Nanorods 3 μm long and 300 nm in diameter were synthesized by electrochemical deposition of nickel into alumina templates as described previously (Paxton et al., 2004; Dhar et al., 2010; Ghazvini et al., 2015). The magnetized nickel nanorods were dispersed in a 90% isopropyl alcohol, 10% water solution.

For magnetic microrheology we have custom built electromagnets (Figure 1A) using 5 inches long iron cores (Ed Fagan Inc., alloy 79, 0.750^′′ diameter) wrapped around with multiple layers of magnet wire (Tech Fixx Inc., 22 awg).

The theory of elasticity measurement follows (Wilhelm et al., 2002; Celedon et al., 2011). Let ϕ and θ denote the direction of the magnetic moment of the particle and the external field in the xy plane, respectively. The torque T_magnetic of the magnetic field B₀ acting on a particle with magnetization m is (1)Tmagnetic=mB0sin(θ-ϕ). Within an elastic material, the torque T_elastic resisting the rotation of the particle in the x-y plane is (2)Telastic=-μf(ϕ-ϕ0) where μ = E/[2(1 + ν)] is the shear modulus, f = πℓ³/[3ln(ℓ/4r)] is a geometric factor and ϕ₀ denotes the particle's direction in the absence of external forces or fields (Wilhelm et al., 2002; Celedon et al., 2011). Similarly, the torque associated with a viscous drag is (3)Tvisc=-ηfϕ. where η is the viscosity, and ϕ. is the angular velocity of the nanorod.

In the Kelvin-representation of the standard linear solid (SLS), an elastic and a Kelvin-Voigt material are in series: the short term response is hence elastic, followed by a slower viscoelastic relaxation to a new elastic equilibrium. In this approximation the rotation of the material Δϕ = ϕ−ϕ₀ is decomposed into the sum Δϕ = ϕ₁ + ϕ₂, where the terms indicate the initial elastic and the subsequent viscoelastic responses, respectively. Thus, the torque balance for a magnetic particle embedded in an SLS material is (4)Tmagnetic=μ1fϕ1=μ2fϕ2+ηfϕ2. For small deformations Δϕ ≪ 1, we approximate T_magnetic as a Taylor series: (5)Tmagnetic=mB0sin(θ-ϕ0)-mB0cos(θ-ϕ0)Δϕ+... Unless ϕ₀ and θ are parallel, |sin(θ−ϕ₀)|≫|cos(θ−ϕ₀)Δϕ|, thus T_magnetic remains a constant during small deformations. Under such conditions, the solutions of Equation (4) are: (6)ϕ1=Tmagneticμ1f and (7)ϕ2=A[1-exp(-t/τ)] where A = T_magnetic/(μ₂f) and the characteristic relaxation time is (8)τ=η/μ2. In the steady state elastic torques resists all the externally imposed T_magnetic in the Kelvin-Voigt unit, hence (9)Tmagnetic=μ2fϕ2max. Thus, the ratio of the viscoelastic and pure elastic response is obtained as (10)ϕ1ϕ2max=μ2μ1.

Fertile wild type quail (Coturnix coturnix japonica) eggs (Ozark Egg Co., Stover, MO) were incubated for varying periods of time (from 20 to 36 h) at 37°C to reach Hamburger and Hamilton (HH) stage 4 (Hamburger and Hamilton, 1951). Embryos were then isolated, injected and cultured as in (Aleksandrova et al., 2015), modified from (Chapman et al., 2001) to reach HH10 when they were subjected to experimental analysis.

Monoclonal antibodies directed against fibrillin-2 and fibronectin ECM proteins (JB3, B3D6; DSHB, Iowa City, IA) were directly conjugated to AlexaFluor 488, 555, or 647 (Molecular Probes) according to the manufacturer's instructions (Czirok et al., 2006). The direct conjugates were injected into the lateral plate mesoderm as 5–40 nl boluses using a PLI-100 (Harvard Instruments) microinjector as described in Little and Drake (2000). Microinjections were performed 30–60 min prior to the beginning of the image acquisition to allow for antibody diffusion and antigen binding.

The embryos were dehydrated through graded ethanol series, placed in acrylamide containing infiltration solution for an hour under vacuum, and embedded in an acrylamide-agarose resin. Subsequently, 100 um sections were cut using a vibratome (Germroth et al., 1995).

Microrheological measurements were performed on the powered stage of a dissecting microscope (Leica M205FA) equipped with epifluorescence illumination and a Planapo 2.0x objective. The imaging system recorded 1,392 × 1,040 pixel images at a rate of 15.44 frames/s and at a resolution of 0.4 μm /pixel.

