DyCo Dynamiques Couplées -- Coupled Dynamics

Colloquium Branching networks

From experiment to theory

*Podospora anserina* thallus growth

Biological or other physical networks can emerge from the growth of a population of growing apex by a combination of filament extension, orientation, branching and annihilation. High spatial and temporal resolution timelapses of such dynamics are currently being acquired by multiple teams across the world. These allow to track at the same time the behaviour of individual apex and the whole network formation.

How are these datasets being acquired? What data analysis tools can be put in place to analyse such complex dynamics? What kind of theoretical framework can help interpreting those results?

This workshop aims at gathering international scientists that are involved in the acquisition, analysis or theoretical understanding of branching network growth. We believe the field is at a turning point and it is time for researcher to meet and share ideas, results and techniques.

Contact and informations

The workshop is organized by Corentin Bisot (AMOLF), Thibault Chassereau (LIED), Éric Herbert (LIED) and Annemiek Cornelissen (MSC).

Scientific comitee is composed of Corentin Bisot (AMOLF), Thibault Chassereau (LIED), Éric Herbert (LIED) and Annemiek Cornelissen (MSC) and Amandine Veber

The workshop will take place over two days, on 26 and 27 June 2025, on the Paris rive gauche campus of the Université Paris Cité (Paris 13). Presentations will take place in room 322 of the Lamarck building, 35 rue Hélène Brion, nearest metro station Bibliothèque de France, metro line 14.

Program

Day 1 will be kicked off by Tom Shimizu and Mark Fricker giving an introductory duo talk presenting the history of the study of growing networks in biology and the latest advancement in high throughput data acquisition. We will continue by discovering different experimental system and watching living (and maybe non living) systems grow : mosses, fungi, but also networked organs. How is this data acquired? How is it processed? The afternoon will start with a presentation by Marc Barthelemy on spatial network, the specific class of network that all our data belongs to. What general properties to these networks have? What can be considered a trait of a network and what is simply a consequence of spatial embedding? A first dive into theory.

In day 2, we’ll indeed slowly move from timelapse datasets to theory and models. The day will open with a presentation by Stephane Douady on “ways”, an underlying structure of spatial networks that inherits important informations about their growth. We’ll then learn about different examples where network timelapses can be used to extract key growth parameters that are also important ecological traits. The afternoon will be started by Edouard Hannezo presenting a general class of branching models that reproduces the dynamics of various systems. This will be followed by two presentations presenting variations around these models to answer ecologically relevant questions.

Program will be updated with titles and abstracts.

In addition to the presentations, posters can be displayed in the room. Please use A0 format and vertical (portrait) orientation. We can take care of the printing. Please send an email to the organisers.

  26th June 27th June
9h Coffee reception Coffee reception
9h30 Mark Fricker and Tom Shimizu Stéphane Douady
10h15 Loai Gandeel Stanislaw Żukowski
10h45 Pause Pause
11h15 Carlos Aguilar Thibault Chassereau
11h45 Allon Weiner Lena Kuwata
12h15 Annemiek Cornelissen Rishabh Sharma
12h45 Lunch Lunch
14h15 Marc Barthelemy Edouard Hannezo
15h Jeanne Abitbol Maxime Lucas
15h30 Matthieu Platre John Casey
16h Discussion Discussion
17h30 Poster & drinks Poster & drinks

Titles and Abstracts

Thursday 26 June

Mark Fricker and Tom Shimizu

resp. Department of Plant Sciences University of Oxford and Amolf
To be added

Loai Gandeel

INRAE
To be added

Carlos Aguilar

University of Jyväskylä
Testing the extreme plastic mycelium hypothesis: Does grazing induce developmental plasticity in saprotrophic fungi?

