The kinetic behavior of lysozyme-catalyzed reactions of cell-wall oligosaccharides is analyzed. The model considers the various ways in which any oligomer can associate with the enzyme, and assumes that the association constant for any mode depends only on which subsites of the enzyme site are filled. Rates of cleavage of bound substrate to form a glycosyl enzyme intermediate and rates of hydrolysis or transfer of the intermediate to an acceptor are assumed to be the same for any productively bound substrate. The model can be solved by numerical integration with a digital computer, and has been fit to experimental data by a least-squares procedure. Using the parameters so obtained, further reactions can be satisfactorily modelled. The general behavior of the reactions and the significance of the values of the parameters are discussed. Nonproductive binding is seen to be of major importance in the reactions of small oligomers, which are hydrolyzed chiefly via pathways in which they react first as transglycosylation acceptors. Nonproductive binding is also seen to have implications for the mechanism of lysozyme action. The model used can be extended to deal with other endocatenases having transferase activity.
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