a, Sketch showing a lateral view of a ten-somite stage embryo highlighting the posterior region of the body (dotted black rectangle) where mesodermal progenitors progressively differentiate as they transit from the MPZ to the PSM (i). Confocal sections along the sagittal plane of posterior extending tissues in membrane-labelled Tg(actb2:MA-Citrine) embryos (inverted) containing ferrofluid droplets (cyan) in different regions along the AP axis, namely the A-PSM, the posterior PSM (P-PSM) and the MPZ (ii). V, ventral; D, dorsal; A, anterior; P, posterior. The red dashed contours highlight each region (A-PSM, P-PSM and MPZ). b, Confocal section of droplet (cyan) during actuation (magnetic field ON; membrane label, inverted; i). Red dashed line indicates droplet contour and arrows indicate the direction of forces applied by the droplet. Sketches defining the induced droplet elongation e along the direction of the applied magnetic field H and the droplet pre-elongation before actuation, e₀ (ii). Dashed lines indicate the unelongated droplet. c, Mean (dots) and median (lines) values of cell size (diameter, d; grey) and junctional length (?; red) in the MPZ and PSM, reanalysed from the literature²⁷. The inset at the right shows illustrates the parameters. Error bars, s.e.m. d, Examples of the time evolution of droplet deformation (normalized droplet extension, e/d¯, where d¯ is the average cell size (diameter); induced strain) during actuation cycles (OFF?ON?OFF) for different values of the applied magnetic field, leading to varying e_M values. Both e₀ and e_R are defined in the inset. e,f, Residual droplet elongation normalized by average cell size, eR?e0/d¯ (e) or by average junctional length, eR?e0/?¯ (f), for varying values of the applied maximal droplet elongation (e_M ? e₀) normalized by average cell size (e) or junctional length (f) in the posterior paraxial mesoderm. Vertical red lines in e and f indicate the onset of plastic, irreversible deformation. Median and interquartile range are shown. P values were obtained from one-sample two-tailed t-tests. NS, not significant; **P = 0.0025, ****P < 0.0001. g, Snapshots showing confocal sections of tissue next to a droplet (dotted red line) during an actuation cycle (OFF?ON?OFF) causing T1 transitions that lead to plastic changes in the local tissue architecture (bottom).

Source data

a, Confocal sections showing the temporal changes in cell junction length (white outline) over 400 seconds, and time traces of junction length for cells in different regions of the tissue, showing that junction length is less variable in the A-PSM than in the MPZ. b, Normalized frequency (distribution) of the magnitude of relative variations in junction lengths ???¯t/?¯t (endogenous applied strain at cell junctions) in the A-PSM and P-PSM (N of approximately 3,500 junctions in each region; four embryos), as well as the MPZ (N = 7,896; three embryos). The average endogenous applied strains at cell junctions (inset) are much smaller than the yield strain in the tissue (red dotted line). c, Confocal sections of PSM tissue in mosaic membrane-labelled embryos showing cell protrusions between cells. The length of each protrusion ?p (inset) can be measured at each time point. d, Kymograph showing the fluorescence intensity along a protrusion path, enabling the determination of the time evolution of the protrusion length (white line), ?p(t). e, Normalized frequency of maximal protrusion strains ?pM??¯p/?¯ in the different regions. Average protrusion strains (inset) are largest in the MPZ but much smaller than the yield strain in the tissue (red dotted line). Number of protrusions, N = 78 (A-PSM), 67 (P-PSM) or 73 (MPZ). f,g, Normalized frequency of the number of protrusions per cell (f) and their maximal lengths (g), with the average protrusion number per cell and average protrusion length shown in the insets of f and g, respectively. Mean ± s.d.; in f, number of cells N = 45 (A-PSM), 56 (P-PSM) or 45 (MPZ); number of protrusions N = 62 (A-PSM), 67 (P-PSM) or 66 (MPZ); in g, number of protrusions N = 45 (A-PSM), 35 (P-PSM) or 38 (MPZ).

