Short-range correlation of stress chains near solid-to-liquid transition in active monolayers.

Using a three-dimensional model of cell monolayers, we study the spatial organization of active stress chains as the monolayer transitions from a solid to a liquid state. The critical exponents that characterize this transition map the isotropic stress percolation onto the two-dimensional random percolation universality class, suggesting short-range stress correlations near this transition. This mapping is achieved via two distinct, independent pathways: (i) cell-cell adhesion and (ii) active traction forces. We unify our findings by linking the nature of this transition to high-stress fluctuations, distinctly linked to each pathway. The results elevate the importance of the transmission of mechanical information in dense active matter and provide a new context for understanding the non-equilibrium statistical physics of phase transition in active systems.

Mechanical basis and topological routes to cell elimination.

Cell layers eliminate unwanted cells through the extrusion process, which underlines healthy versus flawed tissue behaviors. Although several biochemical pathways have been identified, the underlying mechanical basis including the forces involved in cellular extrusion remains largely unexplored. Utilizing a phase-field model of a three-dimensional cell layer, we study the interplay of cell extrusion with cell-cell and cell-substrate interactions in a flat monolayer. Independent tuning of cell-cell versus cell-substrate adhesion forces reveals that extrusion events can be distinctly linked to defects in nematic and hexatic orders associated with cellular arrangements. Specifically, we show that by increasing relative cell-cell adhesion forces the cell monolayer can switch between the collective tendency towards fivefold, hexatic, disclinations relative to half-integer, nematic, defects for extruding a cell. We unify our findings by accessing three-dimensional mechanical stress fields to show that an extrusion event acts as a mechanism to relieve localized stress concentration.

Three-dimensional full-field velocity measurements in shock compression experiments using stereo digital image correlation.

Shock compression plate impact experiments conventionally rely on point-wise velocimetry measurements based on laser-based interferometric techniques. This study presents an experimental methodology to measure the free surface full-field particle velocity in shock compression experiments using high-speed imaging and three-dimensional (3D) digital image correlation (DIC). The experimental setup has a temporal resolution of 100 ns with a spatial resolution varying from 90 to 200 µm/pixel. Experiments were conducted under three different plate impact configurations to measure spatially resolved free surface velocity and validate the experimental technique. First, a normal impact experiment was conducted on polycarbonate to measure the macroscopic full-field normal free surface velocity. Second, an isentropic compression experiment on Y-cut quartz-tungsten carbide assembly is performed to measure the particle velocity for experiments involving ramp compression waves. To explore the capability of the technique in multiaxial loading conditions, a pressure shear plate impact experiment was conducted to measure both the normal and transverse free surface velocities under combined normal and shear loading. The velocities measured in the experiments using digital image correlation are validated against previous data obtained from laser interferometry. Numerical simulations were also performed using established material models to compare and validate the experimental velocity profiles for these different impact configurations. The novel ability of the employed experimental setup to measure full-field free surface velocities with high spatial resolutions in shock compression experiments is demonstrated for the first time in this work.

Dynamic Strength of Iron at High Pressures and Strain Rates.

Accurate modeling of meteorite impacts, and deformation of planetary cores require characterization of the flow strength and in-elasticity of iron in its different phases. In this Letter, we investigate the flow strength of both the ambient α phase and high-pressure ε phase of iron at strain rates of 1×10^{5} s^{-1} and pressures up to 42 GPa using high-pressure-pressure shear plate impact experiments. We report the strength of the ε iron to be significantly higher than α phase but consequently one order smaller than the previously reported dynamic strength at high pressures. The complete stress-strain response of the ε phase is reported for the first time.

Cell wall and cytoskeletal contributions in single cell biomechanics of Nicotiana tabacum.

Studies on the mechanics of plant cells usually focus on understanding the effects of turgor pressure and properties of the cell wall (CW). While the functional roles of the underlying cytoskeleton have been studied, the extent to which it contributes to the mechanical properties of cells is not elucidated. Here, we study the contributions of the CW, microtubules (MTs) and actin filaments (AFs), in the mechanical properties of Nicotiana tabacum cells. We use a multiscale biomechanical assay comprised of atomic force microscopy and micro-indentation in solutions that (i) remove MTs and AFs and (ii) alter osmotic pressures in the cells. To compare measurements obtained by the two mechanical tests, we develop two generative statistical models to describe the cell's behaviour using one or both datasets. Our results illustrate that MTs and AFs contribute significantly to cell stiffness and dissipated energy, while confirming the dominant role of turgor pressure.

Cells exploit a phase transition to mechanically remodel the fibrous extracellular matrix.

