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Biology — Petri Net: Enzyme Kinetics

Michaelis-Menten as a token-flow reaction network.

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Enzyme kinetics (Michaelis-Menten)Enzyme≤1Substrate≤5E + S -> ESenabledComplex≤1ES -> E + PProduct≤5Reachable markings114 places · 2 transitionsTerminatesyes1 final markingLive transitions2/2every one firesSafe places2/4bound ≤ 1 tokenConservation laws2every place covered11 reachable markings, 4 places, 2 transitions — bounded, deadlock-free, and every transition fires: it stops at 1 final marking, each of them a net that used up what it wa…Place `Product` 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 the title …This net runs to completion and stops at Enzyme 1 · Product 5. Nothing is enabled there, and it is not a deadlock: every transition still short of an input is short of one that NOTHING in this net …Conservation law: Substrate + Complex + Product = 5, 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 …Conservation law: Enzyme + Complex = 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.

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title Enzyme kinetics (Michaelis-Menten)

place E tokens 1 "Enzyme"
place S tokens 5 "Substrate"
transition bind "E + S -> ES"
place ES tokens 0 "Complex"
transition cat "ES -> E + P"
place P tokens 0 "Product"

E -> bind
S -> bind
bind -> ES
ES -> cat
cat -> E
cat -> P