Preprint Review Version 1 Preserved in Portico This version is not peer-reviewed

Living Cell’s Feeling of Holes: The Mathematics of Cavities in Biophysical Structures

Version 1 : Received: 16 April 2022 / Approved: 18 April 2022 / Online: 18 April 2022 (06:14:33 CEST)

How to cite: Tozzi, A. Living Cell’s Feeling of Holes: The Mathematics of Cavities in Biophysical Structures. Preprints 2022, 2022040156 (doi: 10.20944/preprints202204.0156.v1). Tozzi, A. Living Cell’s Feeling of Holes: The Mathematics of Cavities in Biophysical Structures. Preprints 2022, 2022040156 (doi: 10.20944/preprints202204.0156.v1).

Abstract

Mechanical properties such as shape, volume and size affect the dynamics of biological systems. Most of the current methodological approaches are inclined to remove the existence of holes and impurities from systems’ description, regarding them as routes toward mechanical failure. On the contrary, we suggest that the occurrence of holes might be of utmost functional importance, allowing reversible transformations of cellular structures. The focus here is on the widespread occurrence of intracytoplasmic holes, that deeply modifies the topology of living cells and provides researchers with novel operational tools to investigate intracellular dynamics. We take as example the prokaryotic gas vesicles, i.e., intracellular cavities filled with gases spreading from the nearby medium. The mechanical and topological cellular properties dictated by intracytoplasmic holes are investigated, focusing on the physical constraints imposed by their very existence. For instance, the presence of gas vesicles breaks the cytoplasmic homogeneity, leading to inhomogeneity in functional activities and modifications in intracellular flows. Also, a topological approach to cytoplasmic holes suggests novel physiological roles for gas vesicles. For example, the gas vesicles’ ability to increase/decrease cellular volumes provides a mechanism that counteracts the detrimental effects of the surface/volume ratio. In conclusion, a structural/methodological approach based on the occurrence of holes testifies once again how the simple biophysical structure alone can dictate the function.

Keywords

nanovesicles; flow; homology; vortex; Betti number; Borsuk–Ulam theorem

Subject

LIFE SCIENCES, Biophysics

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