Fig. 2: Contraction pulses in a 1D excitable tissue.
a Sequential snapshots from a dynamic simulation of a 1D chain of excitable cells (in which the rest length, l0, is shorter than the critical length lc), show the propagation of a single contraction pulse from left to right (Supplementary Movie 1). Cells are shown as circles, at their location along the chain, x, with a color representing their length, l. At time t0 all cells are set at their rest length, l0, except the first cell on the left, which is initiated at li > lc, which triggers the pulse. Red asters represent activly contracting cells. b A kymograph representation of the dynamics shows the pulse propagation in the tissue at constant pulse width, W, and speed, V (defined in units of cells and cells per time, respectively). c A cross-section from the kymograph shows the pulse profile: an expansion-front first, and an equal but opposite contraction-front behind it. All cells in between are actively contracting yet found at their rest length. The main pulse characteristics (V-velocity, W-width, amp-amplitude) are shown. d–g Pulse behavior with changing parameter values. Results are shifted by 0.1 in the y-axis in each experiment. Black dots represent activated cells. d–e System snapshots and time series show that increasing the contraction force, fc, increases the pulse’s width and speed respectively. f System snapshots show that increasing lc increases the amplitude amp. g System snapshots with different li values show a series of identical pulses is emerging. The number of pulses depends on li. h–j Numerical results of the main pulse characteristics show a collapse into our theoretical predictions, specified on the x axis. The parameters used in the simulations are covering the range \(\tilde f \equiv \frac{{f_{{{{{{{\mathrm{c}}}}}}}}}}{{kl_{{{{{{{\mathrm{c}}}}}}}}}} = 0.1 - 1,\tilde t \equiv \frac{{t_{{{{{{{\mathrm{c}}}}}}}}k}}{\gamma } = 0.1 - 6,{{\tilde \epsilon }} \equiv \frac{{l_c - l_0}}{{l_0}} = 0.01 - 0.05,\) where k is the cell stiffness, γ is the media’s viscosity and tc is the duration of contraction. k Numerical results of the pulse profile show the dependency of the shape on the specified ratio.
