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Deep learning-assisted analysis of single-particle tracking for automated correlation between diffusion and function

Nature Methods volume 22, pages 1091–1100 (2025)Cite this article

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Abstract

Subcellular diffusion in living systems reflects cellular processes and interactions. Recent advances in optical microscopy allow the tracking of this nanoscale diffusion of individual objects with unprecedented precision. However, the agnostic and automated extraction of functional information from the diffusion of molecules and organelles within the subcellular environment is labor intensive and poses a significant challenge. Here we introduce DeepSPT, a deep learning framework integrated in an analysis software, to interpret the diffusional two- or three-dimensional temporal behavior of objects in a rapid and efficient manner, agnostically. Demonstrating its versatility, we have applied DeepSPT to automated mapping of the early events of viral infections, identifying endosomal organelles, clathrin-coated pits and vesicles among others with F1 scores of 81%, 82% and 95%, respectively, and within seconds instead of weeks. The fact that DeepSPT effectively extracts biological information from diffusion alone illustrates that besides structure, motion encodes function at the molecular and subcellular level.

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Fig. 1: DeepSPT, an agnostic, automated approach for extraction of time-dependent behavior in dynamic systems.
Fig. 2: Evaluation of DeepSPT’s temporal behavior segmentation.
Fig. 3: Rapid and precise classification of rotavirus uncoating by DeepSPT based exclusively on diffusional behavior.
Fig. 4: Prediction of endosomal identity and AP2 cellular localization based exclusively on temporal diffusional behavior.

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Data availability

All data are available via the University of Copenhagen repository at https://erda.ku.dk/archives/804ea1ea88f340b79ada3e57141a6d6e/published-archive.html (ref. 67). All biological materials have no restrictions and are available upon reasonable request. We refer to the original publications for the additional experimental data used in this work: refs. 10,26,68.

Code availability

A minimal repository of code is available at https://erda.ku.dk/archives/752e4b0695c0dd16ec3c1a130f6ac70b/published-archive.html (ref. 69). The repository of code and models is available at https://erda.ku.dk/archives/4c5adaaacc5c867f6450bcf89ec55a45/published-archive.html (ref. 70). Both are under a CC BY-NC-ND 4.0 DEED license. In addition, upon publication, the code will also be freely available on GitHub.

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Acknowledgements

We thank members of our laboratories for help and encouragement. We thank S. C. Harrison for the fruitful discussions on the rotavirus data interpretation. We thank N. Kumar Mishra and K. J. Jensen for discussion concerning the preparation and use of insulin for our experiments. This work was funded by the Villum Foundation by being part of BioNEC (grant 18333) to J.K.-H. and N.S.H., the Novo Nordisk foundation challenge center for Optimised Oligo escape (NNF23OC0081287) (N.S.H. PI and T.K., co-PI), the center for 4D cellular dynamics (NNF22OC0075851). N.S.H. is affiliated with The Novo Nordisk Foundation Center for Protein Research funded by a generous donation from the Novo Nordisk Foundation (grant no. NNF14CC0001). J.K.-H., A.J.N., S.V.B. and N.S.H. are members of the Integrative Structural Biology Cluster at the University of Copenhagen. VILLUM FONDEN (40516) for W.B. and N.S.H. The Novo Nordisk Foundation Center for Basic Machine Learning Research in Life Science (NNF20OC0062606) for W.B. T.K. acknowledges support from NIH Maximizing Investigators’ Research Award GM130386, NIH grant AI163019, 1R01, IONIS Pharmaceuticals. M.d.S was supported by NIH/NCI CA13202 grant to S. C. Harrison.

