fisher2

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000122) Biomodels notes: The plot corresponds to Fig 4a of the paper. Simulation result obtained from MathSBML. 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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NFAT and NFkappaB activation in T lymphocytes: a model of differential activation of gene expression.

  • Wayne G Fisher
  • Pei-Chi Yang
  • Ram K Medikonduri
  • M Saleet Jafri
Ann Biomed Eng 2006; 34 (11): 1712-1728
Abstract
Mathematical models for the regulation of the Ca(2+)-dependent transcription factors NFAT and NFkappaB that are involved in the activation of the immune and inflammatory responses in T lymphocytes have been developed. These pathways are important targets for drugs, which act as powerful immunosuppressants by suppressing activation of NFAT and NFkappaB in T cells. The models simulate activation and deactivation over physiological concentrations of Ca(2+), diacyl glycerol (DAG), and PKCtheta using single and periodic step increases. The model suggests the following: (1) the activation NFAT does not occur at low frequencies as NFAT requires calcineurin activated by Ca(2+) to remain dephosphorylated and in the nucleus; (2) NFkappaB is activated at lower Ca(2+) oscillation frequencies than NFAT as IkappaB is degraded in response to elevations in Ca(2+) allowing free NFkappaB to translocate into the nucleus; and (3) the degradation of IkappaB is essential for efficient translocation of NFkappaB to the nucleus. Through sensitivity analysis, the model also suggests that the largest controlling factor for NFAT activation is the dissociation/reassociation rate of the NFAT:calcineurin complex and the translocation rate of the complex into the nucleus and for NFkappaB is the degradation/resynthesis rate of IkappaB and the import rate of IkappaB into the nucleus.

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
1e-06 mole
Id Name Spatial dimensions Size
cytosol cytosol 3.0 0.000000000000269
nucleus nucleus 3.0 0.000000000000113
Id Name Initial quantity Compartment Fixed
Act_C_Cyt Active Calcineurin in cytosol 0.0000091 cytosol (cytosol)
Act_C_Nuc Active Calcineurin in Nucleus 0.0000505 nucleus (nucleus)
Ca_Cyt Calcium in Cytosol 1.0 cytosol (cytosol)
Ca_Nuc Calcium in Nucleus 1.0 nucleus (nucleus)
Inact_C_Cyt Inactive Calcineurin in cytosol 0.0097108 cytosol (cytosol)
Inact_C_Nuc Inactive Calcineurin in nucleus 0.049198 nucleus (nucleus)
NFAT_Act_C_Cyt NFAT Calcineurin complex in cytosol 0.0000061 cytosol (cytosol)
NFAT_Act_C_Nuc NFAT Calcineurin complex in nucleus 0.0009477 nucleus (nucleus)
NFAT_Cyt NFAT_Cyt 0.0001101 cytosol (cytosol)
NFAT_Nuc NFAT_nuc 0.0005219 nucleus (nucleus)
NFAT_Pi_Act_C_Cyt Phosphorylated NFAT Calcineurin complex in cytosol 0.0000022 cytosol (cytosol)
NFAT_Pi_Act_C_Nuc Phosphorylated NFAT Calcineurin complex in nucleus 0.0000025 nucleus (nucleus)
NFAT_Pi_Cyt Phosphorylated NFAT in cytosol 0.0094397 cytosol (cytosol)
NFAT_Pi_Nuc Phosphorylated NFAT in nucleus 0.0002272 nucleus (nucleus)

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
R1 Calcineurin dpdnt NFAT dephosphorylation NFAT_Pi_Nuc + Act_C_Nuc = Act_C_Nuc + NFAT_Nuc

nucleus * (k1 * NFAT_Pi_Nuc - k2 * NFAT_Nuc)
R10 Phosphorylated NFAT transport NFAT_Pi_Cyt = NFAT_Pi_Nuc

cytosol * k3 * NFAT_Pi_Cyt - nucleus * k4 * NFAT_Pi_Nuc
R11 NFAT Calcineurin complex disassembly NFAT_Act_C_Cyt = Act_C_Cyt + NFAT_Cyt

cytosol * (k15 * NFAT_Act_C_Cyt - k16 * NFAT_Cyt * Act_C_Cyt)
R12 Calcineurin dpdnt NFAT dephosphorylation NFAT_Pi_Cyt + Act_C_Cyt = Act_C_Cyt + NFAT_Cyt

