It's possible. Consider the scenario wherein the detergent binds to the same binding site as the inhibitor, thereby competing with it. This could happen if the binding site is hydrophobic.
Another issue is the interaction of the inhibitor with the surface of an assay plate. These plates are made of polystyrene and are very hydrophobic. I always add a sub-CMC concentration of non-ionic detergent to buffers for assay done in assay plates. The detergent binds to the surface of the plate and passivates it so that the protein doesn't stick to it. This could prevent a hydrophobic inhibitor from sticking to the plate, too, which would lower the effective inhibitor concentration.
Are you sure the detergent concentration is below the CMC? Are you sure the compound is not an aggregator?
Is the substrate itself hydrophobic, such that it might interact with the detergent?
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