Structure–property relation and relevance of beam theories for microtubules: a coupled molecular and continuum mechanics study

Abstract

Quasi-one-dimensional microtubules (MTs) in cells enjoy high axial rigidity but large transverse flexibility due to the inter-protofilament (PF) sliding. This study aims to explore the structure–property relation for MTs and examine the relevance of the beam theories to their unique features. A molecular structural mechanics (MSM) model was used to identify the origin of the inter-PF sliding and its role in bending and vibration of MTs. The beam models were then fitted to the MSM to reveal how they cope with the distinct mechanical responses induced by the inter-PF sliding. Clear evidence showed that the inter-PF sliding is due to the soft inter-PF bonds and leads to the length-dependent bending stiffness. The Euler beam theory is found to adequately describe MT deformation when the inter-PF sliding is largely prohibited. Nevertheless, neither shear deformation nor the nonlocal effect considered in the ‘more accurate’ beam theories can fully capture the effect of the inter-PF sliding. This reflects the distinct deformation mechanisms between an MT and its equivalent continuous body.

Modelling on the nanomechanics of cytoskeletal filaments

“…Also, based on the assumptions that the MTs could be equivalent to continuum structures, the continuum mechanics theory was widely used to explain the experimental results of MTs [11,21,56]. Theoretical investigations were also conducted in studying the natures of MTs which the experimental techniques have limited power to provide insights.…”

“…The MSM technique can establish the equivalence between the deformation of the molecular structure of MTs and the deformation of structural frame representation of MTs, and it is able to extract the materials information from MD simulation. The robustness and efficiency of the MSM model have been demonstrated in studying the different mechanical feature of MTs such as vibration and buckling [56,[78][79][80][81][82]].…”

“…It is worth mentioning that in this study, the values of k i r , k i φ , k i τ were obtained from the MD simulations in [70,77,167] and further optimized in [56], i.e.,…”

“…It follows that the variation of MT stiffness may arise from the abnormal interactions between adjacent tubulins due to pathological changes (e.g., the above-mentioned disease-causing substitutions or the cancer progression induced structural remodelling of MTs) in human body [56]. It is thus of great interest to study the dependence of the elastic moduli and vibration frequency of MTs on the strength of tubulin interaction.…”

“…MD simulations were employed to study the interface between MT and water. The obtained properties were then entered into an MSM model of MTs with updated values of force constants [56,77] to examine the effect of MT-cytosol interface on the collective vibration of MTs. The MT vibration in this study was also excited by an alternating EF from a dipole antenna ( Fig.…”