Why is a delay needed for oscillations?

Immediate negative feedback usually settles to a steady state. The mRNA-to-protein-to-repressor chain delays the inhibitory signal, so the system overshoots before repression arrives and then undershoots while repression decays.

What does the light pulse represent?

It is a schematic zeitgeber input that transiently boosts clock-gene transcription. Depending on when it arrives in the cycle, the next peak can occur earlier (phase advance) or later (phase delay).

Is this a full mammalian circadian model?

No. Real clocks include many genes, phosphorylation, degradation complexes, nuclear transport, cell-cell coupling, and entrainment pathways. This is a minimal teaching model for the feedback-and-delay principle.

Circadian Oscillator (Goodwin Clock)

Goodwin-style molecular clock: delayed negative transcriptional feedback, mRNA/protein/repressor phase lag, period readout, and light-pulse phase advance or delay.

This is a compact molecular-clock teaching model. Real circadian clocks add many genes, post-translational regulation, entrainment pathways, and tissue-level coupling.

Live graphs

About this model

This simulator uses a compact Goodwin oscillator to show how a circadian molecular clock can arise from delayed negative feedback. The variable M represents clock-gene mRNA, P a translated protein, and R a nuclear repressor. The repressor inhibits its own transcription through a cooperative Hill term α/(1+Rⁿ). The intermediate protein steps create a delay between mRNA production and repression; with sufficiently strong and cooperative feedback, that delay produces a self-sustained rhythm. The first graph shows the phase-lagged molecular traces, the second compares a control repressor rhythm with a rhythm perturbed by a short light/zeitgeber pulse, and the third plots the phase portrait R vs M. The readouts estimate period, molecular phase lag, and the pulse-induced phase advance or delay.

Who it's for: Students in systems biology, chronobiology, nonlinear dynamics, or biophysics learning delayed feedback oscillators and entrainment concepts.

Key terms

Circadian rhythm
Goodwin oscillator
Delayed negative feedback
Hill repression
Phase shift
Zeitgeber
Entrainment
Limit cycle

How it works

A Goodwin-style circadian rhythm model: delayed negative transcriptional feedback creates oscillations, phase lag between molecular species, and light-pulse phase advances or delays.

Key equations

dM/dt = α/(1+Rⁿ) + L(t) − k_m M, dP/dt = k_s M − k_p P, dR/dt = k_t P − k_r R. Cooperative delayed negative feedback makes the clock.

Frequently asked questions

Why is a delay needed for oscillations?: Immediate negative feedback usually settles to a steady state. The mRNA-to-protein-to-repressor chain delays the inhibitory signal, so the system overshoots before repression arrives and then undershoots while repression decays.
What does the light pulse represent?: It is a schematic zeitgeber input that transiently boosts clock-gene transcription. Depending on when it arrives in the cycle, the next peak can occur earlier (phase advance) or later (phase delay).
Is this a full mammalian circadian model?: No. Real clocks include many genes, phosphorylation, degradation complexes, nuclear transport, cell-cell coupling, and entrainment pathways. This is a minimal teaching model for the feedback-and-delay principle.

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Live graphs

About this model

How it works

Key equations

Frequently asked questions

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Live graphs

About this model

How it works

Key equations

Frequently asked questions