Final answer:
In the state of rigor, adding ATP without free calcium ions will result in continued muscle rigidity. However, adding ATP with a substantial concentration of calcium ions will allow muscle contraction to occur.
Step-by-step explanation:
In a state of rigor, actin and myosin are strongly linked but unable to move. If ATP is added but no free calcium ions are present, the myosin heads will not be able to detach from the actin-binding sites, and the cross-bridges will stay in place, resulting in continued rigidity in the muscles. However, if ATP is added with a substantial concentration of calcium ions, the calcium ions will bind to troponin, causing a conformational change that allows tropomyosin to move away from the myosin binding sites on actin. This will enable cross-bridge formation and muscle contraction to occur.