Just as in clay moulding or glass blowing, physically sculpting biological structures requires the constituent material to locally flow like a fluid while maintaining overall mechanical integrity like a solid. Disordered soft materials, such as foams, emulsions and colloidal suspensions, switch from fluid-like to solid-like behaviours at a jamming transition. Similarly, cell collectives have been shown to display glassy dynamics in 2D and 3D and jamming in cultured epithelial monolayers, behaviours recently predicted theoretically and proposed to influence asthma pathobiology and tumour progression. However, little is known about whether these seemingly universal behaviours occur in vivo and, specifically, whether they play any functional part during embryonic morphogenesis. Here, by combining direct in vivo measurements of tissue mechanics with analysis of cellular dynamics, we show that during vertebrate body axis elongation, posterior tissues undergo a jamming transition from a fluid-like behaviour at the extending end, the mesodermal progenitor zone, to a solid-like behaviour in the presomitic mesoderm. We uncover an anteroposterior, N-cadherin-dependent gradient in yield stress that provides increasing mechanical integrity to the presomitic mesoderm, consistent with the tissue transiting from a wetter to a dryer foam-like architecture. Our results show that cell-scale stresses fluctuate rapidly (within about 1 min), enabling cell rearrangements and effectively 'melting' the tissue at the growing end. Persistent (more than 0.5 h) stresses at supracellular scales, rather than cell-scale stresses, guide morphogenetic flows in fluid-like tissue regions. Unidirectional axis extension is sustained by the reported rigidification of the presomitic mesoderm, which mechanically supports posterior, fluid-like tissues during remodelling before their maturation. The spatiotemporal control of fluid-like and solid-like tissue states may represent a generic physical mechanism of embryonic morphogenesis.

Cell-generated mechanical forces play a critical role during tissue morphogenesis and organ formation in the embryo. However, little is known about how these forces shape embryonic organs, mainly because it has not been possible to measure cellular forces within developing three-dimensional (3D) tissues in vivo. Here we present a method to quantify cell-generated mechanical stresses that are exerted locally within living embryonic tissues using fluorescent, cell-sized, oil microdroplets with defined mechanical properties and coated with surface integrin or cadherin receptor ligands. After introducing a droplet between cells in a tissue, local stresses are determined from the droplet shape deformations, which are obtained via fluorescence microscopy and computerized image analysis. Using this method, we quantify the anisotropic stresses generated by mammary epithelial cells cultured within 3D aggregates and confirm that these stresses (3.4 nN/µm2) are dependent on myosin II activity and more than two-fold larger than the stresses generated by cells of embryonic tooth mesenchyme when analyzed within similar cultured aggregates or in developing whole mouse mandibles.

It is generally believed that the mechanical properties of the cellular microenvironment and their spatiotemporal variations 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 been performed yet. Here we introduce a technique that employs biocompatible 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 one minute) and displays decreasing stiffness and increasing fluidity towards its posterior elongating region. This method opens new avenues to study mechanobiology in vivo, both in embryogenesis and in disease processes, including cancer.

In eukaryotic cells, nanotubes represent a substantial fraction of transport intermediates between organelles. They are extracted from membranes by molecular motors walking along microtubules. We previously showed that kinesins fixed on giant unilamellar vesicles in contact with microtubules are sufficient to form nanotubes in vitro. Motors were attached to the membrane through beads, thus facilitating cooperative effects. Koster et al. proposed that motors could dynamically cluster at the tip of tubes when they are individually attached to the membrane. We demonstrate, in a recently designed experimental system, the existence of an accumulation of motors allowing tube extraction. We determine the motor density along a tube by using fluorescence intensity measurements. We also perform a theoretical analysis describing the dynamics of motors and tube growth. The only adjustable parameter is the motor binding rate onto microtubules, which we measure to be 4.7 ؎ 2.4 s ؊1 . In addition, we quantitatively determine, for a given membrane tension, the existence of a threshold in motor density on the vesicle above which nanotubes can be formed. We find that the number of motors pulling a tube can range from four at threshold to a few tens away from it. The threshold in motor density (or in membrane tension at constant motor density) could be important for the understanding of membrane traffic regulation in cells.giant unilamellar vesicle ͉ intracellular transport ͉ kinesin ͉ membrane tubule ͉ traffic jam

The collective dynamics of N interacting processive molecular motors are considered theoretically when an external force is applied to the leading motor. We show, using a discrete lattice model, that the force-velocity curves strongly depend on the effective dynamic interactions between motors and differ significantly from those of a simple approach where the motors equally share the force. Moreover, they become essentially independent of the number of motors if N is large enough (N * 5 for conventional kinesin). We show that a two-state ratchet model has a very similar behavior to that of the coarse-grained lattice model with effective interactions. The general picture is unaffected by motor attachment and detachment events.

Walled cells have the ability to remodel their shape while sustaining an internal turgor pressure that can reach values up to 10 atmospheres [1-7]. Although it is undisputed that this requires a tight and simultaneous regulation of cell wall assembly and mechanics, previous theoretical studies on tip growth focused either on the mechanical behavior of the cell wall or on its assembly [8-14]. To study the interplay between growth and mechanics in shaping a walled cell, we examine the particularly simple geometry of tip-growing cells [1, 3, 15, 16], which elongate via the assembly and expansion of cell wall in the apical region of the cell. We describe the observed irreversible expansion of the cell wall during growth as the extension of an inhomogeneous viscous fluid shell under the action of turgor pressure, fed by a material source in the neighborhood of the growing tip. This allows us to determine theoretically the radius of the cell and its growth velocity in terms of the turgor pressure and the secretion rate and rheology of the cell wall material. We derive simple scaling laws for the geometry of the cell and find that a single dimensionless parameter, which characterizes the relative roles of cell wall assembly and expansion, is sufficient to explain the observed variability in shapes of tip-growing cells. More generally, our description provides a framework to understand cell growth and remodeling in plants (pollen tubes [17], root hairs, etc. [18]), fungi (hyphal growth [19, 20] and fission and budding yeast [3]), and some bacteria [21], in the context of both tip growth and diffuse growth.

Intracellular transport relies on the action of motor proteins, which work collectively to either carry small vesicles or pull membranes tubes along cytoskeletal filaments. Although the individual properties of kinesin-1 motors have been extensively studied, little is known on how several motors coordinate their action and spatially organize on the microtubule when pulling on fluid membranes. Here we address these questions by studying, both experimentally and numerically, the growth of membrane tubes pulled by molecular motors. Our in vitro setup allows us to simultaneously control the parameters monitoring tube growth and measure its characteristics. We perform numerical simulations of membrane tube growth, using the experimentally measured values of all parameters, and analyze the growth properties of the tube considering various motor cooperation schemes. The comparison of the numerical results and the experimental data shows that motors use simultaneously several protofilaments of a microtubule to pull a single tube, as motors moving along a single protofilament cannot generate the forces required for tube extraction. In our experimental conditions, we estimate the average number of motors pulling the tube to be approximately nine, distributed over three contiguous protofilaments. Our results also indicate that the motors pulling the tube do not step synchronously.

We study the motion of oil drops propelled by actin polymerization in cell extracts. Drops deform and acquire a pearlike shape under the action of the elastic stresses exerted by the actin comet, a tail of cross-linked actin filaments. We solve this free boundary problem and calculate the drop shape taking into account the elasticity of the actin gel and the variation of the polymerization velocity with normal stress. The pressure balance on the liquid drop imposes a zero propulsive force if gradients in surface tension or internal pressure are not taken into account. Quantitative parameters of actin polymerization are obtained by fitting theory to experiment.