The Behavioral Space of Zebrafish Locomotion and Its Neural Network Analog
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{"title"=>"The behavioral space of zebrafish locomotion and its neural network analog", "type"=>"journal", "authors"=>[{"first_name"=>"Kiran", "last_name"=>"Girdhar", "scopus_author_id"=>"44761161400"}, {"first_name"=>"Martin", "last_name"=>"Gruebele", "scopus_author_id"=>"7006230488"}, {"first_name"=>"Yann R.", "last_name"=>"Chemla", "scopus_author_id"=>"6603236123"}], "year"=>2015, "source"=>"PLoS ONE", "identifiers"=>{"issn"=>"19326203", "scopus"=>"2-s2.0-84940986967", "pmid"=>"26132396", "doi"=>"10.1371/journal.pone.0128668", "pui"=>"605761286", "sgr"=>"84940986967"}, "id"=>"f8daeeb9-277f-3084-b1a8-11bdf54d3a00", "abstract"=>"How simple is the underlying controlmechanism for the complex locomotion of verte- brates?We explore this question for the swimming behavior of zebrafish larvae. A param- eter-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 \"eigen- shapes\" 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 aremanifested as trajectories consisting of cycles of shapes repeated in succes- sion. To classify behavioral patterns quantitatively and to understand behavioral varia- tions among an ensemble of fish, we construct a \"behavioral space\" usingmulti- dimensional scaling (MDS). Thismethod turns each cycle of a trajectory into a single point in behavioral space, and clusters points based on behavioral similarity. Clustering analy- sis 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 pos- tural space and behavioral space dynamics compared to real zebrafish.", "link"=>"http://www.mendeley.com/research/behavioral-space-zebrafish-locomotion-neural-network-analog", "reader_count"=>62, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Professor > Associate Professor"=>3, "Student > Doctoral Student"=>3, "Researcher"=>8, "Student > Ph. D. Student"=>17, "Student > Postgraduate"=>1, "Student > Master"=>16, "Other"=>2, "Student > Bachelor"=>7, "Lecturer"=>1, "Professor"=>3}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Professor > Associate Professor"=>3, "Student > Doctoral Student"=>3, "Researcher"=>8, "Student > Ph. D. Student"=>17, "Student > Postgraduate"=>1, "Student > Master"=>16, "Other"=>2, "Student > Bachelor"=>7, "Lecturer"=>1, "Professor"=>3}, "reader_count_by_subject_area"=>{"Engineering"=>4, "Unspecified"=>5, "Biochemistry, Genetics and Molecular Biology"=>5, "Mathematics"=>1, "Agricultural and Biological Sciences"=>12, "Neuroscience"=>11, "Physics and Astronomy"=>6, "Chemistry"=>5, "Computer Science"=>12, "Sports and Recreations"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>4}, "Neuroscience"=>{"Neuroscience"=>11}, "Chemistry"=>{"Chemistry"=>5}, "Physics and Astronomy"=>{"Physics and Astronomy"=>6}, "Sports and Recreations"=>{"Sports and Recreations"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>12}, "Computer Science"=>{"Computer Science"=>12}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>5}, "Mathematics"=>{"Mathematics"=>1}, "Unspecified"=>{"Unspecified"=>5}}, "reader_count_by_country"=>{"United States"=>1, "France"=>1, "Portugal"=>1, "Germany"=>1}, "group_count"=>1}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/2159090"], "description"=>"<p>(A) Still images from a free swimming zebrafish movie. Each snapshot shows the fish backbone reduced to a thin skeleton fitted to a cubic spline fit (cyan) and obtained from the neural simulation (red), respectively. The neural model was optimized against the experimental data as described in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0128668#pone.0128668.s015\" target=\"_blank\">S1 File</a>. (B) Decomposition of simulated swimming traces from neuro-kinematic model into eigenshapes <i>V</i><sub><i>k</i></sub>(<i>s</i><sub><i>j</i></sub>). The eigenshapes from the neural model of a turn (dashed light red, blue, and green lines) match those from experimental data of a turn (solid red, blue, and green). (C) Bar plot of % weights of each eigenshapes <i>V</i><sub><i>k</i></sub>(<i>s</i><sub><i>j</i></sub>) (<i>j</i> = 1, 2… 9) (left axis) and cumulative contribution of each eigenshape (right axis, cyan). The first three eigenshapes contribute 98% in total to the variance in Δ<i>θ</i>. (D) Plot of head-to-tail zebrafish compliance (1/<i>W</i>(<i>s</i><sub><i>j</i></sub>)) obtained after optimization of neuro-kinematic model against experimental data. (E) Simulated neuro-kinematic model trajectory of a turning bout in postural space.