The action of hyaluronidase on oligosaccharides from hyaluronan is complicated due to branched reaction paths containing hydrolysis, transglycosylation and condensation. The unit component of hyaluronan is a disaccharide, namely GlcA-(β1→3)-GlcNAc where GlcA and GlcNAc are d-glucuronic acid and d-N-acetylglucosamine respectively. Hyaluronan is the linear polymer formed by these disaccharide units, linked together with β1→4 glycosidic bonds. Bovine testicular hyaluronidase acts only at β1→4 glycosidic bonds of hyaluronan. The progress of product distribution from short oligosaccharides was simulated with the Monte Carlo method using the probabilistic model. The model consists only of a single enzyme molecule and a finite number of substrate and water molecules. The simulation is based on a simple reaction scheme and proceeds via an algorithm with minimum adjustable parameters generating random numbers and probabilities. The experimental data for bovine testicular hyaluronidase using [GlcA-(β1→3)-GlcNAc]4 as the starting substrate were quantitatively simulated with only three adjustable parameters. The simulated data for [GlcA-(β1→3)-GlcNAc]3 and [GlcA-(β1→3)-GlcNAc]5 as the starting substrates agreed semi-quantitatively with experimental data using the same parameters. The mechanism of the hyaluronidase reaction is a combination of branched probabilistic cycles. The condensation reaction is much weaker than the transglycosylation reaction but contributes to product distribution at the final stage of the reaction, preventing complete hydrolysis of the substrates.

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