Author information

Authors and Affiliations

  1. Department of Chemistry, University of Copenhagen, Copenhagen, Denmark

    Jacob Kæstel-Hansen, Annette Juma Nielsen, Sara Vogt Bleshøy, Konstantinos Tsolakidis & Nikos S. Hatzakis

  2. Center for 4D cellular dynamics, University of Copenhagen, Copenhagen, Denmark

    Jacob Kæstel-Hansen, Annette Juma Nielsen, Sara Vogt Bleshøy, Konstantinos Tsolakidis & Nikos S. Hatzakis

  3. Novo Nordisk Center for Optimised Oligo Escape, University of Copenhagen, Copenhagen, Denmark

    Jacob Kæstel-Hansen, Annette Juma Nielsen, Sara Vogt Bleshøy, Konstantinos Tsolakidis, Tomas Kirchhausen & Nikos S. Hatzakis

  4. Novo Nordisk foundation Center for Protein Research, University of Copenhagen, Copenhagen, Denmark

    Jacob Kæstel-Hansen, Annette Juma Nielsen, Sara Vogt Bleshøy, Konstantinos Tsolakidis & Nikos S. Hatzakis

  5. Department of Biological Chemistry and Molecular Pharmacology, Harvard Medical School, Boston, MA, USA

    Marilina de Sautu

  6. Laboratory of Molecular Medicine, Boston Children’s Hospital, Boston, MA, USA

    Marilina de Sautu

  7. Department of Cell Biology, Harvard Medical School, Cambridge, MA, USA

    Anand Saminathan, Gustavo Scanavachi, Ricardo F. Bango Da Cunha Correia & Tomas Kirchhausen

  8. Department of Pediatrics, Harvard Medical School, Cambridge, MA, USA

    Anand Saminathan, Gustavo Scanavachi, Ricardo F. Bango Da Cunha Correia & Tomas Kirchhausen

  9. Program in Cellular and Molecular Medicine Boston Children’s Hospital, Boston, MA, USA

    Anand Saminathan, Gustavo Scanavachi, Ricardo F. Bango Da Cunha Correia & Tomas Kirchhausen

  10. Department of Computer Science, University of Copenhagen, Copenhagen, Denmark

    Wouter Boomsma

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Contributions

J.K.-H., N.S.H. and T.K. wrote the paper with feedback from all the authors. J.K.-H. performed all computational work with input from T.K., W.B. and N.S.H. M.d.S. performed all rotavirus preparation. A.S., R.F.B.D.C.C. and G.S. performed LLSM imaging with the presence of J.K.-H. in the laboratory of T.K. at Harvard Medical School. A.J.N. and S.V.B. performed SDCM imaging and insulin assays and K.T. wrote the software package in the laboratory of N.S.H. at the University of Copenhagen. J.K.-H. and N.S.H. conceived the project idea. N.S.H. had the overall project management with tight interactions with T.K.

Corresponding authors

Correspondence to Tomas Kirchhausen or Nikos S. Hatzakis.

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Nature Methods thanks Koen Martens and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Rita Strack, in collaboration with the Nature Methods team. Peer reviewer reports are available.

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Extended data

Extended Data Fig. 1 Comparison of classification accuracy of DeepSPT with benchmarks.

Comparison of classification accuracy of DeepSPT, LSTM-based model29, and rolling MSD for various number of diffusion types. a, Confusion matrices of DeepSPT predictions per frame on 2D simulated test set trajectories (N=20000 tracks), Data displayed for either 4 diffusional states, or 3 states normal, directed and confined/subdiffusive, or 2 states normal/directed, confined/subdiffusive. b, Confusion matrices of attention BiLSTM29 predictions per frame on 2D simulated test set trajectories. Data for for 4, 3, 2 diffusional states as above c, Confusion matrices of rolling MSD12,47 predictions per frame on 2D simulated test set trajectories (predicts three classes as it bases predictions on the alpha exponent in a MSD fit based on (subdiffusive alpha)<(normal alpha)<(directed alpha)) Data for for 4, 3, 2 diffusional states as above. d, DeepSPT on 3D test set trajectories when combining classes into three and two respectively.

Extended Data Fig. 2 Investigating DeepSPT’s robustness to simulation parameters for the heterogeneous diffusing test set in 3D.

Investigation of model generalizability and limitations for key simulation parameters for traces containing all 4 diffusional types at random (see Methods for test set elaboration): a, Varying ranges of diffusion coefficients (D) for simulated trajectories (varying D is equivalent to varying temporal resolution for observation of a diffusing particle due to scale invariance of diffusion). b, step length to localization error ratio, i.e ratio of contribution to displacements from actual diffusion and localization error respectively where a value of 1 signifies an equal contribution and >1 signifies actual diffusion being larger. c, Duration of track. Median accuracy and mean accuracy are track-level metrics providing descriptive statistics for the distribution track-level accuracies for each test set track (N=20000). Flattened accuracy measures the accuracy for all frame-level predictions inside each trajectory pooled together.

Extended Data Fig. 3 Investigating DeepSPT’s robustness to simulation parameters for the heterogeneous diffusing test set in 2D.

Investigation of model generalizability and limitations for key simulation parameters for traces containing all 4 diffusional types at random (see Methods for test set elaboration): a, Varying ranges of diffusion coefficients (D) for simulated trajectories (varying D is equivalent to varying temporal resolution for observation of a diffusing particle due to scale invariance of diffusion). b, step length to localization error ratio, i.e ratio of contribution to displacements from actual diffusion and localization error respectively where a value of 1 signifies an equal contribution and >1 signifies actual diffusion being larger. c, Duration of track. Median accuracy and mean accuracy are track-level metrics providing descriptive statistics for the distribution track-level accuracies for each test set track (N=20000). Flattened accuracy measures the accuracy for all frame-level predictions inside each trajectory pooled together.

Extended Data Fig. 4 Evaluation of the effects of tracking errors on DeepSPT temporal segmentation.

1000 trajectories are simulated within a box of varying dimensions and tracked using Trackpy56 (see Methods). The trajectories obtained by Trackpy are analyzed using DeepSPT’s temporal segmentation module. a, Example of trajectories produced by Trackpy showing tracks with one or more linking errors (red), correct/preserved tracks (black), and tracks without linking errors but still differ from the simulated tracks (grey). b, Example of simulated ground truth tracks (colored by ID). c, The median accuracy of DeepSPT in prediction diffusional behavior per time point per track for varying simulated box dimensions, thus varying degrees of linking errors. Median accuracy refers to the median of the distribution of correctly predicted time points in each individual track. Each blue cross represents an independent set of 1000 trajectories. Three sets are simulated per simulated box dimension with black dots and error bars representing the mean and standard deviations across each of the three sets. Red line represents the median accuracy of DeepSPT directly on simulated trajectories. d, Zoom-in, showing the dashed grey box in (c). e, The median accuracy of DeepSPT in prediction diffusional behavior per time point per track versus various degrees of preserved tracks, that is number of tracks perfectly tracked. As in (c) each blue cross represents an independent set of 1000 trajectories with three sets per simulated box dimension with black dots and error bars representing the mean and standard deviations across each of the three sets. Red line represents the median accuracy of DeepSPT directly on simulated trajectories. f, Zoom-in, showing the dashed grey box in (e).

Extended Data Fig. 5 Evaluation of DeepSPT and two AnDi challenge models on AnDi challenge task 3.

Confusion matrix for all individual time point predictions within the 20000 2D (a, c, e) and 3D (b, d) test set trajectories simulated using the 2021 AnDi challenge task 3 open-source framework totalling 4 million predictions. See Muñoz-gil et al.28 for further test set specification. Diagonal entries are correct predictions and off-diagonal indicates confused classes. Each entry reports the percentage of predictions normalized to the actual number of true labels in the given class. a, Confusion matrix for DeepSPT on 2D trajectories. b, Confusion matrix for DeepSPT on 3D trajectories. c, Confusion matrix for Method E on 2D trajectories. d, Confusion matrix for Method E on 3D trajectories. e, Confusion matrix for Method J on 2D trajectories.

Extended Data Fig. 6 Evaluation DeepSPT and two AnDi challenge models on traces with multiple changes between diffusion behaviors from the AnDi challenge.

Confusion matrix for all individual time point predictions within the 20000 2D (a, c, e) and 3D (b, d) test set trajectories simulated by combining the anomalous diffusion behaviors from the 2021 AnDi challenge open-source framework28 into heterogeneous trajectories sampling multiple diffusional behaviors with multiple change points totalling 4 million predictions. Diagonal entries are correct predictions and off-diagonal indicates confused classes. Each entry reports the percentage of predictions normalized to the actual number of true labels in the given class. a, Confusion matrix for DeepSPT on 2D trajectories. b, Confusion matrix for DeepSPT on 3D trajectories. c, Confusion matrix for Method E on 2D trajectories. d, Confusion matrix for Method E on 3D trajectories. e, Confusion matrix for Method J on 2D trajectories.

