Abstract
A tissue is a geometrical, space-filling, random cellular network; it remains in this steady state while individual cells divide. Cell division is a local, elementary topological transformation which establishes statistical equilibrium of the structure. We describe the physical conditions to maintain stationary the epidermis (of mammals or of the cucumber), in spite of the fact that cells constantly divide and die. Specifically, we study the statistical equilibrium of the basal layer, a corrugated surface filled with cells, constituting a two-dimensional topological froth. Cells divide and detach from the basal layer, and these two topological transformations are responsible for the stationary state of the epidermis. The topological froth is capable of responding rapidly and locally to external constraints, and is a good illustration of the plasticity of random cellular networks.
Statistical equilibrium is controlled by entropy, both as a measure of disorder and as information, and is characterized by observable relations between average cell shapes and sizes. The technique can be applied to any random cellular network in dynamical equilibrium. Mitosis as the dominating topological transformation and the fact that the distribution of cell shapes is very narrow are the only inputs specific to biology.
Resume
Un tissu est, à première vue, un pavage aléatoire d'une surface ou d'un volume par des polygones (polyèdres) topologiques, les cellules. Ce pavage reste dans un état stationnaire alors que les cellules se divisent constamment. Nous décrivons les conditions physiques nécessaires à l'état stationnaire de l'épiderme (des mammifères et du concombre), en dépit du fait que ses cellules se divisent et meurent. En particulier, nous étudions l'équilibre statistique de la couche basale, une surface couverte de cellules constituant une mousse topologique aléatoire. Les cellules se divisent et se détachent de la couche basale, et ces transformations topologiques sont responsable de l'état stationnaire de l'épiderme. Cette mousse topologique est capable de répondre rapidement et localement à des contraintes externes. C'est un exemple de plasticité de structures cellulaires aléatoires.
L'équilibre statistique est contrôlé par l'entropie qui est ici à la fois une mesure du désordre et une quantité d'information. Il est caractérisé par des relations facilement observables entre les formes des cellules et leurs dimensions. Les seuls éléments spécifiques aux tissus biologiques sont la mitose comme transformation topologique dominante, et l'étroitesse de la distribution des formes de cellules.
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Rivier, N., Schliecker, G. & Dubertret, B. The stationary state of epithelia. Acta Biotheor 43, 403–423 (1995). https://doi.org/10.1007/BF00713562
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DOI: https://doi.org/10.1007/BF00713562