A Hidden Markov Model for Detecting Confinement in Single Particle Tracking Trajectories

Abstract State-of-the-art single particle tracking (SPT) techniques can generate long trajectories with high temporal and spatial resolution. This offers the possibility of mechanistically interpreting particle movements and behaviour in membranes. To this end, a number of statistical techniques have been developed that partition SPT trajectories into states with distinct diffusion signatures, allowing a statistical analysis of diffusion state dynamics and switching behaviour. Here we develop a confinement model, within a hidden Markov framework, that switches between phases of free diffusion, and confinement in a harmonic potential well. By using a Markov chain Monte Carlo (MCMC) algorithm to fit this model, automated partitioning of individual SPT trajectories into these two phases is achieved, which allows us to analyse confinement events. We demonstrate the utility of this algorithm on a previously published dataset, where gold nanoparticle (AuNP) tagged GM1 lipids were tracked in model membranes. We performed a comprehensive analysis of confinement events, demonstrating that there is heterogeneity in the lifetime, shape, and size of events, with confinement size and shape being highly conserved within trajectories. Our observations suggest that heterogeneity in confinement events is caused by both individual nanoparticle characteristics and the binding site environment. The individual nanoparticle heterogeneity ultimately limits the ability of iSCAT to resolve molecular dynamics to the order of the tag size; homogeneous tags could potentially allow the resolution to be taken below this limit by deconvolution methods. In a wider context, the presented harmonic potential well confinement model has the potential to detect and characterise a wide variety of biological phenomena, such as hop diffusion, receptor clustering, and lipid rafts.