sarma4

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000433) Biomodels notes: The model [M4_K2_QSS_PSEQ] correspond to type M4 with mass-action kinetics K2, in QSS (quasi steady state) and PSEQ (sequestrated ) condition. Figure 5d 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
compartment_2 No Name 3.0 1.0
Id Name Initial quantity Compartment Fixed
species_1 MKKK 300.0 compartment_1 (compartment)
species_10 P2 200.0 compartment_1 (compartment)
species_11 Sig 20.0 compartment_1 (compartment)
species_2 MKKK_P 0.0 compartment_1 (compartment)
species_3 MKK 1199.99994221325 compartment_1 (compartment)
species_4 MKK_P 0.0 compartment_1 (compartment)
species_5 MKK_PP 0.0 compartment_1 (compartment)
species_6 MK 1199.99994221325 compartment_1 (compartment)
species_7 MK_P 0.0 compartment_1 (compartment)
species_8 MK_PP 0.0 compartment_1 (compartment)
species_9 P1 100.0 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 1 species_1 > species_2

compartment_1 * function_1(species_1, parameter_1, k1, species_11)
reaction_10 10 species_7 > species_6

compartment_1 * function_10(species_7, species_5, species_4, species_8, species_3, species_6, species_10, parameter_10, parameter_13, parameter_14, parameter_12, parameter_9, k10b)
reaction_2 2 species_2 > species_1

compartment_1 * function_2(species_2, species_1, species_9, species_5, species_4, species_3, parameter_11, parameter_2, parameter_5, parameter_6, k2a)
reaction_3 3 species_3 > species_4

compartment_1 * function_3(k3, species_2, species_3, parameter_3, species_4, parameter_4)
reaction_4 4 species_4 > species_5

compartment_1 * function_4(k4, species_2, species_4, parameter_4, species_3, parameter_3)
reaction_5 5 species_5 > species_4

compartment_1 * function_5(species_5, species_4, species_7, species_8, species_9, species_3, species_6, k5a, parameter_5, species_1, species_2, k5b, species_10, parameter_13, parameter_6, parameter_11, parameter_2, parameter_14, parameter_12, parameter_10, parameter_9)
reaction_6 6 species_4 > species_3

compartment_1 * function_6(species_9, species_4, species_5, species_7, species_8, species_3, species_6, k6a, parameter_6, species_1, species_2, species_10, parameter_14, parameter_2, parameter_11, parameter_5, k6b, parameter_13, parameter_12, parameter_10, parameter_9)
reaction_7 7 species_6 > species_7

compartment_1 * function_7(k7, species_5, species_6, parameter_7, species_7, parameter_8)
reaction_8 8 species_7 > species_8

compartment_1 * function_8(k7, species_5, species_7, parameter_8, species_6, parameter_7)
reaction_9 9 species_8 > species_7

compartment_1 * function_9(species_8, species_9, species_4, species_7, species_3, species_6, species_10, parameter_9, parameter_13, parameter_14, parameter_12, parameter_10, k9b)

Global parameters

Id Value
parameter_1 100.0
parameter_10 108.6
parameter_11 0.06
parameter_12 0.06
parameter_13 24.3
parameter_14 108.6
parameter_2 54.3
parameter_3 50.5
parameter_4 500.0
parameter_5 24.3
parameter_6 108.6
parameter_7 50.5
parameter_8 500.0
parameter_9 24.3

Local parameters

Id Value Reaction
k1 1.0 reaction_1 (1)
k2a 0.086 reaction_2 (2)
k3 0.01 reaction_3 (3)
k4 15.0 reaction_4 (4)
k5a 0.092 reaction_5 (5)
k5b 0.092 reaction_5 (5)
k6a 0.086 reaction_6 (6)
k6b 0.086 reaction_6 (6)
k7 0.01 reaction_7 (7)
k7 15.0 reaction_8 (8)
k9b 0.092 reaction_9 (9)
k10b 0.086 reaction_10 (10)

Assignment rules

Definition

Rate rules

Definition

Algebraic rules

Definition
Definition
function_10(MK_P, MKK_PP, MKK_P, MK_PP, MKK, MK, P2, K10b, K5b, K6b, Kse2, K9b, k10b) = k10b * P2 * MK_P / K10b / (1 + MKK_PP / K5b + MKK_P / K6b + MKK / Kse2 + MK / Kse2 + MK_P / K10b + MK_PP / K9b)
function_1(MKKK, K1, k1, Sig) = k1 * Sig * MKKK / (K1 + MKKK)
function_2(MKKK_P, MKKK, P1, MKK_PP, MKK_P, MKK, Kse1, K2a, K5a, K6a, k2a) = k2a * MKKK_P * P1 / K2a / (1 + MKKK_P / K2a + MKKK / Kse1 + MKK_PP / K5a + MKK_P / K6a + MKK / Kse1)
function_3(k3, MKKK_P, MKK, K3, MKK_P, K4) = k3 * MKKK_P * MKK / K3 / (1 + MKK / K3 + MKK_P / K4)
function_4(k4, MKKK_P, MKK_P, K4, MKK, K3) = k4 * MKKK_P * MKK_P / K4 / (1 + MKK / K3 + MKK_P / K4)
function_8(k7, MKK_PP, MK_P, K8, MK, K7) = k7 * MKK_PP * MK_P / K8 / (1 + MK / K7 + MK_P / K8)
function_9(MK_PP, MKK_PP, MKK_P, MK_P, MKK, MK, P2, K9b, K5b, K6b, Kse2, K10b, k9b) = k9b * P2 * MK_PP / K9b / (1 + MKK_PP / K5b + MKK_P / K6b + MKK / Kse2 + MK / Kse2 + MK_P / K10b + MK_PP / K9b)
function_7(k7, MKK_PP, MK, K7, MK_P, K8) = k7 * MKK_PP * MK / K7 / (1 + MK / K7 + MK_P / K8)
function_5(MKK_PP, MKK_P, MK_P, MK_PP, P1, MKK, MK, k5a, K5a, MKKK, MKKK_P, k5b, P2, K5b, K6a, Kse1, K2a, K6b, Kse2, K10b, K9b) = k5a * P1 * MKK_PP / K5a / (1 + MKKK_P / K2a + MKKK / Kse1 + MKK_PP / K5a + MKK_P / K6a + MKK / Kse1) + k5b * P2 * MKK_PP / K5b / (1 + MKK_PP / K5b + MKK_P / K6b + MKK / Kse2 + MK / Kse2 + MK_P / K10b + MK_PP / K9b)
function_6(P1, MKK_P, MKK_PP, MK_P, MK_PP, MKK, MK, k6a, K6a, MKKK, MKKK_P, P2, K6b, K2a, Kse1, K5a, k6b, K5b, Kse2, K10b, K9b) = k6a * P1 * MKK_P / K6a / (1 + MKKK_P / K2a + MKKK / Kse1 + MKK_PP / K5a + MKK_P / K6a + MKK / Kse1) + k6b * P2 * MKK_P / K6b / (1 + MKK_PP / K5b + MKK_P / K6b + MKK / Kse2 + MK / Kse2 + MK_P / K10b + MK_PP / K9b)
Trigger Assignments