弹性介质中正交各向异性微管的屈曲分析

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\．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\．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．

Buckling of Embedded Microtubules in Elastic Medium

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 microtubulesNeedleman 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 sustainBrangwynne 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.