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In this article, the mentioned in the introduction that the the optimal shape of epithelia cells in drosophila tissue is hexagonal (packing is approximately 6).

Is there an article that proves experimentally this shape? Or we just depend on mathematics and calculating the average neighbours?

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    $\begingroup$ Welcome to Biology StackExchange! I would suggest you add some references (or explain what you mean exactly) to your claim that the optimal shape is hexagonal. Firstly, there are several biophysical models for the shape of epithelia with varying levels of complexity. Secondly, the tiling is of course not hexagonal, it has to deviate to account for topology and cell division. $\endgroup$
    – Domen
    Jul 4, 2022 at 12:22
  • $\begingroup$ @Domen, I did. Actually I am coming from more physics background. Anyway, you said "several biophysical models". All these models are mentioning that the cells are taking a hexagonal shape (of course before rounding in cell division process). I didn't find something experimental I can fed from. $\endgroup$
    – Remember
    Jul 5, 2022 at 7:46
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    $\begingroup$ You might be missing the second part of the statement in the article: "The optimal cell shape on a flat surface is typically hexagonal as this minimizes surface tension". Therefore, the optimality in the simplest biophysical model is defined as the minimization of surface tension. Under the additional constraint that the cells be the same size, the resulting optimal tiling is the hexagonal one (compare with honeycomb). However, experimentally, we generally see that the tiling is not completely hexagonal, and thus this simple model does not adequateley describe the reality. $\endgroup$
    – Domen
    Jul 5, 2022 at 11:33

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