Take a strong promoter like CMV and make a library coding the first reporter (DsRed)alone and the second one (EGFP) fused in frame within one of the >8000 human proteins X (take the X library from the hORFeome cDNA library). Of course, you need viral IRES to let the ribosome translate two protein from the same mRNA. Then, express the library in your favourite cell line. Once protein X is degradated, if you "believe" also EGFP will be degradated, then you can FACS the EGFP/dsRED ratio obtaining 7 population of cells containing only stable-->unstable proteins in your vector. Make 7 microarrays opportunely designed to find the DNA of your vector and identify which proteins (ORF) are stable/unstable. Give the results to a team of bioinformatics/system biologists and mine the dataset to find correlation between protein stability and roles/pathways/amino acid composition/astrological signs and what else you can get statistically significant. Submit the manuscript to Science.
Take care! It would be possible that the EGFP fusion with X protein, generates a protease site. In that case, the EGFP/dsRED ratio may not be a reliable readout of protein stability. If you don't want to take such risk, hire a PhD student and ask him to made 8000 western blots with 8000 working antibodies. Then, submit the manuscript to Reportergene*
* in 2019, when your PhD student will give you the results, Reportergene will have the biggest impact factor.
H.-C. S. Yen, Q. Xu, D. M. Chou, Z. Zhao, S. J. Elledge (2008). Global Protein Stability Profiling in Mammalian Cells Science, 322 (5903), 918-923 DOI: 10.1126/science.1160489