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Receptor heterogeneity in optical biosensors

Journal of Mathematical Biology volume 76, pages 795–816 (2018)Cite this article

Abstract

Scientists measure rate constants associated with biochemical reactions in an optical biosensor—an instrument in which ligand molecules are convected through a flow cell over a surface to which receptors are immobilized. We quantify transport effects on such reactions by modeling the associated convection-diffusion equation with a reaction boundary condition. In experimental situations, the full PDE model reduces to a set of unwieldy integrodifferential equations (IDEs). Employing common physical assumptions, we may reduce the system to an ODE model, which is more useful in practice, and which can be easily adapted to the inverse problem of finding rate constants. The results from the ODE model compare favorably with numerical simulations of the IDEs, even outside its range of validity.

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Authors and Affiliations

  1. Applied and Computational Mathematics Division, Information and Technology Laboratory, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, MD, 20899, USA

    Ryan M. Evans

  2. Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, USA

    David A. Edwards

Authors
  1. Ryan M. Evans
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  2. David A. Edwards
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Corresponding author

Correspondence to Ryan M. Evans.

Additional information

This work was done with the support of the NSF, under award number NSF-DMS 1312529. The first author would also like acknowledge the support of the National Research Council in the form of a postdoctoral fellowship.

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Evans, R.M., Edwards, D.A. Receptor heterogeneity in optical biosensors. J. Math. Biol. 76, 795–816 (2018). https://doi.org/10.1007/s00285-017-1158-x

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  • DOI: https://doi.org/10.1007/s00285-017-1158-x

Keywords

  • Biochemistry
  • Optical biosensors
  • Kinetic rate constants
  • Partial differential equations
  • Asymptotic analysis
  • Numerical methods

Mathematics Subject Classification

  • 92E20
  • 35Q92
  • 41A60
  • 65D99