Fig 1.
Wave propagation in neonatal rat cardiac monolayers with a large portion of non-conducting cells.
(a) Activation map for a sample with 66% of non-conducting cells. Activation times are colour coded. Red lines show the regions where the wave was blocked. White and black arrows show the main propagation pathways. Yellow square pulse sign indicates the location of the stimulating electrode. Yellow dashed lines outline the areas of slow conduction. The original video (S1 Video) of the wave propagation is available at https://youtu.be/3aDmsT1pl3Y. (b) Velocity decay with the increase of the portion of non-conducting cells in samples. The percolation threshold is shown with the dashed line and was equal to 75 ± 2%.
Fig 2.
Conducting pathway in a monolayer of cardiac tissue with 31% of cardiomyocytes and 69% of non-conducting cells.
The interconnected region is outlined in white. Cardiomyocytes are labeled with anti-α-actinin antibody and coloured in pink. Nuclei are shown in blue.
Fig 3.
Cardiac syncytium in a 3-days culture of the neonatal rat cardiomyocytes.
The cells have formed intercalated discs (ID, bright-green, highlighted with red arrows), aligned their cytoskeletons (the aligned strains on the both sides from ID are shown with white arrows) and formed a branching network. Nuclei are shown in blue (DAPI, labels DNA), and actin strands are shown in green (phalloidin, labels F-actin).
Fig 4.
The schematic of the cell-to-cell interaction in a computational model.
The energy term was assigned to every pair of connected actin bundles in coupled cells. This term depends on the angle between the bundles and reaches its minimal value when the bundles are aligned (α = 0). Left image shows quasi-3D schematic of the cells, middle image shows energy profile and right image shows a view from the top.
Fig 5.
The branching pattern obtained in a computer model (a) compared to one observed in an experiment (b).
(a) A virtual sample with 70% of non-conducting cells. (b) A segmented image of the experimental sample with 66% of non-conducting cells. The original image is shown in Fig 2.
Fig 6.
Wave propagation in virtual cardiac monolayers with a large portion of non-conducting cells.
(a) Activation map for a sample with 70% of non-conducting cells. Activation times are colour coded. Red lines show the regions where the wave was blocked. White and black arrows are showing the main propagation pathways. Yellow square pulse sign indicates the location of the stimulating electrode. (b) Velocity as a function of the density of non-conducting cells. Orange lines represent velocities in virtual samples with cytoskeletons alignment (Ebond = 5), and blue lines without (Ebond = 0). Red dashed lines shows the percolation threshold for a simple model where each cell is represented by a point in a square lattice. Waves propagation in samples with branching patterns (orange) was failing in part of the samples starting from 71% and not possible in all of the samples for ≥75%. For each density, 10 samples with the size of 5 mm × 5 mm were tested. For each sample the mean velocity and its standard deviation are shown (mean ± SD). The original video (S3 Video) of the wave propagation is available at https://youtu.be/elvOvBRwnEM.
Fig 7.
The top-left panel shows the probability of full connectivity in the sample (5 x 5 mm samples, connected from top to bottom and from left to right) depending on the percentage of non-conducting cells. Values of Ebond are shown with different colours. Each point corresponds to the average probability in 40 generated samples. The data was fitted with sigmoid functions. The bottom-left panel shows the percentages of non-conducting cells that correspond to 50% and 10% probability of connected network formation in a sample depending on the value of Ebond. These plots show, that there exists an optimal value of Ebond that provides the highest chance of network formation. On the right, examples of connected networks with 66% non-conducting cells and different values of Ebond are shown. Cardiomyocytes are shown in red, and non-conducting fibroblasts in white.
Fig 8.
Spontaneous formation of the structure, that produces a uni-directional block, which results in reentry formation.
The virtual sample had 29% of cardiomyocytes. Images in the top row show the insets of the place, where a uni-directional block has occurred: the central image shows its morphology and images on the sides show wave propagation in different directions. The voltage in these images is colour coded. In the central image, cardiomyocytes are represented with red tints and non-conducting fibroblasts with cyan. The bottom images show the activation maps in the whole sample. The bottom-left image shows the uni-directional block after the first stimulus, which was applied on the left boundary. The bottom-right image shows the reentry formation after the second stimulus. The activation times are colour coded. The arrows show the main wave paths. The red dashed line represents the reentry cycle. The original video (S4 Video) of the wave propagation is available at https://youtu.be/6LZorTUcJdk.
Table 1.
Parameters of the morphological model used in stimulations.
CM—cardiomyocytes, FB— fibroblasts.