Schedule for: 24w5315 - Formation of Looping Networks - from Nature to Models

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions.

River networks are often presented as the paragon of fractal networks. They can indeed be self-similar over a broad range of scales but, as land-dwelling humans well know, they cover only a small portion of the available continental surface. In other words, there is a cut-off length below which their self-similarity breaks down. At this scale, rivers stop being one-dimensional objects, and the ground around them takes over the transport of the water and sediment that feed them. What sets this length? We will address this question with simple dimensional reasoning.

A river loop is a sedimentary pattern consisting of a bifurcation, where water and sediment fluxes are partitioned between two smaller anabranches, and a confluence, where the two anabranches reconnect in a single trunk. River loops can be encountered as individual features, or as nested components in multi-thread networks like anastomosing and braided rivers. Moreover, the artificial restoration of pristine looping patterns through local channel widening is part of modern paradigms in river engineering techniques, with the aim of recovering morphological and ecological functions of degraded fluvial ecosystems. Recently, the remote sensed analysis of hundreds of river reaches worlwide has shown that there is a considerable degree of universality in the planform properties of individual looping systems. In particular, the mean length of the anabranches has shown to be nearly proportional to the bankfull hydraulic characteristics (width, depth) of the reach. The existence of a characteristic length scale has been suggested to reflect a two-way morphodynamic interaction taking place between the constitutive elements of loops, bifurcations and confluences, which mutually exchange information along the connecting anabranches depending on the mean loop length. Here, we aim to bridge analytical modeling with remotely sensed data to provide insight into how the planform geometry displayed by actual looping systems is related with the coupled morphodynamics of bifurcations and confluences, and thus to the allocation of water and sediment between the anabranches. To this end, we propose a physically-based modeling framework for the long-term state of an idealized fluvial loop that is able to account for configurations where one of the two branches partially, or even totally, ceases to transport both water and sediment, and where the two anabranches have different lengths. The theoretical model suggests that the behaviour of individual river loops displays several characteristic features of dynamical systems, such as critical thresholds, phase transitions and multi-stable equilibrium states, and leads to the identification of a handful of dimensionless parameters that primarily control their long-term state. These parameters are functions of the reach-averaged bankfull geometry and of the planform shape of the loop. Although a certain degree of variation is exhibited, the majority of data displays values of the controlling parameters that cluster in fairly narrow ranges, and indicate the tendency of river loops to manifest themselves preferentially in wide and shallow reaches. When analyzed in the light of theory, the parameter values are placed consistently in the region of active loops that are able to keep both branches open, though just one of them may be morphologically active. Finally, the analysis provides some indications that the spatial organization of multi-thread networks may reflect the morphodynamics of individual loops.

Lung pseudoglandular branching morphogenesis proceeds in three stereotyped modes (domain, planar, and orthogonal branching). Much is known about the molecular players, but less is known of how these signals actuate the different branching patterns. With the aim of identifying mechanisms that may determine the different branching modes, we developed a computational model of the epithelial lung bud and its surrounding mesenchyme. We studied transport of morphogens and localization of morphogen flux at lobe surfaces and lobe edges. We find that a single simple mechanism is theoretically capable of directing an epithelial tubule to elongate, bend, flatten, or bifurcate, depending solely on geometric ratios of the tissues in the vicinity of a growing tubule tip. Furthermore, the same simple mechanism is capable of generating orthogonal or planar branching, depending only on the same geometric ratios.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Urban morphology results from complex processes, the patterns and logic of which can be deciphered by identifying characteristics of the spatial structure. The complex organization of this structure suggests the presence of an underlying order in urban evolution. Among the urban components, road networks endure through time, and present a challenging yet fascinating subject for study. Graph theory offers a mathematical formalization of road networks, enhancing spatial understanding. Our research approaches urban morphology through an analytical lens focused on road networks, emphasizing historical context and structural features induced by their physical layout. It unfolds in four axes: (1) building a relevant element to analyse road network (the way) (2) finding indicators to characterize road network structure, revealing common properties over time ; (3) identifying morphotypes within the road network, associated with morphological evolution processes ; and (4) proposing a simulation model (WayMorph). The findings reveals that urban morphology is the result of complex processes that can be identified by analyzing spatial structure. Understanding urban morphogenesis and past evolution is pivotal for addressing future developmental challenges, aiding decision-making for city stakeholders. Territorial development choices, reflected in road network morphologies, reciprocally influence accessibility disparities and territorial development dynamics. Profound comprehension of road network evolution dynamics can significantly support territorial planning.

A signal on a graph is a function on its vertices. Signals can represent measurements in a sensor network, congestion in a traffic network, or activity levels in regions of the brain. Analysis of such signals can allow us to detect noise, trends, missing data, etc. An important tool in signal processing is the Fourier transform. The Graph Fourier Transform (GFT) is defined as the projection of the graph signal onto an eigenbasis of the adjacency matrix of the graph. The GFT is therefore highly dependent on the specific graph, which can cause problems when the graph changes over time or contains errors. I will describe recent work on a GFT framework that can be defined for an entire class of graphs randomly sampled from a common stochastic model. The model is derived from a limiting graph object called a graphon. A graphon represents a class of graph that have a common structure in terms of number of cycles (loops) and other subgraphs.

Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!

Multicellular organisms develop from a single fertilized egg. The sequence of events leading to the precise positioning of individual cells with the required fate within the developing organism is orchestrated by gene regulation within and between cells, cell proliferation and rearrangements as well as global morphological changes, involving coordinated dynamics at multiple scales, from single molecules, to cells, to tissues. Even though various parts of these processes have been elucidated, a generic framework that would capture the interactions between them is still missing. In particular, the question of how morphology affects and is affected by cell differentiation is still open. We propose to describe a developing organism as a dynamical looping network where each cell correspond to a node, spatial relationships are encoded as the edges and transcriptomic states as labels on the nodes. We will explore how the action of cell proliferation, spatial rearrangement and differentiation dynamics affect the characteristics of these networks in various biological examples.

A common feature of many developing organs is the presence of two or more separate but topologically interlinked complex networks, such as the vascular and ductal networks in the pancreas, or the sinusoidal and canalicular networks in the liver. However, neither the degree to which these networks are topologically interlinked, or, "ensnarled", nor the dynamics of this ensnarling has been the subject of much attention. Indeed, much work on complex, cyclic spatial networks has been done in 2d models and model systems, where ensnarled pairs of networks are impossible. Here, we investigate and model ensnarling in symmetric and disordered model network-pairs as well as in the developing liver, with the ultimate goals of deriving physical rules that govern the ensnarling process, and determining the biological consequence of properly ensnarled states on organ function.

The optimal development and remodeling of transport networks is crucial for their proper functioning. One of the important networks for living species is the cardiovascular system. Various studies analyze processes responsible for its growth, which lead to the creation of patterns efficient in supplying oxygen to the system. Many of these models yield satisfying results but include many complex and sometimes very specific mechanisms, limiting them to only fragmentary regions of the growth. We adopt a different philosophy. In order to explore the basic mechanisms responsible for the growth of such an oxygen supply network, we introduce a minimal physical model capable of forming a vascular network in response to chemical and hydrodynamical stimuli. We consider a network model, in which an initial capillary plexus is remodeled according to three main stimuli: shear stress on the capillary walls, vascular endothelial growth factor (VEGF) released by oxygen-deprived cells, and regulatory signals propagated along the vessels. To mirror the hierarchical structure of the cardiovascular system, we divide our network into three types of edges: arterioles growing from the inlet, venules growing from the outlet, and capillaries connecting them. We consider various geometries of the system, with inlets and outlets either localized at the linear boundaries of a rectangular network or in the center and at the circumference of a circular network. The proposed growth mechanisms are able to create and sustain long loops in the network, efficiently oxygenating even the its remotest areas, regardless of the geometry. We compare patterns obtained from the model with structures observed in experimental studies of the vascular system.

Social insects, such as ants and termites, are well-known for their ability to modify the environment in which they live by building very large and complex nests, and large networks of galleries and foraging trails. These are all self-organised structures whose construction typically involves positive feed-back mechanisms, required to focus the activity of several individual insects at the building or the digging site. Positive feed-back, however, is not easily reconciled with the formation of looping networks with branches and multiple alternative paths to a same destination. In my talk, I will summarise the current knowledge and the open questions surrounding the formation of branching and looping structures by social insect colonies, based on both my own research and the wider published scientific literature.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

Stream networks growing in response to re-emerging ground water flow tend to branch at an angle of $\alpha = 2\pi/5=72^\circ$ [Devauchelle et al. 2012]. This result of Laplacian growth can be obtained as the asymptotic solution of Lowner's equation with one infinite branch and two incipient tips branching at any angle. However, already T. Dunne noted in the 1980s that stream networks also ramify via sidebranches splitting off a major stream. These incipient sidebranches are much smaller than the main channel. Consequently, their dynamics is determined by the competition between the much larger upstream and downstream parts of the main stem ultimately growing towards a branching angle of $\alpha=\pi/2=90^\circ$. Reanalyzing the data of Devauchelle et al. 2012, we find second bifurcation mode at $\pi/2$ for junctions, whose total-upstream length ratio is significantly larger than 1, while still recovering the angle $\alpha=2\pi/5$ for bifurcations formed by two upstream tributaries of equal Horton-Strahler order. These results provide a unified framework for the ramification of stream networks in a diffusive field.

