Session A66: Morphogenesis I

The life cycle of the human brain: From morphogenesis to aging

TBD   

Hierarchical “buckling without bending” and cerebellar shape

While studies of brain shape development have focused on the cerebrum, the cerebellum, otherwise known as the little brain, typically houses more neurons than the cerebrum. Mammalian cerebella have 8-10 primary lobes which subsequently branch into smaller lobes. Recently, a “buckling without bending” model has been introduced to quantify the onset of shape change in the developing cerebellum and other brain organs/organoids. It consists of an inner incompressible core of cells and an outer fluid-like cortical layer of dividing cells encased by a pia membrane. Additionally, there are two types of fibrous cells - ones spanning the cerebellum and ones spanning the cortical layer. The onset of shape change is a consequence of mechanical constraints on the outer fluid-like cortical layer as it proliferates. Predictions of the model have been recently supported by experimental studies of the developing mouse cerebellum. Here, we generalize the model beyond the onset of shape change to predict shape development at later stages. We implement a hierarchical version of the above model to predict subsequent branching of the smaller lobes. Predictions are compared with various mammalian cerebella exhibiting varied counts of branching generations.   

Wrinkles on Tori

Wrinkling patterns in soft materials have been extensively studied due to their important roles in determining surface morphologies in biological structures and developing multifunctional devices. Most existing work focuses on relatively simple geometries, such as flat structures and curved structures with constant curvature such as the cylinder and 2-sphere. In this talk we discuss wrinkling patterns on a torus, the Gaussian and mean curvatures of which vary along the poloidal direction. We observe eight different wrinkling patterns from large-scale finite element simulations and construct a phase diagram for these patterns. We further show that the non-uniform curvature and anisotropic deformation play critical roles in determining the formation and evolution of these wrinkling patterns. The anisotropic deformation along the toroidal and poloidal directions controls pattern transitions from stripes to hexagons and the non-uniform curvatures determine the nucleation sites of the wrinkling patterns. Our results show that global deformations of a torus lead to strong coupling between elasticity and curvature which may enlarge the design space as well as the dynamically control of wrinkling patterns.
  

Pattern formation in elastic bilayer systems through substrate pre-stretching

Compressing a thin film bonded to an elastic substrate beyond a critical stress results in an elastic instability, often referred to as wrinkling or ruga, that generates complex surface deformation. Although the best-known example is the sinusoidal wrinkling that appears under uni-axial compression of the film, other loading conditions and actuation mechanisms result in a diverse range of self-organized patterns. We will present experiments in which the substrate is pre-stretched prior to the adhesion of the film, which when released results in film compression. We will show that with only moderate variations in the system and control parameters we can transition between a wide range of patterns, with a well-defined phase diagram spanning periodic wrinkles, creases, folds, and high aspect ratio ridges. We will also explore the dynamics that control the pattern formation, as well as the effect of repeated unloading and reloading, in an effort to rationalize how the specific details of the pattern are determined.   

Mechanical Principles Underlying Development of Bacterial Biofilm Morphology

Surface-attached bacterial communities called biofilms display diverse morphologies. Our recent experiments demonstrated that growth-induced mechanical instabilities – including wrinkling and delamination – underlie the morphogenesis program of biofilms growing at the air-solid interface, and determine the characteristic wavelength of surface undulations. Yet, how the interplay between mechanics and biofilm growth determines colony expansion and morphogenesis remains unclear. Here, we define the physical mechanism underlying biofilm mechano-morphogenesis by combining microscopic and continuum models. We show that surface friction affects the thickness and edge propagation angle of colony biofilms. Moreover, this friction, along with a non-uniform pattern of growth due to nutrient depletion at the biofilm center, gives rise to anisotropic stress patterns. Interestingly, we also find that the combination of active exponential growth near the edge and linear increase of contour length contributes to a constant accumulation of tangential stress. This residual stress can be relaxed by subsequent mechanical instabilities. Finally, we propose a coarse-grained model to characterize the post-wrinkling/delamination expansion of biofilms.   

