Autoregressive HMM resolves biomolecular transitions from passive optical tweezer force measurements

Optical tweezer (OT) single-molecule force spectroscopy is a powerful method to map out the energy landscape of biological complexes and has found increasing applications in academic and pharmaceutical research. The dominant method to extract molecular conformation transitions from the thermal diffusion-broadened trajectories of the microscopic OT probes attached to the single molecule of interest is through hidden Markov models (HMMs). In standard applications, the HMMs assume a white noise spectrum of the probes superimposed onto the molecular signal. Here, we demonstrate, through theoretical derivation, computer modeling and experimental measurements that this standard white noise HMM (wnHMM) misses key features of real OT data. The deviation is most pronounced at higher frequencies because the white noise model does not account for the overdamped nature of particle diffusion in an OT harmonic potential in aqueous environments. To address this, we derive how to incorporate autoregression between consecutive data points into a HMM, and demonstrate through modeling and experiment that such an autoregressive HMM (arHMM) captures real OT data behavior across all frequency ranges. Through analysis of real OT data we recorded on a single DNA hairpin undergoing folding and unfolding transitions, we show that the wnHMM extracts lifetimes that are at least a factor of 2 faster and less consistent than the arHMM results, which match expectations and prior measurements. Overall, our work suggests that arHMM should be the default model choice for analysis OT single-molecule transitions and that its use will improve the fidelity and accuracy of single-molecule force spectroscopy measurements.