Dynamic behaviors of long and curved microtubules based on an atomistic-continuum model

摘要

This paper analyses dynamic response and vibration characteristics of long microtubules. Mechanical aspects of material properties are described based on an atomistic-continuum model and the use of a higher-order Cauchy-Born rule that bridges the scale between microstructures and continuum description. Long microtubules are simulated with one-dimensional strips, which include microscale interaction among protein molecules and can be dealt with using continuum mechanical approaches under higher-order gradient continuum scheme. Based on Hamilton's principle, the differential equation of motion is established and is incorporated in the higher-order gradient continuum mesh-free framework. The performances of structures of microtubules are determined by direct numerical integration in time domain and applying the Fourier transform technique in frequency domain. Time-histories and frequency spec-trums are obtained to determine vibration characteristics. Curved shapes of microtubules are involved in the study. Different cases are considered and compared, and the results are presented and discussed.