Elasticity and glocality: initiation of embryonic inversion in Volvox.

Elastic objects across a wide range of scales deform under local changes of their intrinsic properties, yet the shapes are glocal, set by a complicated balance between local properties and global geometric constraints. Here, we explore this interplay during the inversion process of the green alga Volvox, whose embryos must turn themselves inside out to complete their development. This process has recently been shown to be well described by the deformations of an elastic shell under local variations of its intrinsic curvatures and stretches, although the detailed mechanics of the process have remained unclear. Through a combination of asymptotic analysis and numerical studies of the bifurcation behaviour, we illustrate how appropriate local deformations can overcome global constraints to initiate inversion.We thank Stephanie H¨ohn, Aurelia R. HonerkampSmith and Philipp Khuc Trong for extensive discussions. This work was supported in part by an EPSRC studentship (PAH), an EPSRC Established Career Fellowship (REG), and a Wellcome Trust Senior Investigator Award (REG).This is the final version of the article. It first appeared from Royal Society Publishing via http://dx.doi.org/10.1098/rsif.2015.067

Nonlinear and nonlocal elasticity in coarse-grained differential-tension models of epithelia.

The shapes of epithelial tissues result from a complex interplay of contractile forces in the cytoskeleta of the cells in the tissue and adhesion forces between them. A host of discrete, cell-based models describe these forces by assigning different surface tensions to the apical, basal, and lateral sides of the cells. These differential-tension models have been used to describe the deformations of epithelia in different living systems, but the underlying continuum mechanics at the scale of the epithelium are still unclear. Here, we derive a continuum theory for a simple differential-tension model of a two-dimensional epithelial monolayer and study the buckling of this epithelium under imposed compression. The analysis reveals how the cell-level properties encoded in the differential-tension model lead to linear and nonlinear elastic as well as nonlocal, nonelastic behavior at the continuum level

Turing's Diffusive Threshold in Random Reaction-Diffusion Systems.

Turing instabilities of reaction-diffusion systems can only arise if the diffusivities of the chemical species are sufficiently different. This threshold is unphysical in most systems with N=2 diffusing species, forcing experimental realizations of the instability to rely on fluctuations or additional nondiffusing species. Here, we ask whether this diffusive threshold lowers for N>2 to allow "true" Turing instabilities. Inspired by May's analysis of the stability of random ecological communities, we analyze the probability distribution of the diffusive threshold in reaction-diffusion systems defined by random matrices describing linearized dynamics near a homogeneous fixed point. In the numerically tractable cases N⩽6, we find that the diffusive threshold becomes more likely to be smaller and physical as N increases, and that most of these many-species instabilities cannot be described by reduced models with fewer diffusing species.Gordon and Betty Moore Foundatio

Morphogenesis in space offers challenges and opportunities for soft matter and biophysics

Abstract The effects of microgravity on soft matter morphogenesis have been documented in countless experiments, but physical understanding is still lacking in many cases. Here we review how gravity affects shape emergence and pattern formation for both inert matter and living systems of different biological complexities. We highlight the importance of building physical models for understanding the experimental results available. Answering these fundamental questions will not only solve basic scientific problems, but will also enable several industrial applications relevant to space exploration

Cut it out: Out-of-plane stresses in cell sheet folding of Volvox embryos

The folding of cellular monolayers pervades embryonic development and disease. It results from stresses out of the plane of the tissue, often caused by cell shape changes including cell wedging via apical constriction. These local cellular changes need not however be compatible with the global shape of the tissue. Such geometric incompatibilities lead to residual stresses that have out-of-plane components in curved tissues, but the mechanics and function of these out-of-plane stresses are poorly understood, perhaps because their quantification has proved challenging. Here, we overcome this difficulty by combining laser ablation experiments and a mechanical model to reveal that such out-of-plane residual stresses exist and also persist during the inversion of the spherical embryos of the green alga Volvox. We show how to quantify the mechanical properties of the curved tissue from its unfurling on ablation, and reproduce the tissue shape sequence at different developmental timepoints quantitatively by our mechanical model. Strikingly, this reveals not only clear mechanical signatures of out-of-plane stresses associated with cell shape changes away from those regions where cell wedging bends the tissue, but also indicates an adaptive response of the tissue to these stresses. Our results thus suggest that cell sheet folding is guided mechanically not only by cell wedging, but also by out-of-plane stresses from these additional cell shape changes.Comment: 10 pages, 3 figures; Supporting Information: 10 pages, 2 figure

Impossible ecologies: Interaction networks and stability of coexistence in ecological communities

