Let's say you're developing an enzyme to catalyze a certain reaction. But the progress of this reaction is only measurable through e.g. fluorescently labelled substrate analogs, i.e. not actually the native substrate. One could imagine that the enzyme could become "overfitted" to accomodate the substrate analog and catalyze the conversion of this very well, but catalyze the conversion of the real, native substrate at the same rate (or slower, even).
Are there any documented cases of this?
Or more generally put, are there any documented cases of substrate analogs that actually yield incorrect results?
The kinetic constants for the substrate analogue would not be "incorrect", they simply would be better than those of the natural substrate.
For a single substrate reaction, there are two such constants, the Km essentially describes substrate binding, the Vmax the turnover of the bound substrate. Of these, Km would be more prone to the effect you describe, but you can control for that by a simple competition experiment. If you measure the turnover of your analogue in the presence of the natural substrate, whose turnover cannot be measured, the substrate would appear kinetically as competitive inhibitor, and its Ki can be obtained. If this were much (at least one order of magnitude) higher than Km, you'd have the problem you describe.
You might, in subsequent rounds of selection, use different substrate analogues carrying different fluorophors, to direct the selective pressure towards the common feature of these substrate analogues. In selection for protein binders, we have used to alter between streptavidin and neutravidin for immobilisation of the target, or between sfGFP and mRuby for FACS selection.
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