To characterize tissue deformation, we first apply our non-invasive, optical flow-based method described in Czirok et al. (2017) for each image of the recording. The displacement field u→(t,x→), calculated relative to the first image as a reference, provides the basis to calculate local tissue rotation. We approximate the local vorticity as (11)|∇×u→(t,x→)|=∂uy∂x-∂ux∂y   ≈uy(x+h,y)-uy(x-h,y)-ux(x,y+h)+ux(x,y-h)2h where h is the resolution of the optical flow-derived grid.

To facilitate microrheology measurements in live embryos, we built a plastic incubator chamber surrounded by two, orthogonal pairs of electromagnets (Figure 1). The plastic construction of the incubator chamber minimizes perturbations of the magnetic field. The incubator chamber consists of two heated indium tin oxide (ITO) glass surfaces that enclose a 35mm dish (Figures 1A,B). In the dish a 3D-printed ring (Gulyas et al., 2018) delineates an inner chamber, filled by low melting point agarose, while the outer chamber is filled with sterile distilled water to provide humidity. Temperature was controlled by heating currents within the ITO surfaces, feedback was provided by a thermometer probe immersed in the water bath surrounding the agarose bed. Quail embryos were cultured at the surface of the agarose bed.

The magnetic field within the incubator chamber could be gradually adjusted up to a value of 30 mT by setting the voltage across the electromagnets (Figure 1C). The approximate Helmholtz pair-like configuration of the electromagnets was designed to provide a spatial homogeneous magnetic field. According to our measurements, within a 10 mm diameter region around the symmetry center the magnetic field changes less than 5% (Figure 1D).

To measure the material properties of embryonic tissues, we microinjected ferromagnetic nanorods into HH stage 4 quail embryos. In the confined space of the injector capillary, the particles formed aggregates, which incorporated into the tissue, and were detectable by transmitted light microscopy for the entire length of ex ovo development (Figures 2A,B). The aggregates also appear as dark areas against the background of ECM immunofluorescence (Figure 2C). As subsequent physical sectioning of the microinjected embryos revealed, most nanorod aggregates were delivered into the ECM rich space separating the mesoderm and the endoderm (Figure 2D).

Microrheological recordings were performed in HH10 embryos—by which time the injury associated with microinjection completely healed. As high framerate transmitted light live imaging reveals, alternating magnetic fields readily induce rotation of the embedded aggregates, accompanied by a profound deformation of the surrounding tissue microenvironment (Figure 3, Supplementary Movie 1). The deformation of the ECM was established by live imaging of fibronectin and fibrillin immunofluorescence (Supplementary Movie 2, Figure 2C). As kymogrphs demonstrate by visualizing movement along the perimeter of a 50 μm radius circle centered at an aggregate, the external force-induced deformation of the ECM and the tissue was similar both in magnitude and timing (Figures 3B,C).

To quantify the tissue deformations induced by the rotation of ferromagnetic aggregates, we modified our image analysis tools used to characterize cardiomyocyte beating activity (Czirok et al., 2017). We compared a sequence of images to a common reference frame by PIV analysis, yielding a displacement field (u). The time-dependent spatial average of u indicates a gradually increasing baseline, upon which the magnetic field-induced changes are superimposed (Figure 4A). The increasing baseline reflects deformations intrinsic to the developing tissue.

Tissue rotation was specifically characterized by calculating vorticity (Figure 4C), the amount of local spinning motion that would be seen by a local observer moving with the tissue. The overall rotation was established based on Stokes' theorem: the sum total of vorticity within an area gives the amount of circulation along the perimeter. Thus, by calculating the sum of vorticity over circles of various sizes, we can determine the spatial extent of the tissue deformation as well as the magnitude of the rotation (Figure 4B).

While we do not know the net magnetic moment of the aggregates, the temporal behavior of tissue rotation allows the characterization of the local viscoelastic response of the tissue using Equations (7) and (8). As Figure 4B shows, the response of the tissue is biphasic: a very fast (less than 0.2 s) adjustment is followed by a slow, creep-like behavior lasting for several seconds. As a quantitative measure of the response, we fitted an exponential function (12)ϕ(t)=aexp(-t/τ)+ϕ∞ to each of the recorded responses—both in the creep and relaxation phases—and then transformed the data so that the asymptotic value ϕ_∞ was shifted to zero. The average time-dependent difference from the estimated equilibrium value |ϕ(t) − ϕ_∞| indeed validates the presence of a slow, exponential relaxation with a characteristic time of 1.3 ± 0.2 s (Figures 4D,E). The presence of a faster and a slower response thus suggest that the ECM-containing early embryonic tissue is well-described as a Zener material (Mainardi and Spada, 2011), represented with a spring in series with a Kelvin-Voigt unit (Figure 4D inset). By fitting the Zener model to data extracted from HH10 embryos (n = 4) we calculated μ₂/μ₁ = 0.45 ± 0.1 and found that the ratio of the viscoelastic and pure elastic response is 45:55%.