Metal-organic frameworks demonstrate a wide variety of behavior in their response to pressure, which can be classified in a rather limited list of categories, including anomalous elastic behavior (e.g., negative linear compressibility, NLC), transitions between crystalline phases, and amorphization. Very few of these mechanisms involve bond rearrangement. Here, we report two novel piezo-mechanical responses of metal-organic frameworks, observed under moderate pressure in two materials of the zinc alkyl gate (ZAG) family. Both materials exhibit NLC at high pressure, due to a structural transition involving a reversible proton transfer between an included water molecule and the linker's phosphonate group. In addition, the 6-carbon alkyl chain of ZAG-6 exhibits a coiling transition under pressure. These phenomena are revealed by combining high-pressure single-crystal X-ray crystallography and quantum mechanical calculations. They represent novel pressure responses for metal-organic frameworks, and pressure-induced proton transfer is a very rare phenomenon in materials in general.