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chen3

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000202) Biomodels notes: Plots correspond to the time profiles of cytosolic and ER Calcium and active STIM1 dimers as depicted in Figure 1 and figure 2. 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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Manuscript information

Dynamic simulation of the effect of calcium-release activated calcium channel on cytoplasmic Ca2+ oscillation.

  • Xiao-fang Chen
  • Cong-xin Li
  • Peng-ye Wang
  • Ming Li
  • Wei-chi Wang
Biophys. Chem. 2008; 136 : 87
Abstract
A mathematical model is proposed to illustrate the activation of STIM1 (stromal interaction molecule 1) protein, the assembly and activation of calcium-release activated calcium (CRAC) channels in T cells. In combination with De Young-Keizer-Li-Rinzel model, we successfully reproduce a sustained Ca(2+) oscillation in cytoplasm. Our results reveal that Ca(2+) oscillation dynamics in cytoplasm can be significantly affected by the way how the Orai1 CRAC channel are assembled and activated. A low sustained Ca(2+) influx is observed through the CRAC channels across the plasma membrane. In particular, our model shows that a tetrameric channel complex can effectively regulate the total quantity of the channels and the ratio of the active channels to the total channels, and a period of Ca(2+) oscillation about 29 s is in agreement with published experimental data. The bifurcation analyses illustrate the different dynamic properties between our mixed Ca(2+) feedback model and the single positive or negative feedback models.

Unit definitions 6

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
— 1e-06 mole litre^(-1.0)
— 1.0 second^(-1.0)
— 1e-06 mole litre^(-1.0) second^(-1.0)
— 1000000.0 mole^(-1.0) litre second^(-1.0)
— 1.0 dimensionless

Compartments 3

Id Name Spatial dimensions Size
Cytoplasm — 3.0 1.0
ER — 3.0 0.185
PM — 3.0 1.0

Species 9

Id Name Initial quantity Compartment Fixed
Ca_Cyt — 0.0 Cytoplasm ✘
Ca_ER — 0.0 ER ✘
IP3_Cyt — 0.0 Cytoplasm ✘
O_o — 0.0 PM ✘
Oc — 0.0 PM ✘
Orai1 — 0.001 PM ✘
S2 — 0.54 ER ✘
S2a — 0.06 ER ✘
S4 — 0.0 ER ✘

Initial assignments 0

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
Reactions 15
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
ER_Channel — Ca_ER > Ca_Cyt

Cytoplasm * (L + P_IP3R * pow(IP3_Cyt, 3) * pow(Ca_Cyt, 3) * pow(h, 3) / (pow(IP3_Cyt + Ki, 3) * pow(Ca_Cyt + Ka, 3))) * (Ca_ER - Ca_Cyt)
PLC — ∅ > IP3_Cyt

Cytoplasm * (V_PLC * pow(Ca_Cyt, 2) / (pow(K_PLC, 2) + pow(Ca_Cyt, 2)))
PMCA — Ca_Cyt > ∅

Cytoplasm * (V_PMCA * pow(Ca_Cyt, q) / (pow(K_PMCA, q) + pow(Ca_Cyt, q)))
PM_Channel — ∅ > Ca_Cyt

Cytoplasm * (k_soc * O_o + V_PMleak) * (Ca_ec - Ca_Cyt)
SERCA — Ca_Cyt > Ca_ER

Cytoplasm * (V_SERCA * pow(Ca_Cyt, p) / (pow(K_SERCA, p) + pow(Ca_Cyt, p)))
act_apoSTIM1_deg — S2a > ∅

ER * k_i * S2a
act_apoSTIM1_syn — ∅ > S2a

ER * k_a * S2
apoSTIM1_oligo_deg — S4 > ∅

ER * kd_oligo * S4
apoSTIM1_oligo_syn — ∅ > S4

ER * (Vs4 * pow(S2, 2) / (pow(S2, 2) + pow(K2, 2)))
close_CRAC_prod — ∅ > Oc

PM * (Vcp * pow(Orai1, n_hill) / (pow(Kc, n_hill) + pow(Orai1, n_hill)))
closed_CRAC_channel_deg — Oc > ∅

PM * kdc * Oc
deg — IP3_Cyt > ∅

Cytoplasm * (kdeg * pow(Ca_Cyt, 2) / (pow(K_deg, 2) + pow(Ca_Cyt, 2))) * IP3_Cyt
open_CRAC_channel_deg — O_o > ∅

PM * kdo * O_o
open_CRAC_channel_prod — Oc > O_o

PM * (kop * pow(S2a, l_hill) * Oc / (pow(Ko, l_hill) + pow(S2a, l_hill)))
open_to_closed — O_o > Oc

PM * kod * O_o

Parameters 0   38

Global parameters

Id Value
A 0.5 uM_1_s_1
Ca_ec 1500.0 uM
K1 5.0 uM
K2 0.14 uM
K_PLC 0.12 uM
K_PMCA 0.45 uM
K_SERCA 0.15 uM
K_deg 0.1 uM
Ka 0.4 uM
Kc 2e-05 uM
Kd 0.4 uM
Ki 1.0 uM
Ko 0.2 uM
L 0.00093 s_1
Orai1_t 0.001 uM
P_IP3R 66.6 s_1
St 0.6 uM
V_PLC 0.5 uM_s_1
V_PMCA 1.0 uM_s_1
V_PMleak 5e-07 s_1
V_SERCA 1.0 uM_s_1
Vcp 0.00018 uM_s_1
Vs4 0.25 uM_s_1
h 0.0 dimensionless
k_a 4.0 s_1
k_i 6.0 s_1
k_soc 2.3 uM_1_s_1
kd_oligo 0.8 s_1
kdc 0.5 s_1
kdeg 0.5 s_1
kdo 0.6 s_1
kod 1.0 s_1
kop 0.5 s_1
l_hill 1.0 dimensionless
n_hill 3.0 dimensionless
p 2.0 dimensionless
q 2.0 dimensionless
r_hill 4.0 dimensionless

Local parameters

Id Value Reaction

Rules 0   1   2

Assignment rules

Definition
Orai1 = Orai1_t - (r_hill * Oc + r_hill * O_o)
S2 = pow(K1, 2.0) / (pow(Ca_ER, 2.0) + pow(K1, 2.0)) * (St - S2a)

Rate rules

Definition
h' = A * (Kd - (Ca_Cyt + Kd) * h)

Algebraic rules

Definition

Events 0

Trigger Assignments