A "competing adsorption" principle is known in polymer composites and nanocomposites. Your experimental system is way more complex, but in theory, I assume that BSA can still act as a displacer to your antibodies. I didn't do the required calculations to verify this hypothesis, though.
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I doubt BSA can replace chemisorbed molecules from the surface. More possible explanation is following: BSA electrostatically adsorbed on the surface of APTMS and formed thick (up to few um) layer and therefore hide the antibodies. At conditions described (pH 7.4) BSA has negative charge whereas APTMS is highly protonated (pKa is about 10). I am not sure, is it possible to distinguish an APTMS surface and any homogeneous polymeric surface from the AFM and FESEM data?