In vivo quantification of spatially varying mechanical properties in developing tissues

Abstract

The mechanical properties of the cellular microenvironment and their spatiotemporal variations are thought to play a central role in sculpting embryonic tissues, maintaining organ architecture and controlling cell behavior, including cell differentiation. However, no direct in vivo and in situ measurement of mechanical properties within developing 3D tissues and organs has yet been performed. Here we introduce a technique that employs biocompatible, magnetically responsive ferrofluid microdroplets as local mechanical actuators and allows quantitative spatiotemporal measurements of mechanical properties in vivo. Using this technique, we show that vertebrate body elongation entails spatially varying tissue mechanics along the anteroposterior axis. Specifically, we find that the zebrafish tailbud is viscoelastic (elastic below a few seconds and fluid after just 1 min) and displays decreasing stiffness and increasing fluidity toward its posterior elongating region. This method opens new avenues to study mechanobiology in vivo, both in embryogenesis and in disease processes, including cancer.

Figure 1. Ferrofluid microdroplets as mechanical actuators

(a) A ferrofluid oil droplet, spherical in the absence of a magnetic field $(\overrightarrow{H}=0)$, deforms into an ellipsoid elongated along the axis defined by the direction (black arrow) of an externally applied, uniform magnetic field $(\overrightarrow{H}\ne 0)$. (b) When a ferrofluid oil droplet, inserted between the cells forming a tissue, is actuated by applying a uniform magnetic field, it deforms and generates a local force dipole (red arrows) in the tissue. Imaging the droplet deformation over time upon controlled actuation allows the quantification of the local tissue mechanical properties within a small neighborhood of the droplet (dashed circle).

Figure 2. Module for ferrofluid droplet actuation

(a) 3D drawing of the module. The uniform magnetic field is generated using an array consisting of eight permanent magnets (yellow). The magnitude and direction of the magnetic field on the sample are specified by controlling the distance between the magnet array and the sample using a piezo stage (red) and the magnet array orientation using a rotatory motor (blue), respectively. (b) Magnified sketch of the system geometry, including the magnets, glass-bottom dish (gray) and sample (red). (c) Picture of the magnet array mounted on a 3D-printed holder. (d–e) Finite element simulation of the magnetic flux density $\overrightarrow{B}$ (direction, blue arrows; magnitude, color coded), or magnetic field $\overrightarrow{H}=\overrightarrow{B}/{\mu }_0$ equivalently, generated by the magnet array in the x-z (d) and x-y planes (e). Homogeneous magnetic fields of up to 1 kG = 0.1 T are achieved at the center of the array (e; red arrows). (f) Measured values of the three components of the magnetic flux density (B_x, B_y B_z) at the center of the array (x=y=0) along the z-axis (inset: log-linear scale; error bands indicate the s.d.; Methods). (g) Measured deviation of B_x in the x-y plane at z=0 from its value at the center (x=y=0). Dashed circle indicates the typical size of a zebrafish embryo (~0.6 mm).

Figure 3. Measuring mechanical properties using ferrofluid droplets

(a) Sketch of a ferrofluid droplet (blue) in a material (red) characterized by viscosity η or stiffness E. Magnetic stresses σ_M deform the ferrofluid droplet into an ellipsoid with major and minor axis b and a, respectively, and are resisted by capillary stress σ_C. (b) Effective 1D diagrams representing the combined system of the droplet within a Newtonian fluid or elastic material, characterized by viscous (μ) and elastic elements (k), respectively. (c) Fluorocarbon-based ferrofluid oil droplet in an immiscible, Newtonian hydrocarbon oil, with (ON) and without (OFF) magnetic field. The strain ε is obtained from the droplet’s aspect ratio, b/a, by detecting the droplet’s elliptical contour (white ellipse). Scale bar, 100 μm. (d) Strain evolution (black dots) upon actuation of the droplet in (c) with a controlled magnetic stress σ_M (orange dashed line), showing an exponential relaxation (inset: log-linear scale). The green line represents the fit to the solution of the 1D rheological model for a Newtonian fluid. (e) Viscosity values of three reference Newtonian hydrocarbon oils (N15000, green square; N62000, orange circle; N450000, blue triangle; Methods) measured using ferrofluid droplets and compared to their reference viscosity values (N=4 samples and 4 actuations per sample). The inset shows the ratio of measured to reference viscosities; error bars indicate the s.d. (f) Interfacial tension of the ferrofluid droplet in the same reference hydrocarbon oils measured using the ferrofluid drop deformation (N=7) and compared to independent bulk measurements using a pendant drop tensiometer (N=7). Error bars indicate the s.d. In all cases, N indicates the number of samples.

