Mathematical Approaches of Branching Morphogenesis

Abstract

Many organs require a high surface to volume ratio to properly function. Lungs and kidneys, for example, achieve this by creating highly branched tubular structures during a developmental process called branching morphogenesis. The genes that control lung and kidney branching share a similar network structure that is based on ligand-receptor reciprocal signalling interactions between the epithelium and the surrounding mesenchyme. Nevertheless, the temporal and spatial development of the branched epithelial trees differs, resulting in organs of distinct shape and size. In the embryonic lung, branching morphogenesis highly depends on FGF10 signalling, whereas GDNF is the driving morphogen in the kidney. Knockout of Fgf10 and Gdnf leads to lung and kidney agenesis, respectively. However, FGF10 plays a significant role during kidney branching and both the FGF10 and GDNF pathway converge on the transcription factors ETV4/5. Although the involved signalling proteins have been defined, the underlying mechanism that controls lung and kidney branching morphogenesis is still elusive. A wide range of modelling approaches exists that differ not only in the mathematical framework (e.g., stochastic or deterministic) but also in the spatial scale (e.g., cell or tissue level). Due to advancing imaging techniques, image-based modelling approaches have proven to be a valuable method for investigating the control of branching events with respect to organ-specific properties. Here, we review several mathematical models on lung and kidney branching morphogenesis and suggest that a ligand-receptor-based Turing model represents a potential candidate for a general but also adaptive mechanism to control branching morphogenesis during development.

Fgf10/Fgfr2b Signaling Orchestrates the Symphony of Molecular, Cellular, and Physical Processes Required for Harmonious Airway Branching Morphogenesis

“…As such, computationally modeling biological systems in general, and branching morphogenesis in particular, has proved challenging. This is evidenced by the number of different models of lung branching morphogenesis which have been proposed (for reviews, see Iber and Menshykau, 2013 ; Miura, 2015 ; Varner and Nelson, 2017 ; Lang et al, 2018 ). Here, we briefly discuss two compatible classes of models which continue to garner interest and support: fractal-based geometric models and ligand-receptor based Turing models.…”

“…There are, in addition, purely physical means by which a structure can branch, which depend upon a set of rules that can be computationally modeled. Researchers are beginning to wed these physical rules to our biological understanding of branching morphogenesis, painting an intriguing picture of the regulatory interplay between physics and biology (see reviews by Iber and Menshykau, 2013 ; Lang et al, 2018 ).…”

Current strategies and opportunities to manufacture cells for modeling human lungs

“…Other critical genes and regulatory networks associated with FGF signaling also contribute to controlling the periodicity of the branched network [ 95 ]. Although elements such as domain specification, bifurcation, rotation and branch generation remain largely undetermined [ 93 , 96 ], new technologies involving high-resolution live imaging, tension sensing, and force-mapping are opening paths to further explore and explain the branching morphogenesis phenomenon [ 97 ].…”

Design Principles of Branching Morphogenesis in Filamentous Organisms

“…In most cases, branched animal tissue development consists of the ramification of an epithelium (i.e,. the outer layer of the duct) embedded in a supporting mesenchyme (i.e., a type of loosely organized connective tissue), and relies on various stereotyped cell behaviors including cell migration, proliferation, rearrangement and deformation (see [9][10][11][12][13] for a detailed account on the cellular basis of branch formation in animal organs). Meanwhile, plant and fungal filamentous organisms form branches from existing filamentous cells rather than from a multicellular epithelium, and must carefully orient their growth since their rigid cell walls make them incapable of the rearrangements observed in animal tissues ( Figure 3).…”

“…Branching is also a conspicuous morphological feature of multicellular organisms with parenchymatous bodies of varying complexity, including land plants [8], and numerous vertebrate and invertebrate animal organs such as the lung, kidney, mammary gland, prostate gland, vasculature (blood vessels) and tracheal system [9,10]. The regulation of their morphogenesis has been extensively investigated at the molecular and cellular levels, and exhaustive reviews have been written on these topics (see for example [9][10][11][12][13] for animal organs, and [14][15][16] for plants). In animals, recent work has successfully combined high-resolution microscopy and computational modeling to gain insight into the three-dimensional organization of branched organs, without extensively addressing the underlying molecular logic.…”