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.

A three-dimensional (3D) transverse vibration was reported based on the molecular structural mechanics (MSM) model for microtubules (MTs), where the bending axis of the cross section rotates in an anticlockwise direction and the adjacent half-waves oscillate in different planes. Herein, efforts were invested to capturing the physics behind the observed phenomenon and identifying the important factors that influence the rotation angle between adjacent two half waves. A close correlation was confirmed between the rotation of the oscillation planes and the helical structures of MTs, showing that the 3D mode is a result of the helicity found in MTs. Subsequently, the wave length-dependence and the boundary condition effects were also investigated for the 3D transverse vibration of MTs. In addition, the vibration frequency was found to remain the same in the presence or absence of the bending axis rotation. This infers that the unique vibration mode is merely due to the bending axis rotation of the cross section but no significant torsion occurs for MTs.

An electric field (EF) has the potential to excite the vibration of polarized microtubules (MTs) and thus enable their use as a biosensor for the biophysical properties of MTs or cells. To facilitate the development, this paper aims to capture the EF-induced vibration modes and the associated frequency for MTs. The analyses were carried out based on a molecular structural mechanics model accounting for the structural details of MTs. Transverse vibration, radial breathing vibration and axial vibration were achieved for MTs subject to a transverse or an axial EF. The frequency shift and stiffness alteration of MTs were also examined due to the possible changes of the tubulin interactions in physiological or pathological processes. The strong correlation achieved between the tubulin interaction and MT vibration excited by EF provides a new avenue to a non-contacting technique for the structural or property changes in MTs, where frequency shift is used as a biomarker. This technique can be used for individual MTs and is possible for those in cells when the cytosol damping on MT vibrations is largely reduced by the unique features of MT–cytosol interface.

A molecular structural mechanics (MSM) model was developed for F-actins in cells, where the force constants describing the monomer interaction were achieved using molecular dynamics simulations. The MSM was then employed to predict the mechanical properties of F-actin. The obtained Young's modulus (1.92 GPa), torsional rigidity (2.36×10-26 Nm 2) and flexural rigidity (10.84×10-26 Nm 2) were found to be in good agreement with existing experimental data. Subsequently, the tension-induced bending was studied for F-actins as a result of their helical structure. Mechanical instability was also investigated for the actin filaments in filopodial protrusion by considering the reinforcing effect of the actin-binding proteins. The predicted buckling load agreed well with the experimentally obtained stall force, showing a pivotal role of the actin-binding protein in regulating the stiffness of F-actin bundles during the formation of filopodia protrusion. Herein, it is expected that the MSM model can be extended to the mechanics of more complex filamentous systems such as stress fibers and actin meshwork.

In cells, the protein cross-linkers lead to a distinct buckling behavior of microtubules (MTs) different from the buckling of individual MTs. This paper thus aims to examine this issue via the molecular structural mechanics (MSM) simulations. The transition of buckling responses was captured as the two-dimensional-linkers were replaced by the three-dimensional (3D) ones. Then, the effects of the radial orientation and the axial density of the 3D-linkers were examined, showing that more uniform distribution of the radial orientation leads to the higher critical load with 3D buckling modes, while the inhomogeneity of the axial density results in the localized buckling patterns. The results demonstrated the important role of the cross-linker in regulating MT stiffness, revealed the physics of the experimentally observed localized buckling and these results will pave the way to a new multi-component mechanics model for whole cells.