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Biology — Petri Net: lac Operon

Lactose inactivates the repressor to switch on transcription.

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Lac operon (induction)LactoseActive repressorLactose binds repress…enabledInactive repressorOperonTranscriptionenabledBeta-galactosidaseω unboundedReachable markings—unbounded — no finite setTerminates—not decidedLive transitions—not decidedSafe places0/51 unboundedConservation laws31 place in none1 place unbounded, so this net has no finite reachable set.Place `Inactive repressor` has no outgoing arc: every token that reaches it stays there. A counter of completed work is exactly this, and so is a token leak — the two are the same drawing, and only…Place `Beta-galactosidase` has no outgoing arc: every token that reaches it stays there. A counter of completed work is exactly this, and so is a token leak — the two are the same drawing, and only…Place `Beta-galactosidase` is UNBOUNDED: there is a firing sequence that raises its token count and it can be repeated for ever, so this net puts no upper bound on what the place holds. That is a p…Conservation law: Active repressor + Inactive repressor = 1, at every reachable marking, for ever. No firing of any transition can change it — that is proved from the incidence matrix, not observed…Conservation law: Lactose + Inactive repressor = 2, at every reachable marking, for ever. No firing of any transition can change it — that is proved from the incidence matrix, not observed over a s…Conservation law: Operon = 1, at every reachable marking, for ever. No firing of any transition can change it — that is proved from the incidence matrix, not observed over a search.+ 1 further findings not listed

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title Lac operon (induction)

place Lactose tokens 2 "Lactose"
place Repressor tokens 1 "Active repressor"
transition inactivate "Lactose binds repressor"
place Inactive tokens 0 "Inactive repressor"
place Operon tokens 1 "Operon"
transition transcribe "Transcription"
place Enzymes tokens 0 "Beta-galactosidase"

Lactose -> inactivate
Repressor -> inactivate
inactivate -> Inactive
Operon -> transcribe
transcribe -> Operon
transcribe -> Enzymes