Connexins dynamics

Gap junctions are important in cardiac muscle: the signal to contract is passed efficiently through gap junctions, allowing the heart muscle cells to contract in unison. The GJ are formed with several types of connexins. The equation that governs the dynamics can be modeled simply as follows:      (Equation 1)  where ΔΦ denotes the difference in intra-cellular electrical potential between two adjacent cells.  The subindice ss indicates the steady state value and τg is the time scale associated with the dynamics and it depends also on ΔΦ. Below we show the characteristic functions that are essential ingredients for our modeling purpose.

Steady state characteristic	Time constant	Action potential

Some examples of connexins dynamics

In the following, I illustrate the dynamics of a strand of connexins (1D system) that is periodically excited by a propagating action potential. The interesting phenomena occur when the characteristics of the connexins are set to mimic a diseased cardiac tissue (ischemic situation). One can lower the overall conductivity (to 40% of its nominal value) and we can also shrink the range of ΔΦ for which the connexin steady state is close to its maximum value as illustrated in the figure below

The newly introduced "shrinking factor" FS quantifies the degree by which the plateau of the steady state connexin characteristics is reduced. We have done several  "exploratory" simulations by varying this factor FS and the results are shown below for 5 different values of the FS. In addition to the space time plots showing the value of the connexin after each stimulation (Period=480 ms) we have also created some animations that are showing the evolution in the "phase" plane (g, ΔΦ) of the different connexins. We have two "stroboscopic" measurements corresponding to the two hallmarks (h1 and h2) represented in the figure above of the propagating action potential. In the animations, the cloud of points on the left corresponds to h1 (depolarization) and the cloud of points on the right corresponds to h2 (repolarization). The color code used to represent the points in the plane (g, ΔΦ) codifies the "residence time" (units are ms), i.e., the time it takes for the wave to travel between two adjacent cells surrounding the given connexin. More details of this study and the explanation of the dynamics can be found in the article by C. Hawks et al. (2019).

Here are some movies to examplify the dynamics (Click on the image to open the corresponding animation)

References