clancy2

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000126) Biomodels notes: The model is according to the paper "Na+ Channel Mutation That Causes Both Brugada and Long-QT Syndrome Phenotypes: A Simulation Study of Mechanism". Original model comes from ModelDB with accession number: 62661. This is the wide type model. All the values and reactions obtained from Data Supplement6: Appendix of the paper. Figure3 has been reproduced by MathSBML. The stimulus v=-30mV during the time from 5ms to 20 ms displayed in the event. The meaning for the keyword, C: Close states; O: Open states; IF: Fast inactivation states; IC: Closed-Inactivation states; IM: Intermediat Inactivation states. 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: Complex physiological interactions determine the functional consequences of gene abnormalities and make mechanistic interpretation of phenotypes extremely difficult. A recent example is a single mutation in the C terminus of the cardiac Na(+) channel, 1795insD. The mutation causes two distinct clinical syndromes, long QT (LQT) and Brugada, leading to life-threatening cardiac arrhythmias. Coexistence of these syndromes is seemingly paradoxical; LQT is associated with enhanced Na(+) channel function, and Brugada with reduced function.
METHODS AND RESULTS: Using a computational approach, we demonstrate that the 1795insD mutation exerts variable effects depending on the myocardial substrate. We develop Markov models of the wild-type and 1795insD cardiac Na(+) channels. By incorporating the models into a virtual transgenic cell, we elucidate the mechanism by which 1795insD differentially disrupts cellular electrical behavior in epicardial and midmyocardial cell types. We provide a cellular mechanistic basis for the ECG abnormalities observed in patients carrying the 1795insD gene mutation.
CONCLUSIONS: We demonstrate that the 1795insD mutation can cause both LQT and Brugada syndromes through interaction with the heterogeneous myocardium in a rate-dependent manner. The results highlight the complexity and multiplicity of genotype-phenotype relationships, and the usefulness of computational approaches in establishing a mechanistic link between genetic defects and functional abnormalities.

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 second
0.001 volt
Id Name Spatial dimensions Size
cell 3.0 1.0
Id Name Initial quantity Compartment Fixed
C1 0.0 cell
C2 0.0 cell
C3 1.0 cell
IC2 0.0 cell
IC3 0.0 cell
IF 0.0 cell
IM1 0.0 cell
IM2 0.0 cell
O open states 0.0 cell

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_0000001 IC3=IC2 IC3 = IC2

cell * (IC3 * a11 - IC2 * b11)
reaction_0000002 IC2=IF IC2 = IF

cell * (IC2 * a12 - IF * b12)
reaction_0000003 IF=IM1 IF = IM1

cell * (IF * a4 - IM1 * b4)
reaction_0000004 IM1=IM2 IM1 = IM2

cell * (IM1 * a5 - IM2 * b5)
reaction_0000005 C3=IC3 C3 = IC3

cell * (C3 * b3 - IC3 * a3)
reaction_0000006 C2=C3 C2 = C3

cell * (C2 * b11 - C3 * a11)
reaction_0000007 C2=IC2 C2 = IC2

cell * (C2 * b3 - IC2 * a3)
reaction_0000008 C1=C2 C1 = C2

cell * (C1 * b12 - C2 * a12)
reaction_0000009 C1=IF C1 = IF

cell * (C1 * b3 - IF * a3)
reaction_0000010 IF=O IF = O

cell * (IF * b2 - a2 * O)
reaction_0000011 O=C1 O = C1

cell * (-C1 * a13 + O * b13)

Global parameters

Id Value
Ena 0.0
Fara 96485.0
Gna 23.5
Ina 0.0
Rk 8314.0
Temp 310.0
a11 0.0
a12 0.0
a13 0.0
a2 0.0
a3 0.0
a4 0.0
a5 0.0
b11 0.0
b12 0.0
b13 0.0
b2 0.0
b3 0.0
b4 0.0
b5 0.0
nai 15.0
nao 140.0
scale 1000.0
v 0.0
vhold -80.0
vtest -30.0

Local parameters

Id Value Reaction

Assignment rules

Definition
a11 = 3.802 / (0.1027 * exp(-v / 17.0) + 0.2 * exp(-v / 150.0))
a12 = 3.802 / (0.1027 * exp(-v / 15.0) + 0.23 * exp(-v / 150.0))
a2 = 9.178 * exp(v / 29.68)
b13 = 0.22 * exp(-(v - 10.0) / 20.3)
b3 = 0.0084 + 2.000000e-05 * v
a4 = (9.178 * exp(v / 29.68)) / 100.0
b4 = 3.7933 * 1.000000e-07 * exp(-v / 7.7)
b5 = (3.7933 * 1.000000e-07 * exp(-v / 7.7)) / 50.0
a5 = (9.178 * exp(v / 29.68)) / (9.5 * 10000.0)
Ena = Rk * Temp / Fara * log(nao / nai)
b11 = 0.1917 * exp(-v / 20.3)
b2 = (3.802 / (0.1027 * exp(-v / 12.0) + 0.25 * exp(-v / 150.0))) * (9.178 * exp(v / 29.68)) * (3.7933 * 1.000000e-07 * exp(-v / 7.7)) / ((0.22 * exp(-(v - 10.0) / 20.3)) * (0.0084 + 2.000000e-05 * v))
b12 = 0.2 * exp(-(v - 5.0) / 20.3)
Ina = Gna * (O / (IC3 + IC2 + IF + IM1 + IM2 + C3 + C2 + C1 + O)) * (v - (Rk * Temp / Fara * log(nao / nai))) / scale
a3 = 3.7933 * 1.000000e-07 * exp(-v / 7.7)
a13 = 3.802 / (0.1027 * exp(-v / 12.0) + 0.25 * exp(-v / 150.0))
v = piecewise(vtest,5.0<time<=300.0,vhold)

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments