Reaction-complexation coupling between an enzyme and its polyelectrolytic substrate: Determination of the dissociation constant of the hyaluronidase-hyaluronan complex from the hyaluronidase substrate-dependence

- The hyaluronan/hyaluronidase system is a reaction-complexation coupling.
- The substrate-dependence combines Michaelis-Menten and binding equations.
- For the first time, the Kd value of the system at low ionic strength is determined.

Hyaluronan (HA) is catalytically hydrolyzed by hyaluronidase (HAase). Depending on pH, HA is able to form a non-productive electrostatic complex with HAase in addition to the classical enzyme-substrate complex. Experiments have shown the strong inhibition of the HA hydrolysis catalyzed by HAase when performed at high HA over HAase concentration ratio and low ionic strength. The substrate-dependence thus shows a non-classic inhibition of HAase at high substrate concentrations due to the sequestration of HAase by HA in the electrostatic complex. The modeling of the HA/HAase system is characteristic of a reaction-complexation coupling and it is very difficult to study reaction or binding, separately. Here, we have established the equation controlling the global system and shown that the substrate-dependence of such a system is a direct combination of a pure Michaelis-Menten equation associated with the reaction and a hyperbolic curve associated with the binding. At low substrate concentrations, the hyperbola, representing the relative part of HAase not sequestered by HA, can be assimilated to a straight line. We have established the relationship between the slope of that straight line and the dissociation constant of the electrostatic HA-HAase complex. Fitting the theoretical equation to the experimental data allowed us to determine, for the first time, the Kd value of the non-productive HA-HAase complex at low ionic strength.