Figure 5.
Simulated spatial cell proliferation pattern in case cells enter the cell cycle
(A–C) (A) randomly (proliferating cells in white) and (B) in the presence of BGC at time t = 3d (C) Corresponding frequency histograms for the number of proliferating cells in the vicinity of a proliferating cell for BGC (pressure-based) control of cell cycle entrance and for random entrance.
(D) Illustration of mechanism. A cell entering the cell cycle (orange in (D, (1))) increases its volume (green arrows) hence increasing the pressure in its neighbor cells (indicated by the red arrows) and itself. In the presence of BGC, a cell (red in (D, (2))) surrounded by proliferating cells (orange in (D, (2))) experiences a high pressure, that, if the pressure exceeds a threshold value pth, will inhibit this cell to also enter the cell cycle. As a consequence, BGC acts as an inhibitor neighbor cell of proliferating cells favoring distance between proliferating cells (D, (3)). The result is a checkerboard-like proliferation pattern as in (B). With no BGC, cells would enter the cell cycle randomly, which can lead to locally much higher-pressure peaks (and compression forces) (D, (4)), resulting in the situation as in (A).
(E) For sufficiently small liver lobules (E, (1)) the overall pressure can still remain under the threshold pressure of BGC (indicated by the green curves) hence all cells can divide, though inhibiting local pressure peaks by forming a checkerboard-like pattern at the cell scale, as the pressure can be released by the shift of the lobule border. A central dividing cell (orange in the center of the lobule in (E, (1))) can enter the cell cycle and push its neighbor cells toward the border, resulting after some time in a small displacement of the cells right at the Glisson capsule and release of the pressure at the position of the central dividing cell. The pressure is smallest at the lobe border (indicated by the green curves in (E)), as only by the expansion of the Glisson capsule, the lobe can gain volume. Beyond a certain lobule size the pressure release is not fast enough anymore (indicated by the light gray zone in which the red curve indicates the threshold pressure at which no cell cycle progression occurs anymore), hence a zone in the interior occurs in which the pressure gets so high that BGC does not permit proliferations anymore (indicated by the red cell in (E, (2)), unless each cell division would be balanced by a cell death event (which is not observed in liver regeneration). Without BGC, cell divisions would continue (E, (3)) leading to further increase in pressure, which is not observed. (Note that (E) is a schematic representation; in the simulations, the lobule shape during the regeneration simulation is approximately conserved (geometrically “similar”) with rounded-off borders probably arising by the smoothing effect of the Glisson capsule (see Figures 2 and 4)).