A Mathematical Model for the Role of Cell Signal Transduction in the Initiation and Inhibition of Angiogenesis
Date
Authors
Major Professor
Advisor
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
Authors
Research Projects
Organizational Units
Journal Issue
Is Version Of
Versions
Series
Department
Abstract
Neovascular formation can be divided into three main stages (which may be overlapping): (1) changes within the existing vessel, (2) formation of a new channel, (3) maturation of the new vessel. In two previous papers, [Levine, H.A. and Sleeman, B.D. (1997) "A system of reaction diffusion equations arising in the theory of reinforced random walks" SIAM J. Appl. Math. 683-730; Levine, H.A., Sleeman, B.D. and Nilsen-Hamilton, M. (2001b) "Mathematical modelling of the onset of capillary formation initiating angiogenesis." J. Math. Biol. 195-238] the authors introduced a new approach to angiogenesis, based on the theory of reinforced random walks, coupled with a Michaelis-Menten type mechanism which views the endothelial vascular endothelial cell growth factor (VEGF) receptors as the catalyst for transforming into a proteolytic enzyme in order to model the first stage. It is the purpose of this paper to present a more descriptive yet not overly complicated mathematical model of the biochemical events that are initiated when VEGF interacts with endothelial cells and which result in the cell synthesis of proteolytic enzyme. We also delineate via chemical kinetics, three mechanisms by which one may inhibit angiogenesis (inhibition of growth factor, growth factor receptor and protease function).
Comments
This is an Accepted Manuscript of an article published by Taylor & Francis as Levine, Howard A., Anna L. Tucker, and Marit Nilsen-Hamilton. "A mathematical model for the role of cell signal transduction in the initiation and inhibition of angiogenesis." Growth factors 20, no. 4 (2003): 155-175. Available online: 10.1080/0897719031000084355. Posted with permission.