Source data

a, Confocal sections showing the temporal changes in cell junction length (white outline) over 400 seconds, and time traces of junction length for cells in different regions of the tissue, showing that junction length is less variable in the A-PSM than in the MPZ. b, Normalized frequency (distribution) of the magnitude of relative variations in junction lengths ???¯t/?¯t (endogenous applied strain at cell junctions) in the A-PSM and P-PSM (N of approximately 3,500 junctions in each region; four embryos), as well as the MPZ (N = 7,896; three embryos). The average endogenous applied strains at cell junctions (inset) are much smaller than the yield strain in the tissue (red dotted line). c, Confocal sections of PSM tissue in mosaic membrane-labelled embryos showing cell protrusions between cells. The length of each protrusion ?p (inset) can be measured at each time point. d, Kymograph showing the fluorescence intensity along a protrusion path, enabling the determination of the time evolution of the protrusion length (white line), ?p(t). e, Normalized frequency of maximal protrusion strains ?pM??¯p/?¯ in the different regions. Average protrusion strains (inset) are largest in the MPZ but much smaller than the yield strain in the tissue (red dotted line). Number of protrusions, N = 78 (A-PSM), 67 (P-PSM) or 73 (MPZ). f,g, Normalized frequency of the number of protrusions per cell (f) and their maximal lengths (g), with the average protrusion number per cell and average protrusion length shown in the insets of f and g, respectively. Mean ± s.d.; in f, number of cells N = 45 (A-PSM), 56 (P-PSM) or 45 (MPZ); number of protrusions N = 62 (A-PSM), 67 (P-PSM) or 66 (MPZ); in g, number of protrusions N = 45 (A-PSM), 35 (P-PSM) or 38 (MPZ).

Source data

a, Sketches of cell protrusions and cell?cell junctions, indicating the measured time-dependent protrusion length and cell?cell junctional length, ?p(t) and ?c(t), respectively. b, Normalized frequency of the absolute value of the protrusion strain rates, showing minimal protrusion persistence timescales in the MPZ (inset). Limitations in protrusion tracking did not allow measurement of strain rates below approximately 0.005 s^?1 (grey band). A-PSM (N = 1,490), P-PSM (N = 977) and MPZ (N = 391). c, Temporal autocorrelation of cell?cell junction length in different regions of the tissue along the AP axis, showing persistence (autocorrelation) timescales of approximately 1 minute (inset). Error bars, s.e.m. d, Fourier transform (FT) mode amplitudes of the time evolution of junction length in the tissue for different regions along the AP axis, showing a peak at frequencies (red line) of approximately 0.5 min^?1. N of approximately 3,500 junctions in A-PSM and P-PSM (four embryos) and 7,896 junctions in MPZ (three embryos) in c and d. Error bars, s.e.m. e?h, Confocal sections of MPZ and PSM tissue regions in embryos with myosin II and membrane labels (e) and in embryos with actin (Utrophin, UTR) and membrane labels (g). Scale bars, 50 µm. Zoomed in yellow rectangular regions shown on right. Highlighted yellow region corresponds to analysis region around cell?cell contact. Scale bars, 10 µm. Measured myosin II (f) and actin (h) signal autocorrelations and the characteristic timescales for myosin II (f, inset) and actin (h, inset) dynamics. N = 12 and two embryos for each condition (MPZ, PSM, actin and myosin II). Error bars, s.e.m. (e,f). i, Simulated tissue dynamics arising from actomyosin-generated tension dynamics at cell?cell contacts (Methods). j, Predicted ratio of cell?cell contact length persistence timescale ?? and tension persistence timescale ?_T, in terms of the ratio between the tension persistence timescale ?_T and the dissipation timescale ?_D. Measured values of these ratios in MPZ (light blue square) and PSM (violet square) are shown. Error band of simulation data (s.d.; N = 6 temporal correlations) and s.e.m. of experimental data are shown.

Source data

a, Schematic representation of the measured mechanics of the microenvironment at different strains and timescales during PSM differentiation. The blue ellipse represents the region mechanically probed by cells in these tissues, as indicated by our measurements (for length scales of >0.5 ?m and timescales of >1 s). Above the yield strain, cell rearrangements (T1 transitions, shown in the inset) occur, leading to plastic (irreversible) remodelling of the tissue architecture. Below yield, the tissue maintains its local cellular configurations (no cell rearrangements; inset) and dissipates stresses at different timescales, ?₁ and ?₂. The perceived microenvironment stiffness below yield (colour coded) decreases over time as stresses are dissipated, eventually reaching a constant low value (yellow) associated with the elasticity of deforming cellular packing configurations. Active cellular probing of the microenvironment (blue ellipse) occurs at timescales (~1?2 min) longer than all microenvironment relaxation timescales and at small strains (~10?30%), indicating that during PSM differentiation, cells probe the stiffness associated with the local, foam-like tissue architecture. b, Cortical tension, T, cell adhesion, W, and the volume fraction of extracellular spaces, ?, affect the stiffness, E_T, of the foam-like tissue at supracellular scales for timescales larger than the measured relaxation timescales (~30 s) and smaller than those leading to substantial T1 transitions (~30 min). The equation shows this relationship (?_J being the jamming volume fraction for a disordered 3D foam), and the colours of the parameters in the equation correspond to the colours in the figure at the left.