Analytical method for reconstructing the stress on a spherical particle from its surface deformation.

The mechanical forces that cells experience from the tissue surrounding them are crucial for their behavior and development. Experimental studies of such mechanical forces require a method for measuring them. A widely used approach in this context is bead deformation analysis, where spherical particles are embedded into the tissue. The deformation of the particles then allows to reconstruct the mechanical stress acting on them. Existing approaches for this reconstruction are either very time-consuming or not sufficiently general. In this article, we present an analytical approach to this problem based on an expansion in solid spherical harmonics that allows us to find the complete stress tensor describing the stress acting on the tissue. Our approach is based on the linear theory of elasticity and uses an ansatz specifically designed for deformed spherical bodies. We clarify the conditions under which this ansatz can be used, making our results useful also for other contexts in which this ansatz is employed. Our method can be applied to arbitrary radial particle deformations and requires a very low computational effort. The usefulness of the method is demonstrated by an application to experimental data.

Global and local tension measurements in biomimetic skeletal muscle tissues reveals early mechanical homeostasis.

Tension and mechanical properties of muscle tissue are tightly related to proper skeletal muscle function, which makes experimental access to the biomechanics of muscle tissue formation a key requirement to advance our understanding of muscle function and development. Recently developed elastic in vitro culture chambers allow for raising 3D muscle tissue under controlled conditions and to measure global tissue force generation. However, these chambers are inherently incompatible with high-resolution microscopy limiting their usability to global force measurements, and preventing the exploitation of modern fluorescence based investigation methods for live and dynamic measurements. Here, we present a new chamber design pairing global force measurements, quantified from post-deflection, with local tension measurements obtained from elastic hydrogel beads embedded in muscle tissue. High-resolution 3D video microscopy of engineered muscle formation, enabled by the new chamber, shows an early mechanical tissue homeostasis that remains stable in spite of continued myotube maturation.

Cortical cell stiffness is independent of substrate mechanics.

Cortical stiffness is an important cellular property that changes during migration, adhesion and growth. Previous atomic force microscopy (AFM) indentation measurements of cells cultured on deformable substrates have suggested that cells adapt their stiffness to that of their surroundings. Here we show that the force applied by AFM to a cell results in a significant deformation of the underlying substrate if this substrate is softer than the cell. This 'soft substrate effect' leads to an underestimation of a cell's elastic modulus when analysing data using a standard Hertz model, as confirmed by finite element modelling and AFM measurements of calibrated polyacrylamide beads, microglial cells and fibroblasts. To account for this substrate deformation, we developed a 'composite cell-substrate model'. Correcting for the substrate indentation revealed that cortical cell stiffness is largely independent of substrate mechanics, which has major implications for our interpretation of many physiological and pathological processes.

Collective Cell Migration in Embryogenesis Follows the Laws of Wetting.

Collective cell migration is a fundamental process during embryogenesis and its initial occurrence, called epiboly, is an excellent in vivo model to study the physical processes involved in collective cell movements that are key to understanding organ formation, cancer invasion, and wound healing. In zebrafish, epiboly starts with a cluster of cells at one pole of the spherical embryo. These cells are actively spreading in a continuous movement toward its other pole until they fully cover the yolk. Inspired by the physics of wetting, we determine the contact angle between the cells and the yolk during epiboly. By choosing a wetting approach, the relevant scale for this investigation is the tissue level, which is in contrast to other recent work. Similar to the case of a liquid drop on a surface, one observes three interfaces that carry mechanical tension. Assuming that interfacial force balance holds during the quasi-static spreading process, we employ the physics of wetting to predict the temporal change of the contact angle. Although the experimental values vary dramatically, the model allows us to rescale all measured contact-angle dynamics onto a single master curve explaining the collective cell movement. Thus, we describe the fundamental and complex developmental mechanism at the onset of embryogenesis by only three main parameters: the offset tension strength, α, that gives the strength of interfacial tension compared to other force-generating mechanisms; the tension ratio, δ, between the different interfaces; and the rate of tension variation, λ, which determines the timescale of the whole process.