Memory effects and static disorder reduce information in single-molecule signals

A key theoretical challenge posed by single-molecule studies is the inverse problem of deducing the underlying molecular dynamics from the time evolution of low-dimensional experimental observables. Toward this goal, a variety of low-dimensional models have been proposed as descriptions of single-molecule signals, including random walks with or without conformational memory and/or with static or dynamics disorder. Differentiating among different models presents a challenge, as many distinct physical scenarios lead to similar experimentally observable behaviors such as anomalous diffusion and nonexponential relaxation. Here we show that information-theory-based analysis of single-molecule time series, inspired by Shannons work studying the information content of printed English, can differentiate between Markov (memoryless) and non-Markov single-molecule signals and between static and dynamic disorder. In particular, non-Markov time series are more predictable and thus can be compressed and transmitted within shorter messages (i.e. have a lower entropy rate) than appropriately constructed Markov approximations, and we demonstrate that in practice the LZMA compression algorithm reliably differentiates between these entropy rates across several simulated dynamical models.