No this is not 'homework'. I'm a PhD student, and this was something brought up at the end of a journal club recently, and one of the PIs posed this question and told us to think about it. It sounds simple, but it sort of has me baffled.
Western blot: No. Need a known antigen and so, since we don't know what we're after, this won't work.
Total protein gel: Collect cell lysates from different cell populations that are in different parts of the cell cycle, run it on a gel and observe any cyclic expression. This seems sort of ok but I feel like there are a few problems with it: 1) identifying the cell populations that are in the different cycle stages; 2) other proteins of same/similar size that cannot be differentiated.
Some sort of RNAi, knockdown, etc.: Like the western blot, we don't know what we're dealing with and so can't target anything.
Pulldown assay with mass spec: I don't know a lot about it aside from that it looks at protein-protein interactions. Unsure if it would be appropriate here.
As far as a model, I was thinking either yeast or some immortalized mammalian cell line.