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A guide to single-particle tracking

Nature Reviews Methods Primers volume 4, Article number: 66 (2024) Cite this article

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Abstract

Individual proteins and protein complexes undergo various motion types, including free diffusion, confinement, subdiffusion and directed motion. Different motion behaviours reflect different microenvironments, activity states, kinetics and interaction partners. Single-particle tracking (SPT) is a powerful method for analysing these behaviours directly and in live cells. However, SPT is confounded by multiple sources of experimental noise and biases. Interpreting tracks in terms of quantitative models thus remains a challenging task. We start this Primer by briefly presenting experimental setups and labelling techniques often employed for SPT, followed by a focus on the variety of tools available for analysing noisy tracks with multiple states. This includes tools designed to identify and characterize state fractions and diffusion coefficients, detect and quantify state transitions, predict the number of states and identify and parameterize various motion behaviours. We then highlight some of the many applications of SPT in cellular biology and discuss the limitations of current methods and what future developments are needed to address the current challenges of the SPT analysis.

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Fig. 1: Typical framework for single-particle tracking.
Fig. 2: Methods to estimate state fractions.
Fig. 3: Jump-distance-based methods estimate diffusion coefficients and transition rates.
Fig. 4: ExTrack, an integration method that considers localization error.
Fig. 5: Examples of types of motions.
Fig. 6: Improving transition models.

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Acknowledgements

This work was supported by the Volkswagen Foundation (to S.v.T.) and the Natural Sciences and Engineering Research Council of Canada (NSERC Discovery grant (RGPIN-2021-03208 to S.v.T., RGPIN-2022-05142 to L.E.W.)). S.v.T. and L.E.W. are recipients of salary awards from the Fonds de Recherche du Québec – Santé (FRQS). L.E.W. acknowledges funding from the Canada First Research Excellence Fund (TransMedTech Institute).

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Authors and Affiliations

  1. Department of Engineering Physics, Polytechnique Montréal, Montréal, Québec, Canada

    François Simon & Lucien E. Weiss

  2. Département de Microbiologie, Infectiologie et Immunologie, Faculté de Médecine, Université de Montréal, Montréal, Quebec, Canada

    François Simon & Sven van Teeffelen

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  1. François Simon
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  2. Lucien E. Weiss
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Contributions

All authors contributed equally to the writing of the manuscript. Introduction (F.S., L.E.W. and S.v.T.); Experimentation (F.S., L.E.W. and S.v.T.); Results (F.S., L.E.W. and S.v.T.); Applications (F.S., L.E.W. and S.v.T.); Reproducibility and data deposition (F.S., L.E.W. and S.v.T.); Limitations and optimizations (F.S., L.E.W. and S.v.T.); Outlook (F.S., L.E.W. and S.v.T.); Overview of the Primer (F.S., L.E.W. and S.v.T.).

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Correspondence to François Simon, Lucien E. Weiss or Sven van Teeffelen.

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Nature Reviews Methods Primers thanks Giuseppe Vicidomini, Lehui Xiao and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Glossary

Bayesian inference

A mathematical framework based on Bayes’ theorem to update our knowledge of a phenomenon, called the posterior, given a priori information and new data.

Change-point methods

A class of analysis methods that detect points of transitions between states based on the variations of a metric along a track.

Cost functions

Functions that measure the discrepancy between a given data set and a model that depends on unknown parameters. The parameters are then estimated by minimizing the cost function. The cost function is typically determined by probabilistic methods (for example, maximum likelihood estimation).

Diffusion coefficient

A metric that characterizes the motion of Brownian diffusers in units of length squared per unit time. Frequently estimated from the slope of the mean squared displacement curve.

Diffusion length

The typical displacement of a particle in one time step, Δt; explicitly, d is the standard deviation of the probability distribution of displacements for a Brownian diffuser.

Dirichlet process

A stochastic process used as a prior distribution in Bayesian models with an undetermined number of parameters.

Hidden Markov model

A model in which the observable variables are determined by hidden states that follow a Markov model.

Jump-distance distribution

The distribution of observed displacements between consecutive time points of observation. This measurement depends on both the real displacement and the localization errors of the consecutive observed positions.

Lifetime

The average duration within a state. In a Markov model, the lifetime of a state is the inverse of the sum of the transition rates from that state to the other states.

Markov model

A model in which the states change through time according to fixed transition probabilities that can be summarized in a transition matrix.

Mean squared displacement

(MSD). A metric calculated as the average of all squared displacements for a defined time interval. Brownian motion shows a linear scaling with time, whereas anomalous diffusion is defined as all other behaviours.

Monte Carlo methods

A class of algorithms that use random sampling. This can be used to estimate a deterministic value such as a model parameter. A Markov chain Monte Carlo method samples sequences of states that follow the Markov chain rules.

Sequence of states

Time series of states of motion at each time point.

Variational Bayesian methods

A class of methods that approximate intractable posterior distributions from Bayesian inference.

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Simon, F., Weiss, L.E. & van Teeffelen, S. A guide to single-particle tracking. Nat Rev Methods Primers 4, 66 (2024). https://doi.org/10.1038/s43586-024-00341-3

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