Fig 1.
Schematic of the multiscale model of cardiac conduction.
Ionic currents are linearly proportional to gradients of transmembrane potential inside the cytoplasm, but are non-linearly mediated by gap junctions located at the intercalated discs.
Fig 2.
Circuit representation for the cellular models.
Fig 3.
Normalized conductance of gap junctions as a function of the transjunctional voltage.
(left) Cx43-Cx43 channel, (center) Cx45-Cx45 channel, and (right) Cx43-Cx45 channel. Data extracted from [3]. The (∘) and (•) data corresponds to instantaneous and steady state conductance, respectively.
Table 1.
Parameters for the conductance distribution of gap junctions, taken from [3].
For Vj0, gj,min, z the negative/positive values are presented. The Cx43-Cx45 case considered a modified Boltzmann distribution to improve the fitness to data.
Fig 4.
Impulse conduction features from computational simulations.
The propagating wavefront predicted by the CM clamped, CM voltage-gated, LHM and NOHM are compared for three levels of transjunctional coupling: (top row) high coupling β = 100%, (middle row) low coupling β = 10%, and (bottom row) very low couping β = 1%. In general, the LHM and NOHM drift ahead of their CM counterparts as the GJc is decreased in the case of instantaneous conductance. In contrast, for the case of steady-state conductance the NOHM accurately predicts the CM voltage-gated even for very low coupling levels, whereas the LHM substantially drifts ahead from the CM clamped wavefront.
Fig 5.
Conduction velocity studies on a cardiac strand and the effect of gap-junction coupling for symmetric conductance distributions: (top row) Cx43-Cx43 channel, (bottom row) Cx45-Cx45 channel, (left column) instantaneous conductance, (right column) steady-state conductance.
Black and red colors are used to indicate voltage-independent and voltage-dependent gap-junction conduction, respectively. Voltage-dependent models delivered lower conduction velocities than voltage-independent models of gap-junction conductance, particularly for the steady-state regime.
Fig 6.
Conduction velocity studies on a cardiac strand and the effect of gap-junction coupling for the Cx43-Cx45 channel with non-symmetric conductance distribution: (left) instantaneous conductance case, (right) steady-state conductance case.
Black color denotes voltage-independent models, red and blue colors denote voltage-dependent models. Predictions from gap-junction voltage-independent models CM clamped, and LHM were insensitive to the direction of wave propagation, whereas voltage-dependent models resulted in CVs that strongly depended on the direction of wave propagation for the steady-state conductance case.
Fig 7.
Conduction-velocity restitution curves for the homomeric-heterotypic channel Cx43-Cx45 for high, low and very low GJc: (left) instantaneous conductance case, (right) steady-state conductance case.
CL = cycle length.
Fig 8.
The effect of spatial discretization of the conduction velocity: (left) instantaneous conductance, (right) steady-state conductance.
The conduction velocity in cellular models exhibit a stronger dependence on the mesh size than the continuum models of conduction.