Machine Learning Classification of 3D Intracellular Trafficking Using Custom and Imaris-Derived Motion Features

Abstract

Background: Detecting intracellular diffusion dynamics with high spatiotemporal resolution is critical for understanding the complex molecular mechanisms that govern viral infection, drug delivery, and sustained receptor signaling within cellular compartments. Although considerable progress has been made, accurately distinguishing between different types of diffusion in three dimensions remains a significant challenge. Methods: This study extends a previously established two-dimensional, machine learning-based diffusional fingerprinting approach into a three-dimensional framework to overcome this limitation. It presents an algorithm that predicts intracellular motion types based on a comprehensive feature set, including custom statistical descriptors and standard Imaris-derived trajectory features, which capture subtle variations in individual trajectories. The approach employs an extended gradient-boosted decision trees classifier trained on an array of synthetic trajectories designed to simulate diffusion behaviors typical of intracellular environments. Results: The machine learning classifier demonstrated a classification accuracy of over 90% on synthetic datasets, effectively capturing and distinguishing complex diffusion patterns. Subsequent validation using an experimental dataset confirmed the robustness of the approach. The incorporation of the Imaris track features streamlined diffusion classification and enhanced adaptability across diverse volumetric imaging modalities. Conclusions: This work advances our ability to classify intracellular diffusion dynamics in three dimensions and provides a method that is well-suited for high-resolution analysis of intracellular receptor trafficking, intracellular transport of pathogenic agents, and drug delivery mechanisms.

1. Introduction

Single particle tracking (SPT) is an umbrella term for a family of powerful optical microscopy techniques that enable the observation of individual biomolecules in a live cell roughly ten times below the diffraction limit. The fundamental principle of fluorescence-based SPT is that the position of a single fluorescent emitter, appearing as a non-overlapping blurred spot in the sample volume (x, y, z), can be estimated with sub-voxel accuracy [1,2]. The coordinates of the emitter in a time series are then linked into continuous trajectories that are analyzed to determine global and instantaneous motion parameters. Dramatic technical advances in instrumentation, fluorophore photochemistry and stability, labeling strategies, point emitter detection algorithms, and trajectory reconstruction methods have streamlined the practical adoption of SPT techniques by non-experts and produced important biological insights previously inaccessible via conventional ensemble techniques [3,4,5]. SPT has particularly excelled in the field of receptor biology, revealing that ligand-mediated receptor activation produces significant changes in temporal and spatial patterns of receptor diffusion, dimerization/clustering, interactions with the binding partners, and subcellular trafficking [6,7,8,9,10,11,12].

Recent discoveries have revealed that cell surface receptors can signal not only from the plasma membrane but also from intracellular compartments, such as endosomes and the Golgi apparatus [13,14,15,16]. This non-canonical mode of signaling is thought to be a continuation of plasma membrane activity that persists following receptor endocytosis. Consequently, there is a growing interest in leveraging SPT techniques to study receptor dynamics and activity with high spatiotemporal resolution beyond the plasma membrane. However, much of the SPT research in this field has been conducted in simplified 2D systems, which fail to capture the full 3D complexity of intracellular environments. Moreover, various analytical methods and machine learning tools developed to estimate diffusion types and parameters are largely restricted to 2D implementation [8,9,11,12,17,18,19,20].

Recently, the concept of feature-based supervised machine learning classification of 2D trajectories was introduced [17,18,21,22]. In this approach, a unique identifier (a set of 9 or more custom statistical motion descriptors) is determined for each 2D trajectory of a simulated or experimental particle and then classified using the training data of identifiers estimated for a pool of simulated trajectories undergoing 4 basic types of diffusion: Brownian (normal) diffusion, confined diffusion, anomalous diffusion, and directed motion. Although this 2D methodology is available as the open-source TraJClassifier ImageJ plugin [21] and a Python-based GitHub repository [18], options for classifying 3D trajectories remain limited. This limitation is particularly significant as five-dimensional (x, y, z, time, and lambda), high-resolution (~100 frames/s, ~1 volume/s) imaging of whole cells via lattice light-sheet microscopy (LLSM) is becoming increasingly available [23,24]. Among existing tools, Liu et al. reported a classification algorithm for 3D EGFR trajectories based on three-parameter thresholds (scaling exponent of the MSD curve, directional persistence, and confinement index), reaching 81% accuracy for distinguishing between Brownian diffusion, active transport, confined diffusion, and immobilization [25]. Rosenberg et al. trained a supervised classifier on 36 motion parameters (including speed, direction, volume, intensity, area, location, and duration) of 3D trajectories of T-cell receptor microclusters extracted via the commercially available Imaris software (version 10) [24]. While this technique achieved over 95% accuracy in distinguishing stimulated T-cells from basal T-cells, it did not provide insights into the classification of individual trajectories. More recently, the Hatzakis group sought to extend the 2D “diffusional fingerprint” approach in [18] to 3D information by increasing the number of statistical features to 40 per 3D trajectory and incorporating a deep learning temporal segmentation module based on the U-Net architecture [26].

Building on the 2D framework reported by Pinholt et al. [18], this work extends the feature-based approach into 3D and validates it on a real-world lattice light-sheet microscopy 3D dataset. To achieve this, a pool of simulated particle trajectories in 3D was generated for four distinct motion types—Brownian, Confined, Anomalous, and Directed. From these simulated trajectories, 13 custom motion features and 16 Imaris track features were extracted to capture the spatial and temporal dynamics of particle motion. These features were then used to train a machine-learning classifier capable of accurately distinguishing between the four motion types, with over 90% classification accuracy achieved on synthetic datasets. Finally, the trained classifier was applied to an experimental 3D trajectory dataset to detect the prevalence and spatial heterogeneity of each motion type throughout the entire cell volume.

2. Materials and Methods

Trajectory Simulation. Synthetic trajectories were simulated by adapting the exclusively 2D algorithms employed by Wagner et al. [21], Kowalek et al. [17], and Pinholt et al. [18] to three dimensions. A total of 2000 synthetic trajectories were generated, 500 for each diffusion type. Fixed values were used for two parameters: Δt = 1 s and D = 0.02 µm²/s [21]. The time lag Δt was comparable to the time resolution of a typical volumetric LLSM imaging experiment, ~1 cell volume/s. The value of the diffusion coefficient D corresponds to the average value of D determined for the experimentally acquired trajectories that were used for validation. Other simulation parameters were chosen randomly for each synthetic trajectory using the following bounds [17,21]: length of a trajectory, N = 30–600 positions to vary the trajectory length; boundedness, B = 1–6; active motion to diffusion ratio, R = 1–17; anomalous exponent, α = 0.3–0.7; signal to noise ratio, Q = 1–9.

The degree to which motion is influenced [21] by the active motion was computed according to the following equation:

$$R={\displaystyle \frac{v^{2}N}{6D}}$$

(1)

with v, N, and D being the trajectory velocity, duration, and diffusion coefficient, respectively.

The radius of confinement for trajectories undergoing restricted motion was calculated according to the following equation:

$$r_c=\sqrt{{\displaystyle \frac{DN\Delta t}{B}}}$$

(2)

where D is the diffusion coefficient, N is the trajectory duration, Δt is the time step, and B is the randomly chosen boundedness parameter.

Normal (Brownian) diffusion was simulated according to the equation of the probability distribution of the displacement’s norm d:

$$P_d\left(u\right)={\displaystyle \frac{2u}{4Dt}}exp\left(-{\displaystyle \frac{u^2}{4Dt}}\right)$$

(3)

where t is the duration of the displacement or time lag between positions [27]. A start position of a Brownian particle and a random direction of displacement were randomly chosen; then, the displacements in each dimension (Δx, Δy, Δz) were sampled independently from a Gaussian distribution with a standard deviation of $\sqrt{2Dt}$ and were cumulatively summed to obtain the trajectory. Localization error, modeled as Gaussian noise with a standard deviation σ, was added to simulate measurement uncertainty. Normal diffusion was simulated using the function Gen_normal_diff_3D defined in the sim_tracks_3d.py script.

