lac-operon-sim is a free gene-regulation learning tool that renders an SVG diagram of the E. coli Lac operon (promoter / operator / lacZ-lacY-lacA + LacI + CRP-cAMP) and simulates a delay ODE system (translation τ delay per Bratsun et al. 2005) + allolactose negative allostery (LacI affinity ↓) + cAMP-CRP positive control (glucose ↓ → cAMP ↑ → CRP active → transcription ↑) + three environments (Glu only / Lac only / Glu+Lac diauxic 2-stage) + lacI⁻ (constitutive) / lacI^s (super-repressor) mutant comparison using in-house delayRK4 (Jacob & Monod 1961 J Mol Biol / Alberts Ch.7 / Lodish Ch.7 / Monod 1942 baseline, zero npm).

(1) Static undergrad Lac operon figures → delay ODE dynamic simulation (2) Integrate negative (LacI repressor) + positive (CRP-cAMP) control learning (3) Diauxic growth 2-stage curve (Monod 1942) — glucose vs lactose priority (4) Compare lacI⁻ / lacI^s mutants (Jacob & Monod 1961) (5) Bonus delay ODE numerical methods (translation τ delay) (6) Zero external libs

① Operon SVG diagram (promoter / operator / lacZ-lacY-lacA + LacI + CRP-cAMP) zoom + pan ② Three environment scenarios: • Glucose only: Lac OFF (cAMP ↓ → CRP inactive + LacI active) • Lactose only: Lac ON (allolactose → LacI inactive + cAMP ↑ → CRP active) • Glucose + Lactose: diauxic growth (Glu first, then Lac, 2-stage curve) ③ lacI mutant toggle: • Wild-type • lacI⁻: constitutive expression (mRNA even without Lac) • lacI^s: super-repressor (suppression even with Lac) ④ Delay ODE auto-play ▶ / ⏸ — mRNA / β-galactosidase / lactose / allolactose / cAMP time evolution ⑤ Allolactose negative-allostery affinity slider + cAMP-CRP positive-control strength slider ⑥ Hover 18 academic terms (operon / operator / promoter / repressor / inducer / allolactose / cAMP / CRP / CAP / catabolite repression / diauxic / negative allosteric, etc.)

Example 1) [Glu]=10 mM, [Lac]=0 → Lac OFF (mRNA ≈ 0) Example 2) [Glu]=0, [Lac]=10 mM → Lac ON (mRNA up) Example 3) [Glu]=10 mM, [Lac]=10 mM → diauxic growth: Glu first (Lac OFF) → Lac later (2-stage, Monod 1942) Example 4) lacI⁻ mutant → constitutive (mRNA even without Lac) Example 5) lacI^s super-repressor → suppression even with Lac (Jacob & Monod 1961)