Evidence for a Coupled Oscillator Model of Endocrine Ultradian Rhythms

Abstract

Whereas long-period temporal structures in endocrine dynamics have been well studied, endocrine rhythms on the scale of hours are relatively unexplored. The study of these ultradian rhythms (URs) has remained nascent, in part, because a theoretical framework unifying ultradian patterns across systems has not been established. The present overview proposes a conceptual coupled oscillator network model of URs in which oscillating hormonal outputs, or nodes, are connected by edges representing the strength of node-node coupling. We propose that variable-strength coupling exists both within and across classic hormonal axes. Because coupled oscillators synchronize, such a model implies that changes across hormonal systems could be inferred by surveying accessible nodes in the network. This implication would at once simplify the study of URs and open new avenues of exploration into conditions affecting coupling. In support of this proposed framework, we review mammalian evidence for (1) URs of the gut-brain axis and the hypothalamo-pituitary-thyroid, -adrenal, and -gonadal axes, (2) UR coupling within and across these axes; and (3) the relation of these URs to body temperature. URs across these systems exhibit behavior broadly consistent with a coupled oscillator network, maintaining both consistent URs and coupling within and across axes. This model may aid the exploration of mammalian physiology at high temporal resolution and improve the understanding of endocrine system dynamics within individuals.

Keywords: GBA; HPA; HPG; HPT; biological rhythms; personalized medicine.

Figure 1.. Canonical axes in mammalian physiology exhibit 1–4 hour ultradian rhythms.

The hypothalamus and pituitary (HP) coordinate feedback loops across physiological systems. The Gut Brain Axis influences feeding and digestion, the HP-Thyroid axis influences metabolism, the HP-Adrenal axis regulates the arousal and stress response, and the HP-Gonadal axis regulates reproductive function. 1–4 hour ultradian rhythms occur in outputs of each of these axes, are coupled within and among axes, and modulate body temperature output.

Figure 2.. Hypothetical Coupled Oscillator Network and Properties.

Schematic of the hypothetical ultradian rhythm network with URs represented as sines (A) exemplifying node and edge properties. Oscillating outputs are represented by nodes. The presence of coupling is represented by edges, with edge thickness proportional to the consistency with which a modulation of one node is associated with response in its neighbors (i.e., coupling strength), and edge length indicating the time delay between modulation of one node and response of another. Arrowheads indicate that coupling is directed. Red color indicates a perturbation that spreads from the stomach contraction node to neighboring nodes and indicates that perturbation may propagate through multiple nodes and influence subsequent feedback to the originally perturbed node. B. Hypothetical ACTH ultradian rhythm approximated as a sine wave, with Τau_ACTH indicating period. C. ACTH ultradian rhythm form (B) with overlaid hypothetical CORT ultradian rhythm, illustrating the concept of coupled oscillations with a stable phase difference. D. Hypothetical Core Body Temperature (CBT) ultradian rhythm resulting from combined influence of ACTH, CORT, and stomach contractions, highlighting potential for detecting network disruptions as rhythm perturbations. E. Hypothetical ultradian rhythms in stomach contractions, illustrating a phase advance from a mistimed early meal. This perturbation is visible in the rapid dampening of the composite CBT signal, and in the depressed amplitude as the systems recover and realign (blue and red arrows).

Figure 3.. Real data can be compared to simple models to explore harmonics.

Simulated body temperature data (A, C) was generated by superimposing sinewaves of circadian and ultradian frequencies and compared to four days of real mouse CBT data (B). A. Two ultradian frequencies overlap with an average periodicity of 2 hours, but with each component sine wave set to a non-integer, non-whole-number-multiple (i.e., non-harmonic) of the other. Linear depiction of the simulated waveform (above) across four simulated days; the same data plotted as a raster plot of temperature (color, D), per minute (x-axis) per day (y-axis) allows comparison of peak-timing across days. B. Real mouse data body temperature data (based on data published in Smarr et al., 2017), shows circadian and ultradian rhythms overlapping, as well as reactions to sudden changes in the light: dark cycle (yellow and black bars) not included in our data for the sake of simplicity. C. Simulated data with only one dominant frequency (Tau = 2h) results in perfect ultradian alignment across days. Comparisons across animals and conditions would allow quantitative testing of conditions under which harmonics emerge, as appears to be the case in the real data (B) during the late inactive phase (preceding ZT 0). Notably, UR frequency appears to be modulated at the circadian timescale. D. Color scale bar.