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Dependence of a stimulus-response relationship on internal circadian phase. A rhythmic baseline or a daily change in stimulus availability alone does not demonstrate gating.

A circadian phase specifies position within a circadian rhythm's cycle relative to a chosen reference event.

Entrainment of circadian rhythm synchronizes a circadian clock to a repeating cue, a zeitgeber. One-to-one entrainment of circadian rhythm gives one cycle per environmental cycle with a stable relative circadian phase.^[ref] The stable relation need not put an activity onset exactly at lights-off: a constant offset also expresses phase locking.

For an original local model, let $x_n$ be the activity-onset offset from lights-off on environmental cycle $n$, with a negative value meaning an earlier onset. Choose an intrinsic period $\tau =23.5\mathrm{h}$ and environmental period $T=24\mathrm{h}$. Let $D(x)$ be a stipulated daily delay, measured in hours; positive $D$ moves the next onset later. The recurrence relation isA fixed phase relationship $x_{\ast }$ requires $D(x_{\ast })=T-\tau$: here a half-hour delay balances the half-hour intrinsic advance each cycle. This equality alone describes balance; restoration after a small disturbance also requires fixed point stability for an iteration.

Choose the illustrative local law $D(x)=0.5\mathrm{h}-0.4x$. Thenfor the chosen starting offset $x_0=-3\mathrm{h}$. The error shrinks by a factor of $0.6$ each cycle, proving fixed point stability for an iteration in this model. After five cycles $x_5=-0.23328\mathrm{h}$, about fourteen minutes early. At the fixed point, the imposed delay is $0.5\mathrm{h}$ and the corrected onset interval is $\tau +D(x_{\ast })=24\mathrm{h}$, although the uncoupled period remains $23.5\mathrm{h}$.

The uncorrected comparison has $D=0$ and $x_n=-3\mathrm{h}+n(\tau -T)$, so after five cycles it is $5.5$ hours early. The two traces separate ongoing timekeeping from adjustment to a zeitgeber. The chosen linear delay law is only a local teaching construction: it is not a measured response to light, does not account for wrapping of circadian phase, and does not predict an organism's entrainment range. Nor does it include masking of circadian rhythm. In a real study, tracking several cycles after removal of the cue or after a timed perturbation supplies information that a single activity value under illumination cannot provide.

A free-running circadian rhythm persists without an entraining cycle. Its period $\tau$ separates corresponding circadian phases, such as successive activity onsets, under specified constant conditions.^[ref] A circadian phase tells where the system is within its cycle; a period tells how long one cycle takes. Choosing onset rather than peak as the reference changes the phase label, not the period of an ideal repeating signal.

Consider an original, deliberately idealized model with $\tau =23.5\mathrm{h}$. For seven days prescribe a 12:12 LD cycle with activity starting at hour 12 of each 24-hour day. Then omit the next scheduled dawn and keep the environment dark. Stipulate that the first DD onset retains hour 12, and that every later onset is exactly $23.5\mathrm{h}$ after the previous one. Activity lasts eight hours after each onset. These are chosen model values, not recorded mouse or human data, and the fixed activity window represents an output of the model rather than the molecular mechanism of a circadian clock.

An actogram displays activity against time in successive rows. Here each row spans $T=24\mathrm{h}$, regardless of the circadian rhythm's period. If $t_0$ is the first DD onset and $n$ counts completed free-running cycles, thenThe unwrapped onset displacement $x_n$ is therefore $-0.5n\mathrm{h}$. After eight cycles the onset is four hours earlier than a 24-hour continuation would predict; after sixteen cycles it is eight hours earlier. Because these onsets remain within successive calendar rows in the displayed interval, their row positions are $12,11.5,11,\dots ,4$ hours. The visual slant comes from comparing two different periods, not from cessation of the oscillation.

An alternative phase oscillator description makes the same distinction explicit. Set the circadian phase to zero at $t_0$ and defineThe angular frequency $\omega$ is constant in this model. Onset occurs whenever the unwrapped circadian phase completes another turn. A period longer than $T$ would instead produce later onsets; equality would produce aligned rows even without entrainment of circadian rhythm. Thus aligned rows by themselves do not identify the cause of a daily pattern. Real activity can be noisy, and a free-running circadian rhythm's period can vary with conditions or with time after release; the stipulated straight line assumes a stationary period.

