Deriving Shape-Based Features for C. elegans Locomotion Using Dimensionality Reduction Methods

Abstract

High-throughput analysis of animal behavior is increasingly common following the advances of recording technology, leading to large high-dimensional data sets. This dimensionality can sometimes be reduced while still retaining relevant information. In the case of the nematode worm Caenorhabditis elegans, more than 90% of the shape variance can be captured using just four principal components. However, it remains unclear if other methods can achieve a more compact representation or contribute further biological insight to worm locomotion. Here we take a data-driven approach to worm shape analysis using independent component analysis (ICA), non-negative matrix factorization (NMF), a cosine series, and jPCA (a dynamic variant of principal component analysis [PCA]) and confirm that the dimensionality of worm shape space is close to four. Projecting worm shapes onto the bases derived using each method gives interpretable features ranging from head movements to tail oscillation. We use these as a comparison method to find differences between the wild type N2 worms and various mutants. For example, we find that the neuropeptide mutant nlp-1(ok1469) has an exaggerated head movement suggesting a mode of action for the previously described increased turning rate. The different bases provide complementary views of worm behavior and we expect that closer examination of the time series of projected amplitudes will lead to new results in the future.

Keywords: C. elegans; computational ethology; dimensionality reduction; locomotion; worm tracking.

Figure 1

(A) A typical frame of a worm under the tracking microscope. (B,C) The outline and the curve through the center of the worm. The angle in radians between neighboring points along the centerline is plotted from the tip of the head (s = 1) to the end of the tail (s = 48). (D) As the worm moves, the value of each angle changes, but each subsequent angle provides little additional information because they are highly correlated with each other. (E) Dimensionality reduction methods can reveal more biologically meaningful time-series variables.

Figure 2

(A) Independent component analysis (ICA) returns four basis shapes that explain 97.6% of the variance in the dataset. The graph shows an x-y coordinate representation of the modes with the resampled basis shapes in gray. (B) The fraction of the variance explained along the worm by including an increasing number of basis shapes suggests that the modes can each explain a different part of the worm well. (C) Bivariate histograms for the amplitudes of basis shapes (wild type worm, 15 min, frame rate: 30 Hz). Top row: forward locomotion only, bottom row: all data. Basis shapes 1 and 2 from ICA form a ring in both cases (especially clear when only the forward locomotion is counted), suggesting an oscillatory behavior between them. Similarly, two basis shapes from principal component analysis (PCA) are known to explain an oscillatory behavior, but they also include other information, as evidenced by a lack of clear, continuous ring in their histograms.

Figure 3

(A) Non-negative matrix factorization (NMF) returns five basis shapes that explain 97.6% of the variance in the angle data. The graph shows an x-y coordinate representation of the modes with the resampled basis shapes in gray. (B) Angle representation of the basis shapes in (A; legend in C). (C) The fraction of the variance explained along the worm by including an increasing number of basis shapes suggests that the modes can each explain a different part of the worm well, in this case localized to the five major segments of the worm. (D) Bivariate histograms for the amplitudes of basis shapes (wild type worm, 15 min, frame rate: 30 Hz). Basis shapes 3, 4, 1 and 5 form incomplete rings, suggesting a more diffuse representation of the oscillatory sinusoidal crawling behavior using NMF.

Figure 4

The mean of the absolute projected amplitudes corresponding to each basis shape from NMF is taken for individual worms of four different genotypes. (wild type N2: n = 1303, snf-6: n = 43, nlp-1: n = 22, egg-5: n = 23) snf-6 and nlp-1 worms have significantly increased head motion, but normal movement in the rest of their body in terms of magnitude (p_adj(snf-6) = 3.13 × 10⁻¹⁴, p_adj(nlp-1) = 6.83 × 10⁻⁴), while the opposite can be observed in egg-5 mutants (p_adj(hip) = 8.19 × 10⁻⁵, p_adj(tail) = 2.48 × 10⁻⁶). ***Indicates p < 0.001.

Figure 5

(A) A cosine series was used to generate four basis shapes with increasing frequency. The corresponding x-y representations are shown. (B) The fraction of the variance explained along the worm by including an increasing number of basis shapes. (C) The shapes in the testing set were reconstructed using the four sinusoidal basis shapes and the top four modes of PCA. The histogram of the correlation coefficients (between the reconstructed and the original shapes) suggests a significant, but small difference between the sinusoidal analysis (96.9%) and the data-driven approach (97.1%; t-test, p = 2.49 × 10⁻¹¹).

Figure 6

(A) jPCA is run with 12 components (top six shown here). The graph shows an x-y coordinate representation of the modes with the resampled basis shapes in gray. (B) Bivariate histograms for the amplitudes of basis shapes (wild type worm, 15 min, frame rate: 30 Hz). Basis shapes 1, 2, 3, 4, 5 and 6 all form rings, suggesting an oscillatory behavior between them and independent sinusoidal waves in the corresponding parts of the body.

Figure 7

The amplitude of the jPCA anterior oscillation is measured for individual worms of three different genotypes during forward locomotion and reversals. (wild type N2: n = 1303, tdc-1: n = 19, egg-5: n = 23) tdc-1 has significantly reduced head oscillation during forward locomotion, but suppresses it during reversals to the same magnitude as wild types (p_adj(tdc-1) = 4.80 × 10⁻⁵), while the opposite can be observed in egg-5 mutants (p_adj(egg-5) = 3.71 × 10⁻⁴). During touch-evoked reversals, head oscillation is reduced in both wild type N2 and tdc-1 worms. Both have a significantly smaller ratio (forward/spontaneous reversal) than wild type (p_adj(tdc-1) = 3.73 × 10⁻⁶, p_adj(egg-5) = 6.69 × 10⁻⁶). ***Indicates p < 0.001.