sarma9

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000444) Biomodels notes: Figure 8a 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. 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: 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.

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_0 compartment 3.0 1.0
Id Name Initial quantity Compartment Fixed
species_0 MKKK 999.999903688753 compartment_0 (compartment)
species_1 MKKK_P 0.0 compartment_0 (compartment)
species_10 P3 499.999975922188 compartment_0 (compartment)
species_11 M_PP_n 0.0 compartment_0 (compartment)
species_12 PreP3_mRNA 0.0 compartment_0 (compartment)
species_13 P3mRNA 0.0 compartment_0 (compartment)
species_14 P3_c 0.0 compartment_0 (compartment)
species_15 P3_n 0.0 compartment_0 (compartment)
species_16 M_n 0.0 compartment_0 (compartment)
species_17 M_P_n 0.0 compartment_0 (compartment)
species_2 MKK 3999.9998073775 compartment_0 (compartment)
species_3 MKK_P 0.0 compartment_0 (compartment)
species_4 MKK_PP 0.0 compartment_0 (compartment)
species_5 M 999.999903688753 compartment_0 (compartment)
species_6 M_P 0.0 compartment_0 (compartment)
species_7 M_PP 0.0 compartment_0 (compartment)
species_8 P1 99.9999903688752 compartment_0 (compartment)
species_9 P2 499.999951844377 compartment_0 (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_0 1 species_0 > species_1

compartment_0 * function_4_1_1(A, K1, Ka, V1, species_0, species_7)
reaction_1 3 species_2 > species_3

compartment_0 * function_4_3_1(K3, KI, k3, species_1, species_2, species_3, species_7)
reaction_10 11 species_7 = species_11

compartment_0 * function_1(k11f, species_7, k11b, species_11)
reaction_11 12 ∅ > species_12

compartment_0 * function_2(V12, species_11, n12, K12)
reaction_12 13 species_12 > species_13

compartment_0 * k1 * species_12
reaction_13 14 species_13 > ∅

compartment_0 * k1 * species_13
reaction_14 15 ∅ > species_14

compartment_0 * function_3(k15, species_13)
reaction_15 16 species_14 = species_15

compartment_0 * (k1 * species_14 - k2 * species_15)
reaction_16 17 species_14 > ∅

compartment_0 * k1 * species_14
reaction_17 18 species_15 > ∅

compartment_0 * k1 * species_15
reaction_18 19 species_5 = species_16

compartment_0 * (k1 * species_5 - k2 * species_16)
reaction_19 20 species_6 = species_17

compartment_0 * (k1 * species_6 - k2 * species_17)
reaction_2 4 species_3 > species_4

compartment_0 * function_4_4_1(K4, KI, k4, species_1, species_2, species_3, species_7)
reaction_20 21 species_11 > species_17

compartment_0 * function_4(k21, species_15, species_11, K21, species_17, K21i)
reaction_21 22 species_17 > species_16

compartment_0 * function_5(k22, species_15, species_17, K22, species_11, K22i)
reaction_3 7 species_5 > species_6

compartment_0 * function_4_7_1(K7, k7, species_4, species_5, species_6)
reaction_4 8 species_6 > species_7

compartment_0 * function_4_8_1(K8, k8, species_4, species_5, species_6)
reaction_5 2 species_1 > species_0

compartment_0 * function_4_2_1(K2, k2, species_1, species_8)
reaction_6 5 species_4 > species_3

compartment_0 * function_4_5_1(K5, k5, species_3, species_4, species_9)
reaction_7 6 species_3 > species_2

compartment_0 * function_4_6_1(K6, k6, species_3, species_4, species_9)
reaction_8 9 species_7 > species_6

compartment_0 * function_4_9_1(K9, k9, species_10, species_6, species_7)
reaction_9 10 species_6 > species_5

compartment_0 * function_4_10_1(K10, k10, species_10, species_6, species_7)

