Why is GTP used for nuclear transport and not ATP, given that ATP hydrolysis is used to drive most cellular energonic reactions?
Although this question appears to be either unclear or unanswerable (or both), and shows no evidence of research on the poster’s part, I have chosen to address one aspect of it to emphasize a general concept. This, despite the fact that my knowledge of nuclear transport processes is minimal.
GTP, rather than ATP, is used for nuclear–cytoplasmic transport via importins and exportins, because this process involves one of a large family of ‘G proteins’ that — as their name implies — operate through the use of GTP. Whereas ATP is generally used to drive endergonic molecular reactions, the hydrolysis of GTP in G-protein cycles can be thought as a device to terminate a molecular process. Whether G proteins adopted GTP rather than ATP merely by chance or for a biological reason is a matter of speculation.
NTP hydrolysis — for fun or profit?
It would appear that the question relates to protein-transporting ‘importins and exportins’, which I learn from the Wikipedia article on nuclear transport are regulated by the small G protein, Ran. When complexed to GTP, Ran facilitates the export of proteins by exportins, a process that is terminated by hydrolysis of GTP to GDP. The GDP-bound form facilitates the import of proteins by importins, a process that is terminated by GTP displacing the GDP.
So if we consider the role of the hydrolysis of the nucleotide triphosphate — here GTP — it is clearly not to supply thermodynamic energy for an endergonic process such as muscle contraction, light generation or a chemical reaction with a +ve ΔG:
Rather, it is to produce a conformational change in a protein which allows the termination of a process. This termination is generally through the GDP-bound form of the G protein (grey) interacting with some other protein (black):
This diagram is deliberately simplistic so that the general features of G-protein action can be seen. However, I think it illustrates the same point made in Berg et al. Section 15.6. Other examples are signal transduction of hormone action via cyclic AMP and binding of aminoacyl-tRNA to the ribosome.
Why do G proteins use GTP?
This ‘choice’ of GTP in the original ancestral G protein could have been mere chance, that was subsequently reflected in other G proteins that arose through gene duplication and divergence. That would imply that, at least, it was not disadvantageous. Or as the oldest G proteins are perhaps those involved in protein biosynthesis — a process still catalysed by a ribozyme — the choice of GTP might have reflected an RNA base-pairing interaction in the ‘RNA world’.
Alternatively one might suggest a biological rationale for separating two types of energy-requiring processes — perhaps by regulation of the enzyme that catalyses the conversion of ATP to GTP, dinucleoside-phosphate kinase. However I am not aware of any evidence to support this idea.
Hydrolysis of GTP in other contexts
As mentioned in a comment by @Roland, there are instances where GTP is used to drive endergonic reactions (phosphoenolpyruvate carboxykinase) in a manner analogous to the use of ATP, but this is quite different from hydrolysis of GTP in G proteins. I do not believe that any convincing rationale for this has been propounded, nor for the similar exceptional use of UTP in glycogen synthesis and CTP in phospholipid synthesis. This question has been discussed in another post.