Final answer:
Mice with a defective α subunit of the G protein that cannot hydrolyze GTP to GDP will likely have dark brown fur, as the mutation leads to continuous signaling and increased cAMP levels, stimulating greater pigment production.
Step-by-step explanation:
If a transgenic mouse is genetically engineered to have a defective α subunit of the G protein that cannot hydrolyze GTP to GDP, we can predict the color of the fur of these mice. Normally, the α subunit of the G protein turns itself off by hydrolyzing GTP to GDP. When it cannot perform this hydrolysis, the α subunit remains active, continuously signaling downstream effects in the pathway. This is similar to the case where mice lacking cAMP phosphodiesterase, which normally degrades cAMP, have dark brown fur. The persistent signal would result in elevated cAMP levels in the pigment cells, thus we can predict that mice with the defective α subunit will also have dark brown fur. This is because uninterrupted signaling would stimulate pigment production just as in mice with uncontrolled cAMP levels.