Phase response curve
Encyclopedia
A phase response curve illustrates the transient change 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
In circadian rhythm research, a PRC illustrates the relationship between the timing and the effect of a treatment designed to affect circadian rhythm
s. Normally, the various rhythms will be in synchrony within an individual (human or animal), and sleep–wake is the most obvious of these rhythms. For humans, a treatment designed to affect circadian rhythms will most often be intended to adjust sleep timing, either delaying it to later in the day (night), or advancing it. Extreme morning people may want to delay their sleep timing; extreme evening chronotype
s may wish to advance it.
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. The curve has one peak and one nadir
in each 24 hour cycle. Relative circadian time is plotted vs. phase shift magnitude.
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. Each of these treatments has its own PRC which will vary according to the species being studied; its shape may also vary individually, just slightly. The magnitude is dose-dependent. The discussions below are restricted to the human PRCs for the chronobiotic
s light and melatonin.
Starting about two hours before bedtime, exposure to bright light will delay the circadian phase, causing later wake-up time and later sleep onset. The delaying effect gets stronger as evening progresses. About five hours after usual bedtime, coinciding with the lowest point of the body temperature rhythm (also known as the body temperature nadir
), the PRC peaks and the effect changes abruptly from phase delay to phase advance. Immediately after this peak, bright light exposure has its greatest phase-advancing effect, causing earlier wake-up and sleep onset. The effect diminishes until about two hours after spontaneous wake-up time, when it reaches zero. During the period between two hours after usual wake-up time and two hours before usual bedtime, bright light exposure has little or no effect on circadian phase (slight effects generally cancelling each other out).
Another image of the PRC for light is here.
Light therapy
, typically with a light box producing 10,000 lux
at a prescribed distance, can be used in the evening to delay or in the morning to advance one's sleep timing. Because losing sleep to obtain bright light exposure is considered undesirable by most people, and because it's very difficult to estimate exactly when the greatest effect (the PRC peak) will occur in an individual, the treatment is usually applied just prior to bedtime (to achieve phase delay), or just after spontaneous awakening (to achieve phase advance).
In 2002, Brown researchers, led by David Berson, announced the discovery of special cells in the human eye
, ipRGCs (intrinsically photosensitive retinal ganglion cells), which many researchers now believe control the light entrainment effect of the phase response curve. In the human eye, the ipRGCs have the greatest response to light in the 460–480 nm (blue) range. In one experiment, 400 lux of blue light produced the same effects as 10,000 lux of white light. Furthermore, there is now evidence for a theory of spectral opponency, in which the addition of other spectral colors renders blue light less effective for circadian phototransduction.
(externally-administered) melatonin has a slight phase-delaying effect. The amount of phase-delay increases until about eight hours after wake-up time, when the effect swings abruptly from strong phase delay to strong phase advance. The phase-advance effect diminishes as the day goes on until it reaches zero about bedtime. From usual bedtime until wake-up time, exogenous melatonin has no effect on circadian phase.
The human body produces its own (endogenous
) melatonin starting about two hours before bedtime, provided the lighting is dim. This is known as dim-light melatonin onset, DLMO. This stimulates the phase-advance portion of the PRC and helps keep the body on a regular sleep-wake schedule. It also helps prepare the body for sleep.
Administration of melatonin at any time may have a mild hypnotic
(sleep-inducing) effect. The resultant effect on sleep phase, if any, is governed by the PRC.
All times are approximate and vary among individuals. In particular, there is no convenient way of determining the exact timing of the peaks of these curves in an individual. For this reason, administration of light and/or melatonin should generally be avoided for at least an hour on either side of the expected time of the abrupt change of effect. This provides a safety margin to avoid producing the opposite effect of the intended one.
s, kept in constant darkness, responded to pulses of light exposure. The response varied according to the time of day—that is, the animals' subjective "day"—when light was administered. When DeCoursey plotted all her data relating the quantity and direction (advance or delay) of phase-shift on a single curve, she created the PRC. It has since been a standard tool in the study of biological rhythms.
Experimental estimation of PRC in living, regular-spiking neurons involves measuring the changes in inter-spike interval in response to a small perturbation, such as a transient pulse of current. Notably, the PRC of a neuron is not fixed but may change when firing frequency or neuromodulatory state of the neuron is changed.
Simple harmonic motion
Simple harmonic motion can serve as a mathematical model of a variety of motions, such as the oscillation of a spring. Additionally, other phenomena can be approximated by simple harmonic motion, including the motion of a simple pendulum and molecular vibration....
induced by a perturbation as a function of the phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
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
PRCs in Circadian Rhythms
Circadian rhythm
A circadian rhythm, popularly referred to as body clock, is an endogenously driven , roughly 24-hour cycle in biochemical, physiological, or behavioural processes. Circadian rhythms have been widely observed in plants, animals, fungi and cyanobacteria...
s. Normally, the various rhythms will be in synchrony within an individual (human or animal), and sleep–wake is the most obvious of these rhythms. For humans, a treatment designed to affect circadian rhythms will most often be intended to adjust sleep timing, either delaying it to later in the day (night), or advancing it. Extreme morning people may want to delay their sleep timing; extreme evening chronotype
Chronotype
Chronotype is an attribute of animals, including human beings, reflecting at what time of the day their physical functions are active, change or reach a certain level...
s may wish to advance it.
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. The curve has one peak and one nadir
Nadir
The nadir is the direction pointing directly below a particular location; that is, it is one of two vertical directions at a specified location, orthogonal to a horizontal flat surface there. Since the concept of being below is itself somewhat vague, scientists define the nadir in more rigorous...
in each 24 hour cycle. Relative circadian time is plotted vs. phase shift magnitude.
The two common treatments used to shift the timing of sleep are light therapy
Light therapy
Light therapy or phototherapy consists of exposure to daylight or to specific wavelengths of light using lasers, light-emitting diodes, fluorescent lamps, dichroic lamps or very bright, full-spectrum light, usually controlled with various devices...
, directed at the eyes, and administration of the hormone melatonin
Melatonin
Melatonin , also known chemically as N-acetyl-5-methoxytryptamine, is a naturally occurring compound found in animals, plants, and microbes...
, usually taken orally. Either or both can be used daily. Each of these treatments has its own PRC which will vary according to the species being studied; its shape may also vary individually, just slightly. The magnitude is dose-dependent. The discussions below are restricted to the human PRCs for the chronobiotic
Chronobiotic
Chronobiotic is a substance that is capable of therapeutically re-entering short - term dissociated or long - term desynchronized circadian rhythms, or prophylactically preventing their disruption following an environmental insult. In more simple words, chronobiotic is defined as the agent causes...
s light and melatonin.
Light PRC
Nadir
The nadir is the direction pointing directly below a particular location; that is, it is one of two vertical directions at a specified location, orthogonal to a horizontal flat surface there. Since the concept of being below is itself somewhat vague, scientists define the nadir in more rigorous...
), the PRC peaks and the effect changes abruptly from phase delay to phase advance. Immediately after this peak, bright light exposure has its greatest phase-advancing effect, causing earlier wake-up and sleep onset. The effect diminishes until about two hours after spontaneous wake-up time, when it reaches zero. During the period between two hours after usual wake-up time and two hours before usual bedtime, bright light exposure has little or no effect on circadian phase (slight effects generally cancelling each other out).
Another image of the PRC for light is here.
Light therapy
Light therapy
Light therapy or phototherapy consists of exposure to daylight or to specific wavelengths of light using lasers, light-emitting diodes, fluorescent lamps, dichroic lamps or very bright, full-spectrum light, usually controlled with various devices...
, typically with a light box producing 10,000 lux
Lux
The lux is the SI unit of illuminance and luminous emittance, measuring luminous flux per unit area. It is used in photometry as a measure of the intensity, as perceived by the human eye, of light that hits or passes through a surface...
at a prescribed distance, can be used in the evening to delay or in the morning to advance one's sleep timing. Because losing sleep to obtain bright light exposure is considered undesirable by most people, and because it's very difficult to estimate exactly when the greatest effect (the PRC peak) will occur in an individual, the treatment is usually applied just prior to bedtime (to achieve phase delay), or just after spontaneous awakening (to achieve phase advance).
In 2002, Brown researchers, led by David Berson, announced the discovery of special cells in the human eye
Human eye
The human eye is an organ which reacts to light for several purposes. As a conscious sense organ, the eye allows vision. Rod and cone cells in the retina allow conscious light perception and vision including color differentiation and the perception of depth...
, ipRGCs (intrinsically photosensitive retinal ganglion cells), which many researchers now believe control the light entrainment effect of the phase response curve. In the human eye, the ipRGCs have the greatest response to light in the 460–480 nm (blue) range. In one experiment, 400 lux of blue light produced the same effects as 10,000 lux of white light. Furthermore, there is now evidence for a theory of spectral opponency, in which the addition of other spectral colors renders blue light less effective for circadian phototransduction.
