Actin filaments play significant roles in many essential cellular processes including muscle contraction, cell motility, vesicle and organelle movement, cell signaling, and mechano-sensing mechanism of cells. However, one of the important cellular processes, the mechano-sensing mechanism of cells, is still debatable. To elucidate these mechanisms of cellular processes, it is important to observe the remodeling of the F-actin structure in cells. Although there are many reports about the remodeling of the F-actin structure during cellular processes, it needs to consider that the intracellular and extracellular proteins are fluctuating with thermal energy. We assumed that these small fluctuations affect the mechano-transduction in cells. We focused on an F-actin small fluctuation and tried to observe that in a living cell. Here, we propose the analyzing method of F-actin fluctuation in a living cell using the quasi super-resolution technique. To visualize F-actin filaments in living cells, Lifeact-GFP plasmid vector was transfected to NIH3T3 cells. Ten images of F-actin in living cells were taken every second under static culture conditions. First, we analyzed the small fluctuation of F-actin in living cells with Gaussian smoothed images. In this analysis, the amplitude of F-actin fluctuation was approximately 0.2 to 0.3 m, which is almost the same as the optical resolution. Therefore, we have reconstructed the F-actin image in cell from a cross-sectional fluorescent profile with the quasi super-resolution technique. We analyzed the fluorescent profile at several points along one F-actin filament, and the X and Y coordinates were picked up from the peak fluorescent in each fluorescent profile. From these X and Y coordinates in images, F-actin filament was approximated as a quadratic curve. We reconstructed the F-actin filament each time. The obtained spatial resolution was 0.08 m which was 2.5 times higher than the optical resolution. In quasi super-resolution images, the fluctuation amplitude of F-actin was 0.42 to 0.53 m in the peripheral region and 0.27 m in the center region. The frequency of F-actin fluctuation in both center and peripheral regions was approximately 3 Hz. The F-actin fluctuation was irregular, and several fluctuation patterns were observed. These phenomena might be caused due to the influence of restriction of the cytoskeletal network.

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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 cytoskeleton 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 cone-like 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.

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