Letter | Published:

Network control principles predict neuron function in the Caenorhabditis elegans connectome

Nature volume 550, pages 519523 (26 October 2017) | Download Citation

Abstract

Recent studies on the controllability of complex systems offer a powerful mathematical framework to systematically explore the structure–function relationship in biological, social, and technological networks1,2,3. Despite theoretical advances, we lack direct experimental proof of the validity of these widely used control principles. Here we fill this gap by applying a control framework to the connectome of the nematode Caenorhabditis elegans4,5,6, allowing us to predict the involvement of each C. elegans neuron in locomotor behaviours. We predict that control of the muscles or motor neurons requires 12 neuronal classes, which include neuronal groups previously implicated in locomotion by laser ablation7,8,9,10,11,12,13, as well as one previously uncharacterized neuron, PDB. We validate this prediction experimentally, finding that the ablation of PDB leads to a significant loss of dorsoventral polarity in large body bends. Importantly, control principles also allow us to investigate the involvement of individual neurons within each neuronal class. For example, we predict that, within the class of DD motor neurons, only three (DD04, DD05, or DD06) should affect locomotion when ablated individually. This prediction is also confirmed; single cell ablations of DD04 or DD05 specifically affect posterior body movements, whereas ablations of DD02 or DD03 do not. Our predictions are robust to deletions of weak connections, missing connections, and rewired connections in the current connectome, indicating the potential applicability of this analytical framework to larger and less well-characterized connectomes.

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Acknowledgements

We thank M. Angulo, J. Gao, Y.-Y. Liu, J.-J. Slotine, K. Albrecht, S. P. Cornelius, and A. Li for discussions, and L. Grundy, A. Brown, and E. Yemini for help with analysis of tracking data. We are grateful to V. Butler and the Caenorhabditis Genetics Center, which is funded by National Institutes of Health Office of Research Infrastructure Programs (P40 OD010440), for C. elegans strains. This work is supported by the John Templeton Foundation: Mathematical and Physical Sciences grant number PFI-777; European Commission grant number 641191 (CIMPLEX); Medical Research Council grant number MC-A023-5PB91; Wellcome Trust grant number WT103784MA. P.E.V. is supported by the Medical Research Council grant number MR/K020706/1. Y.L.C. is supported by an EMBO Long Term Fellowship.

Author information

Author notes

    • Gang Yan
    • , Petra E. Vértes
    •  & Emma K. Towlson

    These authors contributed equally to this work.

Affiliations

  1. Center for Complex Network Research and Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA

    • Gang Yan
    • , Emma K. Towlson
    •  & Albert-László Barabási
  2. School of Physics Science and Engineering, Tongji University, Shanghai 200092, China

    • Gang Yan
  3. Department of Psychiatry, Behavioural and Clinical Neuroscience Institute, University of Cambridge, Cambridge CB2 0SZ, UK

    • Petra E. Vértes
  4. Division of Neurobiology, MRC Laboratory of Molecular Biology, Cambridge Biomedical Campus, Francis Crick Avenue, Cambridge CB2 0QH, UK

    • Yee Lian Chew
    • , Denise S. Walker
    •  & William R. Schafer
  5. Center for Cancer Systems Biology, Dana Farber Cancer Institute, Boston, Massachusetts 02115, USA

    • Albert-László Barabási
  6. Department of Medicine, Brigham and Women’s Hospital, Harvard Medical School, Boston, Massachusetts 02115, USA

    • Albert-László Barabási
  7. Center for Network Science, Central European University, H-1051 Budapest, Hungary

    • Albert-László Barabási

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Contributions

A.-L.B., G.Y., and P.E.V. conceived the project. G.Y. did the control analysis. P.E.V. and E.K.T. analysed the results. W.R.S. conceived the experimental validation. Y.L.C. and D.S.W. planned and performed the new experiments. Y.L.C. and W.R.S. analysed the experimental data, and W.R.S. and A.-L.B. discussed the results. A.-L.B., E.K.T., W.R.S., P.E.V., and G.Y. wrote the manuscript, Y.L.C. and D.S.W. edited it. G.Y., Y.L.C., and D.S.W. wrote the Supplementary Information, and W.R.S., E.K.T., and P.E.V. edited it.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Albert-László Barabási.

Reviewer Information Nature thanks C. Bargmann, E. Izquierdo and M. Zhen for their contribution to the peer review of this work.

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Supplementary information

PDF files

  1. 1.

    Supplementary Information

    This file contains the Supplementary Methods and Discussion. It provides details of the mathematical framework, experimental set-up and detailed results, and additional analyses. It also contains Supplementary Tables 1-3, which provide the statistical descriptions of the experimental observations.

  2. 2.

    Reporting Summary

Videos

  1. 1.

    Mock ablation (DD) sample video

    Shown is a short clip from the video mockDD_onfood_L_2016_10_29__13_13_35___7___6_seg.avi. The entire clip is available at https://figshare.com/s/72716a92be1ab0f1e1d4#/articles/5087020

  2. 2.

    DD5 ablation sample video

    Shown is a short clip from the video DD5_onfood_L_2016_10_29__13_13_25___5___6_seg. The entire clip is available at https://figshare.com/s/72716a92be1ab0f1e1d4#/articles/5087020.Shown is a short clip from the video DD5_onfood_L_2016_10_29__13_13_25___5___6_seg. The entire clip is available at https://figshare.com/s/72716a92be1ab0f1e1d4#/articles/5087020.

  3. 3.

    DD2 ablation sample video

    Shown is a short clip from the video DD2_onfood_R_2016_10_30__12_13_57___7___4_seg. The entire clip is available at https://figshare.com/s/72716a92be1ab0f1e1d4#/articles/5087020.

  4. 4.

    Mock ablation (PDB) sample video

    Shown is a short clip from the video mockPDB_on_food_L_2016_11_03__14_16_37___7___1_seg. The animal is executing a ventral omega turn. The entire clip is available at https://figshare.com/s/72716a92be1ab0f1e1d4#/articles/5087020

  5. 5.

    PDB ablation sample video 1

    Shown is a short clip from the video ablPDB_on_food_L_2016_11_03__14_40_04___4___2_seg. The animal is executing a dorsal omega turn. The entire clip is available at https://figshare.com/s/72716a92be1ab0f1e1d4#/articles/5087020.

  6. 6.

    PDB ablation sample video 2

    Shown is a short clip from the video ablPDB_on_food_L_2016_10_22__13_23_05___5___3_seg. The animal is executing a dorsal omega turn. The entire clip is available at https://figshare.com/s/72716a92be1ab0f1e1d4#/articles/5087020

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https://doi.org/10.1038/nature24056

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