Mechanics of human brain organoids

Local Mechanical Modulation-Driven Evagination in Invaginated Epithelia

Local cells can actively create reverse bending (evagination) in invaginated epithelia, which plays a crucial role in the formation of elaborate organisms. However, the precise physical mechanism driving the evagination remains elusive. Here, we present a three-dimensional vertex model, incorporating the intrinsic cell polarity, to explore the complex morphogenesis induced by local mechanical modulations. We find that invaginated tissues can spontaneously generate local reverse bending due to the shift of the apicobasal polarity. Their exact shapes can be analytically determined by the local apicobasal differential tension and the internal stress. Our continuum theory exhibits three regions in a phase diagram controlled by these two parameters, showing curvature transitions from ordered to disordered states. Additionally, we delve into epithelial curvature transition induced by the nucleus repositioning, revealing its active contribution to the apicobasal force generation. The uncovered mechanical principles could potentially guide more studies on epithelial folding in diverse systems.

Wrinkling Instability in Unsupported Epithelial Sheets

We investigate the elasticity of an unsupported epithelial monolayer and we discover that unlike a thin solid plate, which wrinkles if geometrically incompatible with the underlying substrate, the epithelium may do so even in the absence of the substrate. From a cell-based model, we derive an exact elasticity theory and discover wrinkling driven by the differential apico-basal surface tension. Our theory is mapped onto that for supported plates by introducing a phantom substrate whose stiffness is finite beyond a critical differential tension. This suggests a new mechanism for an autonomous control of tissues over the length scale of their surface patterns.

Retina organoids: Window into the biophysics of neuronal systems

With a kind of magnetism, the human retina draws the eye of neuroscientist and physicist alike. It is attractive as a self-organizing system, which forms as a part of the central nervous system via biochemical and mechanical cues. The retina is also intriguing as an electro-optical device, converting photons into voltages to perform on-the-fly filtering before the signals are sent to our brain. Here, we consider how the advent of stem cell derived in vitro analogs of the retina, termed retina organoids, opens up an exploration of the interplay between optics, electrics, and mechanics in a complex neuronal network, all in a Petri dish. This review presents state-of-the-art retina organoid protocols by emphasizing links to the biochemical and mechanical signals of in vivo retinogenesis. Electrophysiological recording of active signal processing becomes possible as retina organoids generate light sensitive and synaptically connected photoreceptors. Experimental biophysical tools provide data to steer the development of mathematical models operating at different levels of coarse-graining. In concert, they provide a means to study how mechanical factors guide retina self-assembly. In turn, this understanding informs the engineering of mechanical signals required to tailor the growth of neuronal network morphology. Tackling the complex developmental and computational processes in the retina requires an interdisciplinary endeavor combining experiment and theory, physics, and biology. The reward is enticing: in the next few years, retina organoids could offer a glimpse inside the machinery of simultaneous cellular self-assembly and signal processing, all in an in vitro setting.

Activity-induced instabilities of brain organoids

We present an analytical and numerical investigation of the activity-induced hydrodynamic instabilities in model brain organoids. While several mechanisms have been introduced to explain the experimental observation of surface instabilities in brain organoids, the role of activity has been largely overlooked. Our results show that the active stress generated by the cells can be a, previously overlooked, contributor to the emergence of surface deformations in brain organoids.

Post-bifurcation behaviour of elasto-capillary necking and bulging in soft tubes

Previous linear bifurcation analyses have evidenced that an axially stretched soft cylindrical tube may develop an infinite-wavelength (localized) instability when one or both of its lateral surfaces are under sufficient surface tension. Phase transition interpretations have also highlighted that the tube admits a final evolved ‘two-phase’ state. How the localized instability initiates and evolves into the final ‘two-phase’ state is still a matter of contention, and this is the focus of the current study. Through a weakly nonlinear analysis conducted for a general material model, the initial sub-critical bifurcation solution is found to be localized bulging or necking depending on whether the axial stretch is greater or less than a certain threshold value. At this threshold value, an exceptionally super-critical kink-wave solution arises in place of localization. A thorough interpretation of the anticipated post-bifurcation behaviour based on our theoretical results is also given, and this is supported by finite-element method simulations.

Influence of the growth gradient on surface wrinkling and pattern transition in growing tubular tissues

Growth-induced pattern formations in curved film-substrate structures have attracted extensive attention recently. In most existing literature, the growth tensor is assumed to be homogeneous or piecewise homogeneous. In this paper, we aim at clarifying the influence of a growth gradient on pattern formation and pattern evolution in bilayered tubular tissues under plane-strain deformation. In the framework of finite elasticity, a bifurcation condition is derived for a general material model and a generic growth function. Then we suppose that both layers are composed of neo-Hookean materials. In particular, the growth function is assumed to decay linearly either from the inner surface or from the outer surface. It is found that a gradient in the growth has a weak effect on the critical state, compared with the homogeneous growth type where both layers share the same growth factor. Furthermore, a finite-element model is built to validate the theoretical model and to investigate the post-buckling behaviours. It is found that the associated pattern transition is not controlled by the growth gradient but by the ratio of the shear modulus between two layers. Different morphologies can occur when the modulus ratio is varied. The current analysis could provide useful insight into the influence of a growth gradient on surface instabilities and suggests that a homogeneous growth field may provide a good approximation on interpreting complicated morphological formations in multiple systems.

Active elasticity drives the formation of periodic beading in damaged axons

In several pathological conditions, such as coronavirus infections, multiple sclerosis, Alzheimer's and Parkinson's diseases, the physiological shape of axons is altered and a periodic sequence of bulges appears. Experimental evidences suggest that such morphological changes are caused by the disruption of the microtubules composing the cytoskeleton of the axon. In this paper, we develop a mathematical model of damaged axons based on the theory of continuum mechanics and nonlinear elasticity. The axon is described as a cylinder composed of an inner passive part, called axoplasm, and an outer active cortex, composed mainly of F-actin and able to contract thanks to myosin-II motors. Through a linear stability analysis we show that, as the shear modulus of the axoplasm diminishes due to the disruption of the cytoskeleton, the active contraction of the cortex makes the cylindrical configuration unstable to axisymmetric perturbations, leading to a beading pattern. Finally, the nonlinear evolution of the bifurcated branches is investigated through finite element simulations.

Physical principles of morphogenesis in mushrooms

Mushroom species display distinctive morphogenetic features. For example, Amanita muscaria and Mycena chlorophos grow in a similar manner, their caps expanding outward quickly and then turning upward. However, only the latter finally develops a central depression in the cap. Here we use a mathematical approach unraveling the interplay between physics and biology driving the emergence of these two different morphologies. The proposed growth elastic model is solved analytically, mapping their shape evolution over time. Even if biological processes in both species make their caps grow turning upward, different physical factors result in different shapes. In fact, we show how for the relatively tall and big A. muscaria a central depression may be incompatible with the physical need to maintain stability against the wind. In contrast, the relatively short and small M. chlorophos is elastically stable with respect to environmental perturbations; thus, it may physically select a central depression to maximize the cap volume and the spore exposure. This work gives fully explicit analytic solutions highlighting the effect of the growth parameters on the morphological evolution, providing useful insights for novel bio-inspired material design.