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

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 spectrums 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.