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Single molecule tracking of heterogeneous diffusion.

J Cao1

  • 1Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2001
PubMed
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Heterogeneous diffusion reveals spatial variations not seen in ensemble measurements. Analysis of single-molecule trajectories uncovers signatures of these heterogeneities through non-Gaussian distributions and correlation functions.

Area of Science:

  • Physics
  • Physical Chemistry
  • Statistical Mechanics

Background:

  • Ensemble measurements of diffusion often mask underlying spatial heterogeneities.
  • The Einstein relation, while fundamental, may not fully capture complex diffusion dynamics.

Purpose of the Study:

  • To identify and quantify spatial heterogeneities in diffusion processes.
  • To develop methods for detecting non-Gaussian diffusion behavior.
  • To probe memory effects in fluctuating diffusion rates.

Main Methods:

  • Analysis of single-molecule diffusional trajectories.
  • Calculation of the time evolution of non-Gaussian distributions.
  • Evaluation of cross-correlation between square displacements at different times.
  • Utilizing the non-Gaussian indicator g(t) and joint moment correlation function f(t,tau).

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Main Results:

  • Spatial heterogeneities are detectable in single-molecule data, not ensemble averages.
  • The non-Gaussian indicator g(t) shows distinct decay or plateau behaviors.
  • The joint moment correlation function f(t,tau) directly probes memory effects.
  • A two-state diffusion model and a stochastic Gaussian model yield consistent results via second cumulant expansion.

Conclusions:

  • Single-molecule tracking is crucial for understanding heterogeneous diffusion.
  • Quantitative measures like g(t) and f(t,tau) provide insights into diffusion complexity.
  • The developed models accurately represent observed diffusion phenomena.