Particles undergoing directed motion were simulated as follows. For a given velocity v with an azimuthal angle β and a polar angle γ, a correction in each Brownian particle’s position due to the active motion was added:

$$d_{x_i},d_{y_i},d_{z_i}=v\Delta tsin\gamma cos\beta ,v\Delta tsin\gamma sin\beta ,v\Delta tcos\gamma$$

(4)

The directed motion trajectories were generated by combining Brownian displacements with a directed component. Displacements were drawn from a normal distribution with a standard deviation of $\sqrt{2Dt}$. A directional drift was then added using Equation (4), with localization noise σ applied to simulate measurement uncertainty, using the function Gen_directed_diff_3D defined in the sim_tracks_3d.py script.

Confined diffusion trajectories were simulated based on the assumption that a particle’s origin is the center of a 3D spherical reflective boundary with a radius of confinement r_c. Each time step Δt was subdivided into smaller intervals (100 substeps) to ensure accurate confinement. At each subinterval, displacements were drawn from a Gaussian distribution with a standard deviation of $\sqrt{2D\Delta \left(\Delta t/100\right)}$. The particle’s new position was accepted only if it remained within the sphere; otherwise, it retained its previous position. Localization error σ was added as Gaussian noise to simulate measurement uncertainty. Confined diffusion was simulated using the function Gen_confined_diff_3D defined in the sim_tracks_3d.py script.

Anomalous subdiffusion trajectories were simulated with the fractional Brownian motion [28] as a continuous-time Gaussian process B_H(t) with its covariance function given by:

$$E\left[B_H\left(t\right)B_H\left(s\right)\right]={\displaystyle \frac{1}{2}}\left({\left|t\right|}^{2H}+{\left|s\right|}^{2H}-{\left|t-s\right|}^{2H}\right)$$

(5)

with the Hurst index H equivalent to one-half α and randomly chosen in α = 0.3–0.7 range for a case of subdiffusion. Anomalous diffusion trajectories were simulated using the function Gen_anomalous_diff_3D defined in the sim_tracks_3d.py script.

Mixed diffusion simulation. A simple case of mixed diffusion was simulated by alternating between two diffusion modes: confined diffusion and either normal or directed diffusion. Each trajectory was 600 frames long, consisting of 12 segments, each lasting 50 frames. For confined and directed diffusion, the parameters (confinement radius, r_c, for confined and velocity, v, for directed) were randomly chosen for each segment to introduce variability. The confined-normal and confined-directed diffusion pairs were selected as they represent biologically relevant transitions, such as particles moving between confined regions and free or active transport. The resulting trajectories were labeled based on their state sequence for subsequent analysis. Mixed diffusion was simulated using the sim_mixed_binary_tracks_3d.py script.

Custom Diffusion Feature Calculation. For each trajectory, mean square displacement (MSD), r²(t), was computed as follows:

$$\begin{array}{c}{r}^2\left(n\Delta t\right)={\displaystyle \frac{1}{N-n}}{{\displaystyle \sum }}_{j=0}^{N-n-1}\{{\left[x\left(j\Delta t+n\Delta t\right)-x\left(j\Delta t\right)\right]}^2+[y\left(j\Delta t+n\Delta t\right)-\\ y\left(j\Delta t\right){]}^2+{\left[z\left(j\Delta t+n\Delta t\right)-z\left(j\Delta t\right)\right]}^2\},\end{array}$$

