Modélisation micro-mécanique des microtubules.

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Arslan, Mélis (2010) Modélisation micro-mécanique des microtubules. Doctorat Mécanique, MAT- Centre des matériaux P.M Fourt, ENSMP p.200.

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Résumé

Les microtubules sont des composants structuraux de cellules et gouvernent des fonctions

cellulaires essentielles telles que les mitoses et le transport des vésicules. Ils sont

composés de deux sous-unités non identiques (tubulines α et β), formant un dimère, et

sont arrangés de sorte à former une structure tubulaire de 20nm de diamètre.

Généralement, ils sont constitués de 13 ou 14 protofilaments arrangés en spirale. Les

liaisons longitudinales entre dimères sont plus rigides et fortes que les liaisons latérales.

Aussi, les microtubules sont des structures fortement anisotropes.

Dans ces travaux de thèse, nous avons pour but de définir l’ensemble des coefficients

élastique qui permet de reproduire leur comportement atomistique ainsi que de rendre

compte de leur réponse mécanique selon des chemins de chargement variés. En

négligeant la discontinuité hélicoïdale souvent observée, un microtubule est représenté

par une structure triangulaire de dimères à partir desquels un volume élémentaire

représentatif est défini. Un potentiel harmonique est utilisé pour décrire les interactions

entre dimères voisins. A partir de l’estimation des constantes élastiques et de l’utilisation

de la méthode proposée par Arslan et Boyce (2006) -alors pour analyser le comportement

mécanique d’un réseau triangulaire de spectrines composant les membranes des globules

rouges-, un modèle continu de comportement mécanique est présenté pour reproduire le

comportement des parois des microtubules. Un modèle numérique éléments finis est

ensuite créé pour modéliser le comportement d'un microtubule dans sa globalité. Des

éléments coques sont utilisés pour reproduire les fines parois des microtubules. Les

propriétés du modèle éléments finis sont ajustées à partir des résultats du modèle présenté

ainsi qu'aux données expérimentales provenant de la littérature. La rigidité de flexion

calculée au cours de simulation des tests de flexion 3 points est en accord avec les valeurs

de la littérature. Ces tests révèlent les mécanismes de déformation en fonction de la

longueur utile du tube utilisé: Flexion et cisaillement locaux de la paroi gouvernent la

déformation pour de "petits" tubes. Pour des longueurs "moyennes" le cisaillement et la

flexion du tube prédominent. Enfin, dans le cas de tubes "longs", la déformation est

uniquement associée aux effets de flexion. Ces résultats témoignent de l’influence de

l'anisotropie du tube sur la réponse observée selon différents mode de sollicitation. Ils

permettent également d’expliquer l'évolution de la rigidité de flexion avec la longueur

utile du tube, comme reportée dans la littérature. Enfin, des micrographes montrent la

propension des extrémités des microtubules à diverger radialement -"à boucler"-. Une

telle géométrie est causée par des instabilités propres aux microtubules et implique un

état précontraint. Un «modèle d'interactions» est alors proposé de manière à considérer

un état précontraint et ainsi reproduire la cinétique des instabilités des microtubules au

cours de la polymérisation/dépolymérisation.

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