Through mechanical forces, biological cells remodel the surrounding collagen network, generating striking deformation patterns. Tethers-tracts of high densification and fibre alignment-form between cells, thinner bands emanate from cell clusters. While tethers facilitate cell migration and communication, how they form is unclear. Combining modelling, simulation and experiment, we show that tether formation is a densification phase transition of the extracellular matrix, caused by buckling instability of network fibres under cell-induced compression, featuring unexpected similarities with martensitic microstructures. Multiscale averaging yields a two-phase, bistable continuum energy landscape for fibrous collagen, with a densified/aligned second phase. Simulations predict strain discontinuities between the undensified and densified phase, which localizes within tethers as experimentally observed. In our experiments, active particles induce similar localized patterns as cells. This shows how cells exploit an instability to mechanically remodel the extracellular matrix simply by contracting, thereby facilitating mechanosensing, invasion and metastasis.

Structure and Biomechanics during Xylem Vessel Transdifferentiation in Arabidopsis thaliana.

Individual plant cells are the building blocks for all plantae and artificially constructed plant biomaterials, like biocomposites. Secondary cell walls (SCWs) are a key component for mediating mechanical strength and stiffness in both living vascular plants and biocomposite materials. In this paper, we study the structure and biomechanics of cultured plant cells during the cellular developmental stages associated with SCW formation. We use a model culture system that induces transdifferentiation of Arabidopsis thaliana cells to xylem vessel elements, upon treatment with dexamethasone (DEX). We group the transdifferentiation process into three distinct stages, based on morphological observations of the cell walls. The first stage includes cells with only a primary cell wall (PCW), the second covers cells that have formed a SCW, and the third stage includes cells with a ruptured tonoplast and partially or fully degraded PCW. We adopt a multi-scale approach to study the mechanical properties of cells in these three stages. We perform large-scale indentations with a micro-compression system in three different osmotic conditions. Atomic force microscopy (AFM) nanoscale indentations in water allow us to isolate the cell wall response. We propose a spring-based model to deconvolve the competing stiffness contributions from turgor pressure, PCW, SCW and cytoplasm in the stiffness of differentiating cells. Prior to triggering differentiation, cells in hypotonic pressure conditions are significantly stiffer than cells in isotonic or hypertonic conditions, highlighting the dominant role of turgor pressure. Plasmolyzed cells with a SCW reach similar levels of stiffness as cells with maximum turgor pressure. The stiffness of the PCW in all of these conditions is lower than the stiffness of the fully-formed SCW. Our results provide the first experimental characterization of the mechanics of SCW formation at single cell level.

A minimal mechanosensing model predicts keratocyte evolution on flexible substrates.

A mathematical model is proposed for shape evolution and locomotion of fish epidermal keratocytes on elastic substrates. The model is based on mechanosensing concepts: cells apply contractile forces onto the elastic substrate, while cell shape evolution depends locally on the substrate stress generated by themselves or external mechanical stimuli acting on the substrate. We use the level set method to study the behaviour of the model numerically, and predict a number of distinct phenomena observed in experiments, such as (i) symmetry breaking from the stationary centrosymmetric to the well-known steadily propagating crescent shape, (ii) asymmetric bipedal oscillations and travelling waves in the lamellipodium leading edge, (iii) response to remote mechanical stress externally applied to the substrate (tensotaxis) and (iv) changing direction of motion towards an interface with a rigid substrate (durotaxis).

Microbuckling of fibrin provides a mechanism for cell mechanosensing.

Biological cells sense and respond to mechanical forces, but how such a mechanosensing process takes place in a nonlinear inhomogeneous fibrous matrix remains unknown. We show that cells in a fibrous matrix induce deformation fields that propagate over a longer range than predicted by linear elasticity. Synthetic, linear elastic hydrogels used in many mechanotransduction studies fail to capture this effect. We develop a nonlinear microstructural finite-element model for a fibre network to simulate localized deformations induced by cells. The model captures measured cell-induced matrix displacements from experiments and identifies an important mechanism for long-range cell mechanosensing: loss of compression stiffness owing to microbuckling of individual fibres. We show evidence that cells sense each other through the formation of localized intercellular bands of tensile deformations caused by this mechanism.

Quantifying cell-induced matrix deformation in three dimensions based on imaging matrix fibers.

During processes such as development and cancer metastasis, cells migrate into three-dimensional fibrous matrices. Previous studies have speculated on the mechanical forces required for migration by observing matrix fiber alignment, densification, and degradation, but these forces remain difficult to quantify. Here we present a new experimental technique to simultaneously measure full-field 3D displacements and structural remodeling of a fibrous matrix, both of which result from cellular forces. We apply this "2-in-1" experimental technique to follow single cells as they invade a physiologically relevant fibrin matrix. We find that cells generate tube-like structures in the matrix by plastically deforming their surroundings, and they re-use these tubes to extend protrusions. Cells generate these tubular structures by applying both pulling and pushing forces.

Contractile forces regulate cell division in three-dimensional environments.