Mechanical Feedback in Gut Looping

The midgut of most organisms consists of a long coiled tube that is dorsally attached to a thin sheet called the mesentery. Previous work has established that the physical foundations of the looping patterns arise from the differential growth between the gut tube and the mesentery in the context of their respective geometric and elastic properties, and that these looping patterns are evolutionarily modulated, at least in part, through species-specific variation in BMP2 levels, affecting the growth rates within the developing mesentey. However, how BMP2 signaling itself is modulated in an endogeneous setting remains unknown. We explore the possibility that tension in the mesentery feedbacks onto the tissue to regulate levels of BMP2, thereby controlling looping morphogenesis, using in-ovo and explant experiments. Quantifying this idea closes the feedback loop linking molecular signaling and gut morphogenesis in the chick embryo, and suggests an evolutionary pathway for exploring gut looping across organisms at a mechanistic level.   

Modeling bio-inspired morphing mechanisms in hydrogel micro capsules

We study changes in shape and size triggered by external stimuli in structures made of soft active materials. In particular, we consider morphing mechanisms driven by hydration and dehydration processes in capsule-like bodies which can hydrate and dehydrate causing the lateral collapse of the capsule body and the change of shape of the capsule. Typical examples come from Nature. In fern sporangium, the cells in the crest to one side of a spherical capsule enclosing the spores lose water by evaporation, so determining tension building up within them, and lateral walls collapsing internally [1,2]. In Sphagnum Moss, dehydration of the capsules cause them to change shape from spherical to cylindrical and to increase the internal air pressure [3].

In both the examples, the coupling between the dehydration process and the change in internal pressure determines a fast mechanism which allows to realize spore dispersal.

The goal of our study is to identify the mechanical determinants of the mechanism and investigate the role of the key geometrical and material parameters.


[1] X. Noblin et al., Science, 2012, 335, 1322.
[2] M. Curatolo et al., Soft Matter 14, 2310–2321, 2018.
[3] Dwight L. Whitake and Joan Edwards, Science, 329, 2010   

Stress-Free Morphing

We study the morphing of soft materials within the framework of non-linear elasticity with large distortions: a distortion field induces a target metric, and the configuration which is effectively realized by a body is the one that minimizes the distance, measured through the elastic energy, between the target metric and the actual one.

Deformations due to distortions, in contrast to those generated by forces, can have a peculiar feature: they can be stress-free; if this is the case, the distortions field is called compatible.

We maintain that the morphing through compatible distortions is a key strategy exploited by many soft biological materials, which can exhibit very large shape-change in response to distortions controlled by chemicals or by temperature changes, while keeping their stress state almost null.

Thus, the study of compatible distortions, and of the related shape-changes, is quite important. Here, we show how the notions of metric tensor and of Riemannian curvature can be used to assess the compatibility of a distortion field.

  

Modeling hemodynamic fluctuations: the brain vasculature as an excitable network

Multiple studies have examined blood oxygen level dependent (BOLD) signals of functional magnetic resonance imaging (fMRI) showing spontaneous fluctuations when the brain is at rest, sleeping or even anesthetized. These fluctuations are found at lower frequencies (around 0.1 Hz) than respiratory or cardiac functions. In addition, recent experimental works seem to rule out their relation with neural activity, suggesting a non-neural origin.

We propose a minimal model for microcirculation that only assumes a nonlinear relation between the current supported by each vessel and the pressure drop between its starting and final nodes, and a dispersive relation for volume accumulation. This simple approach qualitative reproduces the main characteristics of the observed behavior. The fluctuations emerge spontaneously under constant boundary conditions as self-sustained oscillations, forming different patterns depending on the topology of the network.

We expect that this model can shed light on the nature of spontaneous fluctuations on brain vasculature and its interplay with the properties of the network. Finally, the simplicity of the model makes it suitable for its use with different nonlinear flow networks exhibiting complex dynamical behavior.   

