sarma1

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000430) Biomodels notes: The model [M4_K2_USEQ] correspond to type M4 with mass-action kinetics K2, in USEQ (Unsequestrated ) condition. Figure 5a is reproduced by setting P2=5nM and 1000nM. The simulation was done using SBML odeSolver and the plot was generated using Gnuplot. JWS Online curation: This model was curated by reproducing the figures as described in the BioModels Notes. No additional changes were made.

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Abstract
BACKGROUND: The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.
RESULTS: We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.
CONCLUSIONS: Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design.

Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.

Name Definition
0.001 litre
1e-09 mole
Id Name Spatial dimensions Size
compartment_1 compartment 3.0 1.0
Id Name Initial quantity Compartment Fixed
species_1 MK 1200.0 compartment_1 (compartment)
species_10 MKK-P 0.0 compartment_1 (compartment)
species_11 MKK-P_MKKK-P 0.0 compartment_1 (compartment)
species_12 MKK-PP_P2 0.0 compartment_1 (compartment)
species_13 P2 200.0 compartment_1 (compartment)
species_14 MKK-P_P2 0.0 compartment_1 (compartment)
species_15 MKK_P2 0.0 compartment_1 (compartment)
species_16 MKKK 300.0 compartment_1 (compartment)
species_17 MKKK_Sig 0.0 compartment_1 (compartment)
species_18 Sig 10.0 compartment_1 (compartment)
species_19 MKKK-P_P1 0.0 compartment_1 (compartment)
species_2 MKK-PP 0.0 compartment_1 (compartment)
species_20 P1 100.0 compartment_1 (compartment)
species_21 MK-PP_P2 0.0 compartment_1 (compartment)
species_22 MK-P_P2 0.0 compartment_1 (compartment)
species_23 MK_P2 0.0 compartment_1 (compartment)
species_24 MKK-PP_P1 0.0 compartment_1 (compartment)
species_25 MKK-P_P1 0.0 compartment_1 (compartment)
species_26 MKK_P1 0.0 compartment_1 (compartment)
species_27 MKKK_P1 0.0 compartment_1 (compartment)
species_3 MK_MKK-PP 0.0 compartment_1 (compartment)
species_4 MK-P 0.0 compartment_1 (compartment)
species_5 MK-P_MKK-PP 0.0 compartment_1 (compartment)
species_6 MK-PP 0.0 compartment_1 (compartment)
species_7 MKK 1200.0 compartment_1 (compartment)
species_8 MKKK-P 0.0 compartment_1 (compartment)
species_9 MKK_MKKK-P 0.0 compartment_1 (compartment)

Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.

Definition
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
reaction_1 15 species_1 + species_2 = species_3

compartment_1 * (k1 * species_1 * species_2 - k2 * species_3)
reaction_10 6 species_7 + species_8 = species_9

compartment_1 * (k1 * species_7 * species_8 - k2 * species_9)
reaction_11 7 species_9 > species_8 + species_10

compartment_1 * k1 * species_9
reaction_12 8 species_8 + species_10 = species_11

compartment_1 * (k1 * species_10 * species_8 - k2 * species_11)
reaction_13 9 species_11 > species_2 + species_8

compartment_1 * k1 * species_11
reaction_14 10_P2 species_2 + species_13 = species_12

compartment_1 * (k1 * species_2 * species_13 - k2 * species_12)
reaction_15 11_P2 species_12 > species_10 + species_13

compartment_1 * k1 * species_12
reaction_16 12_P2 species_10 + species_13 = species_14

compartment_1 * (k1 * species_10 * species_13 - k2 * species_14)
reaction_17 13_P2 species_14 > species_7 + species_13

compartment_1 * k1 * species_14
reaction_18 14_P2 species_15 = species_7 + species_13

compartment_1 * (k1 * species_15 - k2 * species_7 * species_13)
reaction_19 1 species_16 + species_18 = species_17

compartment_1 * (k1 * species_16 * species_18 - k2 * species_17)
reaction_2 16 species_3 > species_4 + species_2

