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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Figure 1: Ferrofluid microdroplets as mechanical actuators.
Figure 2: Module for ferrofluid droplet actuation.
Figure 3: Measuring mechanical properties using ferrofluid droplets.
Figure 4: In vivo quantification of local, intracellular mechanical properties in early zebrafish embryos.
Figure 5: In vivo and in situ quantification of spatial variations in tissue stiffness and fluidity during zebrafish tailbud elongation.

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Acknowledgements

We thank D. Bothman for help with 3D printing work, O. Sandre and M. Menyo for help with fluorocarbon-based ferrofluids, E. Sletten (University of California, Los Angeles) for sharing custom-made fluorinated dyes, D. Kane and R. Warga (Western Michigan University) for providing pac/N-cadherin mutants, S. Megason (Harvard Medical School) for providing Tg(actb2:MA-Citrine) embryos, 3M for providing free samples of fluorocarbon oils, Ran Biotechnologies for help with fluorinated surfactants, and V. Mansard, T. Squires and M. Valentine for help with bulk rheology measurements. We also thank all Campàs laboratory members, the CNSI microfluidics facility and the UCSB Animal Research Center for support. The MRL Shared Experimental Facilities used for this work are supported by the MRSEC Program of the NSF under award DMR 1121053. F.S. and P.R. gratefully acknowledge financial support from the Alexander von Humboldt Foundation and Otis Williams Foundation, respectively. A.M. was funded by an EMBO Long-Term Fellowship (EMBO ALTF 509-2013). A.M. and P.R. also thank the Errett Fisher Foundation for financial support. This work was partially supported by NIH grant 1R21HD084285-01 (to O.C.) from the Eunice Kennedy Shriver National Institute of Child Health and Human Development.

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Affiliations

Authors

Contributions

O.C. defined and supervised the project; O.C., F.S., A.M. and P.R. designed and discussed the experiments; F.S. and Z.M.H. designed the module to generate magnetic fields; F.S. and D.A.K. built and calibrated the module to generate magnetic fields; F.S. and D.A.K. calibrated the ferrofluid droplets in reference oils; D.A.K. calibrated the ferrofluid droplets in gels; F.S. developed the software to automatically analyze droplet deformations and analyzed the data with help from D.A.K.; F.S. and P.R. derived the 1D effective theoretical description for ferrofluid droplet actuation; A.A.L. performed interfacial tension measurements with a tensiometer; A.M. performed all the experiments in zebrafish with help from F.S. and D.A.K.; A.M., F.S. and O.C. wrote the paper.

Corresponding author

Correspondence to Otger Campàs.

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The authors declare no competing financial interests.

Integrated supplementary information

Supplementary Figure 1 Ferrofluid magnetization curve.

Magnetization curve of a ferrofluid consisting of a 1:1 (v/v) dilution of DFF1 (Ferrotec) fluorocarbon-based ferrofluid in fluorocarbon oil Novec HFE7300 (3M). The magnetization curve was measured using a Quantum Design MPMS 5XL SQUID (superconducting quantum interference device) magnetometer (see Methods). The inset shows the magnetization curve for the range of magnetic fields used in our experiments. The gray bands represent the standard error of the mean (s.e.m) of 5 independent measurements for the same ferrofluid.

Supplementary Figure 2 Ferrofluid droplet actuation in a hydrocarbon oil.

Temporal evolution of the strain (solid black circles) during the actuation cycles shown in Supplementary Video 1. At equilibrium, the magnetic stress (orange dashed line with fill) is balanced by the capillary stress, leading to the saturation of the strain at each actuation cycle. The characteristic time scale of the dynamics depends on the viscosity of the outer medium (in this case a hydrocarbon oil) because the ferrofluid droplet viscosity is negligible (see Methods). Therefore, the dynamics of ferrofluid droplet actuation permits the measurement of the local hydrocarbon oil viscosity around the droplet.

Supplementary Figure 3 Ferrofluid droplet actuation in a polyacrylamide gel.

Temporal evolution of the strain (solid black circles) during the actuation cycles shown in Supplementary Video 2. The inset shows the measured linear stress-strain relation, where the slope corresponds to the apparent elasticity EA that combines the effect of the gel elastic modulus and the droplet capillary stress (see Methods and Supplementary Figure 4).

Supplementary Figure 4 Local elasticity measurements of polyacrylamide gels using ferrofluid droplets.

(a) Measurements of the apparent elasticity EA for three polyacrylamide gels. The apparent elasticity, given by EA= (5/12) (kd+k), combines the material's elastic modulus and the capillary stress (Supplementary Note). Its value is measured by applying a uniform and constant magnetic field to ferrofluid droplets (Supplementary Movie 2) injected into polyacrylamide gels and fitting their equilibrium strain the theoretical predictions from the 1D description (Supplementary Note). Unlike the elastic modulus of the gel, the capillary stress depends on the droplet size (γ/R). Therefore, injecting droplets with different radius R and measuring the apparent elastic modulus EA allows the decoupling of their contributions. To do so, we measured the apparent elasticity of gels with three different elastic moduli (magenta triangles, blue circles and black squares) using droplets with different radius R, thereby changing the scale of capillary stress γ/R. The elastic modulus of the gel surrounding the droplet was obtained by fitting the data using a linear relation (magenta, blue and black lines) and extrapolating this relation for vanishing capillary stress (vanishing 1/R; large radius). The data points in the limit of vanishing $1/R$ (magenta pentagon, blue inverse triangle and black diamond) are measurements using a parallel plate rheometer, which were not included in the fit. (b) Comparison of the values of the elastic modulus measured using ferrofluid droplets and those obtained using a parallel plate rheometer. The local measurement of the elasticity using the ferrofluid droplets agrees well with the bulk measurement technique. The error bars in the elastic modulus E measured using the rheometer represent one standard deviation (s.d.), and the error bars in the elastic modulus E measured using ferrofluid drops correspond to the error associated to the linear fit as 1/R approaches zero.

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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