Living Capillary Bridges

TL;DR

This work compressed cellular aggregates between two solid surfaces and studied their dynamics using microscopy, and computer simulations to propose a new class of active soft matter behavior, where cellular aggregates exhibit liquid-like adaptation to confinement, but with self-organized rupturing driven by biological activity.

Abstract

Biological tissues exhibit complex behaviors with their dynamics often resembling inert soft matter such as liquids, polymers, colloids, and liquid crystals. These analogies enable physics-based approaches for investigations of emergent behaviors in biological processes. A well-studied case is the spreading of cellular aggregates on solid surfaces, where they display dynamics similar to viscous droplets. \textit{In vivo}, however, cells and tissues are in a confined environment with varying geometries and mechanical properties to which they need to adapt. In this work, we compressed cellular aggregates between two solid surfaces and studied their dynamics using microscopy, and computer simulations. The confined cellular aggregates transitioned from compressed spheres into dynamic living capillary bridges exhibiting bridge thinning and a convex-to-concave meniscus curvature transition. We found that the stability of the bridge is determined by the interplay between cell growth and cell spreading on the confining surfaces. This interaction leads to bridge rupture at a critical length scale determined by the distance between the plates. The force distributions, formation and stability regimes of the living capillary bridges were characterized with full 3D computer simulations that included cell division, migration and growth dynamics, directly showing how mechanical principles govern the behavior of the living bridges; cellular aggregates display jamming and stiffening analogously to granular matter, and cell division along the long axis enhances thinning. Based on our results, we propose a new class of active soft matter behavior, where cellular aggregates exhibit liquid-like adaptation to confinement, but with self-organized rupturing driven by biological activity.

Figures (5)

