Frequency and amplitude dependence of nuclear displacement and phase delay in mechanical vibrations for determining cellular natural frequency

Cultured cells biochemically respond to mechanical vibrations. However, the mechanisms of sensing mechanical vibrations and transducing biochemical responses remain unclear. A previous study reported that the expression of the alkaline phosphatase gene of osteoblastic cell under mechanical vibrations peaks at 50 Hz, which seems like a resonance curve in the mechanical vibration theory. Since forced displacement excitation is a dynamic mechanical stimulus that differs from other static mechanical stimuli in that an external force is equivalent to inertia, force is apparently exerted on the mass element by considering the equation of motion. In this study, the method for obtaining the change of a nucleus's relative displacement to an excited dish was refined, and the frequency and acceleration amplitude dependence of the nucleus's relative displacement and phase delay under mechanical vibrations was demonstrated by regarding a cell model as a vibration system. The change of the relative displacement of a HeLa nucleus to an excited dish decreases with increasing frequency in the 12.5-100 Hz range at 0.5 G and increases with increasing acceleration amplitude in the 0.5-2.0 G range at 50 Hz. Phase reversal occurs between 12.5 Hz and 50 Hz, which suggests the existence of the natural frequency of the cell between 12.5 Hz and 50 Hz. The single actin filament tension estimated from the nucleus's relative displacement change was 2.3-10 pN and can be a biochemical response of the mechanotransducer. These findings can contribute to clarifying the mechanism of cell mechanotransduction in dynamic mechanical stimuli.