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The Behavioral Space of Zebrafish Locomotion and Its Neural Network Analog.

Girdhar K, Gruebele M, Chemla YR - PLoS ONE (2015)

Bottom Line: Clustering analysis reveals three known behavioral patterns-scoots, turns, rests-but shows that these do not represent discrete states, but rather extremes of a continuum.The behavioral space not only classifies fish by their behavior but also distinguishes fish by age.With the insight into fish behavior from postural space and behavioral space, we construct a two-channel neural network model for fish locomotion, which produces strikingly similar postural space and behavioral space dynamics compared to real zebrafish.

View Article: PubMed Central - PubMed

Affiliation: Center for Biophysics and Computational Biology, University of Illinois, Urbana, IL, 61801, United States of America.

ABSTRACT
How simple is the underlying control mechanism for the complex locomotion of vertebrates? We explore this question for the swimming behavior of zebrafish larvae. A parameter-independent method, similar to that used in studies of worms and flies, is applied to analyze swimming movies of fish. The motion itself yields a natural set of fish "eigenshapes" as coordinates, rather than the experimenter imposing a choice of coordinates. Three eigenshape coordinates are sufficient to construct a quantitative "postural space" that captures >96% of the observed zebrafish locomotion. Viewed in postural space, swim bouts are manifested as trajectories consisting of cycles of shapes repeated in succession. To classify behavioral patterns quantitatively and to understand behavioral variations among an ensemble of fish, we construct a "behavioral space" using multi-dimensional scaling (MDS). This method turns each cycle of a trajectory into a single point in behavioral space, and clusters points based on behavioral similarity. Clustering analysis reveals three known behavioral patterns-scoots, turns, rests-but shows that these do not represent discrete states, but rather extremes of a continuum. The behavioral space not only classifies fish by their behavior but also distinguishes fish by age. With the insight into fish behavior from postural space and behavioral space, we construct a two-channel neural network model for fish locomotion, which produces strikingly similar postural space and behavioral space dynamics compared to real zebrafish.

No MeSH data available.


Behavioral space of free swimming zebrafish.(A–B) Ensemble of swim bout trajectories (N = 115) embedded by multi-dimensional scaling (MDS) into low-dimensional “behavioral” space. Each cycle of every trajectory is represented by a single point (filled circles for younger larvae (N = 8; 7–8 dpf), open circles for older larvae (N = 12; 9–10 dpf)). The distances between points reflect their behavioral similarities/differences. MDS dimensions 1 and 2 (A) reveal behavioral regions corresponding to turns (red points), scoots (green) and rests (blue). The shaded ellipses demarcate the points from cycles 1–3 of the trajectory (orange, light green, green, respectively. S8A Fig displays the cycles individually). MDS dimensions 2 and 3 (B) reveal differences with zebrafish age (solid ellipse for younger larvae; dotted ellipse for older larvae). The ellipses were determined using PCA analysis of the behavioral space in MDS dimension 1 and dimension 2 for each cycle in (A) and MDS dimension 2 and dimension 3 for cycle 1 in (B). The principal axes of the ellipses are the singular values from PCA. Simulated trajectories from the neuro-kinematic model in Figs 5 and 6 and its training data are shown in diamonds and circles with black outline, respectively. (C) Amplitudes U1, U2, and U3 vs. normalized time of the trajectories in A and B from younger larvae. (D) Same plot for older larvae. Shaded areas demarcate each cycle of the trajectory. (E–F) Postural space representation of the trajectories in C and D, respectively. Throughout, color represents the location in the behavioral space and cycle number: in the RGB colormap, red and green channels correspond to position along MDS dimension 1 and 2, respectively, and the blue channel to the cycle number.
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pone.0128668.g004: Behavioral space of free swimming zebrafish.(A–B) Ensemble of swim bout trajectories (N = 115) embedded by multi-dimensional scaling (MDS) into low-dimensional “behavioral” space. Each cycle of every trajectory is represented by a single point (filled circles for younger larvae (N = 8; 7–8 dpf), open circles for older larvae (N = 12; 9–10 dpf)). The distances between points reflect their behavioral similarities/differences. MDS dimensions 1 and 2 (A) reveal behavioral regions corresponding to turns (red points), scoots (green) and rests (blue). The shaded ellipses demarcate the points from cycles 1–3 of the trajectory (orange, light green, green, respectively. S8A Fig displays the cycles individually). MDS dimensions 2 and 3 (B) reveal differences with zebrafish age (solid ellipse for younger larvae; dotted ellipse for older larvae). The ellipses were determined using PCA analysis of the behavioral space in MDS dimension 1 and dimension 2 for each cycle in (A) and MDS dimension 2 and dimension 3 for cycle 1 in (B). The principal axes of the ellipses are the singular values from PCA. Simulated trajectories from the neuro-kinematic model in Figs 5 and 6 and its training data are shown in diamonds and circles with black outline, respectively. (C) Amplitudes U1, U2, and U3 vs. normalized time of the trajectories in A and B from younger larvae. (D) Same plot for older larvae. Shaded areas demarcate each cycle of the trajectory. (E–F) Postural space representation of the trajectories in C and D, respectively. Throughout, color represents the location in the behavioral space and cycle number: in the RGB colormap, red and green channels correspond to position along MDS dimension 1 and 2, respectively, and the blue channel to the cycle number.

