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Fractional exponential decay in the capture of ligands by randomly distributed traps in one dimension

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Abstract

In many biophysical and biochemical experiments one observes the decay of some ligand population by an appropriate system of traps. We analyse this decay for a one-dimensional system of randomly distributed traps, and show that one can distinguish three different regimes. The decay starts with a fractional exponential of the form exp[−(t/t 0)1/2], which changes into a fractional exponential of the form exp[−(t/t 1)1/3] for long times, which in its turn changes into a pure exponential time dependence, i.e. exp[−t/t 2] for very long times. With these three regimes, we associate three time scales, related to the average trap density and the diffusion constant characterizing the motion of the ligands.

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Literature

  • Agmon, N. and M. L. Glasser. 1986.Phys. Rev. A 34, 656.

    Article  Google Scholar 

  • Carslaw, H. S. and J. C. Jeager. 1959.Conduction of Heat in Solids, equations 12, 13, p. 97. Oxford: Clarendon Press.

    Google Scholar 

  • Copson, E. T. 1967.Asymptotic Expansions, pp. 91–98. Cambridge: Cambridge University Press.

    Google Scholar 

  • Donsker, M. D. and S. R. S. Varadhan. 1975.Communs pure appl. Math. 28, 525.

    MATH  MathSciNet  Google Scholar 

  • Gradshteyn, I. S. and I. M. Rhyzhik. 1965.Table of Integrals, Series and Products, equation 0.234-2. New York: Academic Press.

    Google Scholar 

  • Klafter, J., B. Zumofen and A. Blumen. 1984.J. Physique Lett. 45, L-49.

    Google Scholar 

  • Ngai, K. L. and G. B. Wright (Eds). 1984.Relaxations in Complex Systems. Arlington: Office of Naval Research.

    Google Scholar 

  • Seiferheld, U., H. Baessler and B. Movaghar. 1983.Phys. Rev. Lett. 51, 813.

    Article  Google Scholar 

  • Weiss, G. H. 1986.J. Stat. Phys. 42, 3.

    Article  Google Scholar 

  • Wiegel, F. W. and J. H. J. van Opheusden. 1987. University of Twente, preprint.

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Geurts, B.J., Wiegel, F.W. Fractional exponential decay in the capture of ligands by randomly distributed traps in one dimension. Bltn Mathcal Biology 49, 487–494 (1987). https://doi.org/10.1007/BF02458865

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  • DOI: https://doi.org/10.1007/BF02458865

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