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Biology — Petri Net: Gene Expression

Transcription, translation and degradation as flows.

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Gene expressionGene (on)TranscriptionenabledmRNAω unboundedTranslationProteinω unboundedDegradationReachable markings—unbounded — no finite setTerminates—not decidedLive transitions—not decidedSafe places0/32 unboundedConservation laws12 places in none2 places unbounded, so this net has no finite reachable set.Place `mRNA` 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 proof from the …Place `Protein` 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 proof from t…Conservation law: Gene (on) = 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.2 places are weighted by no conservation law — `mRNA`, `Protein`. Nothing in the structure of this net holds what they hold constant, so their token count is free to drift with the firing sequence.…

Make it your own.

title Gene expression

place Gene tokens 1 "Gene (on)"
transition transcribe "Transcription"
place mRNA tokens 0 "mRNA"
transition translate "Translation"
place Protein tokens 0 "Protein"
transition degrade "Degradation"

Gene -> transcribe
transcribe -> Gene
transcribe -> mRNA
mRNA -> translate
translate -> mRNA
translate -> Protein
Protein -> degrade