Final answer:
The γ (gamma) subunit is the one that rotates within the F1 head of ATP-synthase when protons move through the F0 base membrane channel.
Step-by-step explanation:
When protons move through the membrane via the channel in the F0 base, the γ (gamma) subunit rotates within the F1 head of ATP-synthase. The F1 portion consists of three α (alpha) and three β (beta) subunits arranged alternately, but they do not rotate. Instead, the γ subunit is centrally located and connected to the rotary F0c ring, which is part of the F0 portion that is embedded in the membrane and rotates as protons flow through it. This motion of the γ subunit leads to conformational changes in the α and β subunits, facilitating the synthesis of ATP from ADP and inorganic phosphate (Pi).