Sleep can protect newly acquired information, actively reorganize it, and restore the capacity for subsequent learning. These are distinct claims. Memory consolidation concerns changes after acquisition; better learning the next morning concerns encoding capacity; less interference during an unoccupied interval need not imply an active sleep mechanism. The strongest explanation therefore combines behavioural comparisons with recordings and selective interventions.

A basic retention experiment compares later performance after sleep and waking, ideally relative to an immediate baseline. Yet a night-versus-day comparison also changes circadian phase, interference and alertness at testing. Sleep deprivation adds physiological stress and attentional impairment. Matching acquisition, testing at comparable times, measuring vigilance, and comparing sleep with quiet waking make the inference sharper. A retention advantage after sleep remains compatible with both passive protection and active processing; distinguishing them requires manipulating what happens during the interval.

The active systems consolidation hypothesis provides an active mechanism. Rapid relational encoding by the hippocampus permits later memory reactivation to modify distributed cerebral cortex representations. During NREM sleep, cortical sleep slow oscillations can organize sleep spindles and hippocampal sharp-wave ripples, creating coordinated windows for synaptic plasticity. This is a timing hypothesis about communication, not proof that a complete memory is copied from one anatomical container to another. Systems consolidation and synaptic consolidation can proceed together, and some detailed episodic memories may continue to require hippocampal contributions.

An important recording experiment monitored ensembles of hippocampal place cells in rats during spatial behaviour and during sleep before and after it. Cells active together at particular locations became more likely to fire together in subsequent slow-wave sleep; the pre-experience recording supplied a valuable baseline. This demonstrates experience-related memory reactivation. Pairwise coactivation alone does not establish ordered neural replay, nor does a correlation show that the events improve retention. An apparently memory-related pattern might otherwise be an incidental consequence of prior activity.^[ref]

A stronger causal test interrupted hippocampal sharp-wave ripples during post-training sleep in rats learning a spatial task. An online electrical recording system detected ripple events and triggered brief disruption; a delayed-stimulation comparison helped control stimulation without abolishing the same events. Spatial performance was impaired, while gross sleep architecture was not detectably changed. This supports a functional role for ripple-associated activity beyond simply obtaining sleep. Nevertheless, disruption affects an event and its associated activity, not an experimentally isolated memory message; it does not identify the exact information transferred or establish that all memory consolidation requires the same mechanism.^[ref]

Human targeted memory reactivation offers complementary evidence. Participants learned object locations with an odour present, then received that odour again during polysomnographically identified slow-wave sleep. Retention improved compared with an odourless condition. Crucially, the benefit did not appear when the odour had been absent during learning, or when it was presented during waking or REM sleep; procedural finger-tapping did not show the same benefit. The cue–learning relationship and sleep state therefore mattered. The associated hippocampal activation is consistent with memory reactivation, although activation does not reveal all the represented content. This is stronger evidence for selective processing than an undifferentiated sleep/wake advantage.^[ref]

Sleep could also benefit memory by regulating the substrate for learning. The synaptic homeostasis hypothesis proposes that predominantly waking-associated strengthening requires compensatory renormalization, limiting saturation, energy costs and interference. Selective preservation can improve the contrast of important connections even if average strength of synapses falls. Serial electron-microscopy reconstructions of mouse cortical synapses found smaller axon–spine interfaces after sleep, with an average decrease of roughly 18%; the largest synapses were relatively spared. The comparison included spontaneous and enforced waking. These are structural measurements consistent with selective scaling, not a direct measurement of every synapse's efficacy or proof that the measured changes caused a particular memory benefit.^[ref]

Renormalization and selective strengthening are not mutually exclusive. A learning-related ensemble could be selectively stabilized while less useful background connections weaken. Memory reactivation could help select what survives, and improved capacity after sleep could support the next episode rather than merely preserve the last one. An adequate theory must explain both specificity and restoration, rather than equate more firing or larger synapses with better memory everywhere.

