Entropy-based idealization of complex single-molecule time trajectories from nanoelectronic biosensors: application to the detection and modeling of non-stationary molecular dynamics

Single-molecule field-effect transistors (smFET) have been recently exploited to probe molecular dynamic events occurring at the single-molecule scale. Hidden Markov models (HMMs) are commonly used to model single-molecule kinetic trajectories, but they require restrictive assumptions and a priori knowledge of the likely kinetic model, both rarely met in real experiments. In particular, a major challenge in extracting kinetics from smFET data relies on the non-stationarity of the recorded signals due to noise and drifts. Here, we propose a new approach based on machine learning to retrieve the hidden trajectory between molecular states. Our method is a two-step algorithm based on compression of the raw data using a minimum description length cost function, followed by a k-medoid clustering of the compression patterns. A decision-aid tool automatically selects the multi-state model providing the best-fitting trajectory. Based on tests on synthetic and experimental data, we found that this entropy-based method allows to extract a robust idealized trajectory, without requiring any prior or supervision. We also found that using this idealized trajectory as a prior for HMM analysis provides better performances for the detection and modeling of non-stationary molecular dynamics.