Abstract:
: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.
journal_name
Proc Natl Acad Sci U S Aauthors
Gordon PV,Sample C,Berezhkovskii AM,Muratov CB,Shvartsman SYdoi
10.1073/pnas.1019245108subject
Has Abstractpub_date
2011-04-12 00:00:00pages
6157-62issue
15eissn
0027-8424issn
1091-6490pii
1019245108journal_volume
108pub_type
杂志文章abstract::The principal methyl donor of the cell, S-adenosylmethionine (SAMe), is produced by the highly conserved family of methionine adenosyltranferases (MATs) via an ATP-driven process. These enzymes play an important role in the preservation of life, and their dysregulation has been tightly linked to liver and colon cancer...
journal_title:Proceedings of the National Academy of Sciences of the United States of America
pub_type: 杂志文章
doi:10.1073/pnas.1510959113
更新日期:2016-02-23 00:00:00
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journal_title:Proceedings of the National Academy of Sciences of the United States of America
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doi:10.1073/pnas.77.4.2293
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journal_title:Proceedings of the National Academy of Sciences of the United States of America
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更新日期:2006-01-31 00:00:00
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journal_title:Proceedings of the National Academy of Sciences of the United States of America
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journal_title:Proceedings of the National Academy of Sciences of the United States of America
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journal_title:Proceedings of the National Academy of Sciences of the United States of America
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更新日期:2015-12-15 00:00:00
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journal_title:Proceedings of the National Academy of Sciences of the United States of America
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journal_title:Proceedings of the National Academy of Sciences of the United States of America
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journal_title:Proceedings of the National Academy of Sciences of the United States of America
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journal_title:Proceedings of the National Academy of Sciences of the United States of America
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journal_title:Proceedings of the National Academy of Sciences of the United States of America
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更新日期:1996-10-01 00:00:00
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journal_title:Proceedings of the National Academy of Sciences of the United States of America
pub_type: 杂志文章
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更新日期:1995-05-09 00:00:00