TBA

The fundamental challenge of tissue engineering is to create a functional vascular network that provides oxygen and nutrients to cells. Effectively constructing such networks requires understanding the processes involved in vascular network formation and identifying the factors influencing its growth. From an experimental perspective, we focus on well-controlled systems consisting of individual plastic microbeads coated with endothelial cells or matrices, ie. group of individual microbeads with adjastuble spacing between them. In these systems, the microbeads are placed in hydrogel, acting as an extracellular matrix, supplemented with nutrients, fibroblasts, and vascular endothelial growth factors (VEGF) at controlled concentrations. Such systems exhibit the ability to grow, forming capillary networks built from endothelial cells, with successive stages of growth observed through confocal microscope imaging conducted every 24 hours. To analyze the data, numerical tools for image segmentation have been developed, with the ability to describe networks through numerous parameters. One notable observation is that the onset time, marked by the initial growth of capillaries from a microbead, gets shorter with higher concentrations of VEGF. Additionally, higher concentrations of VEGF result in more branched networks, although they do not significantly affect the speed of growth of individual sprouts. The mean bifurcation angle shows weak dependence on VEGF concentration, typically varying between 60 and 75 degrees. This suggests that the sprout tips tend to follow local VEGF gradients. At high VEGF concentrations, we observe exponential distributions of segment lengths, indicating stochastic branching. To simulate growth of capillary networks in vasculogenesis we employed a cellular Potts model, considering two key factors governing network formation: elastic interactions due to hydrogel deformation by endothelial cells and chemotaxis associated with the diffusion and reaction of VEGF proteins with endothelial cells. Such a numerical model allows us to study vascular network growth under a much wider range of conditions than is experimentally feasible.

Branched structures are a common phenomenon across various biological systems, where they serve critical functions such as efficient fluid transport in organs like the liver, lungs, and salivary and mammary glands. Biophysical modeling has been instrumental in elucidating the basic principles of growth that underpin these ramified architectures and their spatio-temporal development, which predominantly involves the formation of non-looped networks. Conversely, looped networks are often observed in neural networks, where neurons form complex connectivity patterns, such as small-world networks. These networks facilitate feedback and feedforward interactions, leading to diverse self-organized behaviors including synchronization and chaotic dynamics, which have implications for conditions like epilepsy. From a physics perspective, some questions that arise naturally are: what are the minimal ingredients for a system to exhibit branched structures? do (looped or non-looped) branched networks occurs exclusively in non-variational systems, or can they exist in variational systems? Interestingly, even variational systems like forced liquid-crystal cells can display branching dynamics as a mechanism for achieving efficient energy dissipation and complex spatial organization. This talk will highlight our latest research on branching structures in both biological tissues and physical systems, revealing common underlying mechanisms and unique system-specific characteristics.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Studies of patterning in living organisms have been dominated by two theories: reaction-diffusion, and positional information. However, a different paradigm involving the regulated transport of the phytohormone auxin plays a key role in controlling patterning and development in plants. Specifically, the canalization theory [Sachs 1991] proposes an explanation of the vascular patterning in terms of feedback between auxin transport and the localization of auxin transporters within the cells. Experimental studies and computational models have demonstrated the capability of canalization to create branching vascular patterns connecting discreet auxin sources to sinks. Nevertheless, attempts to extend this mechanism to the formation of patterns with loops have not been convincing. In this context I will present two recent models producing vascular patterns with loops consistent with the observed topologies and geometries. The first model [Owens et al. 2024] generates the regular reticulate vascular patterns observed in the flower heads of the common daisy, Bellis perennis, by promoting the creation of approximately equivalent paths from sources to sinks. It also generalizes to the less regular reticulate patterns found in the flower heads of some other members of the Asteracae family. The second model [Zheng et al. 2024] reproduces reticulate patterns characteristic of the leaves of the Chinese money plant, Pilea peperomioides. Interestingly it reveals an unexpected connection between vascular patterns and Voronoi diagrams. In this case, the interaction between auxin and its transporters produces vascular strands which divide the space between sources, rather than connecting sources to sinks. To what extent these models generalize to other plant vascular patterns with loops remains an interesting question. [Owens et al 2024] A. Owens, T. Zhang, P. Gu, J. Hart, J. Stobbs, M. Cieslak, P. Elomaa, and P. Prusinkiewicz, The hidden diversity of vascular patterns in flower heads. New Phytologist, https://doi.org/10.1111/nph.19571, 2024. [Sachs 1991] T. Sachs, Pattern formation in plant tissues. Cambridge University Press, 1991. [Zheng et al 2024] X. Zheng, M. Venezia, E. Blum, U.V. Pedmale, D. Jackson, P. Prusinkiewicz, and S. Navlakha, Reticulate leaf venation in Pilea peperomioides is a Voronoi diagram. In preparation.

The daily cycle of photosynthesis and respiration forces many sediment-dwelling microbes to regularly swim thousands of body lengths through complex pore networks to remain in their preferred chemical environments. Efficient navigation through pores requires cells to balance movement along chemical gradients with obstacle avoidance. Here we experimentally investigate the navigation by a species of colonial bacteria called Magnetoglobus multicellularis as it swims through networks of pores. Bacterial colonies turn to swim along magnetic field lines, which are roughly parallel to the typical chemical gradients in their habitat. When a colony collides with an obstacle, it scatters at a random angle before turning to realign with the geomagnetic field. We show that repeated scattering and realignment lead bacteria to move through the pore space with an average drift velocity and diffusivity that depend only on the ratio of the pore size to the turning radius of a swimming colony. The drift velocity is maximized for a particular ratio of these length scales, suggesting that natural selection must tune the bacterial phenotype to fix the turning radius. The measured magnetic moment, swimming speed, and body size show evidence of this selection pressure. We discuss the relevance of this result to pore space navigation and the evolution of magnetotaxis.

