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Nonlinear Theory of Anomalous Diffusion and Application to Fluorescence Correlation Spectroscopy

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Abstract

The nonlinear theory of anomalous diffusion is based on particle interactions giving an explicit microscopic description of diffusive processes leading to sub-, normal, or super-diffusion as a result of competitive effects between attractive and repulsive interactions. We present the explicit analytical solution to the nonlinear diffusion equation which we then use to compute the correlation function which is experimentally measured by correlation spectroscopy. The theoretical results are applicable in particular to the analysis of fluorescence correlation spectroscopy of marked molecules in biological systems. More specifically we consider the cases of fluorescently labeled lipids in the plasma membrane and of fluorescent apoferritin (a spherically shaped oligomer) in a crowded dextran solution and we find that the nonlinear correlation spectra reproduce very well the experimental data indicating sub-diffusive molecular motion.

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Notes

  1. The analysis has been generalised to include super-diffusion by introducing a similar power law ansatz for the distribution of particle displacements [9].

  2. In the restricted case that the walkers have equal probability to move in any direction, the NLFP reduces to the phenomenological porous media equation [15].

  3. The fluorescence correlation spectrum was also computed analytically from the solution of fractional diffusion equation for sub-diffusive motion [19].

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Acknowledgments

This work was supported in part by the European Space Agency under contract number ESA AO-2004-070.

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  1. Physics Department, Université Libre de Bruxelles, CP 231, 1050, Brussel, Belgium

    Jean Pierre Boon & James F. Lutsko

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  1. Jean Pierre Boon
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  2. James F. Lutsko
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Correspondence to Jean Pierre Boon.

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Boon, J.P., Lutsko, J.F. Nonlinear Theory of Anomalous Diffusion and Application to Fluorescence Correlation Spectroscopy. J Stat Phys 161, 1366–1378 (2015). https://doi.org/10.1007/s10955-015-1315-9

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  • DOI: https://doi.org/10.1007/s10955-015-1315-9

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