Phase response curve

A phase response curve (PRC) illustrates the transient change (phase response) in the cycle period of an oscillation induced by a perturbation as a function of the phase at which it is received. PRCs are used in various fields; examples of biological oscillations are the heartbeat, circadian rhythms, and the regular, repetitive firing observed in some neurons in the absence of noise.^{[better source needed]}

In humans and animals, there is a regulatory system that governs the phase relationship of an organism's internal circadian clock to a regular periodicity in the external environment (usually governed by the solar day). In most organisms, a stable phase relationship is desired, though in some cases the desired phase will vary by season, especially among mammals with seasonal mating habits.

In circadian rhythm research, a PRC illustrates the relationship between a chronobiotic's time of administration (relative to the internal circadian clock) and the magnitude of the treatment's effect on circadian phase. Specifically, a PRC is a graph showing, by convention, time of the subject's endogenous day along the x-axis and the amount of the phase shift (in hours) along the y-axis. Each curve has one peak and one trough in each 24-hour cycle. Relative circadian time is plotted against phase-shift magnitude. The treatment is usually narrowly specified as a set intensity and colour and duration of light exposure to the retina and skin, or a set dose and formulation of melatonin.

These curves are often consulted in the therapeutic setting. Normally, the body's various physiological rhythms will be synchronized within an individual organism (human or animal), usually with respect to a master biological clock. Of particular importance is the sleep–wake cycle. Various sleep disorders and externals stresses (such as jet lag) can interfere with this. Humans with non-24-hour sleep–wake disorder often experience an inability to maintain a consistent internal clock. Extreme chronotypes usually maintain a consistent clock, but find that their natural clock does not align with the expectations of their social environment. PRC curves provide a starting point for therapeutic intervention. The two common treatments used to shift the timing of sleep are light therapy, directed at the eyes, and administration of the hormone melatonin, usually taken orally. Either or both can be used daily. The phase adjustment is generally cumulative with consecutive daily administrations, and — at least partially — additive with concurrent administrations of distinct treatments. If the underlying disturbance is stable in nature, ongoing daily intervention is usually required. For jet lag, the intervention serves mainly to accelerate natural alignment, and ceases once desired alignment is achieved.

Note that phase response curves from the experimental setting are usually aggregates of the test population, that there can be mild or significant variation within the test population, that individuals with sleep disorders often respond atypically, and that the formulation of the chronobiotic might be specific to the experimental setting and not generally available in clinical practice (e.g. for melatonin, one sustained-release formulation might differ in its release rate as compared to another); also, while the magnitude is dose-dependent, not all PRC graphs cover a range of doses. The discussions below are restricted to the PRCs for the light and melatonin in humans.

Starting about two hours before an individual's regular bedtime, exposure of the eyes to light will delay the circadian phase, causing later wake-up time and later sleep onset. The delaying effect gets stronger as evening progresses; it is also dependent on the wavelength and illuminance ("brightness") of the light. The effect is small if indoor lighting is dim (< 3 lux).

About five hours after usual bedtime, coinciding with the body temperature trough (the lowest point of the core body temperature during sleep) the PRC peaks and the effect changes abruptly from phase delay to phase advance. Immediately after this peak, light exposure has its greatest phase-advancing effect, causing earlier wake-up and sleep onset. Again, illuminance greatly affects results; indoor light may be less than 500 lux, while light therapy uses up to 10,000 lux. The effect diminishes until about two hours after spontaneous wake-up time, when it reaches approximately zero.

During the period between two hours after usual wake-up time and two hours before usual bedtime, light exposure has little or no effect on circadian phase (slight effects generally cancelling each other out).