Adaptive transport networks, like blood vessels or river systems, are essential for many natural and human-made systems. Understanding how these networks form and grow is crucial for optimizing their stability and resilience. Even seemingly similar flow systems, like river deltas, may include different morphologies, involving loops or tree-like branching structures. Hydrodynamic fluctuations are known to promote the formation of loops, but their mere presence is not sufficient, as demonstrated by loop-free networks driven by oscillating flows. Here, we explore the stability of a loop formed by fluctuating flows within a scale-free adaptive network. By performing a complete stability analysis, we find a threshold for loop stability that involves an interplay of geometric constraints and hydrodynamic forcing, which we map to the constant and fluctuating flow components. We show that stable loops require fluctuation in the relative size of the flux between nodes, rather than solely a temporal fluctuation in flux at a specific node. Hence, loops are supported when 'Goldilocks' fluctuations are present in the system, with a minimum and a maximum amount of fluctuations relative to the constant-flux component. Our results are robust to the change of the number of nodes and individual loop shape, rendering the result complementary to advances in understanding optimal supply networks and network dynamics that focus on global properties of the networks rather than individual loops.

Existing models of adaptation in biological flow networks consider their constituent vessels (e.g. veins and arteries) to be rigid at short time-scales, thus predicting a non physiological response when the drive (e.g the heart) is dynamic. Here we use a modified adaptation model that incorporates pulsatile driving and the transient spatio-temporal dynamics of elastic vessels, and show that it fundamentally alters the expected long-time structure of branched flow networks. We show that pulsatility stabilizes loops and prevents vascular shunting for a much broader range of metabolic cost functions than predicted by existing theories. We demonstrate how the mechanism of loop stabilization relies on the interactions between the elastic vessels and the dynamic flow, and how it depends on the ensuing resonances. Our work points to the need for a more realistic treatment of adaptation in complex elastic flow networks, especially those driven by a pulsatile source, and provides possible insights into pathologies that emerge when such pulsatility is disrupted in human beings.

Transport of materials within the body is accomplished largely by convection within blood vessels together with diffusion into surrounding tissue. This requires hierarchical network structures to allow efficient flow distribution, together with numerous small terminal vessels to allow short diffusion distances. Such structures emerge by local responses to available biological signals, through the processes of angiogenesis, remodeling and pruning. Theoretical simulations show how these processes can lead to network structures that are capable of meeting varying functional requirements

Intrinsic redundancy given by the presence of loops plays a crucial role in maintaining a healthy vascular network. Our research demonstrates that networks with and without redundancy, despite having equivalent flow resistances in occluded-free conditions, exhibit very different flows when obstructed. Specifically, for densely occluded networks, a redundant network facilitates greater flow compared to its no-redundant counterpart. This investigation enables the quantification of a network's resilience to blockages, provides valuable direction for designing microfluidic devices, and sheds light on the evolutionary advantage of intrinsic redundancy in ensuring vital blood supply at key places of organisms

Organisms often have transport networks that extend throughout their bodies. Looking at the back of a palm, we can see the veins of blood vessels, and pulling a leaf with your hand, we can see the leaf veins. Taking a look at your step on the forest floor, we can see fungal mycelium growing on dead leaves that are turning to leaf litter. Transport networks help multicellular organisms to maintain their large bodies. The transport of nutrients and excretions, and the circulation of signals throughout the system, are thought to be the reason that even a group of many cells can behave as a single entity. Transport networks are an important infrastructure of multicellular systems. The construction of these transport networks takes at least a few weeks to a few months. This is one of the difficulties of experimental studies. However, there is an organism that can do this in a few hours only. It is a plasmodium (giant amoeba) of true slime mold Physarum polycephalum. Because of this advantage, in recent years, the plasmodium of true slime molds have been studied as an instructive model organism for biological transport networks. In this presentation, we will review the transport network in this organism, mainly from the viewpoint of macroscopic physiology, and introduce the environment-dependent formation and re-modeling of the network structure. Physarum plasmodia live in the interior of decaying wood on the forest floor. It is an intricate, porous, three-dimensional space, dotted with nutrients and toxins of various types and sizes. In such an environment, slime molds respond to the ever-changing environmental factors by expanding and retracting their transport networks here and there, and ingest nutrients. Focusing on the complexity of such an environment, we prepared a moderately complex environment in the laboratory to examine the characteristics of transport network formation in slime molds. Specifically, (1) the case in which two food pellets were separated through a maze of obstacles, (2) the case in which there were many places with different degrees of repulsive factor, (3) the case in which 40 food pellets were arranged on a plane, and (4) the case in which escape from a closed space with a specific shape is achieved. A key feature of self-organization of tubular network is the adaptability of each tubular channel to flow through the tube : current-reinforcement rule. Namely, tubular channel gets thicker when flow through the tube is much enough, and getting thinner otherwise. This current-reinforcement rule can be formulated in the model equation of motion, ‘adaptive network model’. Since similar properties of the current reinforcement rule have been observed in transport networks of animals, plants, and fungi, the adaptive network model can be expected to have applicability to other biological systems. A few examples of its extended application are presented.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