Figure 4. In vivo quantification of local, intracellular mechanical properties in early zebrafish embryos

(a–b) Confocal sections showing a ferrofluid droplet (rhodamine label; magenta) within a single blastomere of an 8-cell stage wild type (WT) zebrafish embryo (a) and within the yolk cell of a WT embryo between one- and 8-cell stage (b), with (ON) and without (OFF) applied magnetic field (Tg(actb2:MA-Citrine), membrane label; cyan). (c) Simplest 1D rheological model capturing the two-time scale response observed in all in vivo measurements. The elastic (k_i) and fluid (μ_i) elements in the 1D description (i = 1,2) are related to the stiffnesses (E_i) and viscosities (η_i) of the 3D system via k_i = (12/5)E_i and μ_i = (36/5)η_i (see also Fig. 3b and main text). (d–e) Strain response (black dots) of the cytoplasm of the blastomere (d) and the yolk cell (e), upon actuation with a magnetic field generating a controlled magnetic stress σ_M (orange dashed line). Green lines represent fits to the rheological model in c. (f–g) Measured values of the relaxation time scales (f), as well as time-dependent material properties (g) of both the blastomere cytoplasm (blue squares; N=8) and yolk cell (orange circles; N=6). At short time scales (t < τ₁) both behave as elastic materials, but progressively relax the mechanical stresses (t ~ τ₁) and display pure fluid behavior for t > τ₂. Error bars indicate the s.e.m. Scale bars, 50 μm. In all cases, the measurements involved only a single droplet actuation per embryo, with N indicating the number of embryos (samples).

Figure 5. In vivo and in situ quantification of spatial variations in tissue stiffness and fluidity during zebrafish tailbud elongation

(a) Confocal section showing a ferrofluid droplet (rhodamine label; magenta) embedded between the cells of a developing zebrafish tailbud at 14-somite stage (Tg(actb2:MA-Citrine), membrane label; cyan). Dashed lines highlight the progenitor zone (PZ; pink) and the presomitic mesoderm (PSM; orange). Scale bar, 50 μm. (b) Strain response (black dots) of the PZ tissue, upon actuation with a magnetic field generating a controlled magnetic stress σ_M (orange dashed line). The green line represents the fit to the rheological model in Fig. 4c. (c) Schematic representation showing the spatially-varying mechanical properties along the anterior-posterior (A-P) axis during tailbud extension. The tissue at the posterior-most end of the growing tailbud shows lower viscosity and elasticity compared to mesodermal tissues located anteriorly, closer to the newly forming somites (gray). (d–e) Measured values of the relaxation time scales (d), as well as time-dependent mechanical properties (e) of the PZ tissue of WT (N=11) and pac mutant (N-cadherin^−/−; N=9) embryos, as well as of the PSM tissue of WT embryos (N=11). Measured tissues behave as elastic materials at short time scales (t < τ₁) and display pure fluid behavior for t > τ₂, with a transient crossover (t ~ τ₁). Error bars indicate the s.e.m. In all cases, the measurements involved only a single droplet actuation per embryo, with N indicating the number of embryos (samples).