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.

Anomalous Subdiffusion in Living Cells: Bridging the Gap Between Experiments and Realistic Models Through Collaborative Challenges

“…Moreover, Slator et al [61] implemented the inference of localization noise to infer switches in diffusion coefficient within one trajectory. A similar approach was used to detect confinement [62].…”

Fundamentals of the logarithmic measure for revealing multimodal diffusion

“…However, one must be careful to either ensure that Dt is greater than the characteristic state transition times or to modify the displacement densities to include transient behavior. In this way, our method can provide an alternative to the hidden Markov model analysis methods (15)(16)(17)(18)(19), which capture diffusive state transitions and the corresponding transition state rates.…”

“…By necessity, these methods require long trajectories, which are not always accessible. More sophisticated methods include the hidden Markov models (15)(16)(17)(18)(19)(20), which determine the diffusion coefficients for distinct diffusive states and the transition rates between states but often only consider a predefined fixed number of states, and other advanced trajectory segmentation methods (21). Advanced Bayesian methods (22) and combined hidden Markov model-Bayesian methods (20) can learn both the number of diffusive states and the transition rates but require a high degree of computational proficiency on behalf of the user.…”

Interferometric Scattering (iSCAT) Microscopy and Related Techniques

“…Quantitative iSCAT studies have also enabled clear discrimination of the varying mobility of a lipid diffusing between differently ordered phases within a membrane [176]. Furthermore, the extended duration over which measurement can be performed has inspired researchers to develop new statistical models to interpret the new generation of experimental results [177]. It has to be born in mind, however, that quantitative comparisons of diffusion performed by different methods remains a challenge since each labeling approach might introduce a certain systematic bias, and indeed, diffusion coefficients obtained from different techniques might vary [178].…”