BioModels Database logo

BioModels Database

spacer

BIOMD0000000443 - Sarma2012 - Oscillations in MAPK cascade (S1n)

 

 |   |   |  Send feedback
Reference Publication
Publication ID: 22694947
Sarma U, Ghosh I.
Oscillations in MAPK cascade triggered by two distinct designs of coupled positive and negative feedback loops.
BMC Res Notes 2012; 5: 287
National Centre for Cell Science, Ganeshkhind, Pune, India. uddipans@gmail.com  [more]
Model
Original Model: BIOMD0000000443.xml.origin
Submitter: Uddipan Sarma
Submission ID: MODEL1112190006
Submission Date: 19 Dec 2011 18:18:19 UTC
Last Modification Date: 30 May 2014 17:50:13 UTC
Creation Date: 18 Mar 2013 14:07:04 UTC
Encoders:  Nick Juty
   Vijayalakshmi Chelliah
   Uddipan Sarma
set #1
bqbiol:hasTaxon Taxonomy cellular organisms
set #2
bqmodel:isDerivedFrom BioModels Database Sarma2012 - Oscillations in MAPK cascade (S1)
BioModels Database Nakakuki2010_CellFateDecision_Mechanistic
BioModels Database Nakakuki2010_CellFateDecision_Core
set #3
bqbiol:isVersionOf Gene Ontology MAPK cascade
Notes
Sarma2012 - Oscillations in MAPK cascade (S1n)

Two plausible designs (S1 and S2) of coupled positive and negative feedback loops of MAPK cascade has been described in this paper. Further these models were extended to S1n and S2n, to incorporate the nuclear-cytoplasmic translocation of the MK layer components of the cascade. This model corresponds to model S1n that comprises negative feedback from MK-PP to MKKK-P layer coupled to positive feedback from MK-PP to MKK-PP layer, with the inclusion of nuclear-cytoplasmic translocation.

This model is described in the article:

Sarma U, Ghosh I.
BMC Res Notes. 2012 Jun 13;5:287.

Abstract:

BACKGROUND:
Feedback loops, both positive and negative are embedded in the Mitogen Activated Protein Kinase (MAPK) cascade. In the three layer MAPK cascade, both feedback loops originate from the terminal layer and their sites of action are either of the two upstream layers. Recent studies have shown that the cascade uses coupled positive and negative feedback loops in generating oscillations. Two plausible designs of coupled positive and negative feedback loops can be elucidated from the literature; in one design the positive feedback precedes the negative feedback in the direction of signal flow and vice-versa in another. But it remains unexplored how the two designs contribute towards triggering oscillations in MAPK cascade. Thus it is also not known how amplitude, frequency, robustness or nature (analogous/digital) of the oscillations would be shaped by these two designs.

RESULTS:
We built two models of MAPK cascade that exhibited oscillations as function of two underlying designs of coupled positive and negative feedback loops. Frequency, amplitude and nature (digital/analogous) of oscillations were found to be differentially determined by each design. It was observed that the positive feedback emerging from an oscillating MAPK cascade and functional in an external signal processing module can trigger oscillations in the target module, provided that the target module satisfy certain parametric requirements. The augmentation of the two models was done to incorporate the nuclear-cytoplasmic shuttling of cascade components followed by induction of a nuclear phosphatase. It revealed that the fate of oscillations in the MAPK cascade is governed by the feedback designs. Oscillations were unaffected due to nuclear compartmentalization owing to one design but were completely abolished in the other case.

CONCLUSION:
The MAPK cascade can utilize two distinct designs of coupled positive and negative feedback loops to trigger oscillations. The amplitude, frequency and robustness of the oscillations in presence or absence of nuclear compartmentalization were differentially determined by two designs of coupled positive and negative feedback loops. A positive feedback from an oscillating MAPK cascade was shown to induce oscillations in an external signal processing module, uncovering a novel regulatory aspect of MAPK signal processing.

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: 22694947 Submission Date: 19 Dec 2011 18:18:19 UTC Last Modification Date: 30 May 2014 17:50:13 UTC Creation Date: 18 Mar 2013 14:07:04 UTC
Mathematical expressions
Reactions
1 3 4 7
8 2 5 6
9 10 11 12
13 14 15 17
19 20 16 21
22 18    
Physical entities
Compartments Species
compartment MKKK MKKK_P MKK
MKK_P MKK_PP M
M_P M_PP P1
P2 P3 M_PP_n
PreP3_mRNA P3mRNA P3_c
pP3_c M_n M_P_n
P3_n    
Reactions (22)
 
 1 [MKKK] → [MKKK_P];   {M_PP} , {MKKK} , {M_PP} , {MKKK} , {M_PP}
 
 3 [MKK] → [MKK_P];   {MKKK_P} , {MKK_P} , {M_PP} , {MKKK_P} , {MKK} , {MKK_P} , {M_PP} , {MKKK_P} , {MKK} , {MKK_P} , {M_PP}
 
 4 [MKK_P] → [MKK_PP];   {MKKK_P} , {MKK} , {M_PP} , {MKKK_P} , {MKK} , {MKK_P} , {M_PP} , {MKKK_P} , {MKK} , {MKK_P} , {M_PP}
 
 7 [M] → [M_P];   {MKK_PP} , {M_P} , {MKK_PP} , {M} , {M_P} , {MKK_PP} , {M} , {M_P}
 
 8 [M_P] → [M_PP];   {MKK_PP} , {M} , {MKK_PP} , {M} , {M_P} , {MKK_PP} , {M} , {M_P}
 
 2 [MKKK_P] → [MKKK];   {P1} , {MKKK_P} , {P1} , {MKKK_P} , {P1}
 
 5 [MKK_PP] → [MKK_P];   {P2} , {MKK_P} , {MKK_P} , {MKK_PP} , {P2} , {MKK_P} , {MKK_PP} , {P2}
 
 6 [MKK_P] → [MKK];   {P2} , {MKK_PP} , {MKK_P} , {MKK_PP} , {P2} , {MKK_P} , {MKK_PP} , {P2}
 
 9 [M_PP] → [M_P];   {P3} , {M_P} , {M} , {P3} , {M_P} , {M_PP} , {P3} , {M_P} , {M_PP}
 
 10 [M_P] → [M];   {P3} , {M_PP} , {M} , {P3} , {M_P} , {M_PP} , {P3} , {M_P} , {M_PP}
 
 11 [M_PP] ↔ [M_PP_n];   {M_PP} , {M_PP_n} , {M_PP} , {M_PP_n}
 
 12  → [PreP3_mRNA];   {M_PP_n} , {M_PP_n} , {M_PP_n}
 
 13 [PreP3_mRNA] → [P3mRNA];   {PreP3_mRNA} , {PreP3_mRNA}
 
 14 [P3mRNA] → ;   {P3mRNA} , {P3mRNA}
 
 15  → [P3_c];   {P3mRNA} , {P3mRNA} , {P3mRNA}
 
 17 [P3_c] → ;   {P3_c} , {P3_c}
 
 19 [M] ↔ [M_n];   {M} , {M_n} , {M} , {M_n}
 
 20 [M_P] ↔ [M_P_n];   {M_P} , {M_P_n} , {M_P} , {M_P_n}
 
 16 [P3_c] ↔ [P3_n];   {P3_c} , {P3_n} , {P3_c} , {P3_n}
 
 21 [M_PP_n] → [M_P_n];   {M_P_n} , {P3_n} , {M_PP_n} , {M_P_n} , {P3_n} , {M_PP_n} , {M_P_n} , {P3_n}
 
 22 [M_P_n] → [M_n];   {P3_n} , {M_PP_n} , {P3_n} , {M_P_n} , {M_PP_n} , {P3_n} , {M_P_n} , {M_PP_n}
 
 18 [P3_n] → ;   {P3_n} , {P3_n}
 
Functions (15)
 
 function_4_1_1 lambda(K1, KI, V1, species_0, species_7, V1*species_0/K1/((1+species_0/K1)*(1+species_7/KI)))
 
 function_4_3_1 lambda(A, K3, Ka, k3, species_1, species_2, species_3, species_7, k3*species_1*species_2/K3/(1+species_2/K3+species_3/K3)*(1+A*species_7/Ka)/(1+species_7/Ka))
 
 function_4_4_1 lambda(A, K4, Ka, k4, species_1, species_2, species_3, species_7, k4*species_1*species_3/K4/(1+species_3/K4+species_2/K4)*(1+A*species_7/Ka)/(1+species_7/Ka))
 
 function_4_7_1 lambda(K7, k7, species_4, species_5, species_6, k7*species_4*species_5/K7/(1+species_5/K7+species_6/K7))
 
 function_4_8_1 lambda(K8, k8, species_4, species_5, species_6, k8*species_4*species_6/K8/(1+species_5/K8+species_6/K8))
 
 function_4_2_1 lambda(K2, k2, species_1, species_8, k2*species_8*species_1/K2/(1+species_1/K2))
 
 function_4_5_1 lambda(K5, k5, species_3, species_4, species_9, k5*species_9*species_4/K5/(1+species_4/K5+species_3/K5))
 
 function_4_6_1 lambda(K6, k6, species_3, species_4, species_9, k6*species_9*species_3/K6/(1+species_4/K6+species_3/K6))
 
 function_4_9_1 lambda(K9, k9, species_10, species_6, species_7, k9*species_10*species_7/K9/(1+species_7/K9+species_6/K9))
 
 function_4_10_1 lambda(K10, k10, species_10, species_6, species_7, k10*species_10*species_6/K10/(1+species_7/K10+species_6/K10))
 
 11 lambda(k11f, ppERK_c, k11b, ppERK_n, k11f*ppERK_c-k11b*ppERK_n)
 
