Membrane binding-site density can modulate activation thresholds in enzyme systems

The kinetic equations are analysed for a model system which is motivated by the reactions of blood coagulation, and which involves two zymogen-enzyme pairs each of which can exist in solution phase or bound to a membrane. The enzyme of each pair activates the zymogen of the other pair, and each enzyme is subject to first-order inactivation both in solution and when bound to the membrane. If enzyme activation happens exclusively or predominantly in the membrane phase, then the system displays a threshold response which can be modulated by varying the density of membrane binding sites for the zymogens and enzymes. For low densities of membrane binding sites, the system's response when challenged by a dose of enzyme quickly decays away. For high enough densities of membrane binding sites, the system responds with substantial and sustained enzyme production. Thus variations in surface-binding site densities can serve as a "switch", drastically altering the responsiveness of the system. Such a binding-site-mediated switching mechanism could have profound importance to the regulation of enzyme systems, in particular, the blood coagulation system.