Modified Wavelet Analyses Permit Quantification of Dynamic Interactions Between Ultradian and Circadian Rhythms

Circadian rhythms provide daily temporal structure to cellular and organismal biological processes, ranging from gene expression to cognition. Higher-frequency (intradaily) ultradian rhythms are similarly ubiquitous but have garnered far less empirical study, in part because of the properties that define them-multimodal periods, non-stationarity, circadian harmonics, and diurnal modulation-pose challenges to their accurate and precise quantification. Wavelet analyses are ideally suited to address these challenges, but wavelet-based measurement of ultradian rhythms has remained largely idiographic. Here, we describe novel analytical approaches, based on discrete and continuous wavelet transforms, which permit quantification of rhythmic power distribution across a broad ultradian spectrum, as well as precise identification of period within empirically determined ultradian bands. Moreover, the aggregation of normalized wavelet matrices allows group-level analyses of experimental treatments, thereby circumventing limitations of idiographic approaches. The accuracy and precision of these wavelet analyses were validated using in silico and in vivo models with known ultradian features. Experiments in male and female mice yielded robust and repeatable measures of ultradian period and power in home cage locomotor activity, confirming and extending reports of ultradian rhythm modulation by sex, gonadal hormones, and circadian entrainment. Seasonal changes in day length modulated ultradian period and power, and exerted opposite effects in the light and dark phases of the 24 h day, underscoring the importance of evaluating ultradian rhythms with attention to circadian phase. Sex differences in ultradian rhythms were more prominent at night and depended on gonadal hormones in male mice. Thus, relatively straightforward modifications to the wavelet procedure allowed quantification of ultradian rhythms with appropriate time-frequency resolution, generating accurate, and repeatable measures of period and power which are suitable for group-level analyses. These analytical tools may afford deeper understanding of how ultradian rhythms are generated and respond to interoceptive and exteroceptive cues.