Bacteriophage Lysis–Lysogeny Decision Switch

Infection Conditions

Multiplicity of infection 3

Host nutrient stress 40%

Molecular noise (Ω) 1.0

Repressor / Anti-repressor

Cro

[CI] repressor

0.0

[Cro] antirepressor

0.0

Time since infection

0.0 min

P(lysogeny | MOI)

—

Deciding…

How it works

The λ phage decision circuit is a two-gene mutual-repression toggle: CI (the lysogenic repressor) and Cro (the lytic anti-repressor) each bind the shared operator region and block transcription of the other's gene. As dimers with cooperative (Hill-type) binding, this produces a bistable switch:

d[CI]/dt  =  a1 / (1 + ([Cro]/K)^n)  -  γ[CI]  +  noise
d[Cro]/dt =  a2 / (1 + ([CI]/K)^n)   -  γ[Cro] +  noise

a1 = a1,0 · (1 + kM·MOI) · (1 + kS·stress)   — CI synthesis, boosted by CII
a2 = a2,0 (constitutive PR transcription)
n = 2 (dimer cooperativity), K = half-max operator occupancy

Whichever species crosses its threshold first locks in a positive-feedback loop and represses the other almost to zero — the hallmark of a bistable switch (same class of model as the Gardner–Collins synthetic toggle switch). Two knobs bias the coin flip toward the real biology:

MOI — more phage genome copies per cell make more CII protein, which drives the P_RE promoter and boosts CI synthesis, pulling the odds toward lysogeny.
Nutrient stress — starved, non-dividing cells have lower Hfl protease activity, so CII survives longer; poor growth conditions also favor lysogeny (a phage "waits out" a bad host).
Noise (Ω) — with only tens of protein copies per cell early in infection, stochastic gene-expression noise is what actually breaks the symmetry between the two stable states.
Induce SOS — DNA damage activates RecA, which triggers CI self-cleavage. A lysogen's repressor collapses, Cro's brake is released, and the prophage switches to lysis — this is prophage induction.

Outcome: CI-dominant → lysogeny, the phage DNA integrates into the host chromosome and the cell survives as a lysogen. Cro-dominant → lysis, phage genes for replication and structural proteins turn on, new virions assemble, and the cell bursts.

CI repressor (lysogeny) Cro (lysis) Phage DNA / virions

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