Contact-mediated signaling enables disorder-driven transitions in cellular assemblies

We show that, when cells communicate by contact-mediated interactions, heterogeneity in cell shapes and sizes leads to qualitatively distinct collective behavior in the tissue. For intercellular coupling that implements lateral inhibition, such disorder-driven transitions can substantially alter the asymptotic pattern of differentiated cells by modulating their fate choice through changes in the neighborhood geometry. In addition, when contact-induced signals influence inherent cellular oscillations, disorder leads to the emergence of functionally relevant partially-ordered dynamical states.

Figure 1

Communication between neighboring cells in a closepacked disordered configuration underlie a range of collective behavior. (a) Schematic diagram of the spatial arrangement of hair cells (shown in red) surrounded by supporting cells in the avian basilar papilla, at an early stage of development [24]. (b) Ventral tissue of the marine animal Trichoplax adhaerens illustrated schematically to show the arrangement of monociliated epithelial cells [36, 37, 38]. Each of the cilia engage in periodic motion (“beating,” see inset) that helps propel the organism across a surface [30, 31]. (c)–(e) The key qualitative features of the collective dynamics in such systems are seen to be invariant despite differences in the means by which cells communicate and the dynamics within each cell, e.g., in cells coupled via trans-activation of Notch receptors by Delta ligands resulting in release of a downstream effector (NICD) [shown in (c)], repressilators coupled by Notch-Delta signaling (d) and relaxation oscillators coupled via diffusion of the inactivation variable through intercellular bridges such as gap junctions (e).

Figure 2

Higher disorder in the cellular packing configuration allows a more equitable and robust distribution of cell fates. (a) Spatial patterns formed by the steady state Delta ligand concentration, $L_{SS}$ (see color bar) in an assembly of $N(=900)$ cells resulting from lateral inhibition. The panels show lattices with increasing structural disorder, as indicated by the dispersion of the deviations in cell positions from those in the regular hexagonal lattice: ${\sigma }_P=0$ (top left), 0.01 (top right), 0.1 (bottom left), and 1 (bottom right). As seen from the bimodal distribution in (b), cells either have very low or high values of $L_{SS}$. The increase in the width of the high $L_{SS}$ peak with disorder is quantified in (c) which shows that the number of cells $n_h$ (blue dots) in this state, i.e., cells having $L_{SS}>0.2$, increases with the disorder. We have verified that the specific choice of the threshold value does not qualitatively change our results. The shaded region represents the dispersion in $n_h$. The variance of the cell perimeters [${\sigma }^2\left(l_c\right)$, red dots] also rises with disorder in a qualitatively similar manner. (d) The asymptotic ligand concentration in a cell appears to be correlated with the number of its neighbors $k$. The $L_{SS}$ distributions in cells with a specific $k$ monotonically shift to left with increasing $k$, suggesting that cells in states characterized by higher $L_{SS}$ have fewer neighbors than average. (e) Greater robustness to damage in the cellular array is seen with increased disorder, as evident from the reduced variability of fate distribution (measured in terms of dispersion in $n_h$) with rise in ${\sigma }_P$ when $1\%$ (red) or $5\%$ (blue) of randomly chosen cells are rendered inert.

Figure 3

Disorder promotes the coexistence of qualitatively distinct behaviors (chimera states) in the collective dynamics of cellular oscillators coupled via contact-mediated interactions. (a) Instantaneous states of oscillator arrays that are (top row) ordered (${\sigma }_P=0$), or (bottom row) disordered to the maximum extent (${\sigma }_P=1$), shown at times separated by an interval that is $1/4$ of the oscillation period of an uncoupled cell. Colors represent the expression level of one of the genes ($C$) comprising the oscillating repressilator circuit [41]. (b), (c) The fraction of realizations $f_{ch}$ in which chimera states are observed (b) and the mean fraction of cells that continue to oscillate $f_{\mathrm{osc}}$ (c) shown as a function of the disorder in cellular arrangement (${\sigma }_P$), as well as the strength of inter-cellular interaction induced repression (measured as $1/Q$). (d), (e) Qualitatively similar behaviors in (d) $f_{ch}$ and (e) $f_{\mathrm{osc}}$ are shown by systems of diffusively coupled relaxation oscillators. Increasing the diffusion constant $D$ beyond a critical value leads to cessation of activity through oscillator death. In both systems, increased disorder allows configurations with coexisting oscillating and nonoscillating cells to exist over a much larger range.