment: compartment
Initial concentration: 3.0E-5
 
   MAPKKK inactivator
Compartment: compartment
Initial concentration: 3.0E-4
 
 Mos
Compartment: compartment
Initial concentration: 0.0030
 
 Mos-P
Compartment: compartment
Initial concentration: 0.0
 
 Mek1
Compartment: compartment
Initial concentration: 1.2
 
 Mek1-P
Compartment: compartment
Initial concentration: 0.0
 
 Mek1-PP
Compartment: compartment
Initial concentration: 0.0
 
 Erk2
Compartment: compartment
Initial concentration: 1.2
 
 Erk2-P
Compartment: compartment
Initial concentration: 0.0
 
 Erk2-PP
Compartment: compartment
Initial concentration: 0.0
 
 MAPK-Pase
Compartment: compartment
Initial concentration: 0.12
 
   MAPKK-Pase
Compartment: compartment
Initial concentration: 3.0E-4
 
 E1_Mos
Compartment: compartment
Initial concentration: 0.0
 
 E2_Mos-P
Compartment: compartment
Initial concentration: 0.0
 
 P-Mos_Mek1
Compartment: compartment
Initial concentration: 0.0
 
 P-Mos_P-Mek1
Compartment: compartment
Initial concentration: 0.0
 
 PP-Mek1_Erk2
Compartment: compartment
Initial concentration: 0.0
 
 PP-Mek1_P-Erk2
Compartment: compartment
Initial concentration: 0.0
 
 MAPKK-Pase_PP-Mek1
Compartment: compartment
Initial concentration: 0.0
 
 MAPKK-Pase_P-Mek1
Compartment: compartment
Initial concentration: 0.0
 
 MAPK-Pase_PP-Erk2
Compartment: compartment
Initial concentration: 0.0
 
 MAPK-Pase_P-Erk2
Compartment: compartment
Initial concentration: 0.0
 
   K_PP_norm
Compartment: compartment
 
   KK_PP_norm
Compartment: compartment
 
   KKK_P_norm
Compartment: compartment
 
   relative maximal K_PP
Compartment: compartment
 
Global Parameters (1)
 
 K_PP_norm_max
Value: 0.900049
Constant
 
binding of MAPKKK activator (2)
 
   a1
Value: 1000.0
Constant
 
   d1
Value: 150.0
Constant
 
MAPKKK activation (1)
 
   k2
Value: 150.0
Constant
 
binding of MAPKKK inactivator (2)
 
   a2
Value: 1000.0
Constant
 
   d2
Value: 150.0
Constant
 
MAPKKK inactivation (1)
 
   k2
Value: 150.0
Constant
 
binding P-MAPKKK and MAPKK (2)
 
   a3
Value: 1000.0
Constant
 
   d3
Value: 150.0
Constant
 
phosphorylation of MAPKK (1)
 
   k3
Value: 150.0
Constant
 
binding MAPKK-Pase and P-MAPKK (2)
 
   a4
Value: 1000.0
Constant
 
   d4
Value: 150.0
Constant
 
dephosphorylation of P-MAPKK (1)
 
   k4
Value: 150.0
Constant
 
binding P-MAPKKK and P-MAPKK (2)
 
   a5
Value: 1000.0
Constant
 
   d5
Value: 150.0
Constant
 
phosphorylation of P-MAPKK (1)
 
   k5
Value: 150.0
Constant
 
binding MAPKK-Pase and PP-MAPKK (2)
 
   a6
Value: 1000.0
Constant
 
   d6
Value: 150.0
Constant
 
dephosphorylation of PP-MAPKK (1)
 
   k6
Value: 150.0
Constant
 
binding MAPK and PP-MAPKK (2)
 
   a7
Value: 1000.0
Constant
 
   d7
Value: 150.0
Constant
 
phosphorylation of MAPK (1)
 
   k7
Value: 150.0
Constant
 
binding MAPK-Pase and P-MAPK (2)
 
   a8
Value: 1000.0
Constant
 
   d8
Value: 150.0
Constant
 
dephosphorylation of P-MAPK (1)
 
   k8
Value: 150.0
Constant
 
binding PP-MAPKK and P-MAPK (2)
 
   a9
Value: 1000.0
Constant
 
   d9
Value: 150.0
Constant
 
phosphorylation of P-MAPK (1)
 
   k9
Value: 150.0
Constant
 
binding MAPK-Pase and PP-MAPK (2)
 
   a10
Value: 1000.0
Constant
 
   d10
Value: 150.0
Constant
 
dephosphorylation of PP-MAPK (1)
 
   k10
Value: 150.0
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000009

Curator's comment: (updated: 15 Jul 2013 13:25:23 PDT)

Figure 2B of the reference publication has been reproduced using Copasi 4.10 (Build 55). A logarithmic parameter scan over a range of "MAPKKK activator (Ras)" values with simultaneous calculation of the steady state was performed.

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