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Biology — Petri Net: Action Potential

The ion-flow phases as a token cycle.

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Action potential (ion flow)Resting (-70 mV)≤1Stimulus to thresholdenabledNa+ in (depolarise)≤1K+ outRepolarise≤1Na/K pumpReachable markings33 places · 3 transitionsTerminatesneverruns for everLive transitions3/3every one firesSafe places3/3bound ≤ 1 tokenConservation laws1every place covered3 reachable markings, 3 places, 3 transitions — bounded, deadlock-free, and every transition fires.Conservation law: Resting (-70 mV) + Na+ in (depolarise) + Repolarise = 1, at every reachable marking, for ever. No firing of any transition can change it — that is proved from the incidence matrix…

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title Action potential (ion flow)

place Rest tokens 1 "Resting (-70 mV)"
transition stimulus "Stimulus to threshold"
place Depol tokens 0 "Na+ in (depolarise)"
transition repol "K+ out"
place Repol tokens 0 "Repolarise"
transition recover "Na/K pump"

Rest -> stimulus
stimulus -> Depol
Depol -> repol
repol -> Repol
Repol -> recover
recover -> Rest