Reconstruction of substrate's diffusion landscape by the wavelet analysis of single particle diffusion tracks

TL;DR

This paper introduces a wavelet-based method to analyze single particle diffusion trajectories, enabling the reconstruction of the underlying substrate's diffusion landscape by identifying regions with distinct diffusion coefficients.

Contribution

The novel approach maps particle trajectories into complex oscillating functions and applies wavelet analysis to localize homogeneous regions and determine their diffusion coefficients.

Findings

Successfully applied to test examples

Reconstructed biological membrane properties from real data

Identified distinct diffusion regions in single molecule traces

Abstract

We propose an approach to analysing single trajectories of a particle, which moves randomly on a landscape distinct parts of which result in sufficiently various diffusion coefficients. The method based on the mapping the cumulative sum of step-wise elementary displacement squared into a complex oscillating functions with the subsequent continuous wavelet analysis of the later allows the localisation of relatively homogeneous sub-regions and determining values of the diffusion coefficient within each such sub-region. This approach is applied to demonstrable test examples as well as to the reconstruction of the biological membrane's properties from the real data of single molecule walk tracing.