Table 1.
Characterization of the monolayers: isotropic vs. anisotropic.
Isotropic and anisotropic monolayers are identical for most of the features. The cells differ only in aspect ratio and intercellular conductivities.
Fig 1.
(a) Example of spontaneous APs obtained for Ibias = 2.6 μA/cm2 and Ibias = 3.5 μA/cm2. (b) Total ionic currents corresponding to AP traces in panel a. (c) Stable and unstable fixed points (black and red line respectively), with subcritical Hopf bifurcations H1 and H2 (magenta squares, Ibias = 2.554 and 4.470 μA/cm2). Maximum and minimum membrane potential V values of the stable and unstable cycles (blue and green lines respectively). The stable cycles exists between the two cycle saddle nodes bifurcation SNC1 and SNC2 (Ibias = 2.553 and 4.691 μA/cm2). (d) Autonomous cycle lengths as a function of Ibias (stable cycles only). Dashed lines display cycle length for Ibias = 2.6 μA/cm2 and Ibias = 3.5 μA/cm2, corresponding to AP traces in panel a.
Fig 2.
Disambiguation: density vs. spatial distribution.
(a) Density of 4% with inhomogeneous distribution. (b) Density of 16% with inhomogeneous distribution. (c) Density of 16% with homogeneous distribution.
Fig 3.
Stochastic algorithm governing density and spatial distribution of pacemaker cells: An illustration.
(a) Blank geometry where all cells are quiescent. (b) Random attribution of the 1st pacemaker cell. (c) Determination of M1 available sites for aggregation and M2 available sites for nucleation in red and blue respectively. (d) Random nucleation of the 2nd pacemaker cell in M2 eventually because p ≤ pthr. (e) Determination of M1 and M2. (f) Random aggregation of the 3rd pacemaker cell in M1 eventually because p > pthr.
Fig 4.
Network geometry: Isotropic vs. anisotropic.
Illustration of the 50 x 50 first nodes of 2 monolayers, with pacemaker cells in black and quiescent cells in white. (a) Isotropic monolayer where cells display no preferential orientation. (b) Anisotropic monolayer where cells display preferential orientation along the longitudinal/horizontal axis.
Fig 5.
Characterization of the stochastic algorithm governing density and spatial distribution of pacemaker cells.
(a,d) Average of maximum cluster size Scluster in color scale map as a function of Daut and , for monolayers with isotropic and anisotropic geometries. The size of a cluster is the actual number of pacemaker cells in that cluster. (b,e) Standard deviation of Scluster vs. Daut and
. (c,f) Log10 of number of clusters Ncluster vs. Daut and
. Solid white line is Daut,max (see definition in text) as a function of
.
Fig 6.
Relationship between cluster size transition and cluster fusion.
(a) (average of maximum cluster size) in color scale map as a function a function of Daut and
, for anisotropic networks. Solid white line is Daut,max as a function of
. (b)
as a function of Daut, for first and last
. (c)
(first derivative of
) as a function of Daut, for first and last
. (d) Maximum of
vs. Daut and for all
, plotted as a function Daut,max.
Fig 7.
Electrical activation: isotropic vs. anisotropic.
(a) Isotropic monolayer with Daut = 0.3 and = 0.10 (black sites: PM cells). (b) Electrical activation times (ms) color scale map as a function of node positions for the previously described isotropic monolayer. (c) Anisotropic monolayer with Daut = 0.3 and
= 0.15. (d) Electrical activation times (ms) for the anisotropic monolayer.
Fig 8.
(a-d) For each group, number n of simulations with automaticity is displayed in color scale map as a function Daut and . White spots correspond to [n = 0]. Proportions of pairs (Daut,pthr) with [n = 8] and [0<n<8] are also indicated.
Fig 9.
(a-d) Transition curves from [n = 0] to [0<n<8] (solid line) and from [0<n<8] to [n = 8] (dashed line) are displayed in magenta for ISO-2.6 and ANISO-2.6, and in white for ISO-3.5 and ANISO-3.5. In background is color scale map of either or porosity, both against Daut and
. (e,f) For each group, transition curve to [0<n<8] is subtracted to transition curve to [n = 8].
Fig 10.
(a-d) For all groups, average cycle length is calculated for each pair (Daut,pthr) with [n = 8] and displayed as a color scale map. The corresponding percentage range between the minimum and the maximum values of the
map is also displayed. (e) For each group, mean and s.e.m of values in
map are calculated. (f) For each group, mean and s.e.m of values in Std cycle length σΔTact map (obtained following the same process than
) are calculated.
Table 2.
Summary of simulation results.
Fig 11.
Foci positions: Central vs. border.
(a-d) For each group, and for [n>0], focal position of the last activation is plotted. Central foci are inside the red square, whose side is 50% of the monolayer side. The border foci in the longitudinal x-direction are the foci located outside the red box, exclusively to the left and to the right. The border foci in the transverse y-direction are exclusively at the top and the bottom. Non-exclusive border foci at the corners, i.e. foci that are common to longitudinal and transverse direction are in the blue areas and are not considered in the calculation of border foci anisotropy ratio (r) in Eq (12). (e,f) Proportions of central focals for [n = 8] and [0<n<8].
Fig 12.
(a-d) For all groups, average synchronization time is calculated for each pair (Daut,pthr) with [n = 8] and displayed as a color scale map. The corresponding percentage range between the minimum and the maximum values of the
map is also displayed.(e) For each group, mean and s.e.m of values in
,
,
map are calculated. (f) For each group, mean and s.e.m of values in Std synchronization time σTSync map (obtained following the same process than
) are calculated.