• Figure 1: The concept and geometry of living capillary bridges. a) A scheme of a cellular aggregate confined between two fibronectin (FN) coated glass slides separated by distance $b$, spreading symmetrically on top and bottom surfaces. The aggregate is surrounded by cell culture medium (DMEM). b) Schemes of different active processes in the system. The cell-substrate and cell-cell adhesion energies (WCS, WCC) are based on cell adhesion molecules, from which we highlight integrins (red) and cadherins (blue). c,d) Experimental time series of confined cellular aggregate from side and bottom view ($R_0$ = 180 µm, $C$ = 0.3). Red and blue arrows indicate spreading cell monolayer on the top and bottom surfaces, respectively. Scale bars are 100 µm.
• Figure 2: Dynamics of large living capillary bridges. a) Living capillary bridge geometry. b) Experimental bottom view time series of confined cellular aggregate ($R_0$ = 162 µm; $C$ = 0.4). Scale bars are 500 µm. c) The initial spreading of $R_\mathrm{film}$ as a function of time for confined cellular aggregate ($R_0$ = 180 µm; $C$ = 0.3) on top and bottom plates. The linear fit approximates the spreading velocity $v_\mathrm{s}$. d)$R_\mathrm{film}$ as a function of time for confined cellular aggregate ($R_0$ = 180 µm; $C$ = 0.3) and cellular aggregate spreading on one substrate ($R_0$ = 114 µm). The linear fit approximates the spreading velocity $v_\mathrm{s}$. e) Approximated number of cells $n_\mathrm{cells, film}$ in a spreading film as a function of time. The sector (green area, upper and lower limits based on the range of division time $t_\mathrm{d}$) corresponds to an estimate for cellular film growth based solely on cell migration, and the exponential fit (dashed orange line) corresponds to film growth dominated by cell divisions. f) Time series of a living capillary bridge ($R_0$ = 180 µm; $C$ = 0.3). Scale bar 100 µm. g) Living capillary bridge $R_\mathrm{1}$ and volume $V$ as a function of time ($R_0$ = 180 µm; $C$ = 0.3). The volume estimate is based on the solid of revolution of the bridge outline. h)$R_2$ as a function of time ($R_0$ = 180 µm; $C$ = 0.3). i) Time series of the forced rupture of a living capillary bridge ($R_0 = 160$ µm, $C \approx$ 0.1). Scale bar 200 µm. All error bars in (c)-(h) indicate standard deviation from at least three experiments.
• Figure 3: Dynamics of small living capillary bridges. a) Experimental bottom view time series of a rupturing living capillary bridge ($R_0$ = 81 µm, $C$ = 0.4), and schematic of the rupturing living capillary bridge from side view. The upper (red) and lower (blue) spreading cellular films are visible by changing the focal plane. Scale bar 100 µm. b) Confocal $z$-stack of small living capillary bridge after 4 hours of incubation ($R_0$ = 67 µm; $C$ = 0.4). Scale bar 50 µm. c) Confocal $z$-stacks of small living capillary bridges after 48 hours of incubation ($R_0$ = 87 µm; $C$ = 0.3). The white arrows indicate to rupturing regions. Scale bars are 50 µm. d) $R_\mathrm{film}$ as a function of time ($R_0$$\approx$ 40, 80 µm; $C \approx$ 0.4). The linear fit approximates the spreading velocity $v_\mathrm{s}$. e)$R_1$ as a function of time from five individual living capillary bridges ($R_0$ = 82 µm; $C$ = 0.4). f) Critical bridge radius $R_{1}^*$ 2 hours before rupturing was observed $(R_0=$ 70 $\pm$ 20 µm). All error bars in (d) and (f) indicate standard deviation from at least three bridges.
• Figure 4: Simple model for stable and unstable regimes of living capillary bridges. a) A scheme of the cylindrical approximation of a living capillary bridge. The volume of the bridge increases due to cell growth in the proliferation layer with thickness $\lambda$ and rate determined by division time $t_d$, and decreases due to cell flow on the confining surfaces determined by velocity $v_m$. b) Living capillary bridge $R_\mathrm{1}$ as a function of time for different compression lengths $b$ (compression ratio $C \approx$ 0.4) and initial aggregate sizes ($R_0 =$ 50--160 µm). The colorbar indicates the compression length $b$. Linear fits correspond to model predictions with $b$ = 126 µm (pink line) and 203 µm (blue line) using $t_\mathrm{d} = 18$ h. c)$R_1$ reduction velocity $\Delta R_1 / \Delta t$ as a function of initial confined aggregate radius $R_0$ according to the cylindrical approximation model. The markers correspond to different compression ratios $C$.
• Figure 5: Capillary bridge simulation model and dynamics.a) Schematic representation of the living capillary bridge simulation setup showing the main force components acting on the cells. b) Time series of simulated spreading aggregates ($R_0$ = 100 µm) on a single substrate at time points $t$ = 1 $\tau$, 5 $\tau$, and 84 $\tau$. $\tau$ represents the characteristic time scale of the simulation. The colorbar indicates cell displacement magnitude $\Delta r$ on a logarithmic scale, where $r$ corresponds to the position of the cell center of mass. c) Simulated living capillary bridge ($R_0$ = 100 µm, $C$ = 0.3) at time points $t$ = 1 $\tau$, 5 $\tau$, and 51 $\tau$. The colorbar indicates cell displacement magnitude $\Delta r$ on a logarithmic scale. d) Simulated living capillary bridge film radius as a function of time ($R_0$ = 100 µm, $C$ = 0.3). The linear fit (dashed black line) shows a spreading velocity of $v_s\approx$ 4 µm/$\tau$. The insert plot shows bottom-view visualization of this capillary bridge. The colorbar indicates cell displacement magnitude $\Delta r$ on a logarithmic scale. e) Cell population dynamics on the simulated living capillary bridge spreading film. The green data points corresponds to migrated cells from the initial aggregate (at $t$ = 0), while the orange data points indicate the cell population of the younger cells resulting from cell divisions. The black data points are the total cell number. The dashed lines highlight the overall trends. f) Simulated living capillary bridge ($R_0$ = 100 µm, $C$ = 0.3) meniscus curvature $R_2$ as a function of time. The dashed lines mark half confinement length ($\pm b$/2). g) Distribution of cell friction force at time $t$ = 31 $\tau$ , from simulated living capillary bridge ($R_0$ = 100 µm, $C$ = 0.3) categorized by the spatial location. Gaussian fits: surface (purple, $A$ = 29.8, $\mu$ = 15.2, $\sigma$ = 8.5), bulk (gray, $A$ = 43.7, $\mu$ = 0.5, $\sigma$ = 7.3). Exponential fits: surface (red dashed line, $4.8e^{-F/{26.3}}$) , bulk (blue dashed line, $3.3e^{-F/{17.3}}$). h) Simulated capillary bridge ($R_0$ = 70 µm, $C \approx$ 0.4) at time $t$ = 0 $\tau$ (intact), 10 $\tau$, and 30 $\tau$ (fully ruptured).The last figure depicts the bottom-view visualization of cells on the lower substrate at time $t$ = 30 $\tau$. The colorbar indicates cell displacement magnitude $\Delta r$ on a logarithmic scale