A Computational Model of Simulating Competitive Growth Factor Binding Under Flow

Wensheng Shen
Department of Computational Science
SUNY Brockport
BRockport, NY 14420, USA

Changjiang Zhang
Laboratory for High Performance Scientific Computing and Computer Simulation
Department of Computer Science
University of Kentucky
Lexington, KY 40506-0046, USA

Michael Fannon
Department of Ophthamology and Visual Sciences
University of Kentucky
Lexington, KY 40506, USA

Kimberly Forsten-Williams
Department of Chemical Engineering
Virginia Polytechnic Institute & State University
Blacksburg, VA 24061, USA

Jun Zhang
Laboratory for High Performance Scientific Computing and Computer Simulation
Department of Computer Science
University of Kentucky
Lexington, KY 40506-0046, USA

Abstract

A novel convection-diffusion-reaction model is developed to simulate fibroblast growth factor (FGF-2) binding to cell surface receptors (FGFRs) and heparan sulfate proteoglycans (HSPGs) under flow conditions within a cylindrical-shaped vessel or capillary. The model consists of (1) a set of coupled nonlinear partial differential equations (PDEs), the incompressible Navier-Stokes equations and the convection-diffusion transport equation, and (2) a set of coupled nonlinear ordinary differential equations (ODEs), the local binding and signaling by chemical kinetics. The time-dependent PDE system is discretized and solved by a second order implicit Euler scheme using the finite volume method. The ODE system is solved by a stiff ODE solver VODE using backward differencing formulation (BDF). The transient solution of FGF-2, FGFR, HSPG and their bound complexes for three different flow rates are computed and presented. Simulation results indicate that the model can predict the growth factor transport and binding to receptors with/without the existence of heparan sulfate in flow, as well as the effect of flow rate on growth factor-receptor binding. Findings from this study may provide useful information in understanding the impact of flow on growth factor binding and, ultimately, signaling in circulation.


Key words: Convection-diffusion-reaction, Fibroblast growth factor, Computer modeling, Heparan sulfate proteoglycans, Incompressible Flow.

Mathematics Subject Classification:


Download the PDF file wensheng8.pdf.
Technical Report No. 490-07, Department of Computer Science, University of Kentucky, Lexington, KY, 2007.

This research work was supported in part by NIH under grant R01-HL086644-01.