A multiscale model to predict the elastic property of microtubules

This paper presents a multiscale method to estimate the elastic property of microtubules. A microtubule is viewed as being formed by rolling up its equivalent planar structure into the tubular shape, and the transformation is precisely written into a set of equations with three geometrical parameters. The representative cell is chosen as a triangle unit that contains two tublin monomers and one guanosine triphosphate (GTP) or guanosine diphosphate (GDP) molecule, and its energy is calculated as the sum of one noncovalent bond between one tublin and GDP/GTP molecule and one lateral noncovalent bond between two lateral adjacent tublins. In the proposed multiscale model, the longitudial shift between two adjacent proptofilaments are incroporated into. The longitudial and lateral interactions are modeled with two analytical expressions, and an angle potantial is adopted to compensate the error that is produced by the model of grid balls. The elastic property of microtubule is determined by minimizing the strain energy density, and the elastic constants are calculated in the thereotical scheme of orthotropic elasticity due to the geometrical meanings of three unknown geometrical parameters. It is in detail discussed why the longitudial shift and the angle potential should be used. Copyright © 2012 American Scientific Publishers.