Predicting buckling behavior of microtubules based on an atomistic-continuum model

An atomistic-continuum model is proposed for microtubules. A higher-order gradient continuum constitutive relationship is established, and elasticity and global buckling of microtubules are studied intensively. As a typical macromolecular bio-system, atomic components and structures are much more complicated. Traditional atomistic simulation methods and classical continuum approaches have their own fundamental drawbacks in dealing with this large atomic system. Adopting a homogenization technique, this paper proposes a concept of fictitious bonds for microtubules to link the large atomic structure with continuum description. After selecting a representative unit, the fictitious bond energy equals to the energy stored in the continuum model. The higher-order Cauchy-Born rule is used to approximate the deformation of fictitious bonds under arbitrary loading conditions. A mesh-free numerical scheme is specifically developed for modeling computation. The elastic modulus and critical compressive force are predicted. Representative case studies are presented, and some results are obtained and discussed. (C) 2011 Elsevier Ltd. All rights reserved.