Harmonic oscillation frequencies of cellular contractility support a wave shape model

Animal cell shape changes such as cytokinesis are driven by poorly understood rearrangements of the actomyosin cortical cytoskeleton. To gain novel insights into cell-autonomous cytokinetic contractility, we used the C. elegans zygote as a model cell and imaged cytokinesis with unprecedented temporal resolution. Cytokinetic ring closure underwent cycles of acceleration and deceleration. We quantified contractile oscillations via continuous wavelet transform and mode decomposition. Ring inward displacement dynamics were the composite of co-existing amplitude- and frequency-modulated wave modes with ~ 18, 36 and 72-second periodicity. The periodicities of speed oscillations were only subtly changed by depletion of a panel of conserved actomyosin regulators and structural components, but oscillation amplitudes were suppressed by reduction of force generation, and enhanced by reduction of network crosslinking. As suggested by the relationship of the modes’ periodicities as a fundamental frequency, a harmonic and a subharmonic, the range of speed oscillations was well described by a wave-shape model with a single time-varying amplitude, a single time-varying frequency, and a shape factor. Finally, to retain the spatial relationships among contracting segments of the cytokinetic ring, we performed mode decomposition in three dimensions on a space-time-frequency kymocube of our wavelet transform output. We found three major classes of frequency surfaces varying little over space and time. Principal component analysis of these two-dimensional modes confirmed that the frequencies of contractile oscillations are related as a harmonic and sub-harmonic around a fundamental frequency. We propose that the latter reflects the Rho pacemaker driving contractility, and that the harmonic is emergent due to non-linearities in the system. Dissipation of contractility within the network may explain the slower, sub-harmonic contractile oscillations.