The vascular network can be preserved in fossil leaves, presenting the opportunity to investigate how leaves have evolved and how leaf venation has changed through time. Laminate leaves with a network of veins first appeared in the Devonian and Carboniferous, evolving at least four times independently over a span of fifty million years by about 330 million years ago (and many additional times since then). Similarities of early leaf form suggest a shared sequence of developmental innovations associated with marginal leaf growth across each iterative evolution of leaves—as subsequently tested with interpretation of growth dynamics from vein patterns in living plants for which development can then be directly observed. In addition to informing on mechanisms of leaf development, vascular networks are also directly relevant to hydraulic function. And like with development, fossil leaf venation provides a record of the evolution of physiology. As CO2 is taken up for photosynthetic carbon fixation, water is lost to the atmosphere, a process called transpiration. The greater the rate at which water can be lost, the more photosynthesis can be performed. As the pipes that move water, the leaf vascular network is a key indicator of transpirational and photosynthetic potential. Living and fossil plants attest that the evolution of angiosperms (i.e., the flowering plants) entailed a four-fold increase in the mean and maximum densities of leaf veins. Over almost 400 million years of leaves, all plants averaged about 2 mm of vein length per square mm of leaf and were never more than about 5 mm mm^-2, until angiosperms raised leaf vein densities in the last 100 million years to an average of 8 to 10 mm mm^-2 with maximums greater than 20 mm mm^-2. Flowering plants required a diversity of compensatory changes to cram so many veins into such a small space. Increased vein densities in flowering plants indicate a similarly dramatic increase in the capacity to move water and assimilate carbon via photosynthesis. Although obviously important for the plants themselves, these changes also matter for the Earth system writ large since plants make up the bulk of terrestrial biomass. The recycling of precipitation via angiosperm transpiration would have fostered the spread of high rainfall environments. In climate modeling, the replacement of angiosperm transpiration with the transpiration rates typical of other plants leads to a collapse of rainforest area to 20% of its modern extent. And the two or three-fold increase in primary productivity that angiosperm evolution represented would have been an important restructuring of the carbon cycle, indicating changes to other nutrient cycles as well, like nitrogen and phosphorus. Leaf vascular networks have changed the world.

This presentation demonstates how mass spring models can be utilized to study cracking of elastic materials. Through our simulation system, we'll show how these models can effectively capture material shrinkage phenomena, mirroring real-world scenarios such as drying or cooling processes. By observing shrinkage-induced internal stresses we can gain insight into complex mechanisms behind crack initiation and growth. Furthermore, we will demonstrate how various shrinking conditions can lead to formation of different crack patterns.

Angiogenesis - the growth of new blood vessels from a pre-existing vasculature - is key in both physiological processes and in several pathological scenarios such as cancer progression or diabetic retinopathy. For the new vascular networks to be functional, it is required that the growing sprouts merge either with an existing functional mature vessel or with another growing sprout. This process of forming loops is called anastomosis. In this talk I will present a systematic 2D and 3D computational study of vessel growth in a tissue to address the capability of angiogenic factor gradients to drive anastomosis formation. Furthermore, we verify that this process of anastomose formation increases network morphology resilience towards variations in the endothelial cell’s proliferation and chemotactic response. We use this mathematical model of angiogenesis and anastomose formation to characterize the dynamics of VEGF secretion and turnover in glioblastoma growth. We show that sequestration of VEGF inside glioblastoma cells can be used as a novel target for improved anti-angiogenic-based therapy. With this aim we have engineered a cargo system that allows cellular uptake of anti-VEGF and inhibits VEGF secretion required for angiogenesis activation and development. We show the therapeutic efficacy of this nanocargo in reducing vascularization and tumor cell mass of glioblastoma in vitro and in vivo cancer models.

DIscomedusae are free-swimming medusae which are part of the phylum Cnidaria, the sister group to all animals with bilateral symmetry. Discomedusae possess a gastrovascular system with a canal network distributing nutrients and oxygen to tissues in the subumbrella. A large diversity of canal networks exists, from highly reticulated networks in Rhizostoma pulmo to purely branching networks in Cyanea capillata. The canal network of Aurelia jellyfish has a sparse reticulated network. By day-to-day macroscopic observations, we study the dynamics of the network formation in juvenile Aurelia jellyfish and model it numerically. During the network development, at the circular canal at the rim of the jellyfish umbrella, an instability emerges in form of sprouts. They then grow toward the center of the jellifish and reconnect to already existing radial canals. These reconnections have a bias to reconnect to the younger side radial canal. However, even in clones, there exists a variability towards which canal the reconnections occur. Similar to the morphogenic instability idea of Turing (1952), the canal network pattern is not strictly regulated, but rather grows from an instability, keeping trace of noise, and then self-organizes, guided by physical rules. We show that in Aurelia both the hydrodynamic effects, such as pressure in the canals, and elastic effects, such as deformation of the jellyfish body during swimming, govern the direction toward which the canal sprouts grow. We suggest that these morphogenic instabilities also play a role in the diverse patterns of canal networks in Rhizostoma pulmo and Cyanea capillata

