Because ATP is used for relaxation of muscles, not the contraction.
It is indeed quite counterintuitive, because ATP is always associated with ‘action’. This is different for muscles, so lets first take a quick look at how muscles work.
Knowing all this, the rigidity of muscles after death (rigor mortis) can easily be explained: When breathing and circulation stop, muscles become oxygen deprived and can’t generate ATP aerobically. They might switch momentarily to anaerobic respiration, but they will soon lack sufficient amounts of ATP.
Due to the lack of ATP, step 4 and 5 can’t be carried out: myosin is not released form actin i.e. the muscle stays contracted. In addition, the calcium ions can’t be pumped out of the cell, so resting potential can’t be restored.
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