Does an ecological community allow stable coexistence? Identifying the general principles that determine the answer to this question is a central problem of theoretical ecology. Random matrix theory approaches have uncovered the general trends of the effect of competitive, mutualistic, and predator-prey interactions between species on stability of coexistence. However, an ecological community is determined not only by the counts of these different interaction types, but also by their network arrangement. This cannot be accounted for in a direct statistical description that would enable random matrix theory approaches. Here, we therefore develop a different approach, of exhaustive analysis of small ecological communities, to show that this arrangement of interactions can influence stability of coexistence more than these general trends. We analyse all interaction networks of $N\leqslant 5$ species with Lotka-Volterra dynamics by combining exact results for $N\leqslant 3$ species and numerical exploration. Surprisingly, we find that a very small subset of these networks are "impossible ecologies", in which stable coexistence is non-trivially impossible. We prove that the possibility of stable coexistence in general ecologies is determined by similarly rare "irreducible ecologies". By random sampling of interaction strengths, we then show that the probability of stable coexistence varies over many orders of magnitude even in ecologies that differ only in the network arrangement of identical ecological interactions. Finally, we demonstrate that our approach can reveal the effect of evolutionary or environmental perturbations of the interaction network. Overall, this work reveals the importance of the full structure of the network of interactions for stability of coexistence in ecological communities.Comment: 14 pages, 6 figures, 3 supplementary figure

Shape-Shifting Polyhedral Droplets

Cooled oil emulsion droplets in aqueous surfactant solution have been observed to flatten into a remarkable host of polygonal shapes with straight edges and sharp corners, but different driving mechanisms - (i) a partial phase transition of the liquid bulk oil into a plastic rotator phase near the droplet interface and (ii) buckling of the interfacially frozen surfactant monolayer enabled by drastic lowering of surface tension - have been proposed. Here, combining experiment and theory, we analyse the hitherto unexplored initial stages of the evolution of these 'shape-shifting' droplets, during which a polyhedral droplet flattens into a polygonal platelet under cooling and gravity. Using reflected-light microscopy, we reveal how icosahedral droplets evolve through an intermediate octahedral stage to flatten into hexagonal platelets. This behaviour is reproduced by a theoretical model of the phase transition mechanism, but the buckling mechanism can only reproduce the flattening if surface tension decreases by several orders of magnitude during cooling so that the flattening is driven by buoyancy. The analysis thus provides further evidence that the first mechanism underlies the 'shape-shifting' phenomena.Comment: 11 pages, 12 figure

Histological Correlates of Diffusion-Weighted Magnetic Resonance Microscopy in a Mouse Model of Mesial Temporal Lobe Epilepsy

Mesial temporal lobe epilepsy (MTLE) is the most common type of focal epilepsy. It is frequently associated with abnormal MRI findings, which are caused by underlying cellular, structural, and chemical changes at the micro-scale. In the current study, it is investigated to which extent these alterations correspond to imaging features detected by high resolution magnetic resonance imaging in the intrahippocampal kainate mouse model of MTLE. Fixed hippocampal and whole-brain sections of mouse brain tissue from nine animals under physiological and chronically epileptic conditions were examined using structural and diffusion-weighted MRI. Microstructural details were investigated based on a direct comparison with immunohistochemical analyses of the same specimen. Within the hippocampal formation, diffusion streamlines could be visualized corresponding to dendrites of CA1 pyramidal cells and granule cells, as well as mossy fibers and Schaffer collaterals. Statistically significant changes in diffusivities, fractional anisotropy, and diffusion orientations could be detected in tissue samples from chronically epileptic animals compared to healthy controls, corresponding to microstructural alterations (degeneration of pyramidal cells, dispersion of the granule cell layer, and sprouting of mossy fibers). The diffusion parameters were significantly correlated with histologically determined cell densities. These findings demonstrate that high-resolution diffusion-weighted MRI can resolve subtle microstructural changes in epileptic hippocampal tissue corresponding to histopathological features in MTLE

Corrigendum: Histological Correlates of Diffusion-Weighted Magnetic Resonance Microscopy in a Mouse Model of Mesial Temporal Lobe Epilepsy

In the published article, there were errors in affiliations 2 and 3. Instead of “Experimental Epilepsy Research, Department of Neurosurgery, Medical Center – University of Freiburg, Freiburg, Germany” and “Department Neurosurgery, Experimental Epilepsy Research, Medical Center, University of Freiburg, Freiburg, Germany,” they should be “Faculty of Medicine, University of Freiburg, Freiburg, Germany” and “Experimental Epilepsy Research, Department of Neurosurgery, Medical Center – University of Freiburg, Freiburg, Germany,” respectively. The authors apologize for these errors and state that this does not change the scientific conclusions of the article in any way. The original article has been updated