Light Entrainment Simulator: How the Light-Dark Cycle Sets Your Body Clock

simulator intermediate ~10 min
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ψ = -2.1 h — DLMO 2.1 h before lights-off

With a 12-hour photoperiod at 5000 lux and 24.2-hour intrinsic period, the clock entrains with dim-light melatonin onset (DLMO) occurring 2.1 hours before lights-off — a typical healthy phase angle.

Formula

dφ/dt = (τ - T)/τ + (Z/τ)·PRC(φ) — Winfree entrainment equation
Z_eff = I · (PP/24) · (0.5 + 0.5·B%/25) — effective zeitgeber strength
ψ = arcsin((τ - T) / (A·Z)) — steady-state phase angle

Synchronized by Light

Every morning, photons entering your eyes reset the biological clock with remarkable precision. The retina's ~5000 intrinsically photosensitive ganglion cells (ipRGCs), containing the blue-sensitive photopigment melanopsin, detect environmental light and relay intensity and timing information directly to the suprachiasmatic nucleus (SCN) — the brain's master pacemaker. This light input corrects the small daily drift of the ~24.2-hour internal clock, locking it to exactly 24 hours. Without this daily reset, the clock would progressively shift later, losing synchrony with the solar cycle within weeks.

The Entrainment Zone

Entrainment is not guaranteed — it requires the zeitgeber to be strong enough and the period mismatch small enough. Bright outdoor light (~10,000–100,000 lux) can entrain clocks with intrinsic periods ranging from roughly 23 to 25.5 hours. Dim indoor light (~200 lux) narrows this range dramatically. Individuals whose intrinsic periods fall outside the entrainment range for their light environment will free-run, experiencing the daily phase drift that characterizes Non-24 disorder. This simulation maps the entrainment zone as a function of light intensity and intrinsic period.

Phase Angle: Your Clock's Signature

Once entrained, the clock settles into a stable phase relationship with the light-dark cycle. This phase angle (ψ) determines when you feel sleepy, when melatonin rises, when body temperature dips, and when cortisol surges. Morning chronotypes have a large negative ψ (clock leads the light cycle), while evening types have a smaller ψ. The phase angle depends on intrinsic period — people with longer τ tend toward eveningness because the clock needs more phase advance each day to stay entrained, pushing its equilibrium position later relative to dawn.

Modern Light Environments

Human evolution occurred under natural light conditions: bright days (10,000–100,000 lux) and truly dark nights. Modern indoor living inverts this — dim days (100–500 lux) and artificially lit evenings (100–300 lux). The result is a weakened zeitgeber that incompletely entrains the clock, manifesting as later sleep timing, more variable rhythms, and increased prevalence of circadian disorders. This simulator reveals how light intensity, spectral composition, and photoperiod interact to determine whether your clock is robustly entrained or teetering on the edge of free-running.

FAQ

What is circadian entrainment?

Entrainment is the process by which an external periodic signal (zeitgeber, German for 'time giver') synchronizes the internal circadian clock to a 24-hour cycle. Light is the dominant zeitgeber in mammals, detected by melanopsin-containing intrinsically photosensitive retinal ganglion cells (ipRGCs) that signal directly to the suprachiasmatic nucleus (SCN). Without entrainment, the clock free-runs at its intrinsic period (~24.2 h in humans), drifting later each day.

What is the phase angle of entrainment?

The phase angle (ψ) is the stable time relationship between the clock and the zeitgeber cycle. In healthy entrained humans, dim-light melatonin onset (DLMO) typically occurs 2–3 hours before habitual sleep onset. A more negative ψ (earlier clock relative to lights-off) is associated with morning chronotypes; a less negative or positive ψ characterizes evening types.

Why do blind people often have circadian disorders?

Totally blind individuals who lack functional ipRGCs cannot detect light for circadian entrainment. Their clocks free-run at the intrinsic period (~24.2 h), causing Non-24-Hour Sleep-Wake Disorder — sleep time drifts ~15 minutes later each day, cycling through alignment and misalignment with the social schedule every few months. Tasimelteon (a melatonin agonist) is FDA-approved for this condition.

How does seasonal photoperiod affect the clock?

Longer summer photoperiods compress the clock's subjective night and expand the subjective day. Melatonin secretion duration shortens in summer and lengthens in winter. In susceptible individuals, short winter photoperiods trigger Seasonal Affective Disorder (SAD) through mechanisms involving both circadian phase and melatonin duration. Bright light therapy counteracts this by strengthening the zeitgeber signal.

Sources

Embed

<iframe src="https://homo-deus.com/lab/circadian-biology/light-entrainment/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub