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Biology — Petri Net: Signal Transduction

Ligand-receptor activation driving a response.

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Signal transductionSignal moleculeReceptorReceptor activationenabledActive receptorKinase cascadeCellular responseω unboundedReachable markings—unbounded — no finite setTerminates—not decidedLive transitions—not decidedSafe places0/41 unboundedConservation laws21 place in none1 place unbounded, so this net has no finite reachable set.Place `Cellular response` 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 `Cellular response` 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 pr…Conservation law: Receptor + Active receptor = 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 sea…Conservation law: Signal molecule + Active receptor = 2, at every reachable marking, for ever. No firing of any transition can change it — that is proved from the incidence matrix, not observed ove…1 place is weighted by no conservation law — `Cellular response`. Nothing in the structure of this net holds what it holds constant, so its token count is free to drift with the firing sequence. Th…

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title Signal transduction

place Ligand tokens 2 "Signal molecule"
place Receptor tokens 1 "Receptor"
transition activate "Receptor activation"
place Active tokens 0 "Active receptor"
transition kinase "Kinase cascade"
place Response tokens 0 "Cellular response"

Ligand -> activate
Receptor -> activate
activate -> Active
Active -> kinase
kinase -> Active
kinase -> Response