Global parameters

Id Value
parameter_1 0.022

Local parameters

Id Value Reaction
K3 20.0 reaction_1 (3)
KI 9.0 reaction_1 (3)
k3 0.1 reaction_1 (3)
K4 20.0 reaction_2 (4)
KI 9.0 reaction_2 (4)
k4 0.1 reaction_2 (4)
K7 20.0 reaction_3 (7)
k7 0.1 reaction_3 (7)
K8 20.0 reaction_4 (8)
k8 0.1 reaction_4 (8)
K2 100.0 reaction_5 (2)
k2 0.1 reaction_5 (2)
K5 20.0 reaction_6 (5)
k5 0.02 reaction_6 (5)
A 100.0 reaction_0 (1)
K1 15.0 reaction_0 (1)
Ka 500.0 reaction_0 (1)
V1 6.0 reaction_0 (1)
K6 20.0 reaction_7 (6)
k6 0.02 reaction_7 (6)
K9 20.0 reaction_8 (9)
k9 0.02 reaction_8 (9)
K10 20.0 reaction_9 (10)
k10 0.02 reaction_9 (10)
k11f 10.34 reaction_10 (11)
k11b 2.86 reaction_10 (11)
V12 29.24 reaction_11 (12)
n12 3.97 reaction_11 (12)
K12 169.0 reaction_11 (12)
k1 0.022 reaction_12 (13)
k1 0.0078 reaction_13 (14)
k15 0.0012 reaction_14 (15)
k1 22.56 reaction_15 (16)
k2 15.4 reaction_15 (16)
k1 0.00025 reaction_16 (17)
k1 0.00025 reaction_17 (18)
k1 10.34 reaction_18 (19)
k2 2.86 reaction_18 (19)
k1 10.34 reaction_19 (20)
k2 2.86 reaction_19 (20)
k21 0.68 reaction_20 (21)
K21 10300.0 reaction_20 (21)
K21i 87.0 reaction_20 (21)
k22 0.31 reaction_21 (22)
K22 87.0 reaction_21 (22)
K22i 10300.0 reaction_21 (22)

Assignment rules

Definition

Rate rules

Definition

Algebraic rules

Definition
Definition
function_2(V12, M_PP_n, n12, K12) = V12 * pow(M_PP_n, n12) / (pow(K12, n12) + pow(M_PP_n, n12))
function_4_10_1(K10, k10, species_10, species_6, species_7) = k10 * species_10 * species_6 / K10 / (1 + species_7 / K10 + species_6 / K10)
function_4_9_1(K9, k9, species_10, species_6, species_7) = k9 * species_10 * species_7 / K9 / (1 + species_7 / K9 + species_6 / K9)
function_4_6_1(K6, k6, species_3, species_4, species_9) = k6 * species_9 * species_3 / K6 / (1 + species_4 / K6 + species_3 / K6)
function_5(k22, P3_n, M_P_n, K22, M_PP_n, K22i) = k22 * P3_n * M_P_n / K22 / (1 + M_P_n / K22 + M_PP_n / K22i)
function_4(k21, P3_n, M_PP_n, K21, M_P_n, K21i) = k21 * P3_n * M_PP_n / K21 / (1 + M_PP_n / K21 + M_P_n / K21i)
function_1(k11f, ppERK_c, k11b, ppERK_n) = k11f * ppERK_c - k11b * ppERK_n
function_3(k15, P3mRNA) = k15 * P3mRNA
function_4_5_1(K5, k5, species_3, species_4, species_9) = k5 * species_9 * species_4 / K5 / (1 + species_4 / K5 + species_3 / K5)
function_4_2_1(K2, k2, species_1, species_8) = k2 * species_8 * species_1 / K2 / (1 + species_1 / K2)
function_4_8_1(K8, k8, species_4, species_5, species_6) = k8 * species_4 * species_6 / K8 / (1 + species_5 / K8 + species_6 / K8)
function_4_7_1(K7, k7, species_4, species_5, species_6) = k7 * species_4 * species_5 / K7 / (1 + species_5 / K7 + species_6 / K7)
function_4_4_1(K4, KI, k4, species_1, species_2, species_3, species_7) = k4 * species_1 * species_3 / K4 / ((1 + species_2 / K4 + species_3 / K4) * (1 + species_7 / KI))
function_4_3_1(K3, KI, k3, species_1, species_2, species_3, species_7) = k3 * species_1 * species_2 / K3 / ((1 + species_2 / K3 + species_3 / K3) * (1 + species_7 / KI))
function_4_1_1(A, K1, Ka, V1, species_0, species_7) = V1 * species_0 / K1 / (1 + species_0 / K1) * ((1 + A * species_7 / Ka) / (1 + species_7 / Ka))
Trigger Assignments