Detecting directed motion and confinement in single-particle trajectories using hidden variables

Reviewer #1 (Public Review):

Summary:

Weiss and co-authors presented a versatile probabilistic tool. aTrack helps in classifying tracking behaviors and understanding important parameters for different types of single particle motion types: Brwonian, Confined, or Directed motion. The tool can be used further to analyze populations of tracks and the number of motion states. This is a stand-alone software package, making it user-friendly for a broad group of researchers.

Strengths:

This manuscript presents a novel method for trajectory analysis.

Weaknesses:

(1) In the results section, is there any reason to choose the specific range of track length for determining the type of motion? The starting value is fine, and would be short enough, but do the authors have anything to report about how much is too long for the model?

(2) Robustness to model mismatches is a very important section that the authors have uplifted diligently. Understanding where and how the model is limited is important. For example, the authors mentioned the limitation of trajectory length, do the authors have any information on the trajectory length range at which this method works accurately? This would be of interest to readers who would like to apply this method to their own data.

(3) aTrack extracts certain parameters from the trajectories to determine the motion types. However, it is not very clear how certain parameters are calculated. For example, is the diffusion coefficient D calculated from fitting, and how is the confinement factor defined and estimated, with equations? This information will help the readers to understand the principles of this algorithm.

(4) The authors mentioned the scenario where a particle may experience several types of motion simultaneously. How do these motions simulated and what do they mean in terms of motion types? Are they mixed motion (a particle switches motion types in the same trajectory) or do they simply present features of several motion types? It is not intuitive to the readers that a particle can be diffusive (Brownian) and direct at the same time.

Reviewer #2 (Public Review):

Summary:

The authors present a software package "aTrack" for identification of motion types and parameter estimation in single-particle tracking data. The software is based on maximum likelihood estimation of the time-series data given an assumed motion model and likelihood ratio tests for model selection. They characterized the performance of the software mostly on simulated data and showed that it is applicable to experimental data.

Strengths:

A potential advantage of the presented method is its wide applicability to different motion types.

Weaknesses:

(1) There has been a lot of similar work in this field. Even though the authors included many relevant citations in the introduction, it is still not clear what this work uniquely offers. Is it the first time that direct MLE of the time-series data was developed? Suggestions to improve would include (a) better wording in the introduction section, (b) comparing to other popular methods (based on MSD, step-size statistics (Spot-On, eLife 2018;7:e33125), for example) using the simulated dataset generated by the authors, (c) comparing to other methods using data set in challenges/competitions (Nat. Comm (2021) 12:6253).

(2) The Hypothesis testing method presented here has a number of issues: first, there is no definition of testing statistics. Usually, the testing statistics are defined given a specific (Type I and/or Type II) error rate. There is also no discussion of the specificity and sensitivity of the testing results (i.e. what's the probability of misidentification of a Brownian trajectory as directed? etc). Related, it is not clear what Figure 2e (and other similar plots) means, as the likelihood ratio is small throughout the parameter space. Also, for likelihood ratio tests, the authors need to discuss how model complexity affects the testing outcome (as more complex models tend to be more "likely" for the data) and also how the likelihood function is normalized (normalization is not an issue for MLE but critical for ratio tests).

(3) Relating to the mathematical foundation (Figure 1b). The measured positions are drawn as direct arrows from the real position states: this infers instantaneous localization. In reality, there is motion blur which introduces a correlation of the measured locations. Motion blur is known to introduce bias in SPT analysis, how does it affect the method here?

(4) The authors did not go through the interpretation of the figure. This may be a matter of style, but I find the figures ambiguous to interpret at times.

(5) It is not clear to me how the classification of the 5 motion types was accomplished.

(6) Figure 3. Caption: what is ((d_{est}-0.1)/0.1)? Also panel labeled as "d" should be "e".

Reviewer #3 (Public Review):

Summary:

In this work, Simon et al present a new computational tool to assess non-Brownian single-particle dynamics (aTrack). The authors provide a solid groundwork to determine the motion type of single trajectories via an analytical integration of multiple hidden variables, specifically accounting for localization uncertainty, directed/confined motion parameters, and, very novel, allowing for the evolution of the directed/confined motion parameters over time. This last step is, to the best of my knowledge, conceptually new and could prove very useful for the field in the future. The authors then use this groundwork to determine the motion type and its corresponding parameter values via a series of likelihood tests. This accounts for obtaining the motion type which is statistically most likely to be occurring (with Brownian motion as null hypothesis). Throughout the manuscript, aTrack is rigorously tested, and the limits of the methods are fully explored and clearly visualised. The authors conclude with allowing the characterization of multiple states in a single experiment with good accuracy and explore this in various experimental settings. Overall, the method is fundamentally strong, well-characterised, and tested, and will be of general interest to the single-particle-tracking field.

Strengths:

(1) The use of likelihood ratios gives a strong statistical relevance to the methodology. There is a sharp decrease in likelihood ratio between e.g. confinement of 0.00 and 0.05 and velocity of 0.0 and 0.002 (figure 2c), which clearly shows the strength of the method - being able to determine 2nm/timepoint directed movement with 20 nm loc. error and 100 nm/timepoint diffusion is very impressive.

(2) Allowing the hidden variables of confinement and directed motion to change during a trajectory (i.e. the q factor) is very interesting and allows for new interpretations of data. The quantifications of these variables are, to me, surprisingly accurate, but well-determined.

(3) The software is well-documented, easy to install, and easy to use.

Weaknesses:

(1) The aTrack principle is limited to the motions incorporated by the authors, with, as far as I can see, no way to add new analytical non-Brownian motion. For instance, being able to add a dynamical state-switching model (i.e. quick on/off switching between mobile and non-mobile, for instance, repeatable DNA binding of a protein), could be of interest. I don't believe this necessarily has to be incorporated by the authors, but it might be of interest to provide instructions on how to expand aTrack.

(2) The experimental data does not very convincingly show the usefulness of aTrack. The authors mention that SPBs are directed in mitosis and not in interphase. This can be quantified and studied by microscopy analysis of individual cells and confirming the aTrack direction model based on this, but this is not performed. Similarly, the size of a confinement spot in optical tweezers can be changed by changing the power of the optical tweezer, and this would far more strongly show the quantitative power of aTrack.

(3) The software has a very strict limit on the number of data points per trajectory, which is a user input. Shorter trajectories are discarded, while longer trajectories are cut off to the set length. It is not explained why this is necessary, and I feel it deletes a lot of useful data without clear benefit (in experimental conditions).