# 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.

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### Supplementary Figure 5 Measured values of supracellular (tissue-level) mechanical properties do not depend on droplet size.

(a) Comparison of the experimental outcomes 30 minutes after injection of two sets of ferrofluid droplets with different size range in the PZ tissue: droplets in sets #1 and #2 have average droplet radius of 20 μm and 40 μm, respectively. Data from set #1 and set #2 are shown in red and gray, respectively. The percentage of larvae that do not survive the procedure increases with the size of the droplets (from 2.4% in set #1 to 11.4% in set #2) and fewer of the larger droplets remain in the PZ tissue (69.9% in set #1 and 31.4% in set #2). The percentage of droplets found in the yolk increases from 27.7% in set #1 to 57.1% in set #2 (N=83 in set #1 and N=39 in set #2; N=number of injected embryos). (b) Comparison of the measured mechanical properties for the two sets of droplets. The measured mechanical properties are the same within the error. The obtained values for set #1 are E = 272 ± 45 Pa, η1 = 293 ± 100 Pa s, η2 = 3168 ± 425 Pa s (N=11). The obtained values for set #2 are E = 212 ± 12 Pa, η1 = 191 ± 19 Pa s, η2 = 2919 ± 515 Pa s (N=8). In all cases, the measurements involved only a single droplet actuation per embryo, with N indicating the number of embryos (samples). (c) Correlation analysis of droplet size and measured values of mechanical properties. No correlation between droplet radius and the measured values is observed, as indicated by the Pearson's correlation coefficient, r. Values reported here are mean ± s.e.m.

### Supplementary Figure 6 Droplet injection does not affect normal development.

(a) Trunk and tail of a 2 days post-fertilization (dpf) larvae with a droplet located within skeletal muscle tissue (white dotted inset). Definition of the two lengths, LA and LB, used for the phenotypic analysis. Scale bar, 100 μm. (b) Magnification of the inset region in a showing the droplet and its relative position to the somite boundary. Scale bar, 40 μm. (c) Pie chart showing the experimental outcome 30 minutes after droplet injection: 2.4% of the embryos did not survive, 69.9% presented a drop in the PZ region, and 27.7% had the drop in a non-targeted tissue, often the yolk (N=83 embryos). (d) Definition of the parameters taken in account to quantify the notochord deviation from a straight line. The notochord is sketched as a thick black line. (e) Pie chart showing the location of the droplets identified in 2 dpf larvae: 65.4% of the larvae had a drop embedded within the skeletal muscles, 19.2% in the yolk extension, and 15.4% in the region posterior to the cloaca spanning from the dorsal aorta (DA) to the caudal vein (CV) (N=26 larvae). (f-g) Injected larvae do not show significant alteration of trunk and tail length. The measured lengths LA and LB are LA = 1285 ± 16 μm (N=26) and LB = 2018 ± 30 μm (N=22) for injected larvae, and LA = 1300 ± 9 μm (N=12) and LB = 2121 ± 38 μm (N=12) for control larvae (N is number of larvae). (h) Distance of the droplets from the posterior end of the notochord. Droplets injected in the PZ at 6 somite stage are mainly found in tissues posterior to the cloaca. (i) Effects of droplet injection on tail straightness. No difference was found between injected and control embryos: w/LA = 0.5 ± 0.1 % (N=25) for injected larvae and w/LA = 0.56 ± 0.06 % (N=11) for control larvae (N is number of larvae). (j) Definition of somite angle, α, and somites anterior and posterior to the somite where the droplet is located. Scale bar, 40 μm. (k) Somite angle in trunk and tail regions is not affected in injected larvae: α = 39.3 ± 0.8 degrees in injected larvae (N=24) and α = 39.8 ± 0.6 degrees in control larvae (N=24) (N is the number of somites; 4 somites per larva in the region close to the injected droplet were measured, in a total of 6 larvae). (l) Ratio of somite angle between the somite with droplet and adjacent somites, showing no variation between injected and control larvae: αdropant = 0.99 ± 0.02 (N=8), αdroppos = 1.00 ± 0.03 (N=8), with drop, ant, pos being the somite angle for the somite with a droplet and for the immediately anterior and posterior somites, respectively (N is number of larvae). In all cases, the red line in the plots indicates the mean, and the values here reported are mean ± s.e.m.

## Supplementary information

### Supplementary Text and Figures

Supplementary Figures 1–6 and Supplementary Note. (PDF 1014 kb)

### Ferrofluid droplet actuation in a hydrocarbon oil.

A uniform magnetic field is used to deform the ferrofluid droplet previously inserted in hydrocarbon oil. The droplet is actuated in periodic cycles consisting of turning on and off the magnetic field. The magnetic field is increased at each actuation cycle, leading to larger magnetic stresses, thereby creating larger droplet deformations. The applied magnetic stress starts at a value of 3 Pa in the first cycle and is progressively increased until 29 Pa in the last cycle. The elliptical droplet contour is detected using a homemade algorithm (Methods) and shown in magenta. The resulting temporal strain response is shown in Supplementary Fig. 2. (MOV 5806 kb)

### Ferrofluid droplet actuation in a polyacrylamide gel.

A uniform magnetic field is used to deform a ferrofluid droplet previously inserted into a polyacrylamide gel. The droplet is actuated in periodic cycles consisting of turning on and off the magnetic field, as well as turning the direction of the magnetic field by 90° at each cycle. The magnetic field is increased at each actuation cycle, leading to larger magnetic stresses, thereby creating larger droplet deformations. The applied magnetic stress starts at a value of 25 Pa in the first cycle and is progressively increased until 260 Pa in the last cycle. The characteristic time scale of droplet deformation is on a millisecond timescale (Methods), much faster than the frame rate, leading to instantaneous jumps between equilibrium shapes in our experiments (Supplementary Fig. 3). The elliptical droplet contour is detected using a homemade algorithm (Methods) and shown in magenta. Performing these experiments with droplets of different sizes, we measured the elastic modulus of the polyacrylamide gel surrounding the droplet (Methods and Supplementary Fig. 4). (MOV 1906 kb)

### Ferrofluid droplet actuation in a single blastomere of a 8-cell stage zebrafish embryo.

A uniform magnetic field is used to deform the ferrofluid droplet (magenta) previously injected in the blastomere of a Tg(actb2:MA-Citrine) zebrafish embryo (membrane label; cyan). The droplet is actuated in periodic cycles consisting of turning on and off the magnetic field, as well as turning the direction of the magnetic field by 90° at each cycle (only two cycles of actuation are shown). In these experiments, the magnitude of the magnetic field is the same in each actuation cycle. The raw frames for this movie were filtered with a Gaussian kernel of 1-pixel radius to reduce high frequency noise. (MOV 3266 kb)

### Ferrofluid droplet actuation in the yolk cell of a 2-cell stage zebrafish embryo.

A uniform magnetic field is used to deform the ferrofluid droplet (magenta) previously injected in the yolk cell of a Tg(actb2:MA-Citrine) zebrafish embryo (membrane label; cyan). The droplet is actuated in periodic cycles consisting of turning on and off the magnetic field (only two cycles of actuation are shown). In these experiments, the direction of the magnetic field is the same in each actuation cycle, but the magnitude of the magnetic field is increased at each cycle, leading to larger droplet deformations. The raw frames for this movie were filtered with a Gaussian kernel of 1-pixel radius to reduce high frequency noise. (MOV 6321 kb)

### Ferrofluid droplet actuation in the tailbuid of a 10-somite stage zebrafish embryo.

A uniform magnetic field is used to deform the ferrofluid droplet (magenta) previously injected in the tailbud of a Tg(actb2:MA-Citrine) zebrafish embryo (membrane label; cyan) at 6-somite stage. The droplet is actuated in periodic cycles consisting of turning on and off the magnetic field, as well as turning the direction of the magnetic field by 90° at each cycle (eight cycles of actuation are shown). In these experiments, the magnitude of the magnetic field is the same in each actuation cycle. The raw frames for this movie were filtered with a Gaussian kernel of 1-pixel radius to reduce high frequency noise. (MOV 6341 kb)

### Ferrofluid droplet actuation within trunk skeletal muscles in a 2 days post-fertilization zebrafish larvae.

A ferrofluid droplet was injected at 6-somite stage in the PZ tissue. After 36 hours, the droplet was found embedded within the trunk skeletal muscles, at the level of the yolk extension. The video shows one actuation cycle, showing that ferrofluid droplets can be used to measure tissue mechanical properties at various time points during development. (MOV 3019 kb)

### Supplementary Software

Analysis software to obtain mechanical properties from controlled ferrofluid droplet deformations. (ZIP 3568 kb)

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Serwane, F., Mongera, A., Rowghanian, P. et al. In vivo quantification of spatially varying mechanical properties in developing tissues. Nat Methods 14, 181–186 (2017). https://doi.org/10.1038/nmeth.4101

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