Figure 5. Expansion of a confluent epithelial cell sheet after removal of boundaries positioned at $x=\pm 175$ for two different parameter settings.

(Stiffness parameters ${\displaystyle {\kappa }_P=0.12}$, ${\displaystyle {\kappa }_A=0.18}$; average polarization field ${\displaystyle {ϵ}_0=35}$; signaling radius ${\displaystyle R=2}$; cytoskeletal update rate ${\displaystyle \mu =0.1}$; cell-cell adhesion ${\displaystyle B=12}$; cell-cell dissipation ${\displaystyle \mathrm{\Delta }B=0}$; cell-substrate dissipation ${\displaystyle D=0}$; cell-substrate adhesion penalty ${\displaystyle \phi =0}$; ${\displaystyle 100}$ independent simulations for each set of parameters). (A–D) Tissue expansion for a migration-dominated setup without explicit cell growth and mitosis. (${\displaystyle 3300}$-cell system; maximum cell polarity $\mathrm{\Delta }ϵ=30$). (E–H) Tissue expansion at low density and cell polarizability for a cell sheet comprised of dividing cells. (Initially a ${\displaystyle 2500}$-cell system; maximum cell polarity $\mathrm{\Delta }ϵ=10$; growth time $T_g=180$; division time $T_d=20$; size threshold for cell growth $A_{\text{T}}=1A_{\text{ref}}$, where $A_{\text{ref}}$ is the size of a solitary cell in equilibrium). (A, E) Snapshots of the polarization field $ϵ$; cf. Figure 5—video 1 and Figure 5—video 2. (B, F) Kymographs showing the cell density averaged over the $y$-direction and (top) final snapshots of the cell density profiles. (C, G) Kymographs showing the component ${\sigma }_{xx}$ of the stress tensor averaged over the $y$-direction and (top) final snapshots of the stress profiles. (D, H) Kymographs showing the component $v_x$ of the cell velocities averaged over the $y$-direction and (top) final snapshot of the velocity profiles.

Figure 5—figure supplement 1. Monolayer expansion depends on dissipation and cell polarizability.

Cell monolayer expansion depends on the cell-cell dissipation, cell-substrate dissipation, and maximum cell polarity. (Initially a ${\displaystyle 2500}$-cell system; stiffness parameters ${\kappa }_P=0.12$, ${\kappa }_A=0.18$; average polarization field ${ϵ}_0=35$; maximum cell polarity $\mathrm{\Delta }ϵ=10$; signalling radius $R=2$; cytoskeletal update rate $\mu =0.1$; cell-cell adhesion $B=12$; cell-substrate adhesion penalty $\phi =0$; growth time $T_g=180$; division time $T_d=20$; size threshold for cell growth $A_{\text{T}}=1A_{\text{ref}}$, where $A_{\text{ref}}$ is the size of a solitary cell in equilibrium; ${\displaystyle 100}$ independent simulations for each set of parameters). (A,B) Cell monolayer expansion depends on the cell-cell dissipation $\mathrm{\Delta }\mathbf{}B$ (maximum cell polarity $\mathrm{\Delta }ϵ=10$; cell-substrate dissipation $D=0$). (A) Maximal monolayer extension and roughness (we exclude an initial time interval of 200 MCS because it takes at least that long for first daughter cells to appear). Inset: Relative roughness of the spreading monolayer relative to its size. (B) Time traces for selected values of $\mathrm{\Delta }B$. (C,D) Cell monolayer expansion depends on the cell-substrate dissipation $D$ (maximum cell polarity $\mathrm{\Delta }ϵ=10$; cell-cell dissipation $\mathrm{\Delta }B=0$). (C) Maximal monolayer extension and roughness (we exclude an initial time interval of 200 MCS because it takes at least that long for first daughter cells to appear). (D) Time traces for selected values of $D$. (E,F) Cell monolayer expansion depends on the maximum cell polarity $\mathrm{\Delta }\mathbf{}ϵ$ (cell-cell dissipation $\mathrm{\Delta }B=0$; cell-substrate dissipation $D=0$). (E) Maximal monolayer extension and roughness (we exclude an initial time interval of 200 MCS because it takes at least that long for first daughter cells to appear). (F) Time traces for selected values of $\mathrm{\Delta }ϵ/{\kappa }_P$. .

Figure 5—video 1. Motility-dominated tissue dynamics.

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Figure 5—video 2. Proliferation-dominated tissue dynamics.

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