Study on Vibrational Behavior of Cytoskeletons Modeled by Cylindrical Tensegrity Structure

The dynamic mechanism of a cellular cytoskeleton is essential for the role of the cell, and its accurate characterization has been a long-standing problem for cell scientists. A cytoskeletons vibrations are highly influenced by interactions of filamentous proteins mediated by axial vibration of the stiff microtubules (compressive member) and lateral vibration of F-actin (tensile member). Among various structures in a cell, the cytoplasmic contractile bundles, lamellipodia, and filipodia cells can be modeled by a symmetrical cylinder-shaped self-equilibrium tensegrity structure with different radii at the top and bottom of the cylinder. The truncated conelike cylinder model is made to be small in height compared to both radii. This study investigates the tensegrity self-vibrational behavior of the cellular cytoskeleton to calculate its natural frequencies, composed of the individual vibration of microtubules and F-actins from measured data. The spectral element method is adopted based on the Wittrick-Williams procedure to solve the vibrational behaviors of the cellular cytoskeleton. Various n-polygon cylindrical truncated cone-shaped tensegrity structures to mimic the cellular cytoskeletons are presented to demonstrate the robustness of the present study.