A cross-frequency architecture links biological and behavioral periodicities

Spontaneous behaviors, e.g., walking and speaking, are thought to rely on an internal sense of time that provides a scaffold for precise temporal coordination. Yet endogenous rates of many behavioral processes often diverge from arbitrarily defined unit of objective time, raising a fundamental question: what temporal reference frame coordinates behavior? Using high temporal resolution multimodal recordings, we show that endogenous body-brain periodicities (including pupil fluctuations, saccadic eye movements, respiration, cardiac activity and neural oscillations) as well as spontaneous behaviors such as tapping, walking, and speaking, form a cross-frequency architecture organized as an arithmetic progression in a natural logarithmic frequency space. Successive rates are spaced by about {varphi} (golden ratio {approx} 1.618 1), while the ratio between rhythm classes are captured by e (e {approx} 2.72 2). The absence of power law scaling and harmonic anchoring to individual heart rates excluded the possibility that the frequency architecture scales to, and depends uniquely on, a single pacemaker. Rather, the irrational scaling suggests each rate to be principally independent and maximally de-coupled from others, yet capable to dynamically engage in cross-frequency interactions. We propose that the body-brain frequency architecture may provide an emergent temporal reference frame to scaffold perception and action.