Hadrien Oliveri

Plant morphogenesis relies on dynamic growth deformations at the cell and tissue scales driven by osmotic fluxes. A mechanistic understanding of this phenomenon demands a physical framework that integrates cell imbibition, tissue mechanics and water fluxes, as well as their biophysical and molecular regulations, within a theory of plant active matter capturing the open-system and out-of-equilibrium properties of tissues. Building on historical insights into growth geometry, physics and mechanics, combined with recent experimental results, we outline the key challenges in modelling plant growth and propose steps towards a unified physical theory of plant morphogenesis, in which biological regulation, mechanical forces and water fluxes interact to shape biological form through the fundamental principles of living matter.

Mathematical network models are extremely useful to capture complex propagation processes between different regions (nodes), e.g. the spread of an infectious agent between different countries, or the transport and replication of toxic proteins across different brain regions in neurodegenerative diseases. In these models, transport is modelled at the macroscale through an operator, the so-called graph Laplacian , based on the edge properties and topology, capturing the fluxes between different nodes of the network. However, this phenomenological approach fails to take into account the physical processes taking place, at the microscale, within the edge. A fundamental problem is then to obtain a transport operator from mechanistic principles based on the underlying transport process. Using advection-reaction-diffusion as a generic mechanism for inter-nodal exchanges, we derive a multiscale network transport model and derive the corresponding linear transport operator at the macroscale from first principles. This effective graph Laplacian is fully determined by the transport mechanisms along the edges at the microscale. We show that this operator correctly captures the transport, and we study its scaling properties with respect to edge length.

Rôle de la rétroaction mécanique dans la morphogenèse des plantes: L'acquisition de la forme - ou morphogenèse - chez les systèmes vivants, est largement contrôlée par les gènes. Néanmoins, le lien précis entre, d'une part, les processus chimiques locaux associés aux gènes, et, d'autre part, la géométrie des tissus, n'est pas complètement identifié. Ce lien est vraisemblablement très indirect et médié par des processus mécaniques. Ainsi, il est aujourd'hui admis que les processus chimiques intracellulaires régulent les propriétés mécaniques des cellules seulement localement, et que la forme émerge comme la résolution globale de contraintes mécaniques. Ce paradigme, dit biomécanique, est employé dans cette thèse dans le cas de la morphogenèse des plantes, qui repose majoritairement sur la croissance cellulaire. Le contrôle local de cette croissance est crucial pour la stabilité et la robustesse de la morphogenèse, et implique différents mécanismes de régulation. En particulier, selon une hypothèse récente, les cellules pourraient adapter dynamiquement leur croissance en réponse aux forces qu'elles subissent.Cette régulation locale s'intègre à une échelle multicellulaire de manière non intuitive. Dans cette thèse, j'ai exploré i/ une formalisation mathématique de la régulation de la croissance par les contraintes mécaniques et ii/ le comportement macroscopique émergent d'un tel mécanisme. Pour cela, j'ai adopté une approche de modélisation multi-échelle basée sur une formulation mathématique continue de la croissance cellulaire (développée précédemment dans le cadre de la théorie de la morphoélasticité), et sur une description moyenne des processus moléculaires locaux étant supposés impliqués dans la mécano-perception et le contrôle de l'élasticité des cellules. J'ai d'autre part conçu des algorithmes dédiés à l'étude de ce modèle, intégrés dans un environnement logiciel existant, basé sur la méthode des éléments finis. Ce modèle est en particulier utilisé dans l'étude de la stabilité d'organes à fort degré d'asymétrie, tels que les feuilles, en suggérant qu'un contrôle de la croissance basé sur les forces peut permettre l'amplification d'asymétries initiales.

Plant morphogenesis relies on dynamic growth deformations at the cell and tissue scales driven by osmotic fluxes. A mechanistic understanding of this phenomenon demands a physical framework that integrates cell imbibition, tissue mechanics, and water fluxes, as well as their biophysical and molecular regulations, within a theory of plant active matter capturing the open-system and out-of-equilibrium properties of tissues. Building on historical insights into growth geometry, physics, and mechanics, combined with recent experimental results, we outline the key challenges in modelling plant growth and propose steps towards a unified physical theory of plant morphogenesis, in which biological regulation, mechanical forces, and water fluxes interact to shape biological form through the fundamental principles of living matter.

Mathematical network models are extremely useful to capture complex propagation processes between different regions (nodes), for example the spread of an infectious agent between different countries, or the transport and replication of toxic proteins across different brain regions in neurodegenerative diseases. In these models, transport is modeled at the macroscale through an operator, the so-called graph Laplacian, based on the edge properties and topology, capturing the fluxes between different nodes of the network. However, this phenomenological approach fails to take into account the physical processes taking place at the microscale within the edge. A fundamental problem is then to obtain a transport operator from mechanistic principles based on the underlying transport process. Using advection-reaction-diffusion as a generic mechanism for inter-nodal exchanges, we derive a multiscale network transport model and obtain the corresponding linear transport operator at the macroscale from first principles. This effective graph Laplacian is fully determined by the transport mechanisms along the edges at the microscale. We show that this operator correctly captures the transport, and we study its scaling properties with respect to edge length.

Neurotoxic protein fragments such as amyloid-beta and tau accumulate in characteristic staging patterns in Alzheimer’s disease (AD). The brain clears such metabolic substances via multiple different systems, including via the glymphatic (extracellular/extravascular) pathway. Here, we ask how the distinct features that characterize human glymphatic function would affect the prion-like cascade of protein invasion associated with AD. To address this question, we extract and analyze individual clearance rates from human glymphatic MRI (gMRI) data sets. These clearance rates define subject-specific maps of glymphatic clearance that vary both across cortical lobes and Braak staging regions. We apply these clearance maps as initial states in a computational network model linking misfolded proteins, tissue damage, and local clearance to simulate a series of individual proteinopathy trajectories. Our results show that the spatial heterogeneity in initial clearance induces characteristic propagation patterns, delaying and redirecting the disease progression. Moreover, reducing this spatial heterogeneity accelerates disease progression and induces staging patterns typically associated with AD. A comparison between well-rested subjects and subjects who underwent a single night of sleep deprivation did not reveal differences in initial clearance maps nor in simulated disease progression. These findings suggest that spatial heterogeneity in brain clearance may be a key factor for neurodegenerative resilience.

The growth of plants is a hydromechanical phenomenon in which cells enlarge by absorbing water, while their walls expand and remodel under turgor-induced tension. In multicellular tissues, where cells are mechanically interconnected, morphogenesis results from the combined effect of local cell growths, which reflects the action of heterogeneous mechanical, physical, and chemical fields, each exerting varying degrees of nonlocal influence within the tissue. To describe this process, we propose a physical field theory of plant growth. This theory treats the tissue as a poromorphoelastic body, namely a growing poroelastic medium, where growth arises from pressure-induced deformations and osmotically-driven imbibition of the tissue. From this perspective, growing regions correspond to hydraulic sinks, leading to the possibility of complex non-local regulations, such as water competition and growth-induced water potential gradients. More in general, this work aims to establish foundations for a mechanistic, mechanical field theory of morphogenesis in plants, where growth arises from the interplay of multiple physical fields, and where biochemical regulations are integrated through specific physical parameters.