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Biology — Cross-bridge Cycle (Petri Net)

Myosin heads cycle to slide the filaments.

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Muscle contraction (cross-bridge cycle)ATP≤4Myosin head (cocked)≤2Cross-bridge bound≤2Calcium (troponin)≤2Rigor state, stroke…≤2Head binds actinenabledPower strokeATP detaches headReachable markings105 places · 3 transitionsTerminatesyes1 final markingLive transitions3/3every one firesSafe places0/5bound ≤ 1 tokenConservation laws12 places in none10 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 wa…This net runs to completion and stops at ATP 2 · Myosin head (cocked) 2. Nothing is enabled there, and it is not a deadlock: every transition still short of an input is short of one that NOTHING in…Conservation law: Myosin head (cocked) + Cross-bridge bound + Rigor state, stroke complete = 2, at every reachable marking, for ever. No firing of any transition can change it — that is proved from…2 places are weighted by no conservation law — `ATP`, `Calcium (troponin)`. Nothing in the structure of this net holds what they hold constant, so their token count is free to drift with the firing…

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title Muscle contraction (cross-bridge cycle)

place ATP tokens 4 "ATP"
place Myosin tokens 2 "Myosin head (cocked)"
place Bound tokens 0 "Cross-bridge bound"
place Calcium tokens 2 "Calcium (troponin)"
place Rigor tokens 0 "Rigor state, stroke complete"
transition attach "Head binds actin"
transition powerstroke "Power stroke"
transition detach "ATP detaches head"

Calcium -> attach
Myosin -> attach
attach -> Bound
Bound -> powerstroke
powerstroke -> Rigor
Rigor -> detach
ATP -> detach
detach -> Myosin