Phenotypic plasticity—the ability of a genotype to alter its phenotype in response to environmental changes—can play a crucial role in maximizing fitness in fluctuating environments. However, plasticity comes at a cost, as the energy required to transform a phenotype imposes limits on its extent. While limits to plasticity are well-documented in many organisms, they are not well understood in modular organisms like filamentous fungi. Fungi have highly flexible morphologies, allowing individual organisms to adjust their phenotype in response to local environmental conditions. This flexibility has led to speculation that fungi exhibit “extreme phenotypic plasticity,” making them an interesting system for studying plasticity mechanisms. To test this idea, we analyzed the grazer-induced morphological plasticity of four cord-forming fungal species exposed to different soil microfauna with varying feeding behaviors, using a phenotypic trajectory analysis framework. We hypothesized that grazing would drive convergence towards a common “grazing-resistant phenotype” across species, due to the extreme flexibility of fungal mycelia. Alternatively, we proposed that species would follow unique developmental trajectories in response to grazers, reflecting species-specific plasticity limits. Our results showed that fungal species accounted for most of the morphological variation, with grazers having only a small but significant effect. Moreover, we did not observe convergence towards a common grazing-resistant phenotype; instead, each species followed distinct developmental pathways within species-specific limits, which varied widely. Some species altered up to 30% of their phenotype in response to grazers, while others showed as little as 1% variation. These findings suggest a more nuanced view of fungal plasticity, where morphological plasticity might not be the most effective response to grazing pressure. We speculate that the observed differences in plasticity limits may correlate with the complexity of cord formation in different species. These constraints on fungal morphological plasticity offer new insights into how fungi adapt to dynamic ecological conditions and underscore the need to explore alternative phenotypic responses to environmental pressures. Our study highlights the need to refine plasticity theories, particularly for organisms with complex, modular structures like fungi.

Allon Weiner

Centre d’Immunologie et des Maladies Infectieuses (Cimi), Inserm, Sorbonne University
Invasion of epithelial layers by the fungal pathogen Candida albicans studied by live cell imaging and volum electron microscopy

The opportunistic fungal pathogen Candida albicans is normally commensal, residing in the mucosa of most healthy individuals. In susceptible hosts, its filamentous hyphal form can invade epithelial layers leading to superficial or severe systemic infection. We study the mechanisms of epithelial invasion and host damage in vitro using live cell imaging combined with real-time damage-sensitive reporters and three-dimensional volume electron microscopy. We recently showed that C. albicans can invade successive epithelial cells without membrane breaching by inducing the formation of multi-layered host-membrane derived trans-cellular tunnels.

Lachat, J., et al. Trans-cellular tunnels induced by the fungal pathogen Candida albicans facilitate invasion through successive epithelial cells without host damage. Nat Commun 13, 3781 (2022)

Annemiek Cornelissen

MSC Université Paris Cité
morphogenesis of branching vascular networks

Marc Barthelemy

Institut de Physique théorique, IPhT, Orsay
titre: Structure and evolution of spatial networks

Many systems — from cities, transportation systems to veination patterns in leaves — can be represented as networks embedded in physical space, known as spatial networks. These networks are central to a wide range of disciplines, including physics, geography, epidemiology, urban planning, and biology. Understanding how they are structured and how they evolve over time is key to studying many complex processes. In this talk, I will provide an overview of major insights gained in recent years and highlight some of the main open challenges and promising directions for future research.

