Final answer:
The two regulatory proteins in the thin filament are Troponin and Tropomyosin, both essential for muscle contraction regulation.
Step-by-step explanation:
The two regulatory proteins that are part of the thin filament in muscle cells are Troponin and Tropomyosin. These proteins play critical roles in muscle contraction. Troponin is attached to the actin filament and has a binding site for calcium ions. When calcium ions bind to troponin, it causes a conformational change that moves tropomyosin away from the myosin-binding sites on actin. This process allows myosin heads to bind to actin, leading to muscle contraction. Tropomyosin is a fibrous protein that wraps around the actin filament, blocking the myosin binding sites on actin when the muscle is at rest, thereby preventing contraction.