Connexin43 contributes to electrotonic conduction across scar tissue in the intact heart

Studies have demonstrated non-myocytes, including fibroblasts, can electrically couple to myocytes in culture. However, evidence demonstrating current can passively spread across scar tissue in the intact heart remains elusive. We hypothesize electrotonic conduction occurs across non-myocyte gaps in the heart and is partly mediated by Connexin43 (Cx43). We investigated whether non-myocytes in ventricular scar tissue are electrically connected to surrounding myocardial tissue in wild type and fibroblast-specific protein-1 driven conditional Cx43 knock-out mice (Cx43fsp1KO). Electrical coupling between the scar and uninjured myocardium was demonstrated by injecting current into the myocardium and recording depolarization in the scar through optical mapping. Coupling was significantly reduced in Cx43fsp1KO hearts. Voltage signals were recorded using microelectrodes from control scars but no signals were obtained from Cx43fsp1KO hearts. Recordings showed significantly decreased amplitude, depolarized resting membrane potential, increased duration and reduced upstroke velocity compared to surrounding myocytes, suggesting that the non-excitable cells in the scar closely follow myocyte action potentials. These results were further validated by mathematical simulations. Optical mapping demonstrated that current delivered within the scar could induce activation of the surrounding myocardium. These data demonstrate non-myocytes in the scar are electrically coupled to myocytes, and coupling depends on Cx43 expression.

expected Mendelian ratios, with 50% of the homozygous floxed Cx43 mice carrying the FSP1 Cre transgene. The colony is maintained by inbreeding of littermates. The mice used in this study have been backcrossed for at least 14 generations. Littermate Cx43 flox/flox Cre negative mice were used as controls for the studies that included FSP1 Cx43 KO mice. Conduction system reporter mice (Cntn2-EGFP, CD1.Tg(Cntn2-EGFP)344sat) have been previously described 2 and are currently maintained in a CD1 background.

MATHEMATICAL SIMULATIONS
Simulations were performed using a previously described model for mouse ventricular myocytes. 3 The action potential model was modified by removing the non-inactivating steady state potassium current.
This change increased action potential duration to more closely fit control experimental results.
The monodomain equation was used to simulate the electrical activity of a 2D square of tissue of dimensions 5mm x 5mm, with no-flux boundary conditions: Here is trans-membrane voltage, is the capacitance of cell membrane (per unit area), is the membrane surface area per unit volume. Conductivity was set to be homogenous (no preferential fiber direction) with values of mS/cm along each axis. The action potential model that was used to calculate is the Li mouse ventricular model, 3 modified by removing the non-inactivating steady state potassium current to provide an increased action potential duration that was more in line with our control experimental results. The initial conditions for the Li model state variables were set to the pseudo-steady values at 150 ms pacing cycle length (evaluated after 10,000 paces).
is the stimulus current, which is applied along x = 0 at time t = 10.0 ms to allow the lesion region to settle to an equilibrium with the myocytes before the wavefront arrives.
The scar was modeled by introducing a circular region of 2 mm diameter in the center of the tissue where a fibroblast action potential model was used instead of the mouse ventricular myocyte model. 4 Inside the scar no stimulus current is applied, so we can simplify the equation above to be equal to zero. We can then divide through by to give: This equation reveals that a parameter governs tissue behavior, and this parameter can be altered to represent: (i) a change in density of membrane surface area in the tissue ( ); (ii) a change in the cell-to-cell coupling ( ); or (iii) both at once. Interestingly this shows, for instance, that a reduction to 10% conductivity together with 10% total cell membrane area gives , i.e. the behavior of the model would be unchanged. In other words, doubling the surface area of fibroblasts present in a given volume of the tissue has precisely the same effect as halving how well coupled they are, in terms of the evolution of the transmembrane voltage.
To simulate the initial injury we say that cell-cell coupling has been reduced dramatically (p=0.001). In this case the signals obtained from the lesion are substantially attenuated. We then simulate different levels of fibroblast coupling and cell density by varying ρ between 0.1 and 100 in factors of 10.
Simulations were also performed to investigate the possible 3D source-sink effects of the reduced tissue thickness in the lesion (see Supplemental Video 9). Altering tissue thickness did not significantly differ compared with the 2D cases shown. The study was also performed with a 'neutral' action potential model in which is set to zero. The results for this simulation were again similar, suggesting the choice of fibroblast model does not strongly influence the findings of the model.

Numerical Implementation
Chaste 5 was used to solve the equations, using a finite element discretization with a space step of 0.005 cm and a PDE time step of 0.1 ms. The CVODE Backwards Differentiation Formulae solver 6 was used for solution of action potential model ODEs. Tthis solver takes adaptive time steps within the 0.1 ms PDE step to provide speed whilst meeting relative and absolute tolerances set to 10 -5 and 10 -7 respectively. All of the code that was used is available open source as a bolt-on project for Chaste v3.   Figure 3E.

Supplemental Video 3.
Optical mapping movie of an S1 paced beat (100 ms cycle interval) in a cryoinjured heart with transmural incisions. The corresponding activation map is shown in Figure 6C.
The activation map shows discrete points of early activation on the distal border of the scar, indicating electrotonic spread of current through the scar contributes to activation the myocardium at these sites.