Final answer:
At least one kinesin head must always be in contact with the microtubule to facilitate the movement of this motor protein and ensure constant transport of cellular cargo.
Step-by-step explanation:
The minimum number of kinesin heads in contact with a microtubule at all times is one. Kinesin is a motor protein that moves along microtubules in cells, typically transporting various cellular cargoes. It operates by using ATP to produce mechanical work. Kinesins are dimeric, meaning they have two heads, at least one of which attaches to the microtubule to maintain contact and facilitate movement. Even during the 'hand-over-hand' movement of kinesin, when one head releases to move forward, the other remains attached, ensuring continuous contact with the microtubule.