The influence of entropic crowding in cell monolayers

Abstract

Cell-cell interaction dictates cell morphology and organization, which play a crucial role in the micro-architecture of tissues that guides their biological and mechanical functioning. Here, we investigate the effect of cell density on the responses of cells seeded on flat substrates using a novel statistical thermodynamics framework. The framework recognizes the existence of nonthermal fluctuations in cellular response and thereby naturally captures entropic interactions between cells in monolayers. In line with observations, the model predicts that cell area and elongation decrease with increasing cell seeding density-both are a direct outcome of the fluctuating nature of the cellular response that gives rise to enhanced cell-cell interactions with increasing cell crowding. The modeling framework also predicts the increase in cell alignment with increasing cell density: this cellular ordering is also due to enhanced entropic interactions and is akin to nematic ordering in liquid crystals. Our simulations provide physical insights that suggest that entropic cell-cell interactions play a crucial role in governing the responses of cell monolayers.

Figure 1

Graphical representation of the model, its components, and its output. (a) Sketch of the 2D model of the cell in the $x_1-x_2$ on the elastic substrate within the nutrient bath. The cell exchanges nutrients with the bath, with the model of the cell including passive elasticity of the cell and the stress fiber cytoskeleton. The inset shows the representative volume element of the cytoskeleton and the definition of the orientation $\phi$ of the stress fibers. (b) Sketch of a monolayer along with the periodic assumption used to model such a monolayer. (c) A cell morphology, which is an outcome of the simulations along with typical outputs from the simulations. These include the morphology of the nucleus, the distribution of the stress fiber cytoskeleton visualized by actin staining, the focal adhesion distributions visualized by vinculin staining, and the shape and orientation of cells as described by a best fit ellipse.

Figure 2

Cell crowding reduces cell spreading and elongation. (a) Predictions of the distributions of cells within monolayers for four selected values of increasing seeding density ${\rho }_{\text{cell}}$. The inset shows zoom-ins of a few morphologies to show the protein distributions via immunofluorescence-like images shaded to illustrate concentrations of actin (red), vinculin (green), and the nucleus (blue). Comparison between predictions and measurements (26) of the (b) average cell area $A$ and (c) average cell aspect ratio $A_s$ obtained from best fit ellipses for cells in monolayers as a function of the seeding density ${\rho }_{\text{cell}}$. All predictions and measurements are for cells seeded on a glass substrate with compliance $\mathcal{C}=0$.

Figure 3

Increasing cell crowding and substrate compliance have similar effects on cell morphology. Predictions of the dependence of (a) the average cell area $A$, (b) average aspect ratio $A_s$, and (c) normalized homeostatic temperature $1/\hat{\zeta }\equiv 1/\left(\zeta G_{\text{S}}\right)$ on the substrate compliance $\mathcal{C}$ (lower x-axis) for an isolated cell seeded on the elastic substrate. The correspondence predictions for cell monolayers on glass substrates as a function of the seeding density ${\rho }_{\text{cell}}$ (upper x-axis) are also included to illustrate similarities/differences in the qualitative trends.

Figure 4

Free-energy and traction force distribution boxplots indicate differences in the effect of increasing cell crowding and substrate compliance. Box and whisker plots of the normalized (a) free-energy $\hat{G}\equiv G/G_S$ and (b) traction force $\hat{T}\equiv {\mathcal{T}}_{\text{avg}}/{\mu }_C$ for isolated cells on elastic substrates of compliance $\mathcal{C}$. The corresponding plots for the monolayer on a glass substrate: (c) free-energy $\hat{G}$ and (d) traction force $\hat{T}$. In the box and whisker plots the boxes show the median and upper and lower quartiles of the distributions, while the whiskers indicate the maximum and minimum values in the Markov chain used to construct a sample of the homeostatic ensemble.

Figure 5

Single isolated cells in confined patches show similar morphological effects to increasing cell density within monolayers. (a) A representative cell morphology for a cell confined on a square adhesive patch of area A_p = 17,000 μm². The morphology from the simulation shows the protein distributions via an immunofluorescence-like image shaded to illustrate concentrations of actin (red), vinculin (green), and the nucleus (blue). Predictions of the dependence of (b) the average cell area $A$, (c) average aspect ratio $A_s$, and (d) normalized homeostatic temperature $1/\hat{\zeta }\equiv 1/\left(\zeta G_{\text{S}}\right)$ on cell density ${\rho }_{\text{cell}}\equiv 1/A_p$. Results are shown for both the isolated cell confined on an adhesive patch of area $A_p$ as well as cells in a monolayer both seeded on a rigid glass substrate.

Figure 6

Cells align in monolayers and this alignment decreasing with increasing substrate compliance. (a) A selection of morphological microstates from the simulations for three seeding densities ${\rho }_{\text{cell}}$ of cells on the glass substrates. In each case, four periodic microstates are shown in a manner akin to immunofluorescence images with the nucleus (blue) and focal adhesions (green), as well as the stress fiber cytoskeleton (red) shaded in. The inset shows a zoom-in of a microstate for ${\rho }_{\text{cell}}=8000{\text{cells cm}}^{-2}$ with the best fit ellipses drawn to indicate the orientation ${\phi }_i$ of the major axis of the best fit ellipse. (b) Predictions of the order parameter $\text{Θ}$ as a function of ${\rho }_{\text{cell}}$ for cells seeded on the glass substrate as well as elastic Winkler substrates of compliance $\mathcal{C}$.