SUMMARY Little is known about how neutrophils and other cells establish a single zone of actin assembly during migration. A widespread assumption is that the leading edge prevents formation of additional fronts by generating long-range diffusible inhibitors or by sequestering essential polarity components. We use morphological perturbations, cell severing experiments, and computational simulations to show that diffusion-based mechanisms are not sufficient for long-range inhibition by the pseudopod. Instead, plasma membrane tension could serve as a long-range inhibitor in neutrophils. We find that membrane tension doubles during leading edge protrusion, and increasing tension is sufficient for long-range inhibition of actin assembly and Rac activation. Furthermore, reducing membrane tension causes uniform actin assembly. We suggest that tension, rather than diffusible molecules generated or sequestered at the leading edge, is the dominant source of long-range inhibition that constrains the spread of the existing front and prevents the formation of secondary fronts.

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From bone and wood to concrete and carbon fibre, composites are ubiquitous natural and engineering materials. Eshelby's inclusion theory describes how macroscopic stress fields couple to isolated microscopic inclusions, allowing prediction of a composite's bulk mechanical properties from a knowledge of its microstructure. It has been extended to describe a wide variety of phenomena from solid fracture to cell adhesion. Here, we show experimentally and theoretically that Eshelby's theory breaks down for small liquid inclusions in a soft solid. In this limit, an isolated droplet's deformation is strongly size-dependent with the smallest droplets mimicking the behaviour of solid inclusions. Furthermore, in opposition to the predictions of conventional composite theory, we find that finite concentrations of small liquid inclusions enhance the stiffness of soft solids. A straight-forward extension of Eshelby's theory, accounting for the surface tension of the solid-liquid interface, explains our experimental observations. The counterintuitive effect of liquid-stiffening of solids is expected whenever droplet radii are smaller than an elastocapillary length, given by the ratio of the surface tension to Young's modulus of the solid matrix.

Adherent cells, crawling slugs, peeling paint, sessile liquid drops, bearings and many other living and non-living systems apply forces to solid substrates. Traction force microscopy (TFM) provides spatially-resolved measurements of interfacial forces through the quantification and analysis of the deformation of an elastic substrate. Although originally developed for adherent cells, TFM has no inherent size or force scale, and can be applied to a much broader range of mechanical systems across physics and biology. In this paper, we showcase the wide range of applicability of TFM, describe the theory, and provide experimental details and code so that experimentalists can rapidly adopt this powerful technique.

The Johnson-Kendall-Roberts theory is the basis of modern contact mechanics. It describes how two deformable objects adhere together, driven by adhesion energy and opposed by elasticity. Here we characterize the indentation of glass particles into soft, silicone substrates using confocal microscopy. We show that, whereas the Johnson-Kendall-Roberts theory holds for particles larger than a critical, elastocapillary lengthscale, it fails for smaller particles. Instead, adhesion of small particles mimics the adsorption of particles at a fluid interface, with a size-independent contact angle between the undeformed surface and the particle given by a generalized version of the Young's law. A simple theory quantitatively captures this behaviour and explains how solid surface tension dominates elasticity for small-scale indentation of soft materials.