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

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 function with the subsequent continuous wavelet analysis of the later allows the localization 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. • Revealing patches with different diffusivity from a single particle track. • An improved continuous wavelet transform for exploring random walks. • Processing a case study of real biological membrane visited by a walking molecule. [ABSTRACT FROM AUTHOR]