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Biology — Petri Net: Blood Glucose Control

Insulin and glucagon as opposing transitions.

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Blood glucose homeostasisHigh blood glucose≤1Insulin releasedenabledGlycogen stored≤1Low blood glucose≤1Glucagon releasedenabledGlucose released≤1Reachable markings44 places · 2 transitionsTerminatesyes1 final markingLive transitions2/2every one firesSafe places4/4bound ≤ 1 tokenConservation laws2every place covered4 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 was…Place `Glycogen stored` 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…Place `Glucose released` 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 t…This net runs to completion and stops at Glycogen stored 1 · Glucose released 1. Nothing is enabled there, and it is not a deadlock: every transition still short of an input is short of one that NO…Conservation law: Low blood glucose + Glucose released = 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: High blood glucose + Glycogen stored = 1, at every reachable marking, for ever. No firing of any transition can change it — that is proved from the incidence matrix, not observed …

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title Blood glucose homeostasis

place HighGlucose tokens 1 "High blood glucose"
transition insulin "Insulin released"
place Stored tokens 0 "Glycogen stored"
place LowGlucose tokens 1 "Low blood glucose"
transition glucagon "Glucagon released"
place Released tokens 0 "Glucose released"

HighGlucose -> insulin
insulin -> Stored
LowGlucose -> glucagon
glucagon -> Released