The interpretation must remain task-specific. A cueing effect for declarative memory does not assign every procedural memory to REM sleep, and a null cueing result in one stage does not show that stage has no mnemonic function. Sleep-stage manipulations can alter other stages or awaken subjects. Rodent spatial performance provides mechanistic access but does not by itself establish human autobiographical experience. Replicated behavioural effects, adequate controls and selective circuit perturbations are most persuasive when they converge.

Thus sleep is important because it provides a state in which information can be selectively re-expressed and reorganized while conditions at synapses are regulated. Evidence available by April 2022 supports active contributions in addition to passive protection; it does not establish a universal sleep-only route for every kind of learning.

Plants use an entrained circadian clock to change their sensitivity to stimuli, while also responding directly to the current light and temperature environment. The same external stimulus can therefore have different effects at different internal phases. This circadian gating must be distinguished from a daily rhythm caused solely by daily variation in the stimulus itself.

The plant circadian clock contains interlocking regulation of gene expression, protein accumulation and protein activity. Morning-associated regulators such as CCA1 and LHY interact with later-acting components, including TOC1, to generate a sequence of phases rather than a single daily on–off switch. Light information, including inputs involving phytochromes and cryptochromes, and temperature cues adjust the clock through entrainment of circadian rhythm. Under suitably constant conditions, a free-running circadian rhythm persists. Anticipation of dawn or dusk is therefore possible before the corresponding environmental transition occurs.

Clock outputs can modify several points in a stimulus-response pathway. A receptor or transport protein may accumulate at a particular phase; signaling inhibitors may be removed at another. The clock can regulate hormone production, hormone inactivation, transport and sensitivity of downstream transcription factors. Post-translational regulation allows a phase-specific transcript to produce an output only under a second permissive condition. Consequently, a rhythmic hormone concentration and rhythmic responsiveness to that hormone are distinct explanations and may coexist.

Auxin provides direct experimental evidence for sensitivity gating. Timed auxin treatments and transcriptional reporters in Arabidopsis showed that an externally supplied hormone stimulus produces phase-dependent responses; growth responses were also gated. Because the stimulus was supplied experimentally, the result cannot be explained merely by assuming that the plant normally makes more auxin at one time of day. Reporter dynamics and pretreatment baselines still require appropriate controls, and a reporter is not a direct measurement of free hormone.^[ref]

An illustrative local description iswhere $S$ is a small standardized stimulus, $\varphi$ is circadian phase and $\Delta R$ is the response above the matched untreated baseline. A phase-dependent gain $g$ represents gating. In contrast, if $g$ is constant but the baseline response oscillates, observing different absolute values after treatment does not establish gating. Real pathways can saturate or change sign, so this equation illustrates the experimental distinction rather than defining a universal linear law.

Photoperiodism shows how internal time can be combined with an external cue to produce a developmental decision. In Arabidopsis, timed expression of CONSTANS interacts with light-dependent regulation of the protein. In long days, a permissive expression phase overlaps light sufficiently to support FLOWERING LOCUS T activation. The external coincidence model therefore responds to when light occurs relative to the clock, rather than merely adding up photons. Photoreceptor-dependent protein regulation provides a molecular connection between timing and the external environment.^[ref] FT protein can then communicate from leaves to the shoot apex. Phloem-specific expression and grafting experiments support FT protein movement as part of this long-distance floral signal.^[ref]

A convincing demonstration of circadian gating compares matched stimuli at several internal phases under constant external conditions, with untreated controls at every phase. Plants entrained to opposite schedules can help distinguish internal phase from laboratory clock time. Clock perturbations and restoration of clock function strengthen causal interpretation, provided effects on general health and growth are considered. A phase-shifted response in constant conditions supports clock control; disappearance immediately when the environmental cycle is removed suggests direct environmental control, although weak rhythms and altered physiology can complicate that inference. Masking of circadian rhythm, in which an environmental cue directly changes a measured output, can coexist with clock control.

Timing is useful because demands and risks recur. Coordinating stomatal conductance, photosynthetic preparation and growth with expected light availability can improve resource use. Yet the optimum phase depends on temperature, water availability and day length, and a strong acute stress can override a normal daily preference. Plants combine an internal estimate of time with current conditions, changing pathway sensitivity as well as the abundance of signals and response machinery.