A simple developmental model recapitualtes complex insect wing veination patterns (A wingkle in time)

Geometric patterns in nature have long been a matter of fascination and intrigue. Veins bifurcate insect wings into a diverse and complicated menagerie of shapes. For many insect species, even the left and right wings from the same individual have veins with unique topological arrangements, and little is known about how these patterns form. We present a quantitative study of the fingerprint-like “secondary veins.” We compile a dataset of wings from 232 species and 17 families from the order Odonata (dragonflies and damselflies), a group with particularly elaborate vein patterns. We characterize the geometric arrangements of veins and develop a simple model of secondary vein patterning. Last, we show that our model is capable of recapitulating the vein geometries of species from other, distantly related winged insect clades.   

Self-organization of tubular networks by fluid flows

Long-ranged dynamic patterns are important for development and functioning of large-scale organisms. In the tubular networks of plasmodial slime molds the tubes’ periodic contractions organize in a traveling wave on scales of up to several centimeters. What drives communication across the network? What drives the self-organization of the tube’s cortex to form long-wavelength patterns? Searching for the mechanism of signal propagation we find that flows are hijacked by signals to propagate through the network. Signals promote their own transport by invoking a propagating front of increased flow. This mechanism is sufficient to explain complex dynamics of the organism like finding the shortest path through a maze. Importantly, we find that distant parts within the tubular network communicate by fluid flow. We investigate the mechanism behind the self-sustained contractile waves by developing a minimal model, coupling the mechanics of a cell’s cortex to a contraction-triggering chemical. The chemical itself is spread with the fluid flows that arise due to the cortex contractions. Through theoretical and numerical analysis, we find that the oscillatory component of the flows can give rise to robust scaling of contraction waves with system size—much beyond predicted length scales.   

Patterned smooth muscle constrains and constricts the airway epithelium during branching morphogenesis

During branching morphogenesis, a simple tube of cells gives rise to an arborized epithelial network. In the mouse lung, the airway epithelium develops concomitantly with a layer of smooth muscle, which is derived from the surrounding mesenchyme and wraps circumferentially around the airways. We examined the role of smooth muscle in shaping domain branches that establish the underlying architecture of the lung. We found that branches begin as wide buds that thin at their bases as they extend. At the same time, there is an increase in the amount of smooth muscle wrapped around the parent bronchus at the base of each nascent domain branch. Perturbing the pattern of smooth muscle differentiation causes abnormal epithelial branching. Loss of smooth muscle results in ectopic branching events and slows branch thinning. Enhanced smooth muscle differentiation suppresses branch initiation and extension. Combining experiments with computational modeling revealed that patterned smooth muscle wrapping constrains and constricts the growing epithelium to properly position and physically sculpt domain branches.
  

Smooth Muscle Mechanically Sculpts the Airway Epithelium in Birds and Reptiles

The reptilian lung, with its basic sac-like structure, is considered to be the most evolutionarily basic among amniotes. In comparison, mammalian and avian lungs are much more complex and finely branched. Smooth muscle (SM) is required for branching in the early mouse lung but to date this tissue remains uninvestigated in other amniotes. The respiratory system of birds contains a network of connected airways that begin as terminal structures but fuse as embryonic development progresses. We found that prior to airway fusion in the domestic chicken, Gallus gallus, the airways initiate branches in the direction of their target, which will make the first contact. These new branches occur in regions devoid of SM, implying a role for it in shaping the airway epithelium prior to fusion. We have also examined early development of reptile lungs using the brown anole, Anolis sagrei, as a model organism and found that SM is present in a mesh-like arrangement and regulated by the same signaling pathways as in the murine lung. Contraction of SM defines the shape of the epithelium. Despite the fact that the tissue forms at different periods in development and in varying patterns, these data suggest an evolutionarily conserved mechanism for SM as a physical force in airway morphogenesis.