Melatonin PRC
The phase response curve for melatonin is roughly twelve hours out of phase with the phase response curve for light. At spontaneous wake-up time, exogenousExogenous
Exogenous refers to an action or object coming from outside a system. It is the opposite of endogenous, something generated from within the system....
(externally-administered) melatonin has a slight phase-delaying effect. The amount of phase-delay increases until about eight hours after wake-up time, when the effect swings abruptly from strong phase delay to strong phase advance. The phase-advance effect diminishes as the day goes on until it reaches zero about bedtime. From usual bedtime until wake-up time, exogenous melatonin has no effect on circadian phase.
The human body produces its own (endogenous
Endogenous
Endogenous substances are those that originate from within an organism, tissue, or cell. Endogenous retroviruses are caused by ancient infections of germ cells in humans, mammals and other vertebrates...
) melatonin starting about two hours before bedtime, provided the lighting is dim. This is known as dim-light melatonin onset, DLMO. This stimulates the phase-advance portion of the PRC and helps keep the body on a regular sleep-wake schedule. It also helps prepare the body for sleep.
Administration of melatonin at any time may have a mild hypnotic
Hypnotic
Hypnotic drugs are a class of psychoactives whose primary function is to induce sleep and to be used in the treatment of insomnia and in surgical anesthesia...
(sleep-inducing) effect. The resultant effect on sleep phase, if any, is governed by the PRC.
Additive Effects
In a newer study (2006), Victoria L. Revell et al. have shown that a combination of morning bright light and afternoon melatonin, both timed to phase advance according to the respective PRCs, produce a larger phase advance shift than bright light alone, for a total of up to 2 hours.All times are approximate and vary among individuals. In particular, there is no convenient way of determining the exact timing of the peaks of these curves in an individual. For this reason, administration of light and/or melatonin should generally be avoided for at least an hour on either side of the expected time of the abrupt change of effect. This provides a safety margin to avoid producing the opposite effect of the intended one.
Origin of the PRC
The first published usage of the term "phase response curve" was in 1960 by Patricia DeCoursey. The "daily" activity rhythms of her flying squirrelFlying squirrel
Flying squirrels, scientifically known as Pteromyini or Petauristini, are a tribe of 44 species of squirrels .- Description :...
s, kept in constant darkness, responded to pulses of light exposure. The response varied according to the time of day—that is, the animals' subjective "day"—when light was administered. When DeCoursey plotted all her data relating the quantity and direction (advance or delay) of phase-shift on a single curve, she created the PRC. It has since been a standard tool in the study of biological rhythms.
PRC in neurons
Phase response curve analysis can be used to understand the intrinsic properties and oscillatory behavior of regular-spiking neurons. The neuronal PRCs can be classified as being purely positive (PRC type I) or as having negative parts (PRC type II). Importantly, the PRC type exhibited by a neuron is indicative of its input–output function (excitability) as well as synchronization behavior: networks of PRC type II neurons can synchronize their activity via mutual excitatory connections, but those of PRC type I can not.Experimental estimation of PRC in living, regular-spiking neurons involves measuring the changes in inter-spike interval in response to a small perturbation, such as a transient pulse of current. Notably, the PRC of a neuron is not fixed but may change when firing frequency or neuromodulatory state of the neuron is changed.
See also
- Circadian rhythmCircadian rhythmA circadian rhythm, popularly referred to as body clock, is an endogenously driven , roughly 24-hour cycle in biochemical, physiological, or behavioural processes. Circadian rhythms have been widely observed in plants, animals, fungi and cyanobacteria...
- Circadian rhythm sleep disorders
- Delayed sleep phase syndromeDelayed sleep phase syndromeDelayed sleep-phase syndrome , also known as delayed sleep-phase disorder or delayed sleep-phase type , is a circadian rhythm sleep disorder, a chronic disorder of the timing of sleep, peak period of alertness, the core body temperature rhythm, hormonal and other daily rhythms, compared to the...
- ChronobiologyChronobiologyChronobiology is a field of biology that examines periodic phenomena in living organisms and their adaptation to solar- and lunar-related rhythms. These cycles are known as biological rhythms. Chronobiology comes from the ancient Greek χρόνος , and biology, which pertains to the study, or science,...
- ChronotypeChronotypeChronotype is an attribute of animals, including human beings, reflecting at what time of the day their physical functions are active, change or reach a certain level...