Theory of branching morphogenesis by local interactions and global guidance

A biomimetic branching signal-passing tile assembly model with dynamic growth and disassembly

Natural biological branching processes can form tree-like structures at all scales and, moreover, can perform various functions to achieve specific goals; these include receiving stimuli, performing two-way communication along their branches, and dynamically reforming (extending or retracting branches). They underlie many biological systems with considerable diversity, frequency, and geometric complexity; these include networks of neurons, organ tissue, mycorrhizal fungal networks, plant growth, foraging networks, etc. This paper presents a biomimetic DNA tile assembly model (Y-STAM) to implement dynamic branching processes. The Y-STAM is a relatively compact mathematical model providing a design space where complex, biomimetic branch-like growth and behaviour can emerge from the appropriate parametrization of the model. We also introduce a class of augmented models (Y-STAM+) that provide time- and space-dependent modulations of tile glue strengths, which enable further diverse behaviours that are not possible in the Y-STAM; these additional behaviours include refinement of network assemblies, obstacle avoidance, and programmable growth patterns. We perform and discuss extensive simulations of the Y-STAM and the Y-STAM+. We envision that these models could be applied at the mesoscale and the molecular scale to dynamically assemble branching DNA nanostructures and offer insights into complex biological self-assembly processes.

Multilevel neurium-mimetic individualized graft via additive manufacturing for efficient tissue repair

Complicated peripheral nerve injuries or defects, especially at branching sites, remain a prominent clinical challenge after the application of different treatment strategies. Current nerve grafts fail to match the expected shape and size for delicate and precise branched nerve repair on a case-by-case basis, and there is a lack of geometrical and microscale regenerative navigation. In this study, we develop a sugar painting-inspired individualized multilevel epi-/peri-/endoneurium-mimetic device (SpinMed) to customize natural cues, featuring a selectively protective outer sheath and an instructive core, to support rapid vascular reconstruction and consequent efficient neurite extension along the defect area. The biomimetic perineurium dictates host-guest crosslinking in which new vessels secrete multimerin 1 binding to the fibroin filler surface as an anchor, contributing to the biological endoneurium that promotes Schwann cell homing and remyelination. SpinMed implantation into rat sciatic nerve defects yields a satisfactory outcome in terms of structural reconstruction, with sensory and locomotive function restoration. We further customize SpinMed grafts based on anatomy and digital imaging, achieving rapid repair of the nerve trunk and branches superior to that achieved by autografts and decellularized grafts in a specific beagle nerve defect model, with reliable biosafety. Overall, this intelligent art-inspired biomimetic design offers a facile way to customize sophisticated high-performance nerve grafts and holds great potential for application in translational regenerative medicine.

Mechanism of branching morphogenesis inspired by diatom silica formation

The silica-based cell walls of diatoms are prime examples of genetically controlled, species-specific mineral architectures. The physical principles underlying morphogenesis of their hierarchically structured silica patterns are not understood, yet such insight could indicate novel routes toward synthesizing functional inorganic materials. Recent advances in imaging nascent diatom silica allow rationalizing possible mechanisms of their pattern formation. Here, we combine theory and experiments on the model diatom Thalassiosira pseudonana to put forward a minimal model of branched rib patterns-a fundamental feature of the silica cell wall. We quantitatively recapitulate the time course of rib pattern morphogenesis by accounting for silica biochemistry with autocatalytic formation of diffusible silica precursors followed by conversion into solid silica. We propose that silica deposition releases an inhibitor that slows down up-stream precursor conversion, thereby implementing a self-replicating reaction-diffusion system different from a classical Turing mechanism. The proposed mechanism highlights the role of geometrical cues for guided self-organization, rationalizing the instructive role for the single initial pattern seed known as the primary silicification site. The mechanism of branching morphogenesis that we characterize here is possibly generic and may apply also in other biological systems.

Long-term day-by-day tracking of microvascular networks sprouting in fibrin gels: From detailed morphological analyses to general growth rules

Understanding and controlling of the evolution of sprouting vascular networks remains one of the basic challenges in tissue engineering. Previous studies on the vascularization dynamics have typically focused only on the phase of intense growth and often lacked spatial control over the initial cell arrangement. Here, we perform long-term day-by-day analysis of tens of isolated microvasculatures sprouting from endothelial cell-coated spherical beads embedded in an external fibrin gel. We systematically study the topological evolution of the sprouting networks over their whole lifespan, i.e., for at least 14 days. We develop a custom image analysis toolkit and quantify (i) the overall length and area of the sprouts, (ii) the distributions of segment lengths and branching angles, and (iii) the average number of branch generations-a measure of network complexity. We show that higher concentrations of vascular endothelial growth factor (VEGF) lead to earlier sprouting and more branched networks, yet without significantly affecting the speed of growth of individual sprouts. We find that the mean branching angle is weakly dependent on VEGF and typically in the range of 60°-75°, suggesting that, by comparison with the available diffusion-limited growth models, the bifurcating tips tend to follow local VEGF gradients. At high VEGF concentrations, we observe exponential distributions of segment lengths, which signify purely stochastic branching. Our results-due to their high statistical relevance-may serve as a benchmark for predictive models, while our new image analysis toolkit, offering unique features and high speed of operation, could be exploited in future angiogenic drug tests.

Single-neuron analysis of axon arbors reveals distinct presynaptic organizations between feedforward and feedback projections

The morphology and spatial distribution of axon arbors and boutons are crucial for neuron presynaptic functions. However, the principles governing their whole-brain organization at the single-neuron level remain unclear. We developed a machine-learning method to separate axon arbors from passing axons in single-neuron reconstruction from fluorescence micro-optical sectioning tomography imaging data and obtained 62,374 axon arbors that displayed distinct morphology, spatial patterns, and scaling laws dependent on neuron types and targeted brain areas. Focusing on the axon arbors in the thalamus and cortex, we revealed the segregated spatial distributions and distinct morphology but shared topographic gradients between feedforward and feedback projections. Furthermore, we uncovered an association between arbor complexity and microglia density. Finally, we found that the boutons on terminal arbors show branch-specific clustering with a log-normal distribution that again differed between feedforward and feedback terminal arbors. Together, our study revealed distinct presynaptic structural organizations underlying diverse functional innervation of single projection neurons.

Fourteenth Annual ENBDC Workshop: Methods in Mammary Gland Biology and Breast Cancer

The fourteenth annual workshop of the European Network for Breast Development and Cancer (ENBDC) on Methods in Mammary Gland Biology and Breast Cancer was held on April 26th - 29th in Weggis, Switzerland. For the first time, early career researchers organised and took part in an additional ECR workshop on the 26th of April, which was received with great enthusiasm. The topics of the main workshop included mammary branching and morphogenesis, novel experimental systems (model organisms), systemic influences on tumour progression and the tumour microenvironment. Novel and recent findings were shared across excellent oral and poster presentations.

Self-organized and directed branching results in optimal coverage in developing dermal lymphatic networks

Branching morphogenesis is a ubiquitous process that gives rise to high exchange surfaces in the vasculature and epithelial organs. Lymphatic capillaries form branched networks, which play a key role in the circulation of tissue fluid and immune cells. Although mouse models and correlative patient data indicate that the lymphatic capillary density directly correlates with functional output, i.e., tissue fluid drainage and trafficking efficiency of dendritic cells, the mechanisms ensuring efficient tissue coverage remain poorly understood. Here, we use the mouse ear pinna lymphatic vessel network as a model system and combine lineage-tracing, genetic perturbations, whole-organ reconstructions and theoretical modeling to show that the dermal lymphatic capillaries tile space in an optimal, space-filling manner. This coverage is achieved by two complementary mechanisms: initial tissue invasion provides a non-optimal global scaffold via self-organized branching morphogenesis, while VEGF-C dependent side-branching from existing capillaries rapidly optimizes local coverage by directionally targeting low-density regions. With these two ingredients, we show that a minimal biophysical model can reproduce quantitatively whole-network reconstructions, across development and perturbations. Our results show that lymphatic capillary networks can exploit local self-organizing mechanisms to achieve tissue-scale optimization.

Models of Purkinje cell dendritic tree selection during early cerebellar development

We investigate the relationship between primary dendrite selection of Purkinje cells and migration of their presynaptic partner granule cells during early cerebellar development. During postnatal development, each Purkinje cell grows more than three dendritic trees, from which a primary tree is selected for development, whereas the others completely retract. Experimental studies suggest that this selection process is coordinated by physical and synaptic interactions with granule cells, which undergo a massive migration at the same time. However, technical limitations hinder continuous experimental observation of multiple cell populations. To explore possible mechanisms underlying this selection process, we constructed a computational model using a new computational framework, NeuroDevSim. The study presents the first computational model that simultaneously simulates Purkinje cell growth and the dynamics of granule cell migrations during the first two postnatal weeks, allowing exploration of the role of physical and synaptic interactions upon dendritic selection. The model suggests that interaction with parallel fibers is important to establish the distinct planar morphology of Purkinje cell dendrites. Specific rules to select which dendritic trees to keep or retract result in larger winner trees with more synaptic contacts than using random selection. A rule based on afferent synaptic activity was less effective than rules based on dendritic size or numbers of synapses.

Inflationary theory of branching morphogenesis in the mouse salivary gland

The mechanisms that regulate the patterning of branched epithelia remain a subject of long-standing debate. Recently, it has been proposed that the statistical organization of multiple ductal tissues can be explained through a local self-organizing principle based on the branching-annihilating random walk (BARW) in which proliferating tips drive a process of ductal elongation and stochastic bifurcation that terminates when tips encounter maturing ducts. Here, applied to mouse salivary gland, we show the BARW model struggles to explain the large-scale organization of tissue. Instead, we propose that the gland develops as a tip-driven branching-delayed random walk (BDRW). In this framework, a generalization of the BARW, tips inhibited through steric interaction with proximate ducts may continue their branching program as constraints become alleviated through the persistent expansion of the surrounding tissue. This inflationary BDRW model presents a general paradigm for branching morphogenesis when the ductal epithelium grows cooperatively with the domain into which it expands.

Hydrogel-in-hydrogel live bioprinting for guidance and control of organoids and organotypic cultures

Three-dimensional hydrogel-based organ-like cultures can be applied to study development, regeneration, and disease in vitro. However, the control of engineered hydrogel composition, mechanical properties and geometrical constraints tends to be restricted to the initial time of fabrication. Modulation of hydrogel characteristics over time and according to culture evolution is often not possible. Here, we overcome these limitations by developing a hydrogel-in-hydrogel live bioprinting approach that enables the dynamic fabrication of instructive hydrogel elements within pre-existing hydrogel-based organ-like cultures. This can be achieved by crosslinking photosensitive hydrogels via two-photon absorption at any time during culture. We show that instructive hydrogels guide neural axon directionality in growing organotypic spinal cords, and that hydrogel geometry and mechanical properties control differential cell migration in developing cancer organoids. Finally, we show that hydrogel constraints promote cell polarity in liver organoids, guide small intestinal organoid morphogenesis and control lung tip bifurcation according to the hydrogel composition and shape.

Brain-wide dendrites in a near-optimal performance of dynamic range and information transmission

Dendrites receive and process signals from other neurons. The range of signal intensities that can be robustly distinguished by dendrites is quantified by the dynamic range. We investigate the dynamic range and information transmission efficiency of dendrites in relation to dendritic morphology. We model dendrites in a neuron as multiple excitable binary trees connected to the soma where each node in a tree can be excited by external stimulus or by receiving signals transmitted from adjacent excited nodes. It has been known that larger dendritic trees have a higher dynamic range. We show that for dendritic tress of the same number of nodes, the dynamic range increases with the number of somatic branches and decreases with the asymmetry of dendrites, and the information transmission is more efficient for dendrites with more somatic branches. Moreover, our simulated data suggest that there is an exponential association (decay resp.) of overall relative energy consumption (dynamic range resp.) in relation to the number of somatic branches. This indicates that further increasing the number of somatic branches (e.g. beyond 10 somatic branches) has limited ability to improve the transmission efficiency. With brain-wide neuron digital reconstructions of the pyramidal cells, 90% of neurons have no more than 10 dendrites. These suggest that actual brain-wide dendritic morphology is near optimal in terms of both dynamic range and information transmission.

A Guide Toward Multi-scale and Quantitative Branching Analysis in the Mammary Gland

The mammary gland consists of a bilayered epithelial structure with an extensively branched morphology. The majority of this epithelial tree is laid down during puberty, during which actively proliferating terminal end buds repeatedly elongate and bifurcate to form the basic structure of the ductal tree. Mammary ducts consist of a basal and luminal cell layer with a multitude of identified sub-lineages within both layers. The understanding of how these different cell lineages are cooperatively driving branching morphogenesis is a problem of crossing multiple scales, as this requires information on the macroscopic branched structure of the gland, as well as data on single-cell dynamics driving the morphogenic program. Here we describe a method to combine genetic lineage tracing with whole-gland branching analysis. Quantitative data on the global organ structure can be used to derive a model for mammary gland branching morphogenesis and provide a backbone on which the dynamics of individual cell lineages can be simulated and compared to lineage-tracing approaches. Eventually, these quantitative models and experiments allow to understand the couplings between the macroscopic shape of the mammary gland and the underlying single-cell dynamics driving branching morphogenesis.

How to build an epithelial tree

Nature has evolved a variety of mechanisms to build epithelial trees of diverse architectures within different organs and across species. Epithelial trees are elaborated through branch initiation and extension, and their morphogenesis ends with branch termination. Each of these steps of the branching process can be driven by the actions of epithelial cells themselves (epithelial-intrinsic mechanisms) or by the cells of their surrounding tissues (epithelial-extrinsic mechanisms). Here, we describe examples of how these mechanisms drive each stage of branching morphogenesis, drawing primarily from studies of the lung, kidney, salivary gland, mammary gland, and pancreas, all of which contain epithelial trees that form through collective cell behaviors. Much of our understanding of epithelial branching comes from experiments using mice, but we also include examples here from avian and reptilian models. Throughout, we highlight how distinct mechanisms are employed in different organs and species to build epithelial trees. We also highlight how similar morphogenetic motifs are used to carry out conserved developmental programs or repurposed to support novel ones. Understanding the unique strategies used by nature to build branched epithelia from across the tree of life can help to inspire creative solutions to problems in tissue engineering and regenerative medicine.

Spatiotemporal dynamics of self-organized branching in pancreas-derived organoids

The development dynamics and self-organization of glandular branched epithelia is of utmost importance for our understanding of diverse processes ranging from normal tissue growth to the growth of cancerous tissues. Using single primary murine pancreatic ductal adenocarcinoma (PDAC) cells embedded in a collagen matrix and adapted media supplementation, we generate organoids that self-organize into highly branched structures displaying a seamless lumen connecting terminal end buds, replicating in vivo PDAC architecture. We identify distinct morphogenesis phases, each characterized by a unique pattern of cell invasion, matrix deformation, protein expression, and respective molecular dependencies. We propose a minimal theoretical model of a branching and proliferating tissue, capturing the dynamics of the first phases. Observing the interaction of morphogenesis, mechanical environment and gene expression in vitro sets a benchmark for the understanding of self-organization processes governing complex organoid structure formation processes and branching morphogenesis.

Pancreatic ductal adenocarcinomas (PDAC) exhibit complex morphologies challenging to capture in organoid models. Here, the authors develop PDAC organoids that can recreate branched structures and, with the use of a minimal mathematical model, shed light to pathways and processes directing the dynamics of self-organization and branching morphogenesis.

Dynamic instability of dendrite tips generates the highly branched morphologies of sensory neurons

The highly ramified arbors of neuronal dendrites provide the substrate for the high connectivity and computational power of the brain. Altered dendritic morphology is associated with neuronal diseases. Many molecules have been shown to play crucial roles in shaping and maintaining dendrite morphology. However, the underlying principles by which molecular interactions generate branched morphologies are not understood. To elucidate these principles, we visualized the growth of dendrites throughout larval development of Drosophila sensory neurons and found that the tips of dendrites undergo dynamic instability, transitioning rapidly and stochastically between growing, shrinking, and paused states. By incorporating these measured dynamics into an agent-based computational model, we showed that the complex and highly variable dendritic morphologies of these cells are a consequence of the stochastic dynamics of their dendrite tips. These principles may generalize to branching of other neuronal cell types, as well as to branching at the subcellular and tissue levels.