Stochastic fractal behavior in concentration fluctuation and fluorescence correlation spectroscopy
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Updated: Oct 19, 2026

A Fluorescence Fluctuation Spectroscopy Assay of Protein-Protein Interactions at Cell-Cell Contacts
Published on: December 1, 2018
H Qian1, G M Raymond, J B Bassingthwaighte
1Department of Applied Mathematics, University of Washington, Seattle 98195, USA.
Abstract:
Fluctuations in the concentration of Brownian particles in one and two dimensions, or any reasonable measurement of the concentration such as in fluorescence correlation spectroscopy, is shown to be a stochastic fractal with a long tail. Being singular at omega = 0, the power spectrum of the fluctuation S(omega) approximately omega-1/2 for diffusion in one dimension, approximately log omega in two dimensions, but non-singular in three dimensions. This discovery provides one simple physical mechanism for possible long-memory fractal behavior, and its implications to various biological processes are discussed.
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