Compression algorithms reveal memory effects and static disorder in single-molecule trajectories

Abstract

A key challenge in single-molecule studies is deducing underlying molecular kinetics from low-dimensional data, as distinct physical scenarios can exhibit similar observable behaviors such as anomalous diffusion. We show that information-theoretic analysis of single-molecule time series can reliably differentiate Markov (memoryless) from non-Markov dynamics and static from dynamic disorder. This analysis is based on the idea that non-Markov time series can be compressed, using lossless compression algorithms and transmitted within shorter messages than appropriately constructed Markov approximations. In practice, this method detects differences between Markov and non-Markov trajectories even when they are much smaller than the errors of the compression algorithm.