Final answer:
The ion channel that does not participate in the contractile cell action potential is inward rectifying potassium channels.
Step-by-step explanation:
The contractile cell action potential in cardiac cells involves the participation of different ion channels, such as type T calcium channels, type L calcium channels, delayed rectifying potassium channels, and voltage-gated sodium channels. These channels play important roles in the depolarization and repolarization of the cell membrane during the action potential. Inward rectifying potassium channels, on the other hand, are mainly involved in maintaining the resting potential of the cell and are less involved in the generation of action potentials.