</p>", "links"=>[], "tags"=>["Neural Network Analog", "postural space", "mds"], "article_id"=>1471098, "categories"=>["Uncategorised"], "users"=>["Kiran Girdhar", "Martin Gruebele", "Yann R. Chemla"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0128668.g006", "stats"=>{"downloads"=>0, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Minimal_neuro_kinematic_simulation_of_zebrafish_free_swimming_/1471098", "title"=>"Minimal neuro-kinematic simulation of zebrafish free swimming.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-07-01 04:15:02"}
  • {"files"=>["https://ndownloader.figshare.com/files/2159074"], "description"=>"<p>(A) Still images of a representative turning bout during free swimming. As discussed in the text, it is convenient to divide the bout into a “turn” region (<i>t</i> = 50–100 ms) followed by a “scoot” region (100–250 ms). (B) Plot of the amplitudes <i>U</i><sub>1</sub>(<i>t</i>), <i>U</i><sub>2</sub>(<i>t</i>), and <i>U</i><sub>3</sub>(<i>t</i>) of the three collective eigenshapes corresponding to the movie in A. Each amplitude undergoes multiple oscillation cycles before returning to zero. The regions marked by dashed lines and labeled as cycles (1–4) in <i>U</i><sub>1</sub>(<i>t</i>), <i>U</i><sub>2</sub>(<i>t</i>), and <i>U</i><sub>3</sub>(<i>t</i>) are obtained from the oscillation cycles in <i>U</i><sub>1</sub>(<i>t</i>). The colored dots mark time points corresponding to the still images in A. (C) Representation of a turn bout in postural space. The three-dimensional coordinates of the trajectory are the amplitudes <i>U</i><sub>1</sub>(<i>t</i>), <i>U</i><sub>2</sub>(<i>t</i>), and <i>U</i><sub>3</sub>(<i>t</i>) in B. In this space, the bout involves a turn region (<i>t</i> = 50–100 ms), represented as a bent ellipse (cycle 1), followed by a scoot region (<i>t</i> = 100–250 ms) represented as multiple cycles (2–4) along the flat ellipses, and a final return to the rest behavior. Throughout, time (0–250 ms) is represented by the black—magenta colormap. An analysis of a representative scooting bout is shown in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0128668#pone.0128668.s006\" target=\"_blank\">S5 Fig</a>.</p>", "links"=>[], "tags"=>["Neural Network Analog", "postural space", "mds"], "article_id"=>1471093, "categories"=>["Uncategorised"], "users"=>["Kiran Girdhar", "Martin Gruebele", "Yann R. Chemla"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0128668.g003", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Representation_of_free_swimming_zebrafish_in_low_dimensional_postural_space_/1471093", "title"=>"Representation of free swimming zebrafish in low-dimensional postural space.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-07-01 04:15:02"}
  • {"files"=>["https://ndownloader.figshare.com/files/2159073"], "description"=>"<p>(A) Still images of a swim bout from a representative movie of free swimming zebrafish larva, recorded at 500 fps. (B) Spline fit of fish backbone (cyan). Tangent vectors (black arrow) at 10 evenly spaced segments along the backbone from head (<i>s</i><sub>0</sub> = 0) to tail (<i>s</i><sub>9</sub> = 9) point along a direction <i>θ</i>(<i>s</i><sub><i>j</i></sub>). (C) Swim bout from A parameterized by Δ<i>θ</i>(<i>s</i><sub><i>j</i></sub>,<i>t</i><sub><i>i</i></sub>) = <i>θ</i>(<i>s</i><sub><i>j</i></sub>,<i>t</i><sub><i>i</i></sub>)–<i>θ</i>(0,<i>t</i><sub><i>i</i></sub>). (D) Singular value decomposition of Δ<i>θ</i> into eigenshapes <i>V</i><sub><i>k</i></sub>(<i>s</i><sub><i>j</i></sub>) (<i>j</i> = 1, 2… 9), the first three of which are plotted (red, blue, and