Table 1.
Tracking methods in bio-imaging.
Fig 1.
Multi-step EMC2 for tracking neuron activity in calcium imaging data.
a- Time-lapse imaging (N frames) of intermittent fluorescence activity of a neuron in a deforming environment (e.g. behaving animal). b- Fluorescent spots (neurons), that are significantly brighter than background, are automatically detected with a wavelet-based algorithm. c- Tracklets of detectable neurons are robustly reconstructed using probabilistic tracking algorithm (eMHT). d- Short tracklets of detectable particles are used to compute the elastic deformation of the field of view at each time frame. Associated detections in neuron tracklets are used as fiducials, and the whole deformation is interpolated using a poly-harmonic thin-plate spline function. Forward- and backward-propagated positions of tracklet particle positions are shown with a thin blue line. e- After having corrected for the deformation of the field-of-view where neurons are embedded, gaps between the end- and starting-points of tracklets are closed by minimizing the global Euclidean distance between points (dotted line). f- Finally, complete single neuron tracks over the time-lapse sequence are obtained by applying the elastic transformation of the field-of-view to concatenated tracklets.
Fig 2.
Implementation of the EMC2 algorithm in Icy platform.
Time-lapse sequence of fluorescent particles is the input to a multi-step, automatic protocol in Icy. A first series of blocks, highlighted in blue, detects the position of fluorescent neurons (spots) in each frame of the time-lapse sequence. Block 1 uses the wavelet transform of each image and statistical thresholding of wavelet coefficients to determine spots that are significantly brighter than background. To separate close spots that form clusters in the wavelet-based mask of the image, the thresholded sequence is convolved with a log-gaussian kernel to enhance single spots (block 2), and local maxima algorithm is applied (block 3). A second series of blocks, highlighted in red, computes single particle tracks from computed spot positions. First, the Bayesian tracking algorithm (eMHT) computes tracklets of detectable particles (block 4). Due to fluctuating particle detectability, many Bayesian tracklets are terminated prematurely and new tracklets are created when particles can be detected again. To close detection gaps in single particle tracks, block 5 applies the EMC2 algorithm. Final output of the Icy protocol is the collection of single particle tracks over the time-lapse sequence. Tracking protocol can be found here: http://icy.bioimageanalysis.org/protocol/detection-with-cluster-un-mixing-and-tracking-of-neurons-with-emc2/ and is also directly accessible through the search bar of the Icy software (see step-by-step Supplementary Icy tutorial).
Table 2.
Tested tracking algorithms in manual validation.
Fig 3.
Testing EMC2 robustness with synthetic simulations.
For each simulated type of motion (confined diffusion (a), linear motion (b) and “Hydra-like” elastic deformation (c)), we simulated the stochastic firing of neuronal ensembles and corresponding fluorescence dynamics in synthetic time-lapse sequences (see Materials and Methods for details). We then compared the performances of EMC2 (blue) with TrackMate (no motion correction (red) or linear motion correction (magenta)). P-values are obtained with the Wilcoxon rank sum test over n = 10 simulations in each case. (d-e) Using “Hydra-like” synthetic deformation, we measured the accuracy of EMC2 for increasing proportion of stable (i.e. non-blinking) particles (neuronal cells) and increasing number of simulated particles. (f) After having estimated the deformation-field in three different animals (animal 1 (black), 4 (blue) and 6 (green)), we measured the accuracy of EMC2 for simulated sequences with increasing length (25, 50, 100 and 240 seconds. Imaging and simulations were performed at 10 Hz). For comparison purposes, the performance of TrackMate algorithm for 25 seconds (animal 1), extracted from (c), is shown.
Table 3.
Results of synthetic simulations (Hydra-like deformation, increasing length).
Table 4.
Results of statistical extraction of neuronal ensembles in Hydra (n = 8 animals).
Fig 4.
Monitoring the activity of individual neurons in two-photon calcium imaging of mouse visual cortex with EMC2.
a- Two-photon calcium imaging of single neuron activity in visual cortex of awake mice is performed at Day 1, Day 2 and Day 46 during 5 minutes at 12.3 Hz. Tracking of neuron positions is performed with EMC2 and reveals an important turn-over of active neurons across days. Examples of neurons that are active at Day 1, Day 2 or Day 46 are respectively highlighted with red, green or blue arrows. Neurons active at Day 1&2 are highlighted with yellow arrows, at Day 2&46 with cyan arrows, and at Day 1,2&46 with white arrows. The median number of active neurons each day is also plotted (n = 4 animals). The number of neurons that are active from Day 1, 2 or 3 are respectively represented in red, green or blue. b- Single neuron trajectories can be modeled with confined stochastic motion. Two example trajectories are shown (green & blue trajectories) with a maximum excursion distance of ~ 4 pixels. Boxplots of single neuron displacement between two consecutive frames, and maximum excursion distance (in pixels) are plotted (n = 590 trajectories).
Fig 5.
Neuron tracking and mapping of neuronal ensembles in behaving Hydra.
a- Calcium imaging of single neuron activity in behaving Hydra. The images and analysis of the 3rd movie of animal 1 are given as representative examples. b- Single neuron tracks and fluorescence intensity are obtained with EMC2 algorithm. c- For each neuron, spikes are extracted from fluorescence traces. Peaks of activity (highlighted with red stars) correspond to significant co-activity of individual neurons (sum of individual activities (solid red line) > statistical threshold (dashed red line), p = 0.001 see Materials and Methods). Each peak putatively corresponds to the activation of one neuronal ensemble. d- Similarity between activity peaks is computed using the identities of individual neurons that are firing at each peak (see Materials and Methods). e- The optimal number of peak classes (that putatively corresponds to the number of neuronal ensembles) is computed using the Silhouette index on k-means clustering of the similarity matrix (see Material and Methods). Median fluorescence trace of each neuronal ensemble and corresponding activity peaks are shown. The classification of individual neurons in each ensemble is determined based on their firing at ensemble peaks (see Materials and Methods). f- Individual neurons of each ensemble can be dynamically mapped in the original time-lapse sequence.
Table 5.
Parameters used for synthetic simulations.