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

Sea-urchins and other echinoderms like sea-stars, have developed many different appendages like ossicles, spines, teeth, that are made of bio-mineralised calcite. Despite of a great morphological variety, most of these skeletal elements show an internal mesoscopic structure which is a strugglingly similar, made of an intricate and porous scaffolding reminding of minimal surfaces. Inspired by such a peculiar curvature signature, previous literature speculated on the fact that such a structure, called stereom, must originate from some energy-minimization bulk process like phase-separation. Conversely, more recent experiments showed that the growth of these complex structures is an accretion process relying on localised branching and reconnection episodes, mediated by the activity of specialised bio-mineralising cells. I hypothesise that the actions of those skeletogenetic cells may be crucially affected by the local curvature of the substrate that acts as an organising cue. I will review the key pieces of literature that motivated this research, present some on-going experiments aiming to track the progressive growth of the stereom in sea-urchins, and discuss a modelling approach.

Animal evolution is driven by random mutations at the genome level. However, it has long been suggested that there exist physical constraints which limit the set of possible outcomes. In craniate evolution, it has been observed that head features can be ordered in a diagram such that, as the brain expands, the head rocks more forward and face features become less prognathous. When imaging in detail brain development during chicken embryo, one indeed observes a correlation between brain dilation and flexure. A careful study shows that it is due to the physical texture of the vertebrate embryo[1]. Vertebrate embryos, and especially the head, stems from a neural tube. This neural tube is strangled by a small number of cellular rings. However, the material texture of the embryo imparts a similar texture to the vascular pattern. The vascular network in the early head, as imaged by a technique of vascular enhancement by integration[2], shows a specific texture, with a capillary plexus in the brain vesicles, and larger vascular tubes in the valleys. The heart itself mirrors the initial tissue texture. As a consequence, the distribution of blood flow in the early brain contributes to brain expansion and rotation, as shown theoretically and experimentally. Blood pressure in the capillary bed contributes to brain vesicle dilation, while blood flow contributes to forward head flexure. There exists a vascular torque effect in the circulation loop correlating brain dilation and flexure. This shows that the origin of humans, at the anatomical level, is essentially textural, with a dynamical thrust augmented by hemodynamics. [1]Fleury, V., Electrical stimulation of chicken embryo development supports the Inside story scenario of human origin, Scientific Reports, 14, 72450, (2024). https://doi.org/10.1038/s41598-024-56686-y [2]Richard, S., Brun, A., Tedesco, A. , Gallois, B., Taghi, N., Dantan, P., Seguin, J., Fleury, V., Direct imaging of capillaries reveals the mechanism of arteriovenous interlacing in the chick chorioallantoic membrane, Commun Biol 1, 235 (2018).

The canal network of the gastrovascular system of the jellyfish Aurelia aurita transports nutrients and oxygen to the tissues, enabling the jellyfish to swim. In this network, canals have a preferential flow direction followed by the majority of the nutrients. Depending on this direction, the organization of the canals varies, forming either straight canals or a reticulated network. Investigating how the flow is propelled and characterizing the pulsatility inside the network are crucial steps to understand the role of pulsatility in the formation of the network and the differentiation of flow direction. The flow in the canals is propelled by the expansion and contraction of the deformable canals, assisted by the movements of cilia that line the inner walls of the canals. We study the relative contribution of these two mechanisms to understand how they generate an effective flow that facilitates distribution towards the circular canal at the rim of the umbrella and back to the center of the jellyfish. We perform measurements while the jellyfish, both with and without anesthetic, is lying flat on its exumbrella, and the flow inside the canals is analyzed using the PTV method. We observe that cilia alone succeed in transporting particles. Particles are trapped by the cilia and forwarded. Muscle forcing increases the particles' time-averaged velocity in all canals. Additionally, the path of a particle becomes more oriented in the channel. Our observations confirm Southward's 1955 findings that adradial straight canals also transport food particles in the opposite direction. A rich hydrodynamic complexity emerges from circulation in this system. The scyphomedusa Aurelia aurita is part of the phylum Cnidaria, which is the sister group to all animals with bilateral symmetry. We hope that understanding how transport is realized in this ancient phylum will provide insight into how circulatory systems evolved.

