Lewis' law gives a relationship between the size and the shape of epithelial cells. It states that the average apical area of an epithelial cell is linearly related to its neighbor number . It is a phenomenological law that was first described in the cucumber epidermis by the morphologist Frederic Thomas Lewis in 1928.[1] The simplest version of Lewis' law can be expressed as , which reads: The average apical area of a cell with neighbors (divided by the average apical area of all cells) is proportional to its shape. While neighbor number distributions change throughout organogenesis, the average neighbor number of epithelial cells is , which can be traced back to Euler's formula for polygons.[2]

Discovery

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Frederic Thomas Lewis noticed that epidermal cells display a patterning similar to froths, which led him to quantify and analyze the sizes and shapes of epidermal cells.[1]

Confirmation and mechanism

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A variety of empirical studies in different epithelial tissues have confirmed Lewis' law.[3][4][5]

It has been suggested [6] that the emergence of Lewis' law on the apical surface of epithelia is a result of the concurrence of

  • the tendency of cells to minimize intercellular contact surface energy, and
  • the distribution of apical cell areas (as a result of cellular processes such as cell division).

According to this theory, the observed tissue-specific polygon distributions and Lewis' law arise as a compromise in order to maintain tissue integrity.

Importance

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In order to understand morphogenetic events, i.e. the growth and shaping of tissues and organs, it is necessary to analyze the packing of cells into tissues. In that context, an analysis of patterning processes can help to identify the underlying mechanisms that drive morphogenesis.

References

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  1. ^ a b Lewis, Frederic T. (1928). "The correlation between cell division and the shapes and sizes of prismatic cells in the epidermis of cucumis". The Anatomical Record. 38 (3): 341–376. doi:10.1002/ar.1090380305. ISSN 1097-0185.
  2. ^ Rivier, N.; Lissowski, A. (March 1982). "On the correlation between sizes and shapes of cells in epithelial mosaics". Journal of Physics A: Mathematical and General. 15 (3): L143–L148. doi:10.1088/0305-4470/15/3/012. ISSN 0305-4470.
  3. ^ Babu, M. Madan; Freeman, Matthew; Briscoe, James; Kicheva, Anna; Costa, Luciano da F.; Escudero, Luis M. (2011-11-08). "Epithelial organisation revealed by a network of cellular contacts". Nature Communications. 2: 526. Bibcode:2011NatCo...2..526E. doi:10.1038/ncomms1536. ISSN 2041-1723. PMC 3672852. PMID 22068593.
  4. ^ Escudero, Luis M.; Mao, Yanlan; Pascual, Alberto; Barry, Joseph D.; Tozluoglu, Melda; Sánchez‐Gutiérrez, Daniel (2016-01-04). "Fundamental physical cellular constraints drive self‐organization of tissues". The EMBO Journal. 35 (1): 77–88. doi:10.15252/embj.201592374. ISSN 1460-2075. PMC 4718000. PMID 26598531.
  5. ^ Heller, Davide; Hoppe, Andreas; Restrepo, Simon; Gatti, Lorenzo; Tournier, Alexander L.; Tapon, Nicolas; Basler, Konrad; Mao, Yanlan (January 2016). "EpiTools: An Open-Source Image Analysis Toolkit for Quantifying Epithelial Growth Dynamics". Developmental Cell. 36 (1): 103–116. doi:10.1016/j.devcel.2015.12.012. ISSN 1534-5807. PMC 4712040. PMID 26766446.
  6. ^ Kokic, Marco; Iannini, Antonella; Villa-Fombuena, Gema; Casares, Fernando; Iber, Dagmar (2019-03-27). "Minimisation of surface energy drives apical epithelial organisation and gives rise to Lewis' law". bioRxiv: 590729. doi:10.1101/590729. hdl:20.500.11850/390015.