Wound Healing Coordinates Actin Architectures to Regulate Mechanical Work

Abstract

How cells with diverse morphologies and cytoskeletal architectures modulate their mechanical behaviors to drive robust collective motion within tissues is poorly understood. During wound repair within epithelial monolayers in vitro, cells coordinate the assembly of branched and bundled actin networks to regulate the total mechanical work produced by collective cell motion. Using traction force microscopy, we show that the balance of actin network architectures optimizes the wound closure rate and the magnitude of the mechanical work. These values are constrained by the effective power exerted by the monolayer, which is conserved and independent of actin architectures. Using a cell-based physical model, we show that the rate at which mechanical work is done by the monolayer is limited by the transformation between actin network architectures and differential regulation of cell-substrate friction. These results and our proposed mechanisms provide a robust physical model for how cells collectively coordinate their non-equilibrium behaviors to dynamically regulate tissue-scale mechanical output.

Figure 1:. Monolayer Viscoelasticity Depends on Substrate Rigidity

(a-top) Schematic of experimental setup showing laser ablation of an epithelial sheet and subsequent sheet retraction velocity, v. Star marks location of ablation. Cell monolayers adhere to collagen covalently bound to polyacrylamide substrates. Fluorescent particles are embedded within the polyacrylamide substrate allowing the calculation of traction forces. (a-bottom) Kelvin-Voigt model used to quantify retraction. (b) DIC images immediately after ablation on a 1.3 kPa substrate. Scale bar is 25 μm. (c) PIV of initial deformation of the monolayer 0.5s after ablation, compared to immediately prior to ablation. Red star indicates the position of ablation. (d) Average monolayer retraction rate over time and viscoelastic timescale, τ₀, representative of the ratio between monolayer viscosity η_m and elasticity E_m within a Kelvin-Voigt model. (e) τ₀ is a function of substrate elasticity, E (N_total=38). Error bars are mean +/− standard deviation.

Figure 2.. F-actin Architecture Varies with Wound Size and with Substrate Stiffness.

(a) F-actin (red), cadherin (blue), and paxillin (green) stains for a wound closing on a 4.3 kPa substrate. (b) F-Tractin stably transfected in an MDCK monolayer during healing. Ablation occurs at t=0 min. Outlined is the wound area A, and the area of the wound and lamellipodial protrusions, A_L. This yields the fraction of wound area covered by lamellipodia, ψ = (A_L − A)/A_L. (c) Single cells within monolayers expressing LifeAct during healing form either lamellipodia (LP-top) or a purse string (PS-bottom). Stars indicate positions of ablations. Dotted lines show regions used for kymograph analysis. Kymographs (right) indicate the rate of protrusion by both lamellipodium and purse string. (d) Example of lamellipodial fraction ψ as a function of wound area A on a 12.2 kPa substrate with maximimal lamellipodial area fraction ψ_max. Changes in ψ for A>A(ψ_max), vertical line, originate from the maturation of lamellipodia. (d-inset) The purse string fraction, 1- ψ_max, as a function of substrate stiffness, E (N=32). Dashed line is line of best fit with p<0.001. (e) Percent of cells at wound boundary closing via lamellipodia (LP) versus purse string (PS) as determined by eye. (f) F-actin image of wound treated with blebbistatin has pronounced lamellipodial protrusions. (g) F-actin image of wound treated with CK666 has an enhanced purse string. (h) Purse string fraction across drug treatments of wounds closing on 12.2 kPa substrates. (N_control= 9, N_bleb= 3, N_SMIFH2=6, and N_CK666=5). Scale bars are 25 μm. Error bars are mean +/− standard deviation.

Figure 3.. Purse String Coordinates with Lamellipodia to Maintain Closure Time.

(a) DIC images of epithelial wound closure over time on an 8.5 kPa substrate. Red arrows point to boundaries between purse string and lamellipodia. (b) PIV showing accumulated strain of DIC images in (a). (c) Wound area over time, indicating the initial wound size A₀, and exponential decay constants τ₁ and τ₂, where A = A₀e^−t/τ. (d) τ₁ as a function of substrate stiffness (N=36). (e) τ₁ as a function of substrate stiffness separating the samples from (d) into predominantly purse string samples (PS) or lamellipodial crawling (LP). (f) Strain rates during closure on very soft (E=1.8 kPa) and stiff (E=12.2 kPa) gels show difference in sensitivity to myosin-inhibition by blebbistatin (E=1.8kPa: control N=3, 10μM Bleb N=3, 40μM Bleb N=2; E=12.2kPa: control N=4, 40μM Bleb N=4). Error bars are mean +/− standard deviation.

