🧬 Gene Circuit

Circuit

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Repressilator

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Auto-repressor

Hill coefficient n 2.0 Production β 10 Degradation γ 1.0 Threshold K 5.0 Speed 3×

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Behaviour—

Steady state—

Oscillation period—

Bistable—

Each gene makes a protein at rate dP/dt = β·Hill(regulators) − γP. Activation uses Xⁿ/(Kⁿ+Xⁿ), repression Kⁿ/(Kⁿ+Xⁿ). Mutual repression (toggle) gives two stable states; a 3-gene repression ring (repressilator) oscillates. Fire an inducer pulse to flip the toggle. Higher Hill n sharpens the switch and favours oscillation.