 12 lambda(V12, n12, K12, M_PP_n, V12*M_PP_n^n12/(K12^n12+M_PP_n^n12))
 
 15 lambda(k15, P3mRNA, k15*P3mRNA)
 
 21 lambda(M_PP_n, M_P_n, P3_n, k21, K21, K21i, k21*P3_n*M_PP_n/K21/(1+M_PP_n/K21+M_P_n/K21i))
 
 22 lambda(P3_n, M_P_n, M_PP_n, k22, K22, K22i, k22*P3_n*M_P_n/K22/(1+M_P_n/K22+M_PP_n/K22i))
 
 compartment Spatial dimensions: 3.0  Compartment size: 1.0
 
 MKKK
Compartment: compartment
Initial concentration: 999.999903688753
 
 MKKK_P
Compartment: compartment
Initial concentration: 0.0
 
 MKK
Compartment: compartment
Initial concentration: 3999.99961475501
 
 MKK_P
Compartment: compartment
Initial concentration: 0.0
 
 MKK_PP
Compartment: compartment
Initial concentration: 0.0
 
 M
Compartment: compartment
Initial concentration: 999.999903688753
 
 M_P
Compartment: compartment
Initial concentration: 0.0
 
 M_PP
Compartment: compartment
Initial concentration: 0.0
 
 P1
Compartment: compartment
Initial concentration: 99.9999903688752
 
 P2
Compartment: compartment
Initial concentration: 499.999951844377
 
 P3
Compartment: compartment
Initial concentration: 499.999975922188
 
 M_PP_n
Compartment: compartment
Initial concentration: 0.0
 
 PreP3_mRNA
Compartment: compartment
Initial concentration: 0.0
 
 P3mRNA
Compartment: compartment
Initial concentration: 0.0
 
 P3_c
Compartment: compartment
Initial concentration: 0.0
 
 pP3_c
Compartment: compartment
Initial concentration: 0.0
 
 M_n
Compartment: compartment
Initial concentration: 0.0
 
 M_P_n
Compartment: compartment
Initial concentration: 0.0
 
 P3_n
Compartment: compartment
Initial concentration: 0.0
 
1 (3)
 
   K1
Value: 20.0
Constant
 
   KI
Value: 9.0
Constant
 
   V1
Value: 2.5
Constant
 
3 (4)
 
   A
Value: 10.0
Constant
 
   K3
Value: 20.0
Constant
 
   Ka
Value: 500.0
Constant
 
   k3
Value: 0.1
Constant
 
4 (4)
 
   A
Value: 10.0
Constant
 
   K4
Value: 20.0
Constant
 
   Ka
Value: 500.0
Constant
 
   k4
Value: 0.1
Constant
 
7 (2)
 
   K7
Value: 20.0
Constant
 
   k7
Value: 0.1
Constant
 
8 (2)
 
   K8
Value: 20.0
Constant
 
   k8
Value: 0.1
Constant
 
2 (2)
 
   K2
Value: 200.0
Constant
 
   k2
Value: 0.025
Constant
 
5 (2)
 
   K5
Value: 200.0
Constant
 
   k5
Value: 0.1
Constant
 
6 (2)
 
   K6
Value: 200.0
Constant
 
   k6
Value: 0.1
Constant
 
9 (2)
 
   K9
Value: 200.0
Constant
 
   k9
Value: 0.1
Constant
 
10 (2)
 
   K10
Value: 200.0
Constant
 
   k10
Value: 0.1
Constant
 
11 (2)
 
   k11f
Value: 10.34
Constant
 
   k11b
Value: 2.86
Constant
 
12 (3)
 
   V12
Value: 29.24
Constant
 
   n12
Value: 3.97
Constant
 
   K12
Value: 169.0
Constant
 
13 (1)
 
   k1
Value: 0.022
Constant
 
14 (1)
 
   k1
Value: 0.0078
Constant
 
15 (1)
 
   k15
Value: 0.0012
Constant
 
17 (1)
 
   k1
Value: 2.5E-4
Constant
 
19 (2)
 
   k1
Value: 10.34
Constant
 
   k2
Value: 2.86
Constant
 
20 (2)
 
   k1
Value: 10.34
Constant
 
   k2
Value: 2.86
Constant
 
16 (2)
 
   k1
Value: 22.56
Constant
 
   k2
Value: 15.4
Constant
 
21 (3)
 
   k21
Value: 0.68
Constant
 
   K21
Value: 10300.0
Constant
 
   K21i
Value: 87.0
Constant
 
22 (3)
 
   k22
Value: 0.31
Constant
 
   K22
Value: 87.0
Constant
 
   K22i
Value: 10300.0
Constant
 
18 (1)
 
   k1
Value: 2.5E-4
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000443

Curator's comment: (updated: 18 Mar 2013 14:05:31 GMT)

Figure 7a of the reference publication has been reproduced. The data for generating the plot was obtained by simulating the model using Copasi v4.8 (Build 35) and the plot was obtained using Gnuplot.

spacer
spacer