Figure 4.. Mechanical Work, but not Effective Power, is Architecture Dependent.

(a) DIC image sequence of the closing of a wound on E=12.2 kPa and closing principally by purse string (PS). Scale bar is 50 μm. Associated traction force vectors (b) and strain energy maps (c) for the wound in (a) with definition of the wound perimeter, L, and wound thickness, 2δ_+/−. (d) Total strain energy of a wound during closure decreases with time at a constant rate or effective power P*. (e) P* is independent of wound phenotype; E=12.2 kPa control is split into LP (N=12) (ψ_max>0.3) or PS (N=8) (ψ_max<0.3) subsets. (f) Wound perimeter L decreases linearly with time. Change in perimeter with time determines closure velocity v. (g) Wounds maintain a constant energy per unit length during closure. (h) Wound energy densities W/L and closure velocity (i) for LP or PS subsets. (j) Effective power, P, calculated from W/L × v, is independent of wound phenotype. Solid lines in (h-j) represent the average value for all control samples (N=20) before creating LP and PS subsets. (k-m) Wound energy densities, velocities, and effective powers for CK666 (N=8) and Blebbistatin treated monolayers (N=11). Dashed lines are average values for control samples, indicating that both drug treatments decrease mechanical work for a wound. Error bars are mean +/− standard deviation.

Figure 5.. F-actin is Conserved During Lamellipodial to Purse String Transition.

(a) Montage of fluorescent F-actin within a single cell in a MDCK monolayer on a 12.2 kPa substrate showing a transition from lamellipodial crawling to purse string. (b) Kymograph of F-tractin intensities, measuring the quantity of F-actin along the dashed line in (a). Regions outlined are for the cell body (CB), the purse string (PS) and the lamellipodium (LP). (c) The spatial sum of F-actin fluorescence per unit time for the regions outlined in (b). The ratio of mass flux into the purse string m_PS and out of the lamellipodium m_LP shows correlation in F-actin transfer. (d) F-actin fluorescence intensity integrated over the time series in (c). The decrease in F-actin from the lamellipodium is consistent with the sum of F-actin increases in the purse string and cell body. (e) Cartoon schematic of lamellipodial actin being incorporated into the lamellar band to form a purse string. From t=0 to t=t_f (when the wound is closed) the total F-actin intensity along the wound boundary (f) decreases, but the actin density (ρ=I_γ/L) increases (g). Lines are average and grey regions are standard deviation of (N=4). Super-resolution images of F-actin (h) and myosin (i) of a cell at the leading edge. Myosin localizes to lamellar band. Scale bar is 5 μm. (j) In the lamella, the total myosin intensity I_myo scales with the total amount of actin. (k) Force T=W/L depends on actin content of purse string in CK666 treated wounds (N=7). Red dots are from one sample. Error bars are mean +/− standard deviation.

Figure 6.. Differential friction is necessary to balance effective power.

(a) Schematic of vertex model and inset where cells at the leading edge can either exhibit purse string or lamellipodial crawling. (b) Spatial distribution of strain energy measured through the simulation during closure. (c) Vertex model wound area dependence on time. (d) Strain energy-perimeter relation and wound closure velocity. (e) Differences in unbinding probabilities k_off^PS=0.083 min⁻¹ (blue) and k_off^LP=0.208 min⁻¹(green) lead to differences in focal adhesion lifetimes. (e-inset) Equal focal adhesion off-rates k_off^PS= k_off^LP=0.208 min⁻¹ lead to equal focal adhesion lifetimes. (f) Decay time τ₁ as a function of substrate stiffness (E=1 kPa N_LP=26, N_PS=16; E=2 kPa N_LP=29, N_PS=13; E=4 kPa N_LP=24, N_PS=18; E=8 kPa N_LP=22, N_PS=20; E=16 kPa N_LP=24, N_PS=18). (g-i) Energy density, velocity, and effective power for wounds exhibiting either purse string or lamellipodial crawling. k_off^LP>k_off^PS for E=4kPa (N_LP=24, N_PS=18). (j) The effective power of wounds on E=4 kPa substrate is not balanced between LP and PS if k_off^PS= k_off^LP (N_LP=14, N_PS=6). Vertex model and confocal image show focal adhesions parallel to leading edge for purse strings (k) and perpendicular to leading edge for lamellipodia (l). Scale bars are 10μm. (m) Histograms of experimental focal adhesion angular distributions for cells exhibiting PS (N=257) and LP (N=342). (n) Mean focal adhesion size differs between PS (N=412) and LP (N=1075). (o) Experimentally and analytically calculated friction for LP and PS. Error bars are mean +/− standard deviation.