Calcium wave propagation in chains of endothelial cells with nonlinear reaction dynamics: Green's function approach

Pierre A Deymier, Keith A Runge, Martin J. Deymier, James B. Hoying, Jérôme O. Vasseur

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We present a Green's function-based perturbative approach to solving nonlinear reaction-diffusion problems in networks of endothelial cells. We focus on a single component (Ca2+), piecewise nonlinear model of endoplasmic calcium dynamics and trans-membrane diffusion. The decoupling between nonlinear reaction dynamics and the linear diffusion enables the calculation of the diffusion part of the Green's function for network of cells with nontrivial topologies. We verify analytically and then numerically that our approach leads to the known transition from propagation of calcium front to failure of propagation when the diffusion rate is varied relative to the reaction rates. We then derive the Green's function for a semi-infinite chain of cells with various boundary conditions. We show that the calcium dynamics of cells in the vicinity of the end of the semi-infinite chain is strongly dependent on the boundary conditions. The behavior of the semi-infinite chain with absorbing boundary conditions, a simple model of a multicellular structure with an end in contact with the extracellular matrix, suggests behavioral differentiation between cells at the end and cells embedded within the chain.

Original languageEnglish (US)
Article number041913
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume82
Issue number4
DOIs
StatePublished - Oct 18 2010

Fingerprint

Endothelial Cells
Calcium
Wave Propagation
Green's function
calcium
wave propagation
Green's functions
Cell
cells
boundary conditions
Propagation
Boundary conditions
Linear Diffusion
Absorbing Boundary Conditions
Reaction-diffusion Problems
propagation
Reaction Rate
Decoupling
decoupling
Nonlinear Model

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

Calcium wave propagation in chains of endothelial cells with nonlinear reaction dynamics : Green's function approach. / Deymier, Pierre A; Runge, Keith A; Deymier, Martin J.; Hoying, James B.; Vasseur, Jérôme O.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 82, No. 4, 041913, 18.10.2010.

Research output: Contribution to journalArticle

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