(6)

where Δt is the temporal resolution of acquisition, (x(jΔt), y(jΔt), z(jΔt)) is the particle coordinate at t = jΔt, and N is the number of total frames recorded for an individual particle [29]. The resulting MSD curve to a power law to obtain the diffusion coefficient D, α exponent, and the associated goodness-of-fit (R²):

$$MSD=6D{t}^{\alpha }$$

(7)

Step lengths were defined as the Euclidean distances between consecutive positions along the trajectory, and velocities were computed as the step length divided by the time interval of acquisition. Next, the displacement vector for each trajectory point was calculated relative to the starting position as $displacement=\left[x_i-x_0,y_i-y_0,z_i-z_0\right]$. The radial distance (radius) was computed as the Euclidean norm of the displacement vector for each trajectory point. The maximum radial distance was identified as the largest radius in the trajectory, and the range of radius was determined as the difference between the largest and the smallest radius in the trajectory. Trappedness was calculated to measure relative spatial confinement as follows:

$$\mathrm{Trappedness}=1-{\displaystyle \frac{Max Radius}{Mean Radius}}$$

(8)

The radius of gyration (R_G) was calculated as the root mean square distance of all points from the trajectory’s center of mass using the following equation:

$$R_G=\sqrt{{\displaystyle \frac{1}{N}}{{\displaystyle \sum }}_{i=1}^N\left({(x_i-x_{CoM})}^2+{(y_i-y_{CoM})}^2+{(z_i-z_{CoM})}^2\right)}$$

(9)

where $x_{CoM}, y_{CoM}, z_{CoM}$ are the coordinates of the center of mass. Straightness index was defined as the ratio of the Euclidean distance between the trajectory’s start and end points to the total path length. Gaussianity, the extent of deviations from a Gaussian distribution of step lengths, was first introduced by Ernst et al. [30] and is based on the ratio between the square and quadratic displacements of a point within a given trajectory over n frames:

$$g_n={\displaystyle \frac{\langle r_n^4\rangle }{2\langle r_n^2{\rangle }^2}}$$

(10)

Skewness and kurtosis of step lengths were calculated to quantify asymmetry and tailedness of the step length distribution according to the following equations:

$$\mathrm{Skewness}={\displaystyle \frac{\frac{1}{N}{{\displaystyle \sum }}_{i=1}^N{\left(x_i-\mu \right)}^3}{{\sigma }^3}}$$

(11)

$$\mathrm{Kurtosis}={\displaystyle \frac{\frac{1}{N}{{\displaystyle \sum }}_{i=1}^N{\left(x_i-\mu \right)}^4}{{\sigma }^4}}$$

(12)

where x_i are the step lengths, µ is the mean step length, σ is the standard deviation, and N is the number of steps. Additionally, the mean and standard deviation of velocity magnitudes were computed to describe the speed dynamics of the particle. The features were computed using the gen_fingerprints.py script.

Imaris Diffusion Feature Determination. The simulated tracks for the four diffusion types were exported as TrackMate-compatible XML files [31] using the export_sim_as_trackmate_tracks.py and imported into Imaris 10.2. A total of 16 track parameters were automatically extracted and saved as .csv files.

