John S. Biggins

Gyrification from constrained cortical expansion

Significance The convolutions of the human brain are a symbol of its functional complexity and correlated with its information-processing capacity. Conversely, loss of folds is correlated with loss of function. But how did the outer surface of the brain, the layered cortex of neuronal gray matter, get its folds? Guided by prior experimental observations of the growth of the cortex relative to the underlying white matter, we argue that these folds arise due to a mechanical instability of a soft tissue that grows nonuniformly. Numerical simulations and physical mimics of the constrained growth of the cortex show how compressive mechanical forces sculpt it to form characteristic sulci and gyri, consistent with observations across species in both normal and pathological situations. The exterior of the mammalian brain—the cerebral cortex—has a conserved layered structure whose thickness varies little across species. However, selection pressures over evolutionary time scales have led to cortices that have a large surface area to volume ratio in some organisms, with the result that the brain is strongly convoluted into sulci and gyri. Here we show that the gyrification can arise as a nonlinear consequence of a simple mechanical instability driven by tangential expansion of the gray matter constrained by the white matter. A physical mimic of the process using a layered swelling gel captures the essence of the mechanism, and numerical simulations of the brain treated as a soft solid lead to the formation of cusped sulci and smooth gyri similar to those in the brain. The resulting gyrification patterns are a function of relative cortical expansion and relative thickness (compared with brain size), and are consistent with observations of a wide range of brains, ranging from smooth to highly convoluted. Furthermore, this dependence on two simple geometric parameters that characterize the brain also allows us to qualitatively explain how variations in these parameters lead to anatomical anomalies in such situations as polymicrogyria, pachygyria, and lissencephalia.

Limited predictive value of blastomere angle of division in trophectoderm and inner cell mass specification

The formation of trophectoderm (TE) and pluripotent inner cell mass (ICM) is one of the earliest events during mammalian embryogenesis. It is believed that the orientation of division of polarised blastomeres in the 8- and 16-cell stage embryo determines the fate of daughter cells, based on how asymmetrically distributed lineage determinants are segregated. To investigate the relationship between angle of division and subsequent fate in unperturbed embryos, we constructed cellular resolution digital representations of the development of mouse embryos from the morula to early blastocyst stage, based on 4D confocal image volumes. We find that at the 16-cell stage, very few inside cells are initially produced as a result of cell division, but that the number increases due to cell movement. Contrary to expectations, outside cells at the 16-cell stage represent a heterogeneous population, with some fated to contributing exclusively to the TE and others capable of contributing to both the TE and ICM. Our data support the view that factors other than the angle of division, such as the position of a blastomere, play a major role in the specification of TE and ICM.

Surface sulci in squeezed soft solids

The squeezing of soft solids, the constrained growth of biological tissues, and the swelling of soft elastic solids such as gels can generate large compressive stresses at their surfaces. This causes the otherwise smooth surface of such a solid to become unstable when its stress exceeds a critical value. Previous analyses of the surface instability have assumed two-dimensional plane-strain conditions, but in experiments isotropic stresses often lead to complex three-dimensional sulcification patterns. Here we show how such diverse morphologies arise by numerically modeling the lateral compression of a rigidly clamped elastic layer. For incompressible solids, close to the instability threshold, sulci appear as I-shaped lines aligned orthogonally with their neighbors; at higher compressions they are Y-shaped and prefer a hexagonal arrangement. In contrast, highly compressible solids when squeezed show only one sulcified phase characterized by a hexagonal sulcus network.

Localized soft elasticity in liquid crystal elastomers

Synthetic approaches to prepare designer materials that localize deformation, by combining rigidity and compliance in a single material, have been widely sought. Bottom-up approaches, such as the self-organization of liquid crystals, offer potential advantages over top–down patterning methods such as photolithographic control of crosslink density, relating to the ease of preparation and fidelity of resolution. Here, we report on the directed self-assembly of materials with spatial and hierarchical variation in mechanical anisotropy. The highly nonlinear mechanical properties of the liquid crystalline elastomers examined here enables strain to be locally reduced >15-fold without introducing compositional variation or other heterogeneities. Each domain (⩾0.01 mm2) exhibits anisotropic nonlinear response to load based on the alignment of the molecular orientation with the loading axis. Accordingly, we design monoliths that localize deformation in uniaxial and biaxial tension, shear, bending and crack propagation, and subsequently demonstrate substrates for globally deformable yet locally stiff electronics.

Elasticity of polydomain liquid crystal elastomers

Liquid crystal elastomers are rubbery networks of entropically dominated polymer chains that exhibit mobile liquid crystalline order. These materials have been of recent interest for the soft behavior (large deformations at relatively small stresses) observed in monodomain specimens where the director is the same at every point in the relaxed elastomer. This paper concerns the soft behavior of polydomain specimens where the director points in different directions at different points in the relaxed elastomer. We show that there is a significant difference between polydomains cross-linked in homogeneous high symmetry states then cooled to low symmetry polydomain states and those cross-linked directly in the low symmetry polydomain state. Specifically, elastomers cross-linked in the isotropic state then cooled to a nematic polydomain will, in the ideal limit, be perfectly soft, and with the introduction of non-ideality, will deform at very low stress until they are macroscopically aligned. In fact, we expect these samples to exhibit elasticity significantly softer than monodomain samples, as has recently been observed by Urayama et al. Further, the director patterns will be fine-scale structures that are macroscopically isotropic and not schlieren textures. In contrast, polydomains cross-linked in the nematic polydomain state will be mechanically harder and contain characteristic schlieren director patterns. The models we use for polydomain elastomers are spatially heterogeneous extensions of the neo-classical soft and semi-soft free energies used successfully to describe monodomain samples. We elucidate the effective behavior by bounding the energies using Taylor-like (compatible test strain fields) and Sachs-like (equilibrated stress field) bounds, both valid to large deformations. Good agreement is found with experiments. We also analyze smectic polydomain elastomers and propose that polydomain SmC* elastomers cross-linked in the SmA monodomain state are promising candidates for low field electrical actuation.

Digital instability of a confined elastic meniscus

Thin soft elastic layers serving as joints between relatively rigid bodies may function as sealants, thermal, electrical, or mechanical insulators, bearings, or adhesives. When such a joint is stressed, even though perfect adhesion is maintained, the exposed free meniscus in the thin elastic layer becomes unstable, leading to the formation of spatially periodic digits of air that invade the elastic layer, reminiscent of viscous fingering in a thin fluid layer. However, the elastic instability is reversible and rate-independent, disappearing when the joint is unstressed. We use theory, experiments, and numerical simulations to show that the transition to the digital state is sudden (first-order), the wavelength and amplitude of the fingers are proportional to the thickness of the elastic layer, and the required separation to trigger the instability is inversely proportional to the in-plane dimension of the layer. Our study reveals the energetic origin of this instability and has implications for the strength of polymeric adhesives; it also suggests a method for patterning thin films reversibly with any arrangement of localized fingers in a digital elastic memory, which we confirm experimentally.

Understanding the chain fountain

If a chain is initially at rest in a beaker at a height h1 above the ground, and the end of the chain is pulled over the rim of the beaker and down towards the ground and then released, the chain will spontaneously ‘flow’ out of the beaker under gravity. Furthermore, the beads do not simply drag over the edge of the beaker but form a fountain reaching a height h2 above it. We show that the formation of a fountain requires that the beads come into motion not only by being pulled upwards by the part of the chain immediately above the pile, but also by being pushed upwards by an anomalous reaction force from the pile of stationary chain. We propose possible origins for this force, argue that its magnitude will be proportional to the square of the chain velocity and predict and verify experimentally that h2∝h1.

Mechanics of invagination and folding: Hybridized instabilities when one soft tissue grows on another.

We address the folding induced by differential growth in soft layered solids via an elementary model that consists of a soft growing neo-Hookean elastic layer adhered to a deep elastic substrate. As the layer-to-substrate modulus ratio is varied from above unity toward zero, we find a first transition from supercritical smooth folding followed by cusping of the valleys to direct subcritical cusped folding, then another to supercritical cusped folding. Beyond threshold, the high-amplitude fold spacing converges to about four layer thicknesses for many modulus ratios. In three dimensions, the instability gives rise to a wide variety of morphologies, including almost degenerate zigzag and triple-junction patterns that can coexist when the layer and substrate are of comparable softness. Our study unifies these results providing understanding for the complex and diverse fold morphologies found in biology, including the zigzag precursors to intestinal villi, and disordered zigzags and triple junctions in mammalian cortex.

Mechanical bistability in liquid crystal elastomer-wire composite actuators

We investigate a design of a composite combining a spontaneously actuating liquid crystal elastomer (LCE) with heating wires embedded directly into the rubbery matrix. We focus on the bistable configuration of wires at a critical angle to actuation direction, which theoretically provides a second energy minimum for wires deforming within an incompressible matrix. Experiments confirm the practicality of the theory when wires are embedded in a soft matrix. For a LCE-wire composite, the critical angle depends on the intrinsic actuation amplitude of its component LCE layers. It is further demonstrated for a side-chain LCE, an actuation stroke of ∼35% contraction was possible with a double-layer stacking design, while a triple-layer design showed a contracting stroke of ∼25%. Finally, we examine the dynamics of actuation and estimate the performance limit of a generic heat-stimulated LCE composite actuator in terms of its power efficiency and response time.

Towards understanding the roles of position and geometry on cell fate decisions during preimplantation development.

The first lineage segregation event in mouse embryos produces two separate cell populations: inner cell mass and trophectoderm. This is understood to be brought about by cells sensing their position within the embryo and differentiating accordingly. The cellular and molecular underpinnings of this process remain under investigation and have variously been considered to be completely stochastic or alternately, subject to some predisposition set up at fertilisation or before. Here, we consider these views in light of recent publications, discuss the possible role of cell geometry and mechanical forces in this process and describe how modelling could contribute in addressing this issue.