Physical forces direct the orientation of the cell division axis for cells cultured on rigid, two-dimensional (2D) substrates. The extent to which physical forces regulate cell division in three-dimensional (3D) environments is not known. Here, we combine live-cell imaging with digital volume correlation to map 3D matrix displacements and identify sites at which cells apply contractile force to the matrix as they divide. Dividing cells embedded in fibrous matrices remained anchored to the matrix by long, thin protrusions. During cell rounding, the cells released adhesive contacts near the cell body while applying tensile forces at the tips of the protrusions to direct the orientation of the cell division axis. After cytokinesis, the daughter cells respread into matrix voids and invaded the matrix while maintaining traction forces at the tips of persistent and newly formed protrusions. Mechanical interactions between cells and the extracellular matrix constitute an important mechanism for regulation of cell division in 3D environments.

Three-dimensional traction force microscopy: a new tool for quantifying cell-matrix interactions.

The interactions between biochemical processes and mechanical signaling play important roles during various cellular processes such as wound healing, embryogenesis, metastasis, and cell migration. While traditional traction force measurements have provided quantitative information about cell matrix interactions in two dimensions, recent studies have shown significant differences in the behavior and morphology of cells when placed in three-dimensional environments. Hence new quantitative experimental techniques are needed to accurately determine cell traction forces in three dimensions. Recently, two approaches both based on laser scanning confocal microscopy have emerged to address this need. This study highlights the details, implementation and advantages of such a three-dimensional imaging methodology with the capability to compute cellular traction forces dynamically during cell migration and locomotion. An application of this newly developed three-dimensional traction force microscopy (3D TFM) technique to single cell migration studies of 3T3 fibroblasts is presented to show that this methodology offers a new quantitative vantage point to investigate the three-dimensional nature of cell-ECM interactions.

Quantifying cellular traction forces in three dimensions.

Cells engage in mechanical force exchange with their extracellular environment through tension generated by the cytoskeleton. A method combining laser scanning confocal microscopy (LSCM) and digital volume correlation (DVC) enables tracking and quantification of cell-mediated deformation of the extracellular matrix in all three spatial dimensions. Time-lapse confocal imaging of migrating 3T3 fibroblasts on fibronectin (FN)-modified polyacrylamide gels of varying thickness reveals significant in-plane (x, y) and normal (z) displacements, and illustrates the extent to which cells, even in nominally two-dimensional (2-D) environments, explore their surroundings in all three dimensions. The magnitudes of the measured displacements are independent of the elastic moduli of the gels. Analysis of the normal displacement profiles suggests that normal forces play important roles even in 2-D cell migration.

Transmission wavefront shearing interferometry for photoelastic materials.

A general analysis and experimental validation of transmission wavefront shearing interferometry for photoelastic materials are presented. These interferometers applied to optically isotropic materials produce a single interference pattern related to one phase term, but when applied to photoelastic materials, they produce the sum of two different interference patterns with phase terms that are the sum and difference, respectively, of two stress-related phase terms. The two stress-related phase terms may be separated using phase shifting and polarization optics. These concepts are experimentally demonstrated using coherent gradient sensing in full field for a compressed polycarbonate plate with a V-shaped notch with good agreement with theoretical data. The analysis may be applied to any wavefront shearing interferometer by modifying parameters describing the wavefront shearing distance.

Self-healing pulse-like shear ruptures in the laboratory.

Models predict that dynamic shear ruptures during earthquake faulting occur as either sliding cracks, where a large section of the interface slides behind a fast-moving rupture front, or self-healing slip pulses, where the fault relocks shortly behind the rupture front. We report experimental visualizations of crack-like, pulse-like, and mixed rupture modes propagating along frictionally held, "incoherent" interfaces separating identical solids, and we describe the conditions under which those modes develop. A combination of simultaneously performed measurements via dynamic photoelasticity and laser interferometry reveals the rupture mode type, the exact point of rupture initiation, the sliding velocity history, and the rupture propagation speed.

Investigation of twin-wall structure at the nanometre scale using atomic force microscopy.

The structure of twin walls and their interaction with defects has important implications for the behaviour of a variety of materials including ferroelectric, ferroelastic, co-elastic and superconducting crystals. Here, we present a method for investigating the structure of twin walls with nanometre-scale resolution. In this method, the surface topography measured using atomic force microscopy is compared with candidate displacement fields, and this allows for the determination of the twin-wall thickness and other structural features. Moreover, analysis of both complete area images and individual line-scan profiles provides essential information about local mechanisms of twin-wall broadening, which cannot be obtained by existing experimental methods. The method is demonstrated in the ferroelectric material PbTiO(3), and it is shown that the accumulation of point defects is responsible for significant broadening of the twin walls. Such defects are of interest because they contribute to the twin-wall kinetics and hysteresis.