Journal of Computational Neuroscience

, Volume 38, Issue 3, pp 601–616 | Cite as

A network model comprising 4 segmental, interconnected ganglia, and its application to simulate multi-legged locomotion in crustaceans

  • M. Grabowska
  • T. I. Toth
  • C. Smarandache-Wellmann
  • S. Daun-GruhnEmail author


Inter-segmental coordination is crucial for the locomotion of animals. Arthropods show high variability of leg numbers, from 6 in insects up to 750 legs in millipedes. Despite this fact, the anatomical and functional organization of their nervous systems show basic similarities. The main similarities are the segmental organization, and the way the function of the segmental units is coordinated. We set out to construct a model that could describe locomotion (walking) in animals with more than 6 legs, as well as in 6-legged animals (insects). To this end, we extended a network model by Daun-Gruhn and Tóth (Journal of Computational Neuroscience, doi: 10.1007/s10827-010-0300-1, 2011). This model describes inter-segmental coordination of the ipsilateral legs in the stick insect during walking. Including an additional segment (local network) into the original model, we could simulate coordination patterns that occur in animals walking on eight legs (e.g., crayfish). We could improve the model by modifying its original cyclic connection topology. In all model variants, the phase relations between the afferent segmental excitatory sensory signals and the oscillatory activity of the segmental networks played a crucial role. Our results stress the importance of this sensory input on the generation of different stable coordination patterns. The simulations confirmed that using the modified connection topology, the flexibility of the model behaviour increased, meaning that changing a single phase parameter, i.e., gating properties of just one afferent sensory signal was sufficient to reproduce all coordination patterns seen in the experiments.


Central pattern generator Inter-segmental coordination Network model Locomotion Sensory feedback Arthropods 



We would like to thank Dr. A. Büschges for useful discussions in the course of the work. The work was supported by DFG Grants to SDG: DA1182/1-1, GR3690/2-1 and GR3690/4-1.

Conflict of Interest

The authors declare that they have no conflict of interest.


  1. Akay, T., Bässler, U., Gerharz, P., Büschges, A. (2001). The Role of Sensory Signals From the Insect Coxa-Trochanteral Joint in Controlling Motor Activity of the Femur-Tibia Joint. The American Physiological Society Google Scholar
  2. Akay, T., Haehn, S., Schmitz, J., & Büschges, A. (2004). Signals from load sensors underlie interjoint coordination during stepping. Journal of Neurophysiology, 96, 3532–3537.CrossRefGoogle Scholar
  3. Akay, T., Ludwar, B., Goritz, M. L., Schmitz, J., & Büschges, A. (2007). Segment specificity of load signal processing depends on walking direction in the stick insect leg muscle control system. Journal of Neuroscience, 27, 3285–3294.CrossRefPubMedGoogle Scholar
  4. Barnes, W. J. P. (1975). Leg coordination during walking in the crab, Uca pugnax. Journal of Comparative Physiology, 96, 237–256.CrossRefGoogle Scholar
  5. Bässler, U., & Büschges, A. (1998). Pattern generation for stick insect walking movements. Multisensory control of a locomotor program. Brain Research Reviews, 27, 65–68.CrossRefPubMedGoogle Scholar
  6. Borgmann, A., Scharstein, H., & Büschges, A. (2007). Intersegmental coordination: Influence of a single walking leg on the neighboring segments in the stick insect walking system. Journal of Neurophysiology, 98, 1685–1696.CrossRefPubMedGoogle Scholar
  7. Borgmann, A., Hooper, S. L., & Büschges, A. (2009). Sensory feedback induced by front-leg stepping entrains the activity of central pattern generators in caudal segments of the stick insect walking system. Journal of Neuroscience, 29, 2972–2983.CrossRefPubMedGoogle Scholar
  8. Bowerman, R. F. (1977). The control of arthropod walking. Comparative Biochemical and Phvsiology, 56A, 231–247.CrossRefGoogle Scholar
  9. Bucher, D., Akay, T., DiCaprio, R. A., & Büschges, A. (2003). Interjoint coordination in the stick insect leg-control system: the role of positional signaling. Journal of Neurophysiology, 89, 1245–1255.CrossRefPubMedGoogle Scholar
  10. Büschges, A. (1998). Inhibitory synaptic drive patterns motoneuronal activity in rhythmic preparations of isolated thoracic ganglia in the stick insect. Brain Research, 783, 262–271.CrossRefPubMedGoogle Scholar
  11. Büschges, A. (2005). Sensory control and organization of neural networks mediating coordination of multisegmental organs for locomotion. Journal of Neurophysiology, 93, 1127–1135.CrossRefPubMedGoogle Scholar
  12. Büschges, A., Kudwar, B. C., Bucher, D., Schmidt, J., & DiCaprio, R. A. (2004). Synaptic drive contributing to the rhythmic activation of motoneurons in the deafferented stick insect walking system. European Journal of Neuroscience, 19, 1856–1862.CrossRefPubMedGoogle Scholar
  13. Cattaert, D., & Le Ray, D. (2001). Adaptive motor control in crayfish. Progress in Neurobiology, 63, 199–240.CrossRefPubMedGoogle Scholar
  14. Cattaert, D., El Manira, A., Marchand, A., & Clarac, F. (1990). Central control of the sensory afferent terminals from a leg chordotonal organ in crayfish in vitro preparation. Neuroscience Letters, 108, 81–87.CrossRefPubMedGoogle Scholar
  15. Chasserat, C., & Clarac, F. (1983). Quantitative analysis of walking in a decapod crustacean, the rock lobster Jasus lalandii. II. Spatial and temporal regulation of stepping in driven walking. Journal of Experimental Biology, 107, 219–243.Google Scholar
  16. Chrachri, A., & Clarac, F. (1989). Synaptic connections between motor neurons and interneurons in the fourth thoracic ganglion of the crayfish, Procambarus clarkii. Journal of Neurophysiology, 62, 1237–1250.PubMedGoogle Scholar
  17. Clarac, F. (1982). Decapod crustacean leg coordination during walking. In C. F. Herreid & C. R. Fourtner (Eds.), Locomotion and energetics in arthropods (pp. 31–71). New York: Plenum Press.Google Scholar
  18. Clarac, F., & Barnes, W. J. P. (1985). Peripheral influences on the coordination of the legs during walking in decapod crustaceans. In coordination of motor behaviour. In Soc. exp. Biol. Seminar Series 24 (pp. 249–269). Cambridge: Cambridge University Press.Google Scholar
  19. Clarac, F., Wales, W., & Laverack, M. S. (1971). Stress detection at the autotomy plane in the decapod crustacea II. The function of receptors associated with the cuticle of the basi-ischiopodite. Zeitschrift für vergleichende Physiologie, 73, 383–407.CrossRefGoogle Scholar
  20. Clarac, F., Cattaert, D., & Le Ray, D. (2000). Central control components of a ‘simple’ stretch reflex. Trends in Neuroscience, 23, 199–208.CrossRefGoogle Scholar
  21. Collins, J., & Richmond, S. (1994). Hard–wired central pattern generators for quadrupedal locomotion. Biological Cybernetics, 71, 375–385.CrossRefGoogle Scholar
  22. Collins, J., & Stewart, I. (1992). Hexapodal gaits and coupled nonlinear oscillator models. Biological Cybernetics, 68, 287–298.CrossRefGoogle Scholar
  23. Cruse, H. (1985). Which parameters control the leg movement of a walking insect?: I. Velocity control during the stance phase. Journal of Experimental Biology, 116, 343–355.Google Scholar
  24. Cruse, H. (1990). What mechanisms coordinate leg movement in walking arthropods. TINS, 1(13), 15–21.Google Scholar
  25. Cruse, H., & Müller, U. (1986). Two coupling mechanisms which determine the coordination of ipsilateral legs in the walking crayfish. Journal of Experimental Biology, 121, 349–369.Google Scholar
  26. Cruse, H., Dürr, V., Schilling, M., & Schmitz, J. (2009). Principles of insect locomotion. In P. Arena & L. Patanè (Eds.), Spatial Temporal Patterns for Action-Oriented Perception in Roving Robots (pp. 1–57). Berlin: Springer.Google Scholar
  27. Daun, S., Rybak, I. A., & Rubin, J. (2009). The response of a halfcenter oscillator to external drive depends on the intrinsic dynamics of its components: a mechanistic analysis. Journal of Computational Neuroscience, 27, 3–36.CrossRefPubMedCentralPubMedGoogle Scholar
  28. Daun–Gruhn, S. (2011). A mathematical modeling study of inter-segmental coordination during stick insect walking. Journal of Computational Neuroscience. doi: 10.1007/s10827-010-0254-3.Google Scholar
  29. Daun-Gruhn, S., & Toth, T. I. (2011). An inter-segmental network model and its use in elucidating gait-switches in the stick insect. Journal of Computational Neuroscience. doi: 10.1007/s10827-010-0300-1.Google Scholar
  30. Dürr, V., Schmitz, J., & Cruse, H. (2004). Behavior-based modelling of hexapod locomotion: linking biology and technical application. Arthropod Structure and Development, 33, 237–250.CrossRefPubMedGoogle Scholar
  31. Ekeberg, Ö., Blümel, M., & Büschges, A. (2004). Dynamic simulation of insect walking. Arthropod Structure and Development, 33, 287–300.CrossRefPubMedGoogle Scholar
  32. Elson, R. (1996). Neuroanatomy of a crayfish thoracic ganglion: sensory and motor roots of the walking-Leg nerves and possible homologies with insects. Journal of Comparative Neurology, 365, 1–17.CrossRefPubMedGoogle Scholar
  33. Elson, R. C., Sillar, K. T., & Bush, B. M. H. (1992). Identified proprioceptive afferents and motor rhythm entrainment in the crayfish walking system. Journal of Neurophysiology, 67, 530–546.PubMedGoogle Scholar
  34. Grabowska, M. J., Godlewska, E., Schmidt, J., & Daun-Gruhn, S. (2012). Quadrupedal gaits in hexapod animals – inter-leg coordination in free-walking adult stick insects. The Journal of Experimental Biology, 215, 4255–4266.CrossRefPubMedGoogle Scholar
  35. Graham, D. (1985). Pattern and control of walking in insects. Advances in Insect Physiology, 18, 31–140.CrossRefGoogle Scholar
  36. Grillner, S., Markram, H., De Schutter, E., Silberberg, G., & LeBeau, F. E. N. (2005). Microcircuits in action—from CPGs to neocortex. Trends in Neurosciences, 28, 525–533.CrossRefPubMedGoogle Scholar
  37. Hess, D., & Büschges, A. (1999). Role of proprioceptive signals from an insect femur-tibia joint in patterning motoneuronal activity of an adjacent leg joint. Journal of Neurophysiologly, 81, 1856–1865.Google Scholar
  38. Hodgkin, A. L., & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology, 117, 500–544.CrossRefPubMedCentralPubMedGoogle Scholar
  39. Jamom, M., & Clarac, F. (1995). Locomotor patterns in freely moving crayfish (Procambarus clarkii). The Journal of Experimental Biology, 198, 683–700.Google Scholar
  40. Klärner, D., & Barnes, W. J. P. (1986). The cuticular stress detector (CSD2) of the crayfish. II. Activity during walking and influences on the leg coordination. The Journal of Experimental Biology, 122, 161–175.Google Scholar
  41. Klärner, D., & Barth, F. G. (1986). The cuticular stress detector (CSD2) of the crayfish I physiological properties. The Journal of Experimental Biology, 122, 149–159.Google Scholar
  42. Kopell, N., Ermentrout, G. B., & Williams, T. L. (1991). On chains of oscillators forced at one end. SIAM Journal of Applied Mathematics, 51, 1397–1417.CrossRefGoogle Scholar
  43. Libersat, F., Zill, S., & Clarac, F. (1987). Single-unit responses and reflex effects of force sensitive mechanoreceptors of the dactyl of the crab. Journal of Neurophysiology, 57, 1601–1617.PubMedGoogle Scholar
  44. Ludwar, B. C., Göritz, M. L., & Schmidt, J. (2005). Intersegmental coordination of walking movements in stick insects. Journal of Neurophysiology, 93, 1255–1265.CrossRefPubMedGoogle Scholar
  45. MacMillan, D. L. (1975). A physiological analysis of walking in the American Lobster (Homarus americanus). Philosophical Transactions of the Royal Society B, 270, 1–59.CrossRefGoogle Scholar
  46. Matsuoka, K. (1987). Mechanisms of frequency and pattern control in the neural rhythm generators. Biological Cybernetics, 56, 345–353.CrossRefPubMedGoogle Scholar
  47. Müller, U., & Cruse, H. (1991). The contralateral coordination of walking legs in the crayfish Astacus leptodactylus. I. Experimental results. Biologicval Cybernetics, 64, 429–436.CrossRefGoogle Scholar
  48. Parrack, D.W. (1964). Stepping sequences in the crayfish. PhD. Thesis, University of Illinois.Google Scholar
  49. Pearson, K. G. (2000). Neural adaptation in the generation of rhythmic behavior. Annual Reviews in Physiology, 62, 723–753.CrossRefGoogle Scholar
  50. Ritzmann, R. E., & Büschges, A. (2007). Adaptive motor behavior in insects. Current Opinion in Neurobiology, 17, 629–636.CrossRefPubMedGoogle Scholar
  51. Ross, R. B., and Belanger, J. H. (2013). Passive Mechanical Properties of Crustacean Walking Legs. Poster, Sfn, Annual meeting, San Diego Google Scholar
  52. Sillar, K. T., & Skorupski, P. (1986). Central input to primary afferent neurons in the crayfish, Pacifastacus leniusculus, is correlated with rhythmic motor output of thoracic ganglia. Journal of Neurophysiology, 55(4), 678–688.PubMedGoogle Scholar
  53. Sillar, K. T., Skorupski, P., Elson, R. C., & Bush, B. M. H. (1986). Two identified afferent neurones entrain a central locomotor rhythm generator. Nature, 323, 440–443.CrossRefGoogle Scholar
  54. Sillar, I. K., Clarac, F., & Busch, B. M. H. (1987). Intersegmental coordination of central neural oscillators for rhythmic movements of the walking legs in crayfish, Pacifastacus leniusculus. Journal of Experimental Biology, 131, 245–264.Google Scholar
  55. Skinner, K. (1985). The structure of the fourth abdominal ganglion of the crayfish, Procarnbnrus clarhzi (Girard). I. Tracts in the ganglionic core. Journal of Comparative Neurology, 234, 168–181.CrossRefPubMedGoogle Scholar
  56. Skinner, F., Kopell, N., & Marder, E. (1994). Mechanisms for oscillation and frequency control in reciprocally inhibitory model neural networks. Journal of Computational Neuroscience, 1, 69–87.CrossRefPubMedGoogle Scholar
  57. Toth, T.I., Grabowska, M., Rosjat, N., Hellekes, K., Borgmann, A., Daun-Gruhn, S. (2015). Investigating inter-segmental connections between thoracic ganglia in the stick insect by means of experimental and simulated phase response curves. Biological Cybernetics. doi: 10.1007/s00422-015-0647-5
  58. Von Twickel, A., Büschges, A., & Parsemann, F. (2011). Deriving neural network controllers from neuro-biological data: implementation of a single-leg stick insect controller. Biological Cybernetics, 104, 95–119.CrossRefGoogle Scholar
  59. Westmark, S., Oliveira, E. E., & Schmidt, J. (2009). Pharmacological analysis of tonic activity in motoneurons during stick insect walking. Journal of Neurophysiology, 102, 1049–1061.CrossRefPubMedGoogle Scholar
  60. Wilson, D. M. (1966). Insect walking. Annual Review of Entomol, 11, 103–122.CrossRefGoogle Scholar
  61. Zill, S., Schmitz, J., & Büschges, A. (2004). Load sensing and control of posture and locomotion. Arthropod Structure Development, 33, 273–286.CrossRefPubMedGoogle Scholar
  62. Zill, S. N., Keller, B. R., & Duke, E. R. (2009). Sensory signals of unloading in One Leg follow stance onset in another leg: transfer of load and emergent coordination in cockroach walking. Journal of Neurophysiology, 101, 2297–2304.CrossRefPubMedGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • M. Grabowska
    • 1
  • T. I. Toth
    • 1
  • C. Smarandache-Wellmann
    • 2
  • S. Daun-Gruhn
    • 1
    Email author
  1. 1.Heisenberg Research Group of Computational Biology, Department of Animal Physiology, Institute of ZoologyUniversity of CologneCologneGermany
  2. 2.Emmy-Noether Research Group, Department of Animal Physiology, Institute of ZoologyUniversity of CologneCologneGermany

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