A mathematical model for the roles of pericytes and macrophages in the initiation of angiogenesis. I. The role of protease inhibitors in preventing angiogenesis

In this paper, a simple mathematical model developed in H.A. Levine, B.D. S leeman, M. Nilsen-Hamilton [J. Math. Biol., in press] to describe the initi ation of capillary formation in tumor angiogenesis is extended to include t he roles of pericytes and macrophages in regulating angiogenesis. The model also allows for the presence of anti-angiogenic (angiostatic) factors. The model is based on the observation that angiostatin can prevent the degrada tion of fibronectin in the basal lamina by inhibiting the catalytic action of active proteolytic enzyme. That is, it is proposed that the inhibitor 'd eactivates' the protease but that it does not reduce the over all concentra tion of the protease. It consequently explores the possibility of preventin g neovascular capillaries from migrating through the extra-cellular matrix toward the tumor by inhibiting protease action. The model is based on the t heory of reinforced random walks coupled with Michaelis-Menten mechanisms w hich view endothelial cell receptors as the catalysts for transforming both tumor and macrophage derived angiogenic factors into proteolytic enzyme wh ich in turn degrade the basal lamina, A simple catalytic reaction is propos ed for the degradation of the basal lamina by the active proteases, A mecha nism, in which the angiostatin acts as a protease inhibitor is discussed wh ich has been substantiated experimentally. A second mechanism for the produ ction of protease inhibitor from angiostatin by endothelial cells is propos ed to be of Michaelis-Menten type. Mathematically, this mechanism includes the former as a subcase. (C) 2000 Elsevier Science Inc. All rights reserved .