Extended Data Fig. 7 Temporal segmentation and changepoint prediction of simulated trajectories for DeepSPT and benchmark approaches.

a-e, Predicted changepoints (CP) versus true changepoints. Trajectories are constructed by combining two populations with overlapping diffusional properties into individual tracks with one changepoint (see Methods). Black line represents perfect classification. a, HMM-bayes17, 1556 data points compared to 5000 for other approaches due to computational time restraints as HMM-bayes requires several minutes per track. b, Rolling MSD. c, Original diffusional fingerprinting (Pinholt et al.13) d, Method E from the 2021 AnDi Challenge. e, DeepSPT. f, Table of classification metrics for the temporal segmentation of trajectory timepoints as post- and pre-uncoating and changepoint prediction. Median accuracy measures the median accuracy per trajectory (N=100). F1-score measures the F1-score of all individual timepoint predictions. Median frame error measures the median of absolute distances between predicted and true changepoints across all trajectories. Mean frame error measures the mean of absolute distances between predicted and true changepoints across all trajectories. Mean squared error measures the mean of the second norm distances between predicted and true changepoints across all trajectories. R2 measures the coefficient of determination.

Extended Data Fig. 8 Temporal segmentation and changepoint prediction of 3D lattice light sheet rotavirus trajectory timepoints as post- and pre-uncoating for DeepSPT and benchmark approaches.

a-e, Predicted changepoints (CP) versus true changepoints. Black line represents perfect classification. a, HMM-bayes17 b, Rolling MSD. c, Original diffusional fingerprinting (Pinholt et al.13) d, Method E from the 2021 AnDi Challenge. e, DeepSPT. f, Table of classification metrics for the temporal segmentation of trajectory timepoints as post- and pre-uncoating and changepoint prediction. Median accuracy measures the median accuracy per trajectory per time point (N=100), that is all time points before a changepoint is defined as predicted ‘before’, while time points after are defined as predicted ‘after’. These predictions are compared to the ground truth. F1-score measures the F1-score of all individual time point predictions as for median accuracy. Median frame error measures the median of absolute distances between predicted and true changepoints across all trajectories. Mean frame error measures the mean of absolute distances between predicted and true changepoints across all trajectories. Mean squared error measures the mean of the second norm distances between predicted and true changepoints across all trajectories. R2 measures the coefficient of determination.

Extended Data Fig. 9 Benchmark EEA1- versus NPC1- positive endosome predictions.

Confusion matrices displaying classification performance on outputting NPC1 and EAA1 identity based solely on diffusion. a, DeepSPT. b, Original diffusional fingerprinting (Pinholt et al.13). c, Method E of the ANDI challenge. d, Utilizing the anomalous diffusion exponent (alpha) and diffusion coefficient. e, Only variations in diffusion coefficient. f, Only variations in alpha.

Extended Data Fig. 10 Benchmark dorsal versus ventral AP2 predictions.

Confusion matrices displaying classification performance of outputting whether AP2 is dorsal or ventral based solely on diffusion. a, DeepSPT. b, Original diffusional fingerprinting (Pinholt et al.13). c, Method E of the ANDI challenge. d, Utilizing the anomalous diffusion exponent (alpha) and diffusion coefficient. e, Only variations in diffusion coefficient. f, Only variations in alpha.

Supplementary information

Supplementary Information

Supplementary Figs. 1–26, materials and Tables 1–4.

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Supplementary Video 1

Single rotavirus tracking in 3D by LLSM observing viral uncoating along with DeepSPT identification of the event in split channel view.

Supplementary Video 2

Single rotavirus tracking in 3D by LLSM observing viral uncoating along with DeepSPT identification of the event in merged channel view.

Supplementary Video 3

Single-particle trajectories of NPC1-positive endosomes in 3D in live cell by LLSM.

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Kæstel-Hansen, J., de Sautu, M., Saminathan, A. et al. Deep learning-assisted analysis of single-particle tracking for automated correlation between diffusion and function. Nat Methods 22, 1091–1100 (2025). https://doi.org/10.1038/s41592-025-02665-8

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