Jeanne Abitbol

CNRS, ENS de Lyon, RDP
Branching morphogenesis in moss filaments

Branching forms are ubiquitous in nature and evolved repeatedly in the eukaryotic kingdom. In the evolution of plant body plans, the innovation of branching in filaments was likely a key step prior to the innovation of three-dimensional leafy shoots. In the life cycle of mosses, the first tissue that develops from spore germination are tip-growing, branched filaments. Using Physcomitrium patens as a model species, several molecular actors regulating branching morphogenesis in filaments have been identified. However, the mechanisms governing patterning at the macroscopic scale remain unclear. To address this gap, we developed a pipeline to acquire high-resolution 3D images of protonemal filaments in the first days of spore germination. Images were segmented and analyzed to extract the cell organization of filaments. Cell organization was formalized using mathematical trees, which enabled the quantitative analysis of branching patterns. Based on our observations, we propose that branching morphogenesis in P. patens filaments can be modeled using a simple probabilistic approach, in which subapical cells have a defined probability of producing a side-branch between each apical cell division. Additional rules can be integrated to account for specific observations, such as the absence of side-branch in the first subapical cells, or potential lateral inhibition mechanisms. This simple macroscopic model provides a cellular framework for future work investigating the role of underlying molecular mechanisms. Such simple macroscopic models can also provide a unifying theoretical framework to compare macroscopic rules driving development in different species, and identify the design principles driving branching morphogenesis in filamentous organisms across kingdoms.

Matthieu Platre

Institute for Plant Sciences of Montpellier
Study of the adaptative value of the root system architecture cost-performance tradeoff using Pareto optimality framework

The root system is a critical organ to ensure the anchoring, water and nutrients uptake, and photo-assimilates transport, necessary for plant survival. To maintain these functions when exposed to environmental cues the root system altered its 3-dimensional organization in space, defined as the root system architecture (RSA)1. Depending on the environmental changes, one single genotype displays a variety of RSA to adapt accordingly, highlighting its plasticity. Therefore, the RSA plasticity is a key determinant driving plant survival and adaptation. In the context of climate change, the understanding of RSA plasticity is therefore crucial to uncover plant adaptation. The architectural plasticity can be assessed by changes of morphological (e.g. length), geometrical (e.g. depth), dynamical (e.g. growth rate), and topological descriptors. During the last half century, tremendous efforts were made to study those first three aspects due to their relatively easy assessment. Nonetheless, the analysis of RSA topology which consists of studying the efficiency and functions of a transport network remained underexplored notably by the requirements of computational analysis integrating several traits. In this talk, I will reveal how the efficiency of two root system functions, cost (growth) and performance (transport), limit the RSA plasticity finding a cost-performance tradeoff by a modeling approach based on Pareto optimality. Then, I will address how the climate change conditions that impact the root system functions decreasing water and nutrients accessibilities and promoting photo assimilates production modify the cost-performance tradeoff. Finally, I will present the experimental approaches to test the adaptative value of the root system architecture cost-performance tradeoff.

Friday 27 June

Stéphane Douady

MSC Université Paris Cité Ways in networks

Stanislaw Żukowski

Faculty of Physics, University of Warsaw
To be added

Thibault Chassereau

LIED Université Paris Cité
Full identification of a growing and branching network’s spatio-temporal structures

Experimentally monitoring the kinematics of branching network growth is a tricky task, given the complexity of the structures generated in three dimensions. One option is to drive the network in such a way as to obtain two-dimensional growth, enabling a collection of independent images to be obtained. The density of the network generates ambiguous structures, such as overlaps and meetings, which hinder the reconstruction of the chronology of connections. In this talk, we propose a general method for global network reconstruction. Each network connection is defined by a unique label, enabling it to be tracked in time and space. In this work, we distinguish between lateral and apical branches on the one hand, and extremities on the other. Finally, we reconstruct the network after identifying and eliminating overlaps. This method is then applied to the model filamentous fungus Podospora anserina to reconstruct its growing thallus. We derive criteria for differentiating between apical and lateral branches. We find that the outer ring is favorably composed of apical branches, while densification within the network comes from lateral branches. From this, we derive the specific dynamics of each of the two types. Finally, in the absence of any latency phase during growth initiation, we can reconstruct a time based on the equality of apical and lateral branching collections. This makes it possible to directly compare the growth dynamics of different thalli.

