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Subdiffusive target problem: survival probability.

S B Yuste1, Katja Lindenberg

  • 1Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 1, 2008
PubMed
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In low dimensions, a single subdiffusive trap eventually reaches a target, but takes infinite time. In higher dimensions or with many traps, the target is reached with certainty in finite time.

Area of Science:

  • Physics
  • Physical Chemistry
  • Biophysics

Background:

  • Subdiffusion describes anomalous movement patterns observed in various biological and physical systems.
  • Understanding target encounter dynamics is crucial for processes like molecular binding and cellular reactions.

Purpose of the Study:

  • To calculate the asymptotic survival probability of a spherical target interacting with subdiffusive traps.
  • To analyze the influence of trap dimensionality and density on target encounter times.

Main Methods:

  • Mathematical modeling of subdiffusive transport in continuous Euclidean media.
  • Asymptotic analysis of survival probability for single and multiple trap scenarios.

Main Results:

Related Experiment Videos

  • In 1D and 2D, a single subdiffusive trap reaches the target with certainty, exhibiting power-law decay in survival probability.
  • In dimensions >2, a single trap may never reach the target, resulting in a finite survival probability.
  • A sea of subdiffusive traps ensures target encounter with certainty across all dimensions, characterized by stretched exponential decay.

    • Conclusions:

    • The dimensionality and density of subdiffusive traps critically determine target encounter dynamics.
    • Findings have direct implications for understanding enzyme binding kinetics in crowded cellular environments, such as DNA-protein interactions.