When a more mobile phase invades a less mobile one, the interface between them becomes unstable. Viscous fingering, resulting from a viscosity contrast between immiscible fluids is the most studied example of this type of instability. However, similar instabilities can occur in both fractured and porous media, caused by spatial variations in permeability. This talk will focus on instabilities in fracture dissolution, which is a less common topic than porous media, but which plays a larger role in shaping the landscape because of the much higher flow rates. First I will describe how a uniform fracture can develop highly inhomogeneous flow paths, resulting in just a few highly permeable channels. This at least partially resolves a long-standing paradox as to how long conduits can develop in the subsurface. Second I will show how flat fractures can evolve into cylindrical or elliptical tubes, again by flow focusing.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Maze caves are intricate underground networks characterized by complex branching and intersecting passages. Their origins are still debated, but it is likely that multiple processes contribute to the formation of such networks [1]. This talk will explore several mechanisms proposed to explain the development of maze caves and will briefly discuss a new idea linking their formation to the cooling of carbon dioxide-rich geothermal fluids [2]. [1] A.N. Palmer, Origin and morphology of limestone caves", GSA Bull., 103, 1 (1991) [2] R. Roded, E. Aharonov, A. Frumkin, N. Weber, B. Lazar, and P. Szymczak, Cooling of hydrothermal fluids rich in carbon dioxide can create large karst cave systems in carbonate rocks, Commun. Earth Environ., 4, 465 (2023)

Penguins huddling in a cold wind are represented by a two-dimensional, continuum model. The huddle boundary evolves due to three effects: heat loss to the huddle exterior; the reorganisation of penguins to regulate heat production within the huddle; the conservation of huddle size. The huddle propagates slowly compared to the advective timescale of the wind, thus exterior temperature is governed by the steady advection-diffusion equation and interior temperature by a Poisson equation. The wind velocity is the gradient of a harmonic, scalar field and the conformal invariance of the exterior governing equations motivates the use of a conformal mapping approach in the numerical method. The Poisson equation is not conformally invariant, however, so the interior temperature gradient is found numerically using the AAA-least squares algorithm. The results show that, irrespective of the starting shape, penguin huddles evolve into an egg-like steady shape dependent on the wind strength, parameterised by the Péclet number Pe, and a parameter β which effectively measures the strength of the interior self-generation of heat by the penguins. The numerical method developed is applicable to a further five free boundary problems.

This early-stage work aims at developing a mathematical model to understand how intracellular transport influence the formation of axonal and dendritic branches. Our model describes the transport dynamics of material required for neuronal growth as a free boundary problem. We assume that the moving boundary, which corresponds to neurite elongation and stochastic branching, is material-dependent. The modeling approach and preliminary numerical findings will be discussed. We believe this framework could provide new insights into the principles of neuronal development and the interplay between transport dynamics and neuronal morphology.

Transport networks, such as vasculature or river networks, provide key functions in organisms and the environment. They usually contain loops whose significance for the stability and robustness of the network is well documented. However, the dynamics of their formation is usually not considered. The growth of such structures is often driven by the gradient of an external field. During network evolution, extending branches compete for the available flux of the field, which leads to effective repulsion between them and screening of the shorter ones. Yet, in remarkably diverse processes, from unstable fluid flows to the canal system of jellyfish, loops suddenly form near the breakthrough when the longest branch reaches the boundary of the system. We provide a physical explanation for this universal behavior. Using a 1D model, we explain that the appearance of effective attractive forces results from the field drop inside the leading finger as it approaches the outlet. Furthermore, we numerically study the interactions between two fingers, including screening in the system and its disappearance near the breakthrough. Finally, we perform simulations of the temporal evolution of the fingers to show how revival and attraction to the longest finger leads to dynamic loop formation. We compare the simulations to the experiments and find that the dynamics of the shorter finger are well reproduced. Our results demonstrate that reconnection is a prevalent phenomenon in systems driven by diffusive fluxes, occurring both when the ratio of the mobility inside the growing structure to the mobility outside is low and near the breakthrough.

Fluid-driven processes, such as viscous fingering, erosion, and hydraulic fracture, can give rise to intricate branched patterns. The shape of these self-organized branched patterns emerges from the interaction between local rules, set by bulk material properties, and global constraints, imposed through boundary conditions. Our study explores the effect of global constraints on branch shape, by examining the branched looping networks that form when an invading fluid is injected into a defending phase under highly-limiting global constraints. In particular, we inject water from a point source into a Hele-Shaw cell filled with a yield-stress fluid and allow the self-organized pattern to find its way towards a point sink. As we inject water from the point source, the expansion of the branched pattern towards the sink appears to change from a direct (exploitative) to an indirect (exploration) strategy with an increase in flow-rate. We show that this transition is connected to a switch from a viscosity-dominated to an elasticity-dominated response from the yield stress fluid to the invading fluid and that the corresponding flow-rate can be predicted. By reinterpreting the breakthrough process as a searching problem, we find that at the transition from viscosity-dominated to elasticity-dominated branching, the search strategy is most cost-effective in terms of the amount of fluid that needs to be injected to reach the sink. These experiments demonstrate that the shape of self-organized branched networks arises from a balance between bulk properties and boundary conditions and suggest that we can use global constraints to control the shape of self-organized branched networks.

The liver circulatory system is composed of two blood supply vascular trees (the hepatic artery and portal venous networks), the hepatic microcirculation (by the sinusoids), and a blood drainage vascular tree (the hepatic venous network). In a healthy liver, the flow resistance at microcirculation level is very low, and the pressure upstream —in the portal venous network— is almost the same as the sinusoids pressure. However, changes in the vasculature due to fibrosis —predominantly in the sinusoids— cause increased resistance to flow, which in turn leads to increased portal pressure (termed portal hypertension). Here, we present a liver fibrosis/cirrhosis model. We build on our 1D model of healthy liver circulation, which considers the elasticity of vessel walls and the pulsatile behavior of blood flow and pressure, and emulate the deteriorated liver vasculature due to fibrosis. We recreate altered sinusoids by fibrous tissue (stiffened, compressed and splitting sinusoids) and propose boundary conditions to investigate the impact of fibrosis on hemodynamic variables within the organ. We obtain an increased portal venous pressure, as the one clinically observed in fibrotic/cirrhotic patients. We also study the spreading of fibrosis by simulating the fibrotic alterations in an increasingly number of sinusoids. Finally, we calculate the PPG (portal pressure gradient) parameter in the model and obtain values in agreement with those reported in the literature for fibrotic/cirrhotic patients.

Vascular networks, including epithelial and endothelial organs, require a high surface-to-volume ratio to facilitate effective fluid exchange and transport, which can be achieved through branching morphogenesis. While self-organized branching provides a simple mechanism to cover space, it does so at the expense of efficiency, exhibiting large heterogeneities in spatial coverage. A central question is then whether branched transport networks can efficiently occupy a given territory to maximize their functional output. Here, we combined experiments on developing lymphatic vessel networks and mathematical modeling to reveal that lymphatic capillaries tile space in an optimal, space-filling manner. This optimization occurs through an initial unguided invasion, followed by targeted side-branching into less densely populated network regions. Our findings underscore the ability of lymphatic networks to exploit local regulatory cues for tissue-scale optimization. Finally, we contrast this local guidance mechanism with alternative tiling strategies arising in coupled multi-component networks, such as neurovascular systems, to explore diverse principles of space-filling optimization

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

In coastal channel networks on river deltas and other coastlines, loops are found where self-formed channels branch and rejoin around an island of sediment. Such loops can persist for decades to centuries, suggesting stabilizing water and sediment dynamics. Recent theory developed through simple network models and linear stability analyses proposes that their stability might be linked to hydrodynamic fluctuations on short timescales relative to channel evolution (for example, the alternation between river floods and tides). We test this theory with an experimental loop. This loop is composed of three pipes filled with water and sediment that is forced into or out of each pipe junction and allowed to partition freely as a function of accumulated sediment in each pipe. Several preliminary findings are apparent. First, fluctuations at sufficiently rapid timescales can produce new channel stability equilibria that are not reached at long fluctuation timescales. Second, stable flows and certain hydrodynamic fluctuation sets (driven by programmable pumps) drive one pipe to fill almost completely with sediment, while other sets reach an equilibrium where all channels are open, transporting water and sediment. These findings suggest that fluctuation-controlled stability could indeed be the cause of persistent loops within coastal channel networks.

Wormholing is a process in which the interplay of flow, transport and reaction plays a crucial role. In certain flow conditions, in the dissolving rocks, the dissolution front becomes inherently unstable and splits into finger-like shapes, wormholes. The winning finger grows and competes for the available flow and, therefore, consumes more reactant, resulting in the formation of an intricate, branched network inside the rock matrix. The geometrical features of the wormhole also vary with flow conditions. For example, at low flow rates, the formed wormhole has a relatively large diameter that tapers off towards the tip. At intermediate flow rates, the wormhole tends to show minor branching. A further increase in flow rates leads to the formation of a long-and-thin channel with significant branching.

5-day workshop participants are welcome to use BIRS facilities (TCPL ) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 11AM.

By transporting material from the mountains to the ocean, rivers shape the landscapes around us. In recent work, we developed a theory that shows how the amount of sediment transported by laminar rivers in a laboratory affects their shape. How well does this theory apply to actual rivers in nature? Here we adapt this laminar theory to turbulent flow and compare it to detailed measurements collected for over more than 15 years in mountain streams of the US. The main results of the model developed for small laminar laboratory rivers hold remarkably well for natural ones, although with some significant, but mostly quantitative, differences.

We utilize transport systems daily to commute, e.g. via road networks, or bring energy to our houses through the power grid. Our body needs transport networks, such as the lymphatic, arterial or venous system, to distribute nutrients and remove waste. If the transported quantity is information, for example carried by an electrical signal, then even the internet and the brain can be thought of as members of this broad class of webs. Despite our daily exposure to transport networks, their function and physics can still surprise us. This is exemplified by the Braess paradox, where the addition of an extra road in a network, thereby increasing the loopiness of the network, worsens rather than improves traffic contrary to a naïve prediction

Many physical systems present branched structures. With the help of geomorphologists and mathematicians, they are well studied. Networks with loops are less numerous and studied. However, they are very common in biology. If their interest can be easily understood, we still need to understand how they are build (morphogenesis). At first the models that can create branched and reticulated networks are very different. For instance, branched structures are easily obtained with a scalar field, as a concentration of morphogen, while reticulated patterns are more easily obtained with tensor fields, as the mechanical constraints. However, there are several systems where a branched pattern can have a transition toward a reticulated one, as in ferns veins, river deltas, jellyfish… It is thus interesting to investigate these cases and see what type of model allow these transitions.