For muscle contraction, the actin and myosin forms a cross bridge which leads to contraction of muscle.This cross bridge is formed in presence of calcium ( because the calcium ion binds to troponin which releases the active binding site for myosin present on actin).
Also to break these cross bridges, ATP is required . Energy obtained from ATP is used to break the cross bridge and muscle relaxation occur.
Now when the person dies, the muscles become more permeable to calcium. This cause more calcium to move into the cytoplasm of muscle from sarcoplasmic reticulum resulting in contractions. And since person has died, no more ATP will be formed because respiration has stopped. So no ATP are now available to break the cross Bridges. This result in Rigor Mortis.
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