Final answer:
The structure called titin runs the length of the sarcomere through the thick filaments and is crucial for the elastic recoil in muscles, providing stability and elasticity to the myofibrils.
Step-by-step explanation:
The structure that runs the length of the sarcomere through the thick filaments and contributes to the elastic recoil in a muscle is called titin. Titin is a giant protein that spans half of the sarcomere, from the Z-disk to the M-line, and back again to the Z-disk within the opposite half of the sarcomere.
It plays a critical role in the sarcomere's ability to stretch and then spring back to its resting state. Titin anchors the thick filaments to the Z-disk and provides structural stability, flexibility, and elasticity to the myofibrils. During muscle contraction, when the sarcomere shortens, titin ensures that the thick and thin filaments do not overlap too much.
It functions much like a spring, storing potential energy when the muscle is stretched and releasing it during the recoil. Consequently, titin is essential for the passive elastic properties and the overall mechanics of the muscle.