ArticleSIAM journal on applied mathematics2018
INVESTIGATION OF A STRUCTURED FISHER'S EQUATION WITH APPLICATIONS IN BIOCHEMISTRY.
Article in SIAM journal on applied mathematics, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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Who cites it
3 citing papers in PubMed.
- Topologically-based parameter inference for agent-based model selection from spatiotemporal cellular data.PLoS computational biology · 2026Article
- Learning Equations from Biological Data with Limited Time Samples.Bulletin of mathematical biology · 2020Article
- The influence of numerical error on parameter estimation and uncertainty quantification for advective PDE models.Inverse problems · 2019Article
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2 authors.
Funding
Abstract
Recent biological research has sought to understand how biochemical signaling pathways, such as the mitogen-activated protein kinase (MAPK) family, influence the migration of a population of cells during wound healing. Fisher's Equation has been used extensively to model experimental wound healing assays due to its simple nature and known traveling wave solutions. This partial differential equation with independent variables of time and space cannot account for the effects of biochemical activity on wound healing, however. To this end, we derive a structured Fisher's Equation with independent variables of time, space, and biochemical pathway activity level and prove the existence of a self-similar traveling wave solution to this equation. We exhibit that these methods also apply to a general structured reaction-diffusion equation and a chemotaxis equation. We also consider a more complicated model with different phenotypes based on MAPK activation and numerically investigate how various temporal patterns of biochemical activity can lead to increased and decreased rates of population migration.
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