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Biology — Petri Net: Urea Cycle

A cyclic net regenerating ornithine to dispose of ammonia.

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Urea cycleAmmonia≤2Ornithine≤1+ carbamoyl phosphateenabledCitrulline≤1+ aspartateArginine≤1ArginaseUrea (excreted)≤2Reachable markings75 places · 3 transitionsTerminatesyes1 final markingLive transitions3/3every one firesSafe places3/5bound ≤ 1 tokenConservation laws2every place covered7 reachable markings, 5 places, 3 transitions — bounded, deadlock-free, and every transition fires: it stops at 1 final marking, each of them a net that used up what it was…Place `Urea (excreted)` 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 th…This net runs to completion and stops at Ornithine 1 · Urea (excreted) 2. Nothing is enabled there, and it is not a deadlock: every transition still short of an input is short of one that NOTHING i…Conservation law: Ammonia + Citrulline + Arginine + Urea (excreted) = 2, at every reachable marking, for ever. No firing of any transition can change it — that is proved from the incidence matrix, …Conservation law: Ornithine + Citrulline + Arginine = 1, at every reachable marking, for ever. No firing of any transition can change it — that is proved from the incidence matrix, not observed ove…

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title Urea cycle

place NH3 tokens 2 "Ammonia"
place Orn tokens 1 "Ornithine"
transition carbamoyl "+ carbamoyl phosphate"
place Cit tokens 0 "Citrulline"
transition argsucc "+ aspartate"
place Arg tokens 0 "Arginine"
transition cleave "Arginase"
place Urea tokens 0 "Urea (excreted)"

NH3 -> carbamoyl
Orn -> carbamoyl
carbamoyl -> Cit
Cit -> argsucc
argsucc -> Arg
Arg -> cleave
cleave -> Urea
cleave -> Orn