Final answer:
Calcium ions bind to the troponin complex on actin filaments, specifically to troponin C, which leads to conformational changes that allow muscle contraction to begin.
Step-by-step explanation:
The place where calcium binds on actin filaments is on the troponin complex. Specifically, calcium ions bind to troponin C. Troponin is a complex of three proteins that is attached to tropomyosin, which lies along the actin filament and covers the myosin binding sites on the actin molecules when the muscle is in a relaxed state. When calcium ions bind to troponin C, it induces a conformational change in the troponin-tropomyosin complex, causing tropomyosin to move away from the myosin binding sites on actin. This then allows myosin heads to bind to actin and begin the contraction cycle.