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Biomixing by Chemotaxis and Enhancement of Biological Reactions

Publication ,  Journal Article
Kiselev, A; Ryzhik, L
Published in: Communications in Partial Differential Equations
February 1, 2012

Many phenomena in biology involve both reactions and chemotaxis. These processes can clearly influence each other, and chemotaxis can play an important role in sustaining and speeding up the reaction. However, to the best of our knowledge, the question of reaction enhancement by chemotaxis has not yet received extensive treatment either analytically or numerically. We consider a model with a single density function involving diffusion, advection, chemotaxis, and absorbing reaction. The model is motivated, in particular, by studies of coral broadcast spawning, where experimental observations of the efficiency of fertilization rates significantly exceed the data obtained from numerical models that do not take chemotaxis (attraction of sperm gametes by a chemical secreted by egg gametes) into account. We prove that in the framework of our model, chemotaxis plays a crucial role. There is a rigid limit to how much the fertilization efficiency can be enhanced if there is no chemotaxis but only advection and diffusion. On the other hand, when chemotaxis is present, the fertilization rate can be arbitrarily close to being complete provided that the chemotactic attraction is sufficiently strong. Moreover, an interesting feature of the estimates on fertilization rate and timescales in the chemotactic case is that they do not depend on the amplitude of the reaction term. © 2012 Copyright Taylor and Francis Group, LLC.

Duke Scholars

Published In

Communications in Partial Differential Equations

DOI

EISSN

1532-4133

ISSN

0360-5302

Publication Date

February 1, 2012

Volume

37

Issue

2

Start / End Page

298 / 318

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

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Kiselev, A., & Ryzhik, L. (2012). Biomixing by Chemotaxis and Enhancement of Biological Reactions. Communications in Partial Differential Equations, 37(2), 298–318. https://doi.org/10.1080/03605302.2011.589879
Kiselev, A., and L. Ryzhik. “Biomixing by Chemotaxis and Enhancement of Biological Reactions.” Communications in Partial Differential Equations 37, no. 2 (February 1, 2012): 298–318. https://doi.org/10.1080/03605302.2011.589879.
Kiselev A, Ryzhik L. Biomixing by Chemotaxis and Enhancement of Biological Reactions. Communications in Partial Differential Equations. 2012 Feb 1;37(2):298–318.
Kiselev, A., and L. Ryzhik. “Biomixing by Chemotaxis and Enhancement of Biological Reactions.” Communications in Partial Differential Equations, vol. 37, no. 2, Feb. 2012, pp. 298–318. Scopus, doi:10.1080/03605302.2011.589879.
Kiselev A, Ryzhik L. Biomixing by Chemotaxis and Enhancement of Biological Reactions. Communications in Partial Differential Equations. 2012 Feb 1;37(2):298–318.

Published In

Communications in Partial Differential Equations

DOI

EISSN

1532-4133

ISSN

0360-5302

Publication Date

February 1, 2012

Volume

37

Issue

2

Start / End Page

298 / 318

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics