A computational framework for transverse compression of microtubules based on a higher-order Cauchy–Born rule

This work presents a computational framework for the transverse compression of microtubules using the Cauchy–Born rule. Atomistic-continuum simulation and mesh-free method are employed in the computation for the theoretical scheme of the higher-order gradient continuum. Elastic properties and mechanical responses of microtubules under transverse compression are intensively studied. Without tracing each atom in large protein structures, a homogenization technique is proposed to evaluate interatomic energy stored among macromolecules. The concept of fictitious bonds is proposed for microtubules to bridge the gap between the atomistic simulation and the continuum approach, which is of great significance for application of the continuum approach to macromolecular structures. To reflect the inhomogeneous deformations of a cylindrical structure, the higher-order Cauchy–Born rule is employed to calculate the fictitious bond vectors emanating from a given evaluation point during the deformation process. By selecting a representative unit, a higher-order gradient continuum constitutive relationship is established to take atomistic interactions into consideration. Elastic modulus and transverse mechanics, including critical hydrostatic pressure and transverse compression-induced structure transitions, are numerically simulated. Example problems are carefully selected and the obtained results are discussed in detail.