Abstract
Transformation of biological inherent information into the spatial organization of an organism is a major challenge of modern developmental biology. The aim of this paper is to find a complete and sufficient description of the regular spatiotemporal structure of the multicellular organisms using plants as a basic model. The locally reiterative development of the real organism’s structures was regarded as a combinatorial map from a globally regular space with a proper group action. Such a space was considered as a “developmental program” of the organism. The following questions are resolved here: (1) formalistic description of spatiotemporal structure of the real organisms at the cellular and tissue levels of organization in terms of graphs; (2) definition of regularities and flexibility in the structure development in terms of groups acting on graphs; (3) the basic species-specific properties and principles of reiterative work of “developmental program” spaces. We believe that the considerable and appropriate formalization of biological spatiotemporal data opens the possibilities for revealing the correspondence between structural mechanisms at incomparably different levels of organization, such as molecular-genetic, cellular and morphological levels.
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Notes
- 1.
A group element or subgroup generator is written as a left product of group generators. For example, \( ab{{a}^2} = (a(b(aa)) \).
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Acknowledgments
The author would like to thank M. L. Gromov and N. Morozova for their valuable remarks and discussion of many questions touched in this work. The existence of similar species-specific “hyperbolic laws” of cell divisions was suggested earlier by M. Gromov [21], whose work has considerably influenced to the creation of this paper.
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Rudskiy, I.V. (2013). Formalistic Representation of the Cellular Architecture in the Course of Plant Tissue Development. In: Capasso, V., Gromov, M., Harel-Bellan, A., Morozova, N., Pritchard, L. (eds) Pattern Formation in Morphogenesis. Springer Proceedings in Mathematics, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20164-6_19
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