Machine Learning Classification. The extracted features for simulated tracks were compiled into a data frame, where each row corresponded to a trajectory, and each column represented a computed feature. Diffusion-type labels (Normal (ND), Anomalous (AD), Confined (CD), Directed (DM)) were assigned based on ground truth. Features were normalized to zero mean and unit variance using the StandardScaler to ensure uniform scaling. The diffusion types were converted to numerical labels using the LabelEncoder. The dataset was randomly split into training (70%) and testing (30%) subsets to ensure a stratified split for equal representation of diffusion types. The classifier used for this analysis was the XGBoost classifier, a gradient-boosted decision tree algorithm known for its robustness to feature interactions, handling of missing data, and interpretability [32]. While the machine learning pipeline utilized XGBoost due to its excellent performance in similar scenarios, it can be easily modified to incorporate alternative algorithms. Other machine learning methods, such as Random Forest or Support Vector Machines, can replace the XGBoost classifier if desired. The model was configured with 1000 estimators, a maximum tree depth of 5, a learning rate of 0.1, and a multi-class logarithmic loss objective function. The training was performed using the training set to optimize the classifier to distinguish between the diffusion types. The performance of the classifier was evaluated on the test set using precision, recall, F1-score, and accuracy metrics. A confusion matrix was generated to visualize the number of correct and incorrect predictions for each diffusion type. A sliding window approach was applied to classify mixed diffusion trajectories, where overlapping windows of 50 frames were analyzed with a step size of 25 frames. Features were computed for each window, normalized using the pre-trained scaler, and classified using the pre-trained XGBoost model, with final frame labels determined by majority voting across overlapping predictions. The training and classification were implemented in the Spyder IDE (Python 3.9) using the scripts ml_classifier_3d.py, ml_classifier_imaris_3d.py, or ml_classifier_mixed_3d.py.

3. Results

A feature-based approach was employed for trajectory analysis, with 13 descriptive custom parameters computed for each simulated trajectory. The full feature set included general trend descriptors, such as average step size and velocity; results of the power-law fit of the MSD curve, yielding diffusion coefficient (D), alpha exponent, and goodness-of-fit (R²); trajectory shape descriptors, such as kurtosis, radius of gyration, straightness index, and trappedness; and a parameter describing non-Brownian displacements (Gaussianity). A total of 2000 synthetic three-dimensional trajectories were generated in accordance with Wagner et al., Pinholt et al., and Kowalek et al. protocols [17,18,21] for four types of diffusion (500 each) that may be encountered in the complex intracellular environment: normal (Brownian) diffusion, directed motion, confined diffusion, and anomalous diffusion [33,34].

Figure 1 shows all synthetic tracks for each diffusion type and the averaged set of normalized diffusion features for these synthetic tracks in the form of a color-coded heatmap. Confined diffusion exhibited strong positive contributions from trappedness, Gaussianity, skewness, and kurtosis, while features from the MSD power law fit contributed negatively. Directed motion was cahracterized by high positive contributions from maximal radius, range of radii, mean velocity, and radius of gyration, coupled with negative contributions from trappedness and Gaussianity. Anomalous diffusion consistently showed strong negative contributions across most features, with minimal positive influence. Normal diffusion lacked clear defining characteristics. These distinct differences in feature patterns between diffusion types indicated that the pool of extracted features from the entire 3D synthetic dataset could form the basis of a machine-learning classifier.

In the case of automatically derived track features using the Imaris software, the differences between normalized feature patterns were less prominent compared to those of the custom features (Figure 2).

Key quantitative observations included a strong negative contribution of mean Ar1 (the first-order autocorrelation coefficient of a trajectory describing its directional motion persistence) and its components (x, y, and z) to anomalous diffusion, while displacement length showed a strong positive contribution to directed motion. Speed metrics, including maximum and mean speed, also exhibited positive contributions to directed motion, whereas their contributions to other types were minimal.

Next, the diffusion features from simulated trajectories were used to train an XGBoost classifier [32]. The classifier accuracy was evaluated using a confusion matrix, where the rows refer to ground truth, and the columns refer to the predicted motion type (Figure 3a). Anomalous trajectories were classified with high accuracy, with 148 true positives and only 2 false negatives (1.3%), and no misclassifications into other categories. Similarly, the classification of confined trajectories yielded 147 true positives, with only 3 instances (2%) misclassified as anomalous and no misclassifications into directed motion or normal diffusion categories. Directed motion trajectories, while generally well-classified, exhibited some overlap with the normal diffusion class, resulting in 133 true positives and 17 instances (11.3%) misclassified as Brownian. Classification of normal diffusion trajectories also showed good performance, with 135 true positives and 15 instances (10%) misclassified as directed motion. For the confusion matrices presented in Figure 3b (Δt = 1/10), Figure 3c (Δt = 1/30), and Figure 3d (Imaris features), the results were comparable across different time resolutions and feature sets, with overall accuracy greater than 90% for all conditions examined (

Table 1. Machine learning classification report.

