Effects of non-linear GJ channels on the AP propagation : a modelling insight
Résumé
Background: Velocity and pattern of propagation of cardiac AP depends on structural and
functional properties of the tissue, such as conductivity, dynamics of transmembrane ionic
channels and gap junctions (GJ).
Gap junctions are clusters of channels that connect adjacent cells. A gap junction channel
(GJC) is made of proteins named connexins. Electrical behavior of GJCs depend on the type
and arrangement of their connexin composition. The dominating connexins in cardiac
myocytes are Cx43, Cx45 and Cx40.
Methods and results: In current mathematical models, GJCs are considered to be passive.
But, the experimental results, obtained by the dualvoltage clamp
technique, show that GJCs display biophysical electrical properties such as voltage gating,
i.e. a time and voltage dependence.
Here we model Cx43 GJCs. We use the HodgkinHuxley formalism to describe GJCs
conductance via one gating variable
g j = g j (t, V j ). From our experimental results we obtain model parameters: the normalised
steady state conductance and the time constant to reach the steady state, both voltage
dependent. Once we have described the behavior of the single GJC, we write the mathematical model of
the tissue, where we apply GJ current on specific parts of the cells’ membranes.
Numerics and outlook: Some 3D numerical experiments are currently being performed on a
thin strip of cells, in order to compare the model’s results with the experimental
ones. We use a monolayer of 50 × 3 cells, represented by cylinders of 100μm length
and 10μm radius, with 2μm intercellular distance. We model GJCs on the cross sections of the cylinders. Finally, we
apply an external stimulus on the border of the domain, and observe the propagation of the
AP. Our goal is to make a mathematical model of the heterogeneous GJCs, including Cx45
channels, as these have been shown to play a role in arrythmogenesis.
Domaines
Mathématiques [math]Origine | Fichiers produits par l'(les) auteur(s) |
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