Skip to main content
SpringerLink
Log in
Book cover

Advances in the Mathematical Sciences pp 157–172Cite as

Understanding Locomotor Rhythm in the Lamprey Central Pattern Generator

  • Conference paper
  • First Online:

Part of the book series: Association for Women in Mathematics Series ((AWMS,volume 6))

Abstract

The lamprey central pattern generator (CPG) for locomotion consists of a collection of neurons in the spinal cord that is responsible for producing the rhythmic neural activity used for swimming. Mechanoreceptors in the margin of the spinal cord, called edge cells, detect the bending of the body and provide sensory feedback for the CPG. Thus, edge cells are essential for the CPG’s ability to respond to perturbations. To investigate the CPG’s response to perturbations during swimming, we compute entrainment ranges for stochastic bending signals where Gaussian band-limited white noise is added on top of a sinusoidal signal. Experimentally, the lamprey spinal cord was bent back-and-forth to entrain the CPG’s rhythm, and then Gaussian band-limited white noise was added to the sensory stimulus. Correspondingly, we also developed mathematical models of the CPG circuit. Using the same stimuli in the models as was used in the experiment, we examine which properties of the CPG circuit are related to the observed experimental results.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. A. Borgmann, S.L. Hooper, A. Büschges, Sensory feedback induced by front-leg stepping entrains the activity of central pattern generators in caudal segments of the stick insect walking system. J. Neurosci. 21(9), 2972–2983 (2009)

    Google Scholar 

  2. J.T. Buchanan, Identification of interneurons with contralateral, caudal axons in the lamprey spinal cord: Synaptic interactions and morphology. J. Neurophys. 47, 961–975 (1982)

    Google Scholar 

  3. A.H. Cohen, G.B. Ermentrout, T. Kiemel, N. Kopell, K.A. Sigvardt, T.L. Williams, Modeling of intersegmental coordination in the lamprey central pattern generator for locomotion. Trends Neurosci. 15, 434–438 (1992)

    Article  Google Scholar 

  4. A.H. Cohen, P.J. Holmes, R.H. Rand, The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: A mathematical model. J. Exp. Biol. 116, 345–369 (1982)

    MathSciNet  MATH  Google Scholar 

  5. A.H. Cohen, P. Wallén, The neuronal correlate of locomotion in fish. ‘Fictive swimming’ induced in an in vitro preparation of the lamprey. Exp. Brain Res. 41, 11–18 (1980)

    Article  Google Scholar 

  6. Ö. Ekeberg, A combined neuronal and mechanical model of fish swimming. Biol. Cybern. 69, 363–374 (1993)

    Google Scholar 

  7. Ö. Ekeberg, S. Grillner, Simulations of neuromuscular control in lamprey swimming. Phil. Trans. Roy. Soc. Lond. B 354(1385), 895–902 (1999)

    Google Scholar 

  8. N.I. Fisher. Statistical Analysis of Circular Data. (Cambridge University Press, cambridge, 1995)

    Google Scholar 

  9. S. Grillner, On the generation of locomotion in the spinal dogfish. Exp. Brain Res. 20, 459–470 (1974)

    Article  Google Scholar 

  10. S. Grillner, The motor infrastructure: from ion channels to neuronal networks. Nat. Rev. Neurosci. 4, 573–586 (2003)

    Article  Google Scholar 

  11. S. Grillner, A. McClellan, C. Perret, Entrainment of the spinal pattern generators for swimming by mechanosensitive elements in the lamprey spinal cord in vitro. Brain Res. 217, 380–386 (1981)

    Article  Google Scholar 

  12. S. Grillner, T. Williams, P.-Å. Lagerbäck, The edge cell, a possible intraspinal mechanoreceptor. Science 223(4635), 500–503 (1984)

    Google Scholar 

  13. J. Guckenheimer, P. Holmes. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. (Springer, Berlin, 1990)

    Google Scholar 

  14. F.C. Hoppensteadt, E.M. Izhikevich, Weakly Connected Neural Networks (Springer, New York, 1997)

    Book  MATH  Google Scholar 

  15. O. Kiehn, Locomotor circuits in the mammalian spinal cord. Ann. Rev. Neurosci. 29(1), 279–306 (2006)

    Article  Google Scholar 

  16. T. Kiemel, K.M. Gormley, L. Guan, T.L. Williams, A.H. Cohen, Estimating the strength and direction of functional coupling in the lamprey spinal cord. J. Comput. Neurosci. 15, 233–245 (2003)

    Article  Google Scholar 

  17. N. Kopell, G.B. Ermentrout, T.L. Williams, On chains of oscillators forced at one end. SIAM J. Appl. Math. 51, 1397–1417 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  18. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, 1984)

    Book  MATH  Google Scholar 

  19. E. Marder, D. Bucher, Central pattern generators and the control of rhythmic movements. Curr. Biol. 11(23), 986–996 (2001)

    Article  Google Scholar 

  20. N. Massarelli, G. Clapp, K. Hoffman, T. Kiemel. Entrainment ranges for chains of forced neural and phase oscillators. J. Math. Neurosci. 6(6), (2016). doi:10.1186/s13408-016-0038-9

  21. A.D. McClellan, Brainstem command system for locomotion in the lamprey: localization of descending pathways in the spinal cord. Brain Res. 457(2), 338–349 (1988)

    Article  Google Scholar 

  22. A.D. McClellan, K. Sigvardt, Features of entrainment of spinal pattern generators for locomotor activity in the lamprey. J. Neurosci. 8, 133–145 (1988)

    Google Scholar 

  23. D.L. McLean, M.E. Higashijima, J.R. Fetcho, A topographic map of recruitment in the spinal cord. Nature 446(7131), 71–75 (2007)

    Article  Google Scholar 

  24. J. Neu, Large populations of coupled chemical oscillators. SIAM J. Appl. Math 38(2), 305–316 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  25. J. Neu, The method of near-identity transformations and its applications. SIAM J. Appl. Math 38(2), 189–208 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  26. K.G. Pearson, S. Rossignol, Fictive motor patterns in chronic spinal cats. J. Neurophysiol. 66(6), 1874–1887 (1991)

    Google Scholar 

  27. G. Viana di Prisco, P. Wallen, S. Grillner, Synaptic effects of intraspinal stretch-receptor neurons mediating movement-related feedback during locomotion. Brain Res. 530, 161–166 (1990)

    Google Scholar 

  28. C.M. Rovainen, Synaptic interactions of identified nerve cells in the spinal cord of the sea lamprey. J. Comp. Neurol. 154, 189–206 (1974)

    Article  Google Scholar 

  29. E.D. Tytell, A.H. Cohen, Rostral versus caudal differences in mechanical entrainment of the lamprey central pattern generator for locomotion. J. Neurophys. 99(5), 2408–2419 (2008)

    Article  Google Scholar 

  30. P.L. Várkonyi, T. Kiemel, K.A. Hoffman, A.H. Cohen, P. Holmes, On the derivation and tuning of phase oscillator models for lamprey central pattern generators. J. Comp. Neurosci. 25(2), 245–261 (2008)

    Google Scholar 

  31. P. Wallen, T. Williams, Fictive locomotion in the lamprey spinal cord in vitro compared with swimming in the intact and spinal animal. J. Physiol. 347, 225–239 (1984)

    Article  Google Scholar 

  32. J.C. Weeks, Neuronal basis of leech swimming: separation of swim initiation, pattern generation, and intersegmental coordination by selective lesions. J. Neurophysiol. 45(4), 698–723 (1981)

    Google Scholar 

  33. T.L. Williams, Phase coupling by synaptic spread in chains of coupled neuronal oscillators. Science 258, 662–665 (1992)

    Article  Google Scholar 

  34. T.L. Williams, K.A. Sigvardt, Intersegmental phase lags in the lamprey spinal cord: Experimental confirmation of the existence of a boundary region. J. Comput. Neurosci. 1, 61–67 (1994)

    Article  Google Scholar 

  35. T.L. Williams, K.A. Sigvardt, N. Kopell, G.B. Ermentrout, M.P. Remler, Forcing of coupled nonlinear oscillators: Studies of intersegmental coordination in the lamprey locomotor central pattern generator. J. Neurophys. 64, 862–871 (1990)

    Google Scholar 

  36. D.M. Wilson, The central nervous control of flight in a locust. J. Exp. Biol. 38(2), 471–490 (1961)

    Google Scholar 

Download references

Acknowledgments

The authors wish to acknowledge that this work was partially funded by NSF Grant DBI-RCN 1062052, NSF Grant BCS-123011. This material is based upon work supported by, or in part by, the U.S. Army Research Laboratory and the U.S. Army Research Office under contract/grant number W911NF-14-1-0268.

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, MD, 21250, USA

    Nicole Massarelli & Kathleen Hoffman

  2. Tufts University, Medford, MA, 02155, USA

    Allan Yau

  3. Department of Kinesiology, University of Maryland, College Park, MD, 20742, USA

    Tim Kiemel

  4. Department of Biology, Tufts University, Medford, MA, 02155, USA

    Eric Tytell

Authors
  1. Nicole Massarelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Allan Yau
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kathleen Hoffman
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Tim Kiemel
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Eric Tytell
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kathleen Hoffman .

Editor information

Editors and Affiliations

  1. National Security Agency , Fort Meade, Maryland, USA

    Gail Letzter

  2. Microsoft Research, Redmond, Washington, USA

    Kristin Lauter

  3. Department of Mathematics & Comp. Sci., Saint Louis University Department of Mathematics & Comp. Sci., Saint Louis, Missouri, USA

    Erin Chambers

  4. Department of Statistics, University of Missouri–Columbia, Columbia, Missouri, USA

    Nancy Flournoy

  5. Department of Mathematics , Boston College Department of Mathematics, Chestnut Hill, Massachusetts, USA

    Julia Elisenda Grigsby

  6. National Security Agency , Fort Meade, Maryland, USA

    Carla Martin

  7. Department of Mathematics & Comp. Sci., DeSales University Department of Mathematics & Comp. Sci., Center Valley, Pennsylvania, USA

    Kathleen Ryan

  8. Department of Mathematics, University of Maryland Department of Mathematics, College Park, Maryland, USA

    Konstantina Trivisa

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Massarelli, N., Yau, A., Hoffman, K., Kiemel, T., Tytell, E. (2016). Understanding Locomotor Rhythm in the Lamprey Central Pattern Generator. In: Letzter, G., et al. Advances in the Mathematical Sciences. Association for Women in Mathematics Series, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-319-34139-2_6

Download citation

Publish with us

Policies and ethics

Search

Navigation