Mechanics of the cellular microenvironment as probed by cells in vivo during zebrafish presomitic mesoderm differentiation.

Tissue morphogenesis, homoeostasis and repair require cells to constantly monitor their three-dimensional microenvironment and adapt their behaviours in response to local biochemical and mechanical cues. Yet the mechanical parameters of the cellular microenvironment probed by cells in vivo remain unclear. Here, we report the mechanics of the cellular microenvironment that cells probe in vivo and in situ during zebrafish presomitic mesoderm differentiation. By quantifying both endogenous cell-generated strains and tissue mechanics, we show that individual cells probe the stiffness associated with deformations of the supracellular, foam-like tissue architecture. Stress relaxation leads to a perceived microenvironment stiffness that decreases over time, with cells probing the softest regime. We find that most mechanical parameters, including those probed by cells, vary along the anteroposterior axis as mesodermal progenitors differentiate. These findings expand our understanding of in vivo mechanosensation and might aid the design of advanced scaffolds for tissue engineering applications.

A fluid-to-solid jamming transition underlies vertebrate body axis elongation.

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 transition1-4. Similarly, cell collectives have been shown to display glassy dynamics in 2D and 3D5,6 and jamming in cultured epithelial monolayers7,8, behaviours recently predicted theoretically9-11 and proposed to influence asthma pathobiology8 and tumour progression12. However, little is known about whether these seemingly universal behaviours occur in vivo13 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.

In vivo quantification of spatially varying mechanical properties in developing tissues.

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.

Two cases of reciprocal relations for electric and hydrodynamic currents: A rigid polymer in a nano-channel and a polyelectrolyte gel.

We illustrate an Onsager-type linear response theory of electrohydrodynamic coupling for two examples, namely, a long nano-channel blocked partially by a rigid polymer and a gel of semi-flexible polyelectrolyte chains. We calculate the hydrodynamic and electric currents driven by an external voltage and pressure and the corresponding Onsager coefficients for these systems. Our consideration clarifies the effect of the electro-osmotic flow on the effective charge of the polymer inside the channel. It also makes it possible to explore the dependence of the currents through the gel on the electric screening radius and salt concentration.

Mechanical control of tissue shape and morphogenetic flows during vertebrate body axis elongation.

Shaping embryonic tissues into their functional morphologies requires cells to control the physical state of the tissue in space and time. While regional variations in cellular forces or cell proliferation have been typically assumed to be the main physical factors controlling tissue morphogenesis, recent experiments have revealed that spatial variations in the tissue physical (fluid/solid) state play a key role in shaping embryonic tissues. Here we theoretically study how the regional control of fluid and solid tissue states guides morphogenetic flows to shape the extending vertebrate body axis. Our results show that both the existence of a fluid-to-solid tissue transition along the anteroposterior axis and the tissue surface tension determine the shape of the tissue and its ability to elongate unidirectionally, with large tissue tensions preventing unidirectional elongation and promoting blob-like tissue expansions. We predict both the tissue morphogenetic flows and stresses that enable unidirectional axis elongation. Our results show the existence of a sharp transition in the structure of morphogenetic flows, from a flow with no vortices to a flow with two counter-rotating vortices, caused by a transition in the number and location of topological defects in the flow field. Finally, comparing the theoretical predictions to quantitative measurements of both tissue flows and shape during zebrafish body axis elongation, we show that the observed morphogenetic events can be explained by the existence of a fluid-to-solid tissue transition along the anteroposterior axis. These results highlight the role of spatiotemporally-controlled fluid-to-solid transitions in the tissue state as a physical mechanism of embryonic morphogenesis.

Electrophoretic capture of a DNA chain into a nanopore.

Based on our formulation of the DNA electrophoresis near a pore [Rowghanian and Grosberg, Phys. Rev. E (to be published)], we address the electrophoretic DNA capture into a nanopore as a steady-state process of particle absorption to a sink placed on top of an energy barrier. Reproducing the previously observed diffusion-limited and barrier-limited regimes as two different limits of the particle absorption process and matching the data, our model suggests a slower growth of the capture rate with the DNA length for very large DNA molecules than the previous model, motivating more experiments beyond the current range of electric field and DNA length. At moderately weak electric fields, our model predicts a different effect, stating that the DNA length dependence of the capture rate first disappears as the field is reduced and eventually reverses to a decreasing trend with N.

Electrophoresis of a DNA coil near a nanopore.

Motivated by DNA electrophoresis near a nanopore, we consider the flow field around an "elongated jet," a long thin source which injects momentum into a liquid. This solution qualitatively describes the electro-osmotic flow around a long rigid polymer, where due to electrohydrodynamic coupling, the solvent receives momentum from the electric field. Based on the qualitative behavior of the elongated jet solution, we develop a coarse-grained scheme which reproduces the known theoretical results regarding the electrophoretic behavior of a long rigid polymer and a polymer coil in a uniform field, which we then exploit to analyze the electrophoresis of a polymer coil in the nonuniform field near a nanopore.

Propagation of tension along a polymer chain.

We study the propagation of tension caused by an external force along a long polymeric molecule in two different settings, namely along a free polymer in three-dimensional (3D) space being pulled from one end, and along a prestretched circular polymer, confined in a narrow circular tube. We show that in both cases, the tension propagation is governed by a diffusion equation, and in particular, the tension front propagates as t(1/2) along the contour of the chain. The results are confirmed numerically, and by molecular dynamics simulations in the case of the 3D polymer. We also compare our results with the previously suggested ones for the translocation setting, and discuss why tension propagation is slower in that case.

Force-driven polymer translocation through a nanopore: an old problem revisited.

We consider DNA translocation through a pore in a planar membrane. The pore is so narrow that only one DNA segment can fit in. Assuming that the biasing force f acts inside the pore only, and that the DNA monomer number N is asymptotically large, we modify the previously developed treatment of the stretched part of the pre-translocated polymer by introducing the concept of "iso-flux trumpet". We show that friction of a moving chain in the trumpet, although it determines the speed of the process, provides only a marginal fraction of overall dissipation in the process. The dominant dissipation turns out to be due to irreversible entropic squeezing of the chain into the small pore. We also discover that because of the role of the membrane a much larger amount of heat of order k(B)T per monomer gets transferred from the heat bath on the post-translocation side to that on the pre-translocation side.