cytosol * (k1 * NFAT_Pi_Cyt - k2 * NFAT_Cyt)
R13 Calcineurin activation {3.0}Ca_Cyt + Inact_C_Cyt = Act_C_Cyt

cytosol * (k19 * Inact_C_Cyt * pow(Ca_Cyt, 3) - k20 * Act_C_Cyt)
R14 Calcineurin activation {3.0}Ca_Nuc + Inact_C_Nuc = Act_C_Nuc

nucleus * (k19 * Inact_C_Nuc * pow(Ca_Nuc, 3) - k20 * Act_C_Nuc)
R15 Inactive Calcineurin transport Inact_C_Cyt = Inact_C_Nuc

cytosol * k5 * Inact_C_Cyt - nucleus * k6 * Inact_C_Nuc
R16 Calcium transport Ca_Cyt = Ca_Nuc

cytosol * k21 * Ca_Cyt - nucleus * k22 * Ca_Nuc
R17 Phosphorylated NFAT Calcineurin complex transport NFAT_Pi_Act_C_Cyt = NFAT_Pi_Act_C_Nuc

cytosol * k7 * NFAT_Pi_Act_C_Cyt - nucleus * k8 * NFAT_Pi_Act_C_Nuc
R2 NFAT Calcineurin complex formation Act_C_Nuc + NFAT_Nuc = NFAT_Act_C_Nuc

nucleus * (k16 * NFAT_Nuc * Act_C_Nuc - k15 * NFAT_Act_C_Nuc)
R3 NFAT transport NFAT_Nuc = NFAT_Cyt

nucleus * k18 * NFAT_Nuc - cytosol * k17 * NFAT_Cyt
R4 Active Calcineurin transport Act_C_Nuc = Act_C_Cyt

nucleus * k6 * Act_C_Nuc - cytosol * k5 * Act_C_Cyt
R5 NFAT Calcineurin complex phosphorylation NFAT_Act_C_Nuc = NFAT_Pi_Act_C_Nuc

nucleus * (k14 * NFAT_Act_C_Nuc - k13 * NFAT_Pi_Act_C_Nuc)
R6 Phosphorylated NFAT Calcineurin complex disassembly NFAT_Pi_Act_C_Nuc = Act_C_Nuc + NFAT_Pi_Nuc

nucleus * (k12 * NFAT_Pi_Act_C_Nuc - k11 * NFAT_Pi_Nuc * Act_C_Nuc)
R7 NFAT Calcineurin complex transport NFAT_Act_C_Nuc = NFAT_Act_C_Cyt

nucleus * k10 * NFAT_Act_C_Nuc - cytosol * k9 * NFAT_Act_C_Cyt
R8 NFAT Calcineurin complex phosphorylation NFAT_Act_C_Cyt = NFAT_Pi_Act_C_Cyt

cytosol * (k14 * NFAT_Act_C_Cyt - k13 * NFAT_Pi_Act_C_Cyt)
R9 Phosphorylated NFAT Calcineurin complex disassembly NFAT_Pi_Act_C_Cyt = Act_C_Cyt + NFAT_Pi_Cyt

cytosol * (k12 * NFAT_Pi_Act_C_Cyt - k11 * NFAT_Pi_Cyt * Act_C_Cyt)

Global parameters

Id Value
Time_in_Seconds 100.0
k1 0.0000256
k10 0.005
k11 6.63
k12 0.00168
k13 0.5
k14 0.00256
k15 0.00168
k16 6.63
k17 0.0015
k18 0.00096
k19 1.0
k2 0.00256
k20 1.0
k21 0.21
k22 0.5
k3 0.005
k4 0.5
k5 0.0019
k6 0.00092
k7 0.005
k8 0.5
k9 0.5

Local parameters

Id Value Reaction

Assignment rules

Definition

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments
and(leq(Time_in_Seconds - time, 0), lt(time, 1500)) Ca_Cyt = 1; Ca_Nuc = 1; Time_in_Seconds = Time_in_Seconds + 100
geq(time, 1500) Ca_Cyt = 0.1; Ca_Nuc = 0.1
and(leq(Time_in_Seconds - time, 90), lt(time, 1500)) Ca_Cyt = 0.1; Ca_Nuc = 0.1