ArticleThe Journal of chemical physics2011
Ordinary differential equation for local accumulation time.
Article in The Journal of chemical physics, 2011. 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.
- Quantifying Temperature Compensation of Bicoid Gradients with a Fast T-Tunable Microfluidic Device.Biophysical journal · 2020Article
- Kinetics of receptor occupancy during morphogen gradient formation.The Journal of chemical physics · 2013Article
- Physical interpretation of mean local accumulation time of morphogen gradient formation.The Journal of chemical physics · 2011Article
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1 author.
Funding
Abstract
Cell differentiation in a developing tissue is controlled by the concentration fields of signaling molecules called morphogens. Formation of these concentration fields can be described by the reaction-diffusion mechanism in which locally produced molecules diffuse through the patterned tissue and are degraded. The formation kinetics at a given point of the patterned tissue can be characterized by the local accumulation time, defined in terms of the local relaxation function. Here, we show that this time satisfies an ordinary differential equation. Using this equation one can straightforwardly determine the local accumulation time, i.e., without preliminary calculation of the relaxation function by solving the partial differential equation, as was done in previous studies. We derive this ordinary differential equation together with the accompanying boundary conditions and demonstrate that the earlier obtained results for the local accumulation time can be recovered by solving this equation.
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