Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 32, Issue 5, Pages 3039-3070Publisher
SIAM PUBLICATIONS
DOI: 10.1137/090779693
Keywords
systems biology; numerical methods; advection-reaction-diffusion equation; level set methods
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Funding
- NIH [R01-GM079271, R01-GM078994]
- NATIONAL INSTITUTE OF GENERAL MEDICAL SCIENCES [R01GM079271] Funding Source: NIH RePORTER
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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.
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