Vol. 5, No. 1, 2010

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ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
A cut-cell method for simulating spatial models of biochemical reaction networks in arbitrary geometries

Wanda Strychalski, David Adalsteinsson and Timothy Elston

Vol. 5 (2010), No. 1, 31–53
Abstract

Cells use signaling networks consisting of multiple interacting proteins to respond to changes in their environment. In many situations, such as chemotaxis, spatial and temporal information must be transmitted through the network. Recent computational studies have emphasized the importance of cellular geometry in signal transduction, but have been limited in their ability to accurately represent complex cell morphologies. We present a finite volume method that addresses this problem. Our method uses Cartesian-cut cells in a differential algebraic formulation to handle the complex boundary dynamics encountered in biological systems. The method is second-order in space and time. Several models of signaling systems are simulated in realistic cell morphologies obtained from live cell images. We then examine the effects of geometry on signal transduction.

Keywords
systems biology, numerical methods, reaction-diffusion equation
Mathematical Subject Classification 2000
Primary: 92-08, 65M06
Milestones
Received: 24 June 2009
Revised: 4 December 2009
Accepted: 13 December 2009
Published: 31 January 2010
Authors
Wanda Strychalski
Carolina Center for Interdisciplinary Applied Mathematics
Department of Mathematics
University of North Carolina at Chapel Hill
Chapel Hill, NC 27599
United States
http://www.unc.edu/~wandastr
David Adalsteinsson
Carolina Center for Interdisciplinary Applied Mathematics
Department of Mathematics
University of North Carolina at Chapel Hill
Chapel Hill, NC 27599
United States
http://amath.unc.edu/David/David
Timothy Elston
Department of Pharmacology
University of North Carolina at Chapel Hill
Chapel Hill, NC 27599
United States
http://www.amath.unc.edu/Faculty/telston/