A molecular structural mechanics (MSM) method has been implemented to investigate the free vibration of microtubules (MTs). The emphasis is placed on the effects of the configuration and the imperfect boundaries of MTs. It is shown that the influence of protofilament number on the fundamental frequency is strong, while the effect of helix-start number is almost negligible. The fundamental frequency is also found to decrease as the number of the blocked filaments at boundaries decreases. Subsequently, the Euler-Bernoulli beam theory is employed to reveal the physics behind the simulation results. Fitting the Euler-Bernoulli beam into the MSM data leads to an explicit formula for the fundamental frequency of MTs with various configurations and identifies a possible correlation between the imperfect boundary conditions and the length-dependent bending stiffness of MTs reported in experiments.

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.

The size scale effect on the pyroelectric properties is studied for gallium nitride (GaN) nanowires (NWs) based on molecular dynamics simulations and the theoretical analysis. Due to the significant influence of the surface thermoelasticity and piezoelectricity at the nanoscale, the pyroelectric coefficient of GaN NWs is found to depend on the cross-sectional size. This size-dependent pyroelectric coefficient of GaN NWs together with the size-dependent dielectric constant reported in our previous study is employed to study the pyroelectric potential of GaN NWs subjected to heating. The results show that the size scale effect is significant for thin NWs (cross-sectional size in nanometers) and may raise the pyroelectric potential of GaN NWs by over 10 times. Such a size scale effect on the pyroelectric properties of NWs originates from the influence of thermoelasticity, piezoelectricity, and dielectricity at the nanoscale and decreases with increasing cross-section of GaN NWs. It is expected that the present study may have strong implication in the field of energy harvesting at the nanoscale, as pyroelectricity offers a new avenue to the design of novel nanogenerators.

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.