Rat skin tissue has been homogenized using liquid nitrogen. Lysis buffer is then added along with protease inhibitor. Samples are then used for BCA. Following the BCA the samples will be used for an ELISA procedure.
could you maybe adopt the method used normally for removal of bacterial endotoxin or other lipido-philic components with TritonX114 differential fractionation? If you mix your sample with Triton X114 on ice (especially if there is some dye such as bromophenol blue present), it is readily miscible. Then if you warm the samples >25˚C for some time and spin the samples at high speed, the Tx114 becomes a separate lipid layer, taking fat-soluble components (including the blue dye) of the buffer with it. Remove the aqueous layer containing your proteins. Do this 2 or 3 times and you should be able to remove the fat layer fairly effectively, although you'd need to be careful not to lose yield.
Otherwise, are there no methods to mechanically adsorb the fat layer off the surface of the liquid using Whatman paper or something similar?
If your target protein is >10k, cold acetone precipitation would seem to be the way to go as it will remove fat as well the excess detergent (SDS?) that may interfere with the Bradford assay. One point to consider is whether your ELISA requires the protein to be in its native (folded) form (Then Robin's way is better ). If denaturated is OK, then go for organic solvent (alternative: Methanol/chloroform for an even stronger cleaning, with phase separation). I hope this helps