	Precision				Recall				F1 Score
	Δt = 1	1/10Δt	1/30Δt	Imaris	Δt = 1	1/10Δt	1/30Δt	Imaris	Δt = 1	1/10Δt	1/30Δt	Imaris
Anomalous	0.98	0.98	0.99	0.94	0.99	0.99	0.97	0.98	0.98	0.98	0.98	0.96
Confined	1.00	0.99	0.97	0.93	0.98	0.97	0.99	0.94	0.99	0.98	0.98	0.93
Directed	0.90	0.96	0.92	0.93	0.89	0.89	0.89	0.89	0.89	0.92	0.91	0.91
Normal	0.88	0.88	0.89	0.89	0.90	0.95	0.92	0.88	0.89	0.92	0.90	0.88

).

Analysis of mixed diffusion trajectories using a sliding window approach via the XGBoost classifier (Δt = 1) demonstrated variable classification performance across the diffusion modes. Ground-truth binary labels and classifications of confined + normal and confined + directed diffusion mixed traces are visualized in Figure 4, with 3D trajectory segments color-coded according to their respective modes.

For confined + directed traces, classification achieved high precision and recall for both confined diffusion (precision = 1.00, recall = 0.90, F1 score = 0.95) and directed motion (precision = 1.00, recall = 0.81, F1 score = 0.89) diffusion, with an overall accuracy of 85%. Similarly, in the confined + normal classification, confined diffusion showed high precision (0.97) but moderate recall (0.66) and an F1 score of 0.78, while normal diffusion had perfect precision (1.00) with comparable recall (0.65) and an F1 score of 0.79, yielding an overall accuracy of 65%.

The experimental dataset was acquired via volumetric time-lapse imaging of Cos7 cells transiently transfected with mEmerald-Rab5a and Golgi7-tdTomato on a commercially available ZEISS Lattice Lightsheet 7 [35]. Briefly, 200-time points were acquired in 2 channels, one volume (85 × 80 × 20 µm³) every 3.2 s, 205 planes per volume, and a total of 41,000 frames in just under 11 min. After acquisition, the raw data were deconvolved, deskewed, and cover glass transformed using ZEN, resulting in a processed file with 0.145 µm pixel size in x, y, and z. The 3D trajectories of Golgi7-tdTomato-labeled vesicles were reconstructed in ImageJ 1.54p using the TrackMate plugin [31]. The Laplacian-of-Gaussian detector was employed to identify individual vesicles (estimated diameter 2 µm, quality threshold 5, median filter), and complete trajectories were reconstructed using the Simple Linear Assignment Problem tracker (linking max distance 3 µm, gap-closing max distance 3 µm, max frame gap 2) [36]. Only trajectories with more than 30 spots were used for further analysis via the trained classifier. Classification of these experimental particle trajectories into distinct diffusion modes was performed, as visualized in Figure 5. Figure 5a displays an Imaris-rendered 3D visualization of all trajectories, color-coded by temporal progression. Figure 5b,c panels show the classification results from two pre-trained classifiers: the Imaris features classifier and the custom features classifier. Figure 5b shows the 2D projection of classified trajectories, while Figure 5c presents a 3D perspective of spatial trajectory clustering and diffusion class distribution. The prediction results from the Imaris features classifier identified 67 trajectories as normal, 34 as directed, 16 as confined, and 15 as anomalous. In contrast, the custom features classifier categorized 53 trajectories as normal, 37 as directed, 1 as confined, and 41 as anomalous.

