Abstract
Negative-feedback (inhibitory) and positive-feedforward (stimulatory) processes regulate physiological systems. Whether such processes are themselves rhythmic is not known. Here, we apply cross-approximate entropy (cross-ApEn), a noninvasive measurement of joint (pairwise) signal synchrony, to inferentially assess hypothesized circadian and ultradian variations in feedback coupling. The data comprised simultaneous measurements of three pituitary and one peripheral hormone (LH, FSH, prolactin, and testosterone) in 12 healthy men each sampled every 10 min for 4 days (5,760 min). Ergodicity, due to the time series stationarity of the measurements over the 4 days, allows for effective estimation of parameters based upon the 12 subjects. Cross-ApEn changes were quantified via moving-window estimates applied to 4-day time series pairs. The resultant ordered windowed cross-ApEn series (in time) were subjected to power spectrum analysis. Rhythmicity was assessed against the null hypothesis of randomness using 1,000 simulated periodograms derived by shuffling the interpulse-interval hormone-concentration segments and redoing cross-ApEn windows and spectral analysis. By forward cross-ApEn analysis, paired LH-testosterone, LH-prolactin, and LH-FSH synchrony maintained dominant rhythms with periodicities of 18-22.5, 18, and 22.5 h, respectively (each P < 0.001). By reverse (feedback) cross-ApEn analysis, testosterone-LH, testosterone-prolactin, and testosterone-FSH synchrony cycles were 30, 18, and 30-45 h, respectively (each P ≤ 0.001). Significant 8- or 24-h rhythms were also detected in most linkages, and maximal bihormonal synchrony occurred consistently at ∼0400-0500. Collectively, these analyses demonstrate significant ultradian (<24 h), circadian (∼24 h), and infradian (>24 h) oscillations in pituitary-testis synchrony, wherein maximal biglandular coordination is strongly constrained to the early morning hours.