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Dimensionality and Dynamics in the Behavior of C. elegans

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  • Greg J Stephens
  • Bethany Johnson-Kerner
  • William Bialek
  • William S Ryu

Abstract

A major challenge in analyzing animal behavior is to discover some underlying simplicity in complex motor actions. Here, we show that the space of shapes adopted by the nematode Caenorhabditis elegans is low dimensional, with just four dimensions accounting for 95% of the shape variance. These dimensions provide a quantitative description of worm behavior, and we partially reconstruct “equations of motion” for the dynamics in this space. These dynamics have multiple attractors, and we find that the worm visits these in a rapid and almost completely deterministic response to weak thermal stimuli. Stimulus-dependent correlations among the different modes suggest that one can generate more reliable behaviors by synchronizing stimuli to the state of the worm in shape space. We confirm this prediction, effectively “steering” the worm in real time.Author Summary: A great deal of work has been done in characterizing the genes, proteins, neurons, and circuits that are involved in the biology of behavior, but the techniques used to quantify behavior have lagged behind the advancements made in these areas. Here, we address this imbalance in a domain rich enough to allow complex, natural behavior yet simple enough so that movements can be explored exhaustively: the motions of Caenorhabditis elegans freely crawling on an agar plate. From measurements of the worm's curvature, we show that the space of natural worm postures is low dimensional and can be almost completely described by their projections along four principal “eigenworms.” The dynamics along these eigenworms offer both a quantitative characterization of classical worm movement such as forward crawling, reversals, and Omega-turns, and evidence of more subtle behaviors such as pause states at particular postures. We can partially construct equations of motion for this shape space, and within these dynamics we find a set of attractors that can be used as a rigorous definition of behavioral state. Our observations of C. elegans reveal a precise and complete language of motion and new aspects of worm behavior. We believe this is a lesson with promise for other organisms.

Suggested Citation

  • Greg J Stephens & Bethany Johnson-Kerner & William Bialek & William S Ryu, 2008. "Dimensionality and Dynamics in the Behavior of C. elegans," PLOS Computational Biology, Public Library of Science, vol. 4(4), pages 1-10, April.
    • Handle: RePEc:plo:pcbi00:1000028
    DOI: 10.1371/journal.pcbi.1000028
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    References listed on IDEAS

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    1. Gürol M. Süel & Jordi Garcia-Ojalvo & Louisa M. Liberman & Michael B. Elowitz, 2006. "An excitable gene regulatory circuit induces transient cellular differentiation," Nature, Nature, vol. 440(7083), pages 545-550, March.
    2. Leslie C. Osborne & Stephen G. Lisberger & William Bialek, 2005. "A sensory source for motor variation," Nature, Nature, vol. 437(7057), pages 412-416, September.
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    Cited by:

    1. Jeffrey P Nguyen & Ashley N Linder & George S Plummer & Joshua W Shaevitz & Andrew M Leifer, 2017. "Automatically tracking neurons in a moving and deforming brain," PLOS Computational Biology, Public Library of Science, vol. 13(5), pages 1-19, May.
    2. Laetitia Hebert & Tosif Ahamed & Antonio C Costa & Liam O’Shaughnessy & Greg J Stephens, 2021. "WormPose: Image synthesis and convolutional networks for pose estimation in C. elegans," PLOS Computational Biology, Public Library of Science, vol. 17(4), pages 1-20, April.
    3. Stanislav Nagy & Marc Goessling & Yali Amit & David Biron, 2015. "A Generative Statistical Algorithm for Automatic Detection of Complex Postures," PLOS Computational Biology, Public Library of Science, vol. 11(10), pages 1-23, October.
    4. Steffen Werner & Jochen C Rink & Ingmar H Riedel-Kruse & Benjamin M Friedrich, 2014. "Shape Mode Analysis Exposes Movement Patterns in Biology: Flagella and Flatworms as Case Studies," PLOS ONE, Public Library of Science, vol. 9(11), pages 1-21, November.
    5. Li-Chun Lin & Han-Sheng Chuang, 2017. "Analyzing the locomotory gaitprint of Caenorhabditis elegans on the basis of empirical mode decomposition," PLOS ONE, Public Library of Science, vol. 12(7), pages 1-14, July.
    6. Elke Braun & Bart Geurten & Martin Egelhaaf, 2010. "Identifying Prototypical Components in Behaviour Using Clustering Algorithms," PLOS ONE, Public Library of Science, vol. 5(2), pages 1-15, February.
    7. Christophe Restif & Carolina Ibáñez-Ventoso & Mehul M Vora & Suzhen Guo & Dimitris Metaxas & Monica Driscoll, 2014. "CeleST: Computer Vision Software for Quantitative Analysis of C. elegans Swim Behavior Reveals Novel Features of Locomotion," PLOS Computational Biology, Public Library of Science, vol. 10(7), pages 1-12, July.
    8. Chang Woo Ji & Young-Seuk Park & Yongde Cui & Hongzhu Wang & Ihn-Sil Kwak & Tae-Soo Chon, 2020. "Analyzing the Response Behavior of Lumbriculus variegatus (Oligochaeta: Lumbriculidae) to Different Concentrations of Copper Sulfate Based on Line Body Shape Detection and a Recurrent Self-Organizing ," IJERPH, MDPI, vol. 17(8), pages 1-15, April.
    9. Chongbin Zheng & Evelyn Tang, 2024. "A topological mechanism for robust and efficient global oscillations in biological networks," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    10. Markus Reischl & Mazin Jouda & Neil MacKinnon & Erwin Fuhrer & Natalia Bakhtina & Andreas Bartschat & Ralf Mikut & Jan G Korvink, 2019. "Motion prediction enables simulated MR-imaging of freely moving model organisms," PLOS Computational Biology, Public Library of Science, vol. 15(12), pages 1-16, December.
    11. Sepideh Bazazi & Frederic Bartumeus & Joseph J Hale & Iain D Couzin, 2012. "Intermittent Motion in Desert Locusts: Behavioural Complexity in Simple Environments," PLOS Computational Biology, Public Library of Science, vol. 8(5), pages 1-10, May.

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