Mentions: We next used multidimensional scaling (MDS) [25] to quantify the differences between trajectories (and between the cycles of trajectories), and to determine whether they cluster into discrete behavioral patterns. Past behavioral studies have used both non-linear and linear clustering methods [19, 20], and here we applied a linear method to ensure robustness. MDS takes as input the Euclidean “distance” dαβ between every pair of postural space trajectories α and β over one oscillation cycle (see Materials and Methods and S1 File), and determines the optimal low-dimensional space required to embed the distance data. In this space, shown in Fig 4A, each oscillation cycle of a trajectory is represented by a point, and the distance between two points represents how similar the trajectories in the pair are. Thus, MDS generates a “behavioral space” in which distinct behavioral patterns would appear as well-separated clusters of points.


The Behavioral Space of Zebrafish Locomotion and Its Neural Network Analog.

Girdhar K, Gruebele M, Chemla YR - PLoS ONE (2015)

Behavioral space of free swimming zebrafish.(A–B) Ensemble of swim bout trajectories (N = 115) embedded by multi-dimensional scaling (MDS) into low-dimensional “behavioral” space. Each cycle of every trajectory is represented by a single point (filled circles for younger larvae (N = 8; 7–8 dpf), open circles for older larvae (N = 12; 9–10 dpf)). The distances between points reflect their behavioral similarities/differences. MDS dimensions 1 and 2 (A) reveal behavioral regions corresponding to turns (red points), scoots (green) and rests (blue). The shaded ellipses demarcate the points from cycles 1–3 of the trajectory (orange, light green, green, respectively. S8A Fig displays the cycles individually). MDS dimensions 2 and 3 (B) reveal differences with zebrafish age (solid ellipse for younger larvae; dotted ellipse for older larvae). The ellipses were determined using PCA analysis of the behavioral space in MDS dimension 1 and dimension 2 for each cycle in (A) and MDS dimension 2 and dimension 3 for cycle 1 in (B). The principal axes of the ellipses are the singular values from PCA. Simulated trajectories from the neuro-kinematic model in Figs 5 and 6 and its training data are shown in diamonds and circles with black outline, respectively. (C) Amplitudes U1, U2, and U3 vs. normalized time of the trajectories in A and B from younger larvae. (D) Same plot for older larvae. Shaded areas demarcate each cycle of the trajectory. (E–F) Postural space representation of the trajectories in C and D, respectively. Throughout, color represents the location in the behavioral space and cycle number: in the RGB colormap, red and green channels correspond to position along MDS dimension 1 and 2, respectively, and the blue channel to the cycle number.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4489106&req=5

