During animal development numerous organs with functions ranging from fluid transport to signal propagation develop into highly branched shapes and forms. To ensure organ function, the formation of their geometrical and topological as well as size-dependent properties is crucial. For example, organ geometry serves to maximize exchange area with its surroundings and organ topology controls the response to fluctuations and damage. Most importantly, organ size and proportion need to scale throughout animal growth to meet the demands of increasing body size. However, how organ geometry and topology are established and scaled in a self-organized manner, remains poorly understood. In this thesis, we present a novel theoretical framework to study the self-organized growth and scaling of branched organs. In this framework, we represent the organ outline by an infinitely thin interface and consider morphogen-controlled interface evolution in growing domains. We demonstrate that an instability in interface motion can lead to the self-organized formation of complex branched morphologies and show how the interplay between interface motion, morphogen dynamics, and domain growth controls the geometrical, topological, and size-dependent properties of the resulting structures.
To understand the formation of branched structures from instabilities in morphogen-controlled interface growth, we first consider a range of different interface growth scenarios in non-growing domains. In a first approach, we present a stochastic lattice model with interface growth driven by a morphogen concentration gradient. We find a range of branched morphologies extending from self-similar fractal structures to almost circular structures with only a few branches depending on the morphogen gradient length scale. We present the Euler characteristic as an example of a topological invariant and employ it to introduce topological constraints into interface growth, leading to the formation of tree-like structures. In a second approach, we study a continuum model for morphogen-controlled interface growth. In this model, the interface has a constant tendency to grow and is inhibited by morphogen concentration. Additionally, we take into account a curvature dependency of interface growth, which leads to an effective stabilization of interface motion at small length scales. We identify branch distance and thickness as key morphological properties and discuss their regulation. We relate branch distance regulation to the interplay of destabilization from morphogen inhibition and stabilization from the curvature dependency of interface growth and explain branch thickness regulation in terms of mutual branch inhibition.
By considering interface instability in different scenarios, we overall demonstrate the robustness of our approach.
Finally, we apply our theoretical framework to study the branching morphogenesis of the planarian gut. The planarian gut is a highly branched organ that spans the entire organism and is responsible for the delivery of nutrients to the planarian body. Planarians undergo massive body size changes of more than one order of magnitude in organism length and thus constitute an ideal model organism to study the growth and scaling of branched organs. We reconsider our continuum model and include novel features needed to account for the organization of the planarian gut. We take into account external guiding cues that alter the orientation of branches and, most importantly, consider branching morphogenesis in a growing domain.
We demonstrate that our model can account for the geometrical and topological properties of the gut and show that gut scaling can arise from to the interplay of branch growth and organism growth.
Overall, we present a novel theoretical framework to study the growth and scaling of branched organs. In this framework, we demonstrate the self-organized formation of branched morphologies from instabilities in morphogen-controlled interface growth and show how the interplay of interface motion, morphogen dynamics, and system size determine geometry, topology, and size-dependent properties of the resulting structures.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:92326 |
| Date | 09 July 2024 |
| Creators | Hanauer, Christian |
| Contributors | Jülicher, Frank, Kruse, Karsten, Technische Universität Dresden, Max-Planck-Institut für Physik komplexer Systeme |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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