4. Discussion

The distinct differences observed in diffusion feature patterns provide a solid foundation for accurate machine learning differentiation of diffusion types. The trained classifiers based on either custom or Imaris-derived features effectively distinguished most simulated trajectory types, with minor misclassifications observed primarily between the directed motion and Brownian diffusion categories, and enabled clear classification of experimental trajectories. While the XGBoost classifier achieved high accuracy on single-state simulated trajectories (with overall accuracies exceeding 90%), the performance on mixed diffusion synthetic trajectories revealed challenges. The sliding window approach highlighted lower recall in the transition regions between diffusion types, especially for confined and normal diffusion. Optimizing the sliding window size or incorporating additional features, such as step variability or mean squared displacement trends, could improve recall and accuracy for more complex scenarios. On the other hand, one should note that 100% classification accuracy is inherently difficult because pure random walks transiently exhibit the movement patterns of confined or directed diffusion [25].

Despite variations in the classification criteria and sensitivities of the two approaches, normal diffusion and directed motion occurrences in the experimental dataset were in good ageement between the Imaris features classifier and the custom features classifier. The largest discrepancy was observed in the classification of anomalous versus confined diffusion, where the custom features classifier identified substantially more anomalous trajectories (41 compared to 15 by the Imaris classifier) and far fewer confined trajectories (1 compared to 16 by the Imaris classifier). Golgi7 vesicles, which are involved in intracellular trafficking, are expected to exhibit subdiffusive behavior, such as confined motion within vesicular docking sites or anomalous motion as they navigate through crowded intracellular environments. Decoding these subdiffusive patterns, such as confined and anomalous motion, is inherently challenging due to overlapping features and transition dynamics and has been the subject of several particle-tracking challenges [22,37].

Finally, this study demonstrates the transition from traditional 2D techniques to the 3D trajectory analysis. The established 2D techniques have primarily been limited to studying diffusion processes in the membrane (Phase I) or within a given optical slice. Consequently, very few studies have explored the full endocytosis and intracellular transport dynamics, which can generally consist of membrane penetration (Phase II), active transport within the cytoplasm (Phase III), and delivery to the endosomal-lysosomal system (Phase IV). The extension to 3D trajectory analysis in this study lays the foundation for detecting and characterizing these processes throughout the entire cell volume. This capability is particularly important given that hotspots for preferential endocytosis or subcellular signaling may exist within specific compartments of the cell [8,38].

5. Conclusions

This study extends the 2D feature-based diffusion classification approach to three dimensions to capture the intricate complexities of intracellular 3D motion. Synthetic trajectories representing four diffusion types (Normal, Directed, Confined, and Anomalous) relevant to intracellular dynamics were generated using stochastic simulations. For each synthetic trajectory, a custom comprehensive set of features was computed to capture spatial and temporal dynamics in a supervised manner. Additionally, Imaris-derived track features were incorporated into a parallel classifier for the first time to enhance the feature space and motion type classification potential. An XGBoost machine learning classifier was trained on normalized feature data from synthetic trajectories to achieve high precision and recall across all diffusion types and conditions, with overall accuracy exceeding 90% for each set of data. The trained classifiers were applied to experimental 3D trajectories of Golgi-associated vesicles to infer diffusion type and provide new insights into intracellular dynamics.

The open-source scripts associated with this study will be of significant interest to researchers investigating intracellular receptor trafficking, drug delivery, and virus infection in three dimensions. The modular classification pipeline can be further improved by expanding the feature set to include higher-order dynamic descriptors and integrating elements of deep learning for rapid, unbiased characterization of whole-cell trafficking dynamics. With the incorporation of deep learning architectures, such as convolutional neural networks [39,40,41] or recurrent neural networks [42], the approach could achieve even greater accuracy and scalability while automating the detection of diffusion modes as well as hotspots for endocytosis or signaling across entire cellular volumes. These advancements hold great promise for enhancing our understanding of intracellular processes and developing novel therapeutic strategies aimed at addressing trafficking deficits.