Direct observation of enzyme substrate complexes by stopped-flow fluorescence: Mathematical analyses

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Abstract
The fluorescence changes which occur upon the interaction of enzyme and substrate under stopped-flow conditions can provide a sensitive means to directly observe ES complexes. The interconversion of the intermediates during catalysis causes changes in fluorescence, signaling directly their existence, and allowing their quantitation. We have studied extensively and approach which measures radiationless energy transfer (RET) between enzyme tryptophanyl residues and a fluorescent peptide or ester substrate. Our studies of a number of proteolytic enzymes have validated the approach, which is sensitive and applicable to a variety of enzymes under a wide range of experimental conditions, including subzero temperatures. Direct excitation of fluorescent substrates can also be used to observe ES complex formation and breakdown and is complementary to the RET approach. Here we review both the RET and direct excitation kinetic approaches, with particular emphasis on the mathematical foundations we have developed which are critical to the successful interpretation of these or any other spectroscopic approach which yields a signal that is unique to ES complex.