弹性介质中正交各向异性微管的屈曲分析  

Buckling of Embedded Microtubules in Elastic Medium

作　　者：穆罕默德·塔杰[1] 张俊乾[1,2] 

机构地区：[1]上海大学力学系,上海市应用数学和力学研究所,上海200072 [2]上海大学上海市力学在能源工程中的应用重点实验室,上海200072

出　　处：《应用数学和力学》2011年第3期279-285,共7页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10772105);上海市重点学科建设资助项目(S30106)

摘　　要：已有实验表明,处于细胞质中的微管可以比自由微管承受更大的压力而不发生屈曲.基于嵌入式碳纳米管屈曲的Winkler模型,利用正交各向异性情形的Winkler模型研究了细胞质中充当细胞骨架的微管的屈曲行为.计算表明,本模型可以较好地预测嵌入弹性介质中的微管较自由微管承受更大屈曲压力这一现象,而且所得到的临界屈曲压力与微管受压屈曲的实验值吻合[Needleman D J,Ojeda-Lopez M A,Kai Ewert U R,Miller H P,Wilson L,Safiny C R.Biophys J,2005,89(5):3410-3423;Needleman D J,Ojeda-Lopez M A,Raviv U,Ewert K,Jones J B,Miller HP L,Wilso L,Safinya C R.Phys Rev Lett,2004,93(19):1981041-1981044.].同时,所得的结果也表明周围介质与微管的相互作用可以极大地提高微管抵抗屈曲的能力,该结果很好地阐释了介质与微管相互作用从而提高微管抗屈曲压力的相互作用机制[Brangwynne C P,MacKintosh F C,Ku-mar S,Geisse N A,Talbot J,Mahadevan L,Parker K K,Ingber D E,Weitz D A.The Journal of CellBiology,2006,173(5):733-741].模拟结果表明,所给出的模型可以对嵌入弹性介质中的微管的屈曲行为进行很好地模拟.Motivated by the application of Winkler-like model for buckling analysis of embedded carbon nanotubes,an orthotropic Winkler-like model was developed to study buckling behavior of embedded cytoskeletal microtubules within cytoplasm.Experimental observations of buckling of embedded cytoskeletal microtubules reveal that embedded microtubules bear a large compressive force as compared to free microtubules.Our theoretical model predicts that embedded microtubules in elastic medium bear large compressive forces than free microtubules.The estimated critical pressure is found not only in good agreement with the experimental values of pressure-induced buckling of microtubules [Needleman D J,Ojeda-Lopez M A,Kai Ewert U R,Miller H P,Wilson L,Safiny C R.Biophys J,2005,89（5）： 3410-3423;Needleman D J,Ojeda-Lopez M A,Raviv U,Ewert K,Jones J B,Miller H P L,Wilso L,Safinya C R.Phys Rev Lett,2004,93（19）： 1981041-1981044.].But also,due to mechanical coupling of microtubules with surrounding elastic medium,critical buckling force has increased considerably,which well explains the theory that mechanical coupling of microtubules with the elastic medium increases compressive forces that microtubules can sustain [Brangwynne C P,MacKintosh F C,Kumar S,Geisse N A,Talbot J,Mahadevan L,Parker K K,Ingber D E,Weitz D A.The Journal of Cell Biology,2006,173（5）： 733-741] suggesting that the present model is a good approximation for buckling analysis of embedded microtubules.

关 键 词：微管 屈曲 正交各向异性Winkler模型 弹性介质 

分 类 号：O343[理学—固体力学] Q66[理学—力学]