green, respectively). The light colors correspond to eigenshapes determined from analyzing individual fish from a population, and dark colors are the collective eigenshapes from analyzing the entire population at once. (E) Bar plot of % weights (<math><mrow><msub><mi>S</mi><mrow><mi>k</mi><mi>k</mi></mrow></msub><mo>/</mo><mo>∑</mo><mrow><mi>k</mi><mo>′</mo><mo>=</mo><mn>1</mn></mrow><mrow><mn>10</mn></mrow><mrow><msub><mi>S</mi><mrow><mi>k</mi><mo>′</mo><mi>k</mi><mo>′</mo></mrow></msub></mrow></mrow></math>, where <i>S</i><sub><i>kk</i></sub> are the singular values) of each eigenfunction <i>V</i><sub><i>k</i></sub>(<i>s</i><sub><i>j</i></sub>). The right axis in cyan shows the cumulative contribution of each eigenshape. The first three eigenshapes contribute 96% of the total variance in Δ<i>θ</i>.</p>", "links"=>[], "tags"=>["Neural Network Analog", "postural space", "mds"], "article_id"=>1471092, "categories"=>["Uncategorised"], "users"=>["Kiran Girdhar", "Martin Gruebele", "Yann R. Chemla"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0128668.g002", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Decomposition_of_free_swimming_zebrafish_larval_backbone_shapes_into_orthonormal_basis_/1471092", "title"=>"Decomposition of free swimming zebrafish larval backbone shapes into orthonormal basis.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-07-01 04:15:02"}
  • {"files"=>["https://ndownloader.figshare.com/files/2159087"], "description"=>"<p>(A–B) Ensemble of swim bout trajectories (<i>N</i> = 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 (<i>N</i> = 8; 7–8 dpf), open circles for older larvae (<i>N</i> = 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. <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0128668#pone.0128668.s009\" target=\"_blank\">S8A Fig</a> 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 <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0128668#pone.0128668.g005\" target=\"_blank\">5</a> and <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0128668#pone.0128668.g006\" target=\"_blank\">6</a> and its training data are shown in diamonds and circles with black outline, respectively. (C) Amplitudes <i>U</i><sub>1</sub>, <i>U</i><sub>2</sub>, and <i>U</i><sub>3</sub> 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.</p>", "links"=>[], "tags"=>["Neural Network Analog", "postural space", "mds"], "article_id"=>1471095, "categories"=>["Uncategorised"], "users"=>["Kiran Girdhar", "Martin Gruebele", "Yann R. Chemla"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0128668.g004", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Behavioral_space_of_free_swimming_zebrafish_/1471095", "title"=>"Behavioral space of free swimming zebrafish.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-07-01 04:15:02"}
  • {"files"=>["https://ndownloader.figshare.com/files/2159088"], "description"=>"<p>(A) Schematic of neuro-kinematic model depicting the fish backbone divided into ten segments on the right and left sides. (B) Spike train generated by an optimized neural model. The right and left spike trains are shown in red and green, respectively. The height of each spike represents the amplitude <i>a</i> of the stimulus. <i>τ</i><sub><i>f</i></sub> is the firing time for each spike in the head segment. The segment-to-segment delay <i>d</i> is the time difference between spikes in adjacent segments of the fish backbone.</p>", "links"=>[], "tags"=>["Neural Network Analog", "postural space", "mds"], "article_id"=>1471096, "categories"=>["Uncategorised"], "users"=>["Kiran Girdhar", "Martin Gruebele", "Yann R. Chemla"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0128668.g005", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Spike_train_of_zebrafish_free_swimming_/1471096", "title"=>"Spike train of zebrafish free swimming.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-07-01 04:15:02"}
