Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 108, Issue 15, Pages 6157-6162Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1019245108
Keywords
robustness; tissue regulation; concentration gradient
Categories
Funding
- United States-Israel Binational Science Foundation [2006-151]
- National Institutes of Health, Center for Information Technology
- National Science Foundation (NSF) [DMS-0718027, DMS-0908279, DMS-0718604]
- National Institutes of Health [GM078079]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1119714] Funding Source: National Science Foundation
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0908279] Funding Source: National Science Foundation
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Some aspects of pattern formation in developing embryos can be described by nonlinear reaction-diffusion equations. An important class of these models accounts for diffusion and degradation of a locally produced single chemical species. At long times, solutions of such models approach a steady state in which the concentration decays with distance from the source of production. We present analytical results that characterize the dynamics of this process and are in quantitative agreement with numerical solutions of the underlying nonlinear equations. The derived results provide an explicit connection between the parameters of the problem and the time needed to reach a steady state value at a given position. Our approach can be used for the quantitative analysis of tissue patterning by morphogen gradients, a subject of active research in biophysics and developmental biology.
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