Analysis of DNA Looping Kinetics in Tethered Particle Motion Experiments using Hidden Markov Models

Abstract

Tethered particle motion (TPM) is a powerful method for measuring DNA-protein interactions at the single molecule level. TPM experiments monitor the Brownian motion of beads tethered to a microscope cover slip. The Brownian motion changes when a protein binds to and deforms the DNA 'leash', for example in the formation of a DNA loop. A complicating factor in the interpretation of TPM data is that the number of observable states, corresponding to different conformations of the DNA-protein complex, is often not known in advance. Moreover, conformational transitions that occur on time scales comparable to the diffusive motion of the bead are difficult to extract from the data. We present an analysis method for TPM data that overcomes these limitations in existing approaches. Our method relies on variational Bayesian inference on a variant of the Hidden Markov model. This variational approach allows us to determine the number of states directly from the data in a statistically principled manner. Moreover, by operating directly on the position data, we achieve significantly better time resolution compared to methods based on running averages of the bead root-mean-square distance from the tethering point. Finally, we show that hierarchical techniques developed in the context of single molecule FRET experiments can be adapted to our TPM methods to perform pooled analysis on many trajectories. This increases the accuracy of the method despite considerable bead-to-bead variability, and allows a more precise characterization of rare events. We apply our method to Lac-mediated loop formation on a short (107 bp) construct, and demonstrate direct interconversion between two different looped states, with implications for structual models of the looped Lac-DNA complex.