Nonlinear reaction-diffusion: a microscopic approach

• Authors: Jean Boon , James Lutsko , Christopher Lutsko
• Languages of publication: EN

Abstracts

EN

A microscopic theory for reaction-difusion (R-D) processes is developed from Einstein’s master equation including a reactive term. The mean field formulation leads to a generalized R-D equation for the n-th order annihilation reaction A + A + A + ... + A → 0, and the steady state solutions exhibit long range power law behavior showing the relative dominance of sub-diffusion over reaction effects in constrained systems, or conversely short range concentration distribution with finite support describing situations where diffusion is slow and extinction is fast. We apply the theory to analyze experimental data for morphogen gradient formation in the wing disc of the Drosophila embryo.

Keywords

EN

reaction-diffusion; nonlinear processes; morphogen gradient

• Journal: Open Physics
• Year: 2012
• Volume: 10
• Issue: 3
• Pages: 631-636

Dates

published

1 - 6 - 2012

online

17 - 6 - 2012

Contributors

author

Jean Boon

• Center for Nonlinear Phenomena and Complex Systems CP 231, Université Libre de Bruxelles, 1050, Bruxelles, Belgium,

author

James Lutsko

• Center for Nonlinear Phenomena and Complex Systems CP 231, Université Libre de Bruxelles, 1050, Bruxelles, Belgium,

author

Christopher Lutsko

• International School of Brussels, Kattenberg 19, 1170, Bruxelles, Belgium

References

• [1] O. Wartlick, A. Kicheva, M. Gonzalez-Gaitan, Cold. Spring Harb. Perspect. Biol. 1, a001255 (2011) http://dx.doi.org/10.1101/cshperspect.a001255[Crossref]
• [2] E. Abad, S. B. Yuste, K. Lindenberg, Phys. Rev. E 81, 031115 (2010)
• [3] S. B. Yuste, E. Abad, K. Lindenberg, Phys. Rev. E 82, 061123 (2010)
• [4] Y. He, S. Burov, R. Metzler, E. Barkai, Phys. Rev. Lett. 101, 058101 (2008) http://dx.doi.org/10.1103/PhysRevLett.101.058101[Crossref]
• [5] M. Magdrziarz, A. Weron, K. Burnecki, J. Klafter, Phys. Rev. Lett. 103, 180602 (2009) http://dx.doi.org/10.1103/PhysRevLett.103.180602[Crossref]
• [6] J. Szymanski, M. Weiss, Phys. Rev. Lett. 103, 038102 (2009) http://dx.doi.org/10.1103/PhysRevLett.103.038102[Crossref]
• [7] M. R. Horton, F. Hofling, J. O. Radler, T. Franosch Soft Matter. 6, 2648 (2010) http://dx.doi.org/10.1039/b924149c[Crossref]
• [8] J. F. Lutsko, J. P. Boon, Phys. Rev. E 77, 051103 (2008)
• [9] D. O. Kharchenko, V. O. Kharchenko, Physica A 354, 262 (2005) http://dx.doi.org/10.1016/j.physa.2005.01.057[Crossref]
• [10] A. Eldar, D. Rosin, B.-Z. Shilo, N. Barkai, Dev. Cell. 5, 635 (2003) http://dx.doi.org/10.1016/S1534-5807(03)00292-2[Crossref]
• [11] C. Han, D. Yan, T.Y. Belenkaya, X. Lin, Development 132, 667 (2005) http://dx.doi.org/10.1242/dev.01636[Crossref]

Identifiers

DOI

10.2478/s11534-012-0020-4