Genetic Toggle Switch: Synthetic Biology Circuit

Inducer Pulses

Circuit Parameters

Promoter 1 strength α₁ (LacI synthesis) 2.5

Promoter 2 strength α₂ (TetR synthesis) 2.5

Repressor cooperativity (Hill n) 2.0

Circuit State

Balanced — flip with a pulse

LacI (u) · RFP

TetR (v) · GFP

u — LacI level

0.50

v — TetR level

0.50

Sim time

0.0 τ

Active inducer

none

How it works

This is the Gardner–Collins–Cantor genetic toggle switch (Nature, 2000) — the founding circuit of synthetic biology. Two promoters are wired so each one's gene product represses the other's promoter:

du/dt = α₁ / (1 + v_eff^n) − u     (LacI, repressed by TetR)
dv/dt = α₂ / (1 + u_eff^n) − v     (TetR, repressed by LacI)

u_eff = u / (1 + [IPTG]·K)   v_eff = v / (1 + [aTc]·K)

With cooperative repression (Hill coefficient n > 1) the system is bistable: it settles into one of two stable steady states — "u-high / v-low" or "u-low / v-high" — separated by an unstable middle point. Left alone it stays wherever it last settled; that's the circuit's memory.

+ IPTG — a real inducer that binds and inactivates LacI protein, reducing its effective concentration (u_eff) and letting TetR (v) rise, flipping the switch to the "GFP-on" state.
+ aTc — binds and inactivates TetR, letting LacI (u) rise, flipping the switch to the "RFP-on" state.
α₁ / α₂ — maximum promoter output (ribosome-binding-site / promoter strength) for each gene.
Hill n — repressor binding cooperativity; below n≈1 the switch loses bistability and only has one steady state — try dragging it down to see the two particle clouds merge into one.

Real-world relevance: this exact circuit topology (mutually-repressing promoters) underlies engineered "genetic memory" used in biosensors, cell-fate recorders, and industrial strains that need to switch metabolic states — e.g. delaying biofuel-pathway expression until a population reaches a target density.

LacI / RFP protein TetR / GFP protein

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.