Simulating Biochemical Signaling Networks in Complex Moving Geometries

  • Authors:

  • Wanda Strychalski;David Adalsteinsson;Timothy C. Elston

  • Affiliations:

  • wandastr@email.unc.edu and david@unc.edu;-;telston@med.unc.edu

  • Venue:
  • SIAM Journal on Scientific Computing
  • Year:
  • 2010

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Abstract

Signaling networks regulate cellular responses to environmental stimuli through cascades of protein interactions. External signals can trigger cells to polarize and move in a specific direction. During migration, spatially localized activity of proteins is maintained. To investigate the effects of morphological changes on intracellular signaling, we developed a numerical scheme consisting of a cut cell finite volume spatial discretization coupled with level set methods to simulate the resulting advection-reaction-diffusion system. We then apply the method to several biochemical reaction networks in changing geometries. We found that a Turing instability can develop exclusively by cell deformations that maintain constant area. For a Turing system with a geometry-dependent single or double peak solution, simulations in a dynamically changing geometry suggest that a single peak solution is the only stable one, independent of the oscillation frequency. The method is also applied to a model of a signaling network in a migrating fibroblast.