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

Abstract

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 Shannon's 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.

Challenges in Inferring the Directionality of Active Molecular Processes from Single-Molecule Fluorescence Resonance Energy Transfer Trajectories

“…Such effects, fundamentally, cannot be neglected, and they can be detected with appropriate data analysis. , If discovering and quantifying the directionality of the observed dynamics are the objectives, it may also be desirable to estimate entropy production (eq ) directly from raw experimental time series (e.g., the photon sequence in Figure ) rather than after postprocessing the data using, e.g., hidden Markov models. In this regard, histogram entropy estimators and compression algorithm-based estimators appear to be promising, ,, although, to the best of our knowledge, they have not yet been applied to photon sequences. On the theory side, there have been recent developments addressing the question of how measures of irreversibility such as the entropy production can be deduced from partial observations such as some but not all transitions; , application of those ideas to experimental trajectories is a promising new direction.…”