Mechanical plasticity of cell membranes enhances epithelial wound closure

During epithelial wound healing, cell morphology near the healed wound and the healing rate vary strongly among different developmental stages even for a single species like Drosophila. We develop deformable particle (DP) model simulations to understand how variations in cell mechanics give rise to distinct wound closure phenotypes in the Drosophila embryonic ectoderm and larval wing disc epithelium. We find that plastic deformation of the cell membrane can generate large changes in cell shape consistent with wound closure in the embryonic ectoderm. Our results show that the embryonic ectoderm is best described by cell membranes with an elasto-plastic response, whereas the larval wing disc is best described by cell membranes with an exclusively elastic response. By varying the mechanical response of cell membranes in DP simulations, we recapitulate the wound closure behavior of both the embryonic ectoderm and the larval wing disc.

Figure 1

(a) Normalized wound area $A\left(t\right)/A\left(0\right)$ plotted as a function of time $t$ during wound closure in wing discs (black circles) and embryos (filled red triangles), fit to a sum of two exponential functions (dashed lines). (b) Cell shape parameter $\mathcal{A}\left(t\right)$ averaged over cells adjacent to the wound boundary and plotted vs time during wound closure for the same data in (a). We include a moving average of the data in (b) with a 20-minute window size (solid lines). The data for $A\left(t\right)/A\left(0\right)$ and $\mathcal{A}\left(t\right)$ are from five wing disc wounds and two embryo wound experiments conducted in Ref. [3]. Example cell outlines reproduced from Ref. [3] are shown during wound closure for a single (c) wing disc and (d) embryo, with the wound shaded in gray. The scale bars are 3 $\mu$ in (c) and 5 $\mu \text{m}$ in (d).

Figure 2

(a) Schematic of a deformable particle (or cell) with area $a_i$ and segment lengths $l_{\alpha i}=|{\vec{r}}_{\alpha i}-{\vec{r}}_{(\alpha -1)i}|$ representing the cell membrane. (b) The distance vector ${\vec{d}}_{\alpha i,\beta j}$ between vertex $\alpha$ on cell $i$ and membrane segment ${\vec{l}}_{\beta j}$ on cell $j$ has no component along ${\vec{l}}_{\beta j}$. (c) A cell with $\mathcal{A}=1$ is uniaxially compressed. An elastic cell returns to its undeformed shape (left) after the strain is removed, whereas a plastic cell is permanently deformed (right). (d) A simulated wound is initialized as a cell monolayer, followed by removal of central cells such that the wound size is similar to those in Ref. [3]. Inset: Close-up of the purse string (PS), modeled as a collection of vertices (blue) along the edge of the wound (red). PS vertices are connected by springs (blue lines) with rest lengths ${\lambda }_0$, and each PS vertex is bonded to one DP vertex (yellow lines).

Figure 3

(a) Cell shape parameter $\mathcal{A}$ in the healed system plotted vs the cell bulk modulus $B$ and plastic relaxation timescale $\tau$. (b) Closure rate $dA/dt$ plotted using the data in (a). Parameters indicated by the squares represent predictions for $B$ and $\tau$ of embryo (red) and wing disc (black) cells. $dA/dt$ is defined as $95\%$ of the maximum wound area divided by the time it takes for the wound to shrink to $5\%$ of its maximum size. Averaging at a given $\tau$ and $\beta$ is performed over 25 simulations with different initial conditions. Simulations are carried out at $B$ and $\tau$ given by the grid points, and contours are obtained via interpolation between grid points.

Figure 4

(a) Normalized wound area $A\left(t\right)/A\left(0\right)$ plotted vs time $t$ for simulations of wound closure in embryo (red triangles) and wing disc cells (black triangles) using parameters in Fig. 3. (b) $\mathcal{A}\left(t\right)$ averaged over cells adjacent to the wound for the simulations in (a). Solid lines indicate the moving average of $\mathcal{A}\left(t\right)$ from experiments. Results from simulations using Eq. (10) are included in (a) and (b) to account for shape memory of wing disc cells (black squares). Snapshots of these simulations are shown for (c) embryo and (d) wing disc parameters.