The role of membrane patch size and flow in regulating a proteolytic feedback threshold on a membrane: possible application in blood coagulation

Positive feedback controls in proteolytic systems are characterized by thre sholds which are regulated by the concentration of the initial stimulus and the kinetic parameters for enzyme generation and inhibition. Significant c omplexity is added when a positive feedback is localized on a membrane in c ontact with a flowing medium, such as seen in the early steps of blood coag ulation. A partial differential equation model of an archetypal feedback lo op is examined in which a proteolytic enzyme catalyzes its own formation fr om a zymogen on a membrane in contact with a flowing medium. As predicted f rom prior solution-phase and membrane-phase analyses, the threshold conditi ons for activation of the system are regulated by the kinetics of enzyme ge neration and inhibition and by the density of reactant-binding sites on the membrane; but the present analysis also establishes how the feedback thres hold is controlled by the flow rate of the adjacent medium and the physical size of the membrane patch on which the feedback loop is localized. For gi ven systems of particular kinetic properties, lower flow rates or larger ac tive patches of membrane can result in the activation threshold being excee ded, whereas higher flow rates or smaller membrane patches can prevent init iation. In addition to numerical simulation, a simplified non-flowing model is analyzed to formulate an approximate mathematical statement of the depe ndence of the minimum activatable patch size on the kinetic and other param eters. (C) 2001 Published by Elsevier Science Inc.