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  1. Evaluation Summary:

    The authors describe new approaches to improve the analysis of single-molecule tracking data to uncover multiple diffusive states of proteins in living cells. This paper will be of interest to researches from the fields of experimental biology, who are interested in tracking of proteins using microscopy, as well as computational scientists who are interested in devising novel methodologies for analysis of multiple-particle tracking data. The paper presents two advanced techniques for estimation of motion parameters (such as diffusion coefficients) and contains rigorous evaluation using simulated and real biological data.

    (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #3 agreed to share their name with the authors.)

  2. Reviewer #1 (Public Review):

    This work addresses the problem of accurately estimating dynamics parameters in single particle tracking applications. The authors give a very extensive overview of the current problems and solutions while dealing with imaging of diffusive motion of subcellular particles and challenges that one faces while trying to estimate the main parameters of interest, such as diffusion constants. The authors properly address the issues with short trajectories, which are typical in practice and propose two advanced approached, which successfully deal with the mentioned shortcomings (short trajectories from which it is difficult to estimate parameters reliably, and the measurement errors that contaminate the input data). The proposed techniques are very interesting, and the way how those pure mathematical (and long existing) concepts are applied for this specific application of single particle tracking is rather novel. The proposed methodology is supported by a thorough validation, which includes simulations of all possible conditions (numbers of trajectories, distributions of the diffusion constants within the population of particles, the levels of inaccuracies in the measurements, etc.). Additionally, the experiments with the real data are also very convincing. The authors do focus on a regular Brownian diffusion and hopefully will show the applicability of these approaches to more typical applications containing anomalous diffusion. The availability of the code, which the authors provide on github, is very important, especially to less (technically) skilled audience from the field of experimental biology, who would like to apply those techniques to their data.

  3. Reviewer #2 (Public Review):

    This paper will be of interest to the cellular biologists who perform single-particle tracking experiments and develop new tracking methodologies. The authors investigate a new way of estimating an unknown number of diffusion states from short single-molecule trajectories. Ideas developed in the paper are likely to be used for further algorithm development. The authors give the users access to a repository on GitHub that contains comprehensive code that supports the paper.

    Comments:

    1. The authors claim in their abstract that their algorithm works on tracks with variable localization precision. However, in their simulation section, they investigate only a single localization precision value per diffusion state. This doesn't match the reality since intensity and background from molecules (and over the field) is never a single value, but follows a distribution. To make this simulation realistic the authors would need to generate datasets where the localization precision comes from a distribution with different parameters per diffusion coefficient (e.g. a different mean and variance).
    2. In the introduction the authors claim that they also address the problem of having an unknown number of diffusion states. However, I don't think that the paper addresses this issue, because with their current approach it is not possible to classify trajectory segments into a state.

  4. Reviewer #3 (Public Review):

    Single-molecule tracking is a powerful technique to uncover the dynamic properties of biomolecules at the single-molecule level. However, interpretation of the data is challenged by technical limitations of the fluorophores and image acquisition, such as photobleaching and limited depth of view. Several approaches have been proposed to overcome these challenges and to improve quantitative analysis of single-molecule data. Heckert et al. present in this manuscript novel methods that make use of Bayesian inference to uncover present diffusive states more accurately than common methods such as mean-square-displacement analysis. The advantage of their method compared to existing developed methods such as Spot-On and vbSPT is that it is possible to obtain an estimated diffusion coefficient per tracked molecule. This allows for spatial analysis of diffusion patterns within the cell and to correlate the mobility of molecules directly with underlying cellular organization.

    The major strength of this work lies in their presentation of the current technical challenges (limited focus depth, photo bleaching, localization error) in single-molecule tracking and propose useful solutions to these limitations of single-molecule tracking. As an experimental biologist it is difficult for me to assess the analytical approaches entirely, but I do think that they extensively describe the methodology in the main text and in the additional computational methods. Their presentation of several simulations with relevant variables to validate their methods help to appreciate the validity of their approach.

    Although I think their methods could be very useful to more accurately describing biological processes, the novel biological insights presented in this paper are limited. While in their simulations it is clear that their methods are more accurate I would suggest the authors to compare the results from their biological experiments with existing methods, such as MSD analysis. I think this could help to convince possible users of this analysis methods to apply these methods in their experiments.