compartment_1 * k1 * species_3
reaction_20 2 species_17 > species_8 + species_18

compartment_1 * k1 * species_17
reaction_21 3 species_8 + species_20 = species_19

compartment_1 * (k1 * species_8 * species_20 - k2 * species_19)
reaction_22 4 species_19 > species_16 + species_20

compartment_1 * k1 * species_19
reaction_23 10_P1 species_2 + species_20 = species_24

compartment_1 * (k1 * species_2 * species_20 - k2 * species_24)
reaction_24 5 species_27 = species_16 + species_20

compartment_1 * (k1 * species_27 - k2 * species_16 * species_20)
reaction_25 11_P1 species_24 > species_10 + species_20

compartment_1 * k1 * species_24
reaction_26 12_P1 species_10 + species_20 = species_25

compartment_1 * (k1 * species_10 * species_20 - k2 * species_25)
reaction_27 13_P1 species_25 > species_7 + species_20

compartment_1 * k1 * species_25
reaction_28 14_P1 species_26 = species_7 + species_20

compartment_1 * (k1 * species_26 - k2 * species_7 * species_20)
reaction_3 17 species_4 + species_2 = species_5

compartment_1 * (k1 * species_4 * species_2 - k2 * species_5)
reaction_4 18 species_5 > species_6 + species_2

compartment_1 * k1 * species_5
reaction_5 19 species_6 + species_13 = species_21

compartment_1 * (k1 * species_6 * species_13 - k2 * species_21)
reaction_6 20 species_21 > species_4 + species_13

compartment_1 * k1 * species_21
reaction_7 21 species_4 + species_13 = species_22

compartment_1 * (k1 * species_4 * species_13 - k2 * species_22)
reaction_8 22 species_22 > species_1 + species_13

compartment_1 * k1 * species_22
reaction_9 23 species_23 = species_1 + species_13

compartment_1 * (k1 * species_23 - k2 * species_1 * species_13)

Global parameters

Id Value
parameter_1 0.0

Local parameters

Id Value Reaction
k1 0.02 reaction_1 (15)
k2 1.0 reaction_1 (15)
k1 0.01 reaction_2 (16)
k1 0.032 reaction_3 (17)
k2 1.0 reaction_3 (17)
k1 15.0 reaction_4 (18)
k1 0.045 reaction_5 (19)
k2 1.0 reaction_5 (19)
k1 0.092 reaction_6 (20)
k1 0.01 reaction_7 (21)
k2 1.0 reaction_7 (21)
k1 0.086 reaction_8 (22)
k1 0.0 reaction_9 (23)
k2 0.0 reaction_9 (23)
k1 0.02 reaction_10 (6)
k2 1.0 reaction_10 (6)
k1 0.01 reaction_11 (7)
k1 0.032 reaction_12 (8)
k2 1.0 reaction_12 (8)
k1 15.0 reaction_13 (9)
k1 0.045 reaction_14 (10_P2)
k2 1.0 reaction_14 (10_P2)
k1 0.092 reaction_15 (11_P2)
k1 0.01 reaction_16 (12_P2)
k2 1.0 reaction_16 (12_P2)
k1 0.086 reaction_17 (13_P2)
k1 0.0 reaction_18 (14_P2)
k2 0.0 reaction_18 (14_P2)
k1 0.02 reaction_19 (1)
k2 1.0 reaction_19 (1)
k1 1.0 reaction_20 (2)
k1 0.02 reaction_21 (3)
k2 1.0 reaction_21 (3)
k1 0.086 reaction_22 (4)
k1 0.045 reaction_23 (10_P1)
k2 1.0 reaction_23 (10_P1)
k1 0.092 reaction_25 (11_P1)
k1 0.01 reaction_26 (12_P1)
k2 1.0 reaction_26 (12_P1)
k1 0.086 reaction_27 (13_P1)
k1 0.0 reaction_28 (14_P1)
k2 0.0 reaction_28 (14_P1)
k1 0.0 reaction_24 (5)
k2 0.0 reaction_24 (5)

Assignment rules

Definition

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments