Critical time scales for morphogen gradient formation: Concentration or gradient criteria?

被引：4

作者：

Simpson, Matthew J. ^{[1
]}

机构：

[1] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia

来源：

INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER | 2017年 / 106卷

基金：

澳大利亚研究理事会;

关键词：

Reaction-diffusion; Steady state; Transient; Critical time; Mean action time; LONG;

D O I：

10.1016/j.ijheatmasstransfer.2016.09.026

中图分类号：

O414.1 [热力学];

学科分类号：

摘要：

We extend some recent analysis regarding an approximation of the time scale required for a transient morphogen concentration profile to approach steady state. Motivated by experimental observations, we consider the time scale required for the spatial gradient of morphogen concentration to approach steady state. The analysis shows that the spatial gradient approaches steady state faster than the associated concentration profile approaches steady state. For typical parameter values, this difference in time scales appears to be significant because it is comparable to the time scale of a typical experiment. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：570 / 572

页数：3

共 18 条

[1] Decapentaplegic and growth control in the developing Drosophila wing [J].

Akiyama, Takuya ;

Gibson, Matthew C. .

NATURE, 2015, 527 (7578) :375-+

[2] The interpretation of morphogen gradients [J].

Ashe, HL ;

Briscoe, J .

DEVELOPMENT, 2006, 133 (03) :385-394

[3] Formation of morphogen gradients: Local accumulation time [J].

Berezhkovskii, Alexander M. ;

Sample, Christine ;

Shvartsman, Stanislav Y. .

PHYSICAL REVIEW E, 2011, 83 (05)

[4] How Long Does It Take to Establish a Morphogen Gradient? [J].

Berezhkovskii, Alexander M. ;

Sample, Christine ;

Shvartsman, Stanislav Y. .

BIOPHYSICAL JOURNAL, 2010, 99 (08) :L59-L61

[5] Morphogen rules: design principles of gradient-mediated embryo patterning [J].

Briscoe, James ;

Small, Stephen .

DEVELOPMENT, 2015, 142 (23) :3996-4009

[6] DIFFUSION IN EMBRYOGENESIS [J].

CRICK, F .

NATURE, 1970, 225 (5231) :420-&

[7] Moments of action provide insight into critical times for advection-diffusion-reaction processes [J].

Ellery, Adam J. ;

Simpson, Matthew J. ;

McCue, Scott W. ;

Baker, Ruth E. .

PHYSICAL REVIEW E, 2012, 86 (03)

[8] Critical time scales for advection-diffusion-reaction processes [J].

Ellery, Adam J. ;

Simpson, Matthew J. ;

Mccue, Scott W. ;

Baker, Ruth E. .

PHYSICAL REVIEW E, 2012, 85 (04)

[9] Critical times in single-layer reaction diffusion [J].

Hickson, R. I. ;

Barry, S. I. ;

Sidhu, H. S. ;

Mercer, G. N. .

INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 2011, 54 (11-12) :2642-2650

[10] Critical times in multilayer diffusion. Part 2: Approximate solutions [J].

Hickson, R. I. ;

Barry, S. I. ;

Mercer, G. N. .

INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 2009, 52 (25-26) :5784-5791

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