Campus Units

Biochemistry, Biophysics and Molecular Biology, Roy J. Carver Department of, Mathematics

Document Type

Article

Publication Version

Accepted Manuscript

Publication Date

6-11-2009

Journal or Book Title

Growth Factors

Volume

20

Issue

4

First Page

155

Last Page

175

DOI

10.1080/0897719031000084355

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.

Copyright Owner

Taylor & Francis

Language

en

File Format

application/pdf

Published Version

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