Behavioural Classification in C. elegans: a Spatio-Temporal Analysis of Locomotion

TL;DR

The paper tackles the problem of characterizing C. elegans behaviour from center-of-mass trajectories in scenarios where full-body tracking is impractical, particularly at high density. It compares two pipelines: (i) hand-designed atomic behaviours and (ii) an unsupervised automatic segmentation that uses center-point features, UMAP dimensionality reduction, and KMeans clustering, evaluated within an agent-based probabilistic finite-state model with transitions $p_{s\rightarrow s'}(k) = (m_{s'}\,k + q_{s'})\, l_{s\rightarrow s'}$. Results show the automatic method better reproduces observed movement and reveals important temporal dependencies, yielding distinct behavioural states even from point-tracking; the agent-based model demonstrates higher likelihood fits and closer distributions to real worm movement when using automatic states. This work demonstrates that meaningful spatio-temporal behavioural states can be inferred from simplified centre-point tracking, enabling scalable analysis of single- and collective-worm locomotion and guiding future automated behavioural pipelines.

Abstract

The 1mm roundworm C. elegans is a model organism used in many sub-areas of biology to investigate different types of biological processes. In order to complement the n-vivo analysis with computer-based investigations, several methods have been proposed to simulate the worm behaviour. These methods extract discrete behavioural units from the flow of the worm movements using different types of tracking techniques. Nevertheless, these techniques require a clear view of the entire worm body, which is not always achievable. For example, this happens in high density worm conditions, which are particularly informative to understand the influence of the social context on the single worm behaviour. In this paper, we illustrate and evaluate a method to extract behavioural units from recordings of C. elegans movements which do not necessarily require a clear view of the entire worm body. Moreover, the behavioural units are defined by an unsupervised automatic pipeline which frees the process from predefined assumptions that inevitably bias the behavioural analysis. The behavioural units resulting from the automatic method are interpreted by comparing them with hand-designed behavioural units. The effectiveness of the automatic method is evaluated by measuring the extent to which the movement of a simulated worm, with an agent-based model, matches the movement of a natural worm. Our results indicate that spatio-temporal locomotory patterns emerge even from single point worm tracking. Moreover, we show that such patterns represent a fundamental aspect of the behavioural classification process.

Figures (6)

• Figure 1: (a) Average silhouette score obtained from clustering via KMeans the embedded feature space while varying the number of clusters $k$. The maximum value is achieved for $k^*=5$ and the resulting clustering of the embedded feature space is shown in (b).
• Figure 2: Distributions of speed (skyblue) and angle change (light green) for each atomic behaviour (top) and each automatic behaviour (bottom) when classifying our dataset. We overlay the distributions obtained from our agent-based simulator when using $1000$ agents for $1800$ time steps (speed in orange, angle change in red) and report the Kolmogorov-Smirnoff (KS) statistic in Table \ref{['tab:ks_atomic_and_automatic']}. For the atomic behaviours, speed and angle change are computed for state (a) sharp turn, (b) reversal, (c) pause, (d) lines, (e) arcs and (f) loops. For the automatically defined behaviours, speed and angle changes are computed for states (g) slow-line ($0$), (h) straight-turn ($1$), (i) loop-turn ($2$), (j) crawl ($3$) and (k) high-turning ($4$).
• Figure 3: Shapley values of the features for each state obtained from the automatic behaviour method after an optimised XGBoost predictor was trained on the features to classify the state labels after the KMeans clustering on the embedded feature space with $k^*=5$ clusters. We show only the $3$ most influent Shapley values for state (a) slow-line ($0$), (b) straight-turn ($1$), (c) loop-turn ($2$), (d) crawl ($3$) and (e) high-turning ($4$).
• Figure 4: Ordered confusion matrix of the two classification methods: rows represent labels obtained by applying the atomic method, whereas columns represent labels obtained by the automatic classification. Each cell contains the number of data points through time where the two systems agree and is normalised column-wise, thus showing how each automatic state maps to the atomic states.
• Figure 5: Transition matrices for the atomic (a) and automatic (b) methods computed as the overall count of transitions between behavioural states, excluding self-transitions and normalised row-wise.