  • {"files"=>["https://ndownloader.figshare.com/files/2159072"], "description"=>"<p>(A) Snapshots of a larval zebrafish free swimming movie in which the fish backbone is fitted to a 10-point spline. (B) A linear combination of three “eigenshapes” accurately reconstructs the backbone shapes of the zebrafish. (C) A swimming bout is represented as a trajectory in the “postural space” spanned by the three eigenshapes. (D) A “behavioral space” generated by multi-dimensional scaling reduces each cycle of a trajectory to a point, and clusters them by their similarity. (E) A 2-channel neuro-kinematic model is constructed based on the observed behavioral patterns and evaluated using the same work flow.</p>", "links"=>[], "tags"=>["Neural Network Analog", "postural space", "mds"], "article_id"=>1471091, "categories"=>["Uncategorised"], "users"=>["Kiran Girdhar", "Martin Gruebele", "Yann R. Chemla"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0128668.g001", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Workflow_from_swim_observation_to_neuro_kinematic_model_/1471091", "title"=>"Workflow from swim observation to neuro-kinematic model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2015-07-01 04:15:02"}
  • {"files"=>["https://ndownloader.figshare.com/files/2159095", "https://ndownloader.figshare.com/files/2159096", "https://ndownloader.figshare.com/files/2159097", "https://ndownloader.figshare.com/files/2159098", "https://ndownloader.figshare.com/files/2159099", "https://ndownloader.figshare.com/files/2159100", "https://ndownloader.figshare.com/files/2159101", "https://ndownloader.figshare.com/files/2159102", "https://ndownloader.figshare.com/files/2159103", "https://ndownloader.figshare.com/files/2159104", "https://ndownloader.figshare.com/files/2159105", "https://ndownloader.figshare.com/files/2159106", "https://ndownloader.figshare.com/files/2159107", "https://ndownloader.figshare.com/files/2159108", "https://ndownloader.figshare.com/files/2159109", "https://ndownloader.figshare.com/files/2159110", "https://ndownloader.figshare.com/files/2159111", "https://ndownloader.figshare.com/files/2159112", "https://ndownloader.figshare.com/files/2159113", "https://ndownloader.figshare.com/files/2159114", "https://ndownloader.figshare.com/files/2159115"], "description"=>"<div><p>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.</p></div>", "links"=>[], "tags"=>["Neural Network Analog", "postural space", "mds"], "article_id"=>1471103, "categories"=>["Uncategorised"], "users"=>["Kiran Girdhar", "Martin Gruebele", "Yann R. Chemla"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0128668.s001", "https://dx.doi.org/10.1371/journal.pone.0128668.s002", "https://dx.doi.org/10.1371/journal.pone.0128668.s003", "https://dx.doi.org/10.1371/journal.pone.0128668.s004", "https://dx.doi.org/10.1371/journal.pone.0128668.s005", "https://dx.doi.org/10.1371/journal.pone.0128668.s006", "https://dx.doi.org/10.1371/journal.pone.0128668.s007", "https://dx.doi.org/10.1371/journal.pone.0128668.s008", "https://dx.doi.org/10.1371/journal.pone.0128668.s009", "https://dx.doi.org/10.1371/journal.pone.0128668.s010", "https://dx.doi.org/10.1371/journal.pone.0128668.s011", "https://dx.doi.org/10.1371/journal.pone.0128668.s012", "https://dx.doi.org/10.1371/journal.pone.0128668.s013", "https://dx.doi.org/10.1371/journal.pone.0128668.s014", "https://dx.doi.org/10.1371/journal.pone.0128668.s015", "https://dx.doi.org/10.1371/journal.pone.0128668.s016", "https://dx.doi.org/10.1371/journal.pone.0128668.s017", "https://dx.doi.org/10.1371/journal.pone.0128668.s018", "https://dx.doi.org/10.1371/journal.pone.0128668.s019", "https://dx.doi.org/10.1371/journal.pone.0128668.s020", "https://dx.doi.org/10.1371/journal.pone.0128668.s021"], "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_Behavioral_Space_of_Zebrafish_Locomotion_and_Its_Neural_Network_Analog_/1471103", "title"=>"The Behavioral Space of Zebrafish Locomotion and Its Neural Network Analog", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2015-07-01 04:15:02"}

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{"start_date"=>"2015-01-01T00:00:00Z", "end_date"=>"2015-12-31T00:00:00Z", "subject_areas"=>[]}
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