Final answer:
The statement is true; the myosin heads attaching to actin binding sites and pulling the actin filament toward the sarcomere's center is a crucial step in muscle contraction, known as the power stroke. This process requires ATP and continues as long as Ca++ ions and ATP are present.
Step-by-step explanation:
The statement is true: During a muscle contraction, the head of the myosin cross bridges attach to actin binding sites and bend slightly, pulling the actin filament toward the center of the sarcomere. This is part of the cross-bridge cycle which is essential for muscle contraction. The cycle begins when the myosin-binding site on an actin filament is exposed as calcium ions bind to troponin, allowing tropomyosin to move away from the binding sites. As a result, myosin heads can bind to the actin forming cross-bridges. This is followed by what is known as the power stroke; the myosin head pivots and pulls the actin filament toward the sarcomere's center, thereby shortening the sarcomere. This action, along with many sarcomeres contracting in unison, leads to muscle fiber contraction.
The process requires energy, which is supplied by ATP. After the power stroke, myosin heads must be 're-cocked' by breaking down ATP, allowing for detachment and preparation for another cycle of contraction as long as the Ca++ ions and ATP are available.