Lena Kuwata

Université Paris Cité MAP5
Quantifying the impact of different forms of stress on fungal growth

Using a stochastic growth-fragmentation process to model the growth of the mycelial network, we obtain explicit expressions for certain descriptors of fungal growth, which we can then use to infer growth parameters and quantify the impact of various forms of stress. This inference method uses the empirical distribution in length of terminal segments (portions of filament lying between an apex and a branching point) in the mycelium at some large time T and the growth rate of the total number of nodes to estimate the apical and lateral branching rates and the elongation speed. To assess the robustness of these estimates, we compare them to estimates obtained by tracking the dynamics of individual apexes in time and we also compare the experimental data to simulated data from the stochastic model using the estimated parameters.

Rishabh Sharma

Faculty of Physics, University of Warsaw
Influence of rock structure on the morphology of wormhole network

Dissolution is a highly non-linear process in which the interplay of flow, transport, and reaction leads to the emergence of reaction-infiltration instabilities. In dissolving rocks at certain flow conditions, these instabilities give rise to the formation of a network of competing channels known as dissolution channels or wormholes. The wormholes compete for the available flow, with the winning wormhole attracting a larger flow and solute concentration, screening the rest of the network and forming a highly permeable conduit through the rock. In this study, we investigate how the rock structure, such as packed layers of low porosity, can influence the shape of evolving dissolution channels. We analyze the shape of experimentally formed wormhole networks in two different types of limestone using geometric measures that account for tortuosity and branching. These measures indicate that wormholes formed perpendicular to the packed layers are more tortuous and contain more branches compared to those formed along the packed layer in higher porosity regions. We verify these observations by analyzing the pore architecture of the respective samples, obtained from microtomography scans

Edouard Hannenzo

ISTA Austria
Stochastic models of multicellular branching morphogenesis

Branching morphogenesis is a prototypical example of complex three-dimensional organ sculpting, required in multiple developmental settings to maximize the area of exchange surfaces. It requires, in particular, the coordinated growth of different cell types together with complex patterning to lead to robust macroscopic outputs. In recent years, novel multiscale quantitative biology approaches, together with biophysical modelling, have begun to shed new light of this topic. I will discuss some of these recent developments, highlighting the generic design principles that can be abstracted across different branched organs, as well as the implications for the broader fields of stem cell, developmental and systems biology.

Maxime Lucas

Nuamure institute for complex systems
Growth and structure of underground fungal networks

Arbuscular mycorrhizal fungi (AMFs) form symbiotic relationships with the roots of most terrestrial plants, playing a crucial role in nutrient exchange and ecosystem stability. In these organisms, network structure directly impacts functions such as transport efficiency, spatial exploration, and robustness. Yet, network formation is constrained by finite resources, forcing trade-offs between competing functional goals. Some species evolve structures optimized for exploration, others for resilience or efficiency. To investigate these trade-offs, we introduce a minimal spatial model of AMF network growth, based on just three local rules: hyphal growth, branching, and fusion (anastomosis). Despite its simplicity, the model generates a wide range of morphologies and reveals general principles applicable to other biological and artificial systems that self-organize through decentralized, resource-limited dynamics.

John Casey

Lawrence Livermore National Laboratory
Simulation of hyphal network growth and transport

Bioenergy crops like switchgrass benefit from their associations with mycorrhizal fungi, filamentous branching colonies that retrieve nutrients and water from the surrounding soil in exchange for plant carbon, though the partnership is dependent on the environmental context and the particular species pairing. Through imaging of arbuscular mycorrhizal fungi (AMF) colony growth, we have observed diverse morphologies among a collection of species. We are interested in how hyphal network architecture and dynamics might influence the plant-fungi resource economy, and whether we might predict which species pairs would thrive in a particular environment. We developed the Plant-Hyphosphere Resource Economy Emulator (PHREE) to simulate the growth of hyphal colonies and their nutrient return-on-carbon-investment with plants under different environmental conditions. By parameterizing simulations with high-resolution imaging, we are able to re-capture the morphology and growth of several AMF species and identify environmental optima for plant fitness. I will discuss the model design, preliminary results and identify some areas for improvement.