pone.0128668.g004: Behavioral space of free swimming zebrafish.(A–B) Ensemble of swim bout trajectories (N = 115) embedded by multi-dimensional scaling (MDS) into low-dimensional “behavioral” space. Each cycle of every trajectory is represented by a single point (filled circles for younger larvae (N = 8; 7–8 dpf), open circles for older larvae (N = 12; 9–10 dpf)). The distances between points reflect their behavioral similarities/differences. MDS dimensions 1 and 2 (A) reveal behavioral regions corresponding to turns (red points), scoots (green) and rests (blue). The shaded ellipses demarcate the points from cycles 1–3 of the trajectory (orange, light green, green, respectively. S8A Fig displays the cycles individually). MDS dimensions 2 and 3 (B) reveal differences with zebrafish age (solid ellipse for younger larvae; dotted ellipse for older larvae). The ellipses were determined using PCA analysis of the behavioral space in MDS dimension 1 and dimension 2 for each cycle in (A) and MDS dimension 2 and dimension 3 for cycle 1 in (B). The principal axes of the ellipses are the singular values from PCA. Simulated trajectories from the neuro-kinematic model in Figs 5 and 6 and its training data are shown in diamonds and circles with black outline, respectively. (C) Amplitudes U1, U2, and U3 vs. normalized time of the trajectories in A and B from younger larvae. (D) Same plot for older larvae. Shaded areas demarcate each cycle of the trajectory. (E–F) Postural space representation of the trajectories in C and D, respectively. Throughout, color represents the location in the behavioral space and cycle number: in the RGB colormap, red and green channels correspond to position along MDS dimension 1 and 2, respectively, and the blue channel to the cycle number.
Mentions: We next used multidimensional scaling (MDS) [25] to quantify the differences between trajectories (and between the cycles of trajectories), and to determine whether they cluster into discrete behavioral patterns. Past behavioral studies have used both non-linear and linear clustering methods [19, 20], and here we applied a linear method to ensure robustness. MDS takes as input the Euclidean “distance” dαβ between every pair of postural space trajectories α and β over one oscillation cycle (see Materials and Methods and S1 File), and determines the optimal low-dimensional space required to embed the distance data. In this space, shown in Fig 4A, each oscillation cycle of a trajectory is represented by a point, and the distance between two points represents how similar the trajectories in the pair are. Thus, MDS generates a “behavioral space” in which distinct behavioral patterns would appear as well-separated clusters of points.

Bottom Line: Clustering analysis reveals three known behavioral patterns-scoots, turns, rests-but shows that these do not represent discrete states, but rather extremes of a continuum.The behavioral space not only classifies fish by their behavior but also distinguishes fish by age.With the insight into fish behavior from postural space and behavioral space, we construct a two-channel neural network model for fish locomotion, which produces strikingly similar postural space and behavioral space dynamics compared to real zebrafish.

View Article: PubMed Central - PubMed

Affiliation: Center for Biophysics and Computational Biology, University of Illinois, Urbana, IL, 61801, United States of America.

ABSTRACT
How simple is the underlying control mechanism for the complex locomotion of vertebrates? We explore this question for the swimming behavior of zebrafish larvae. A parameter-independent method, similar to that used in studies of worms and flies, is applied to analyze swimming movies of fish. The motion itself yields a natural set of fish "eigenshapes" as coordinates, rather than the experimenter imposing a choice of coordinates. Three eigenshape coordinates are sufficient to construct a quantitative "postural space" that captures >96% of the observed zebrafish locomotion. Viewed in postural space, swim bouts are manifested as trajectories consisting of cycles of shapes repeated in succession. To classify behavioral patterns quantitatively and to understand behavioral variations among an ensemble of fish, we construct a "behavioral space" using multi-dimensional scaling (MDS). This method turns each cycle of a trajectory into a single point in behavioral space, and clusters points based on behavioral similarity. Clustering analysis reveals three known behavioral patterns-scoots, turns, rests-but shows that these do not represent discrete states, but rather extremes of a continuum. The behavioral space not only classifies fish by their behavior but also distinguishes fish by age. With the insight into fish behavior from postural space and behavioral space, we construct a two-channel neural network model for fish locomotion, which produces strikingly similar postural space and behavioral space dynamics compared to real zebrafish.

No MeSH data available.