Final answer:
Gradient-driven pumps use the energy from ion gradients for transport such as in the bacterial flagellum, whereas ATP-driven pumps require ATP hydrolysis to move substances against their concentration gradients, like the sodium/potassium pump.
Step-by-step explanation:
For a pump to be gradient-driven means it utilizes the energy from a concentration gradient, such as a proton gradient, to perform work without the direct use of adenosine triphosphate (ATP). A common example of this is the bacterial flagellum, which is powered by proton flow through a membrane system. In contrast, an ATP-driven pump, like the sodium/potassium pump, requires the hydrolysis of ATP to directly fuel the active transport of molecules or ions against their concentration gradients.
An electrochemical gradient, such as the proton gradient mentioned above, is utilized in the process of oxidative phosphorylation, where the flow of protons through ATP-Synthase synthesizes ATP. This is analogous to generating electricity by water flowing through a turbine.
In summary, gradient-driven pumps use the energy stored in ion gradients, while ATP-driven pumps rely on the energy from ATP hydrolysis to transport substances across cell membranes.