Advertisement

Biological Cybernetics

, Volume 92, Issue 3, pp 206–218 | Cite as

Travelling wave patterns in a model of the spinal pattern generator using spiking neurons

  • Alexander KaskeEmail author
  • Nils Bertschinger
Article

Abstract.

The aim of this study is to produce travelling waves in a planar net of artificial spiking neurons. Provided that the parameters of the waves – frequency, wavelength and orientation – can be sufficiently controlled, such a network can serve as a model of the spinal pattern generator for swimming and terrestrial quadruped locomotion. A previous implementation using non-spiking, sigmoid neurons lacked the physiological plausibility that can only be attained using more realistic spiking neurons. Simulations were conducted using three types of spiking neuronal models. First, leaky integrate-and-fire neurons were used. Second, we introduced a phenomenological bursting neuron. And third, a canonical model neuron was implemented which could reproduce the full dynamics of the Hodgkin–Huxley neuron. The conditions necessary to produce appropriate travelling waves corresponded largely to the known anatomy and physiology of the spinal cord. Especially important features for the generation of travelling waves were the topology of the local connections – so-called off-centre connectivity – the availability of dynamic synapses and, to some extent, the availability of bursting cell types. The latter were necessary to produce stable waves at the low frequencies observed in quadruped locomotion. In general, the phenomenon of travelling waves was very robust and largely independent of the network parameters and emulated cell types.

Keywords

Spinal Cord Pattern Generator Model Neuron Wave Pattern Network Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alford, S, Christenson, J, Grillner, S 1991Presynaptic GABAA and GABAB receptor-mediated phasic modulation in axons of spinal motor interneuronsEur J Neurosci310711Google Scholar
  2. Batueva, ,IV, Buchanan, JT, Veselkin, NP, Suderevskaya, EI, Tsetkov, EA 2002aThe effects of serotonin on functionally diverse isolated lamprey spinal cord neuronsNeurosci Behav Physiol3299101Google Scholar
  3. Batueva, ,IV, Buchanan, JT, Veselkin, NP, Suderevskaya, EI, Tsetkov, EA 2002bSerotonin modulates oscillations of the membrane potential in isolated spinal neurons from lampreysNeurosci Behav Physiol32195203Google Scholar
  4. Beer, RD, Chiel, HJ, Gallagher, JC 1999Evolution and analysis of model CPGs for walking: General principles and individual variabilityJ Comput Neurosci7119147Google Scholar
  5. Bekkof, A 1985Development of locomotion in vertebrates: a comparative perspectiveGallin, ES eds. Comparative development of adaptive skills: evolutionary implicationEarlsbaumHillsdale, NJ5794Google Scholar
  6. Bem, T, Cabelguen, JM, Ekeberg, Ö, Grillner, S 2003From swimming to walking: a single basic network for two different behaviorsBiol Cybern887990CrossRefPubMedGoogle Scholar
  7. Bennet, WO, Simons, RS, Brainerd, EL 2001Twisting and bending: the functional role of salamander lateral hypaxial musculatire during locomotionJ Exp Biol20419791989Google Scholar
  8. Bonnot A, Whelan PJ, Mentis GZ, O’Donavan M (2002) Spatiotemporal pattern of motoneuron activation in the rostral lumbar and the sacral segments during locomotor-like activity in the neonatal mouse spinal cord. J Neurosci 22:RC203 (1–6)Google Scholar
  9. Bowtell, G, Williams, TL 1991Anguilliform body dynamics: modeling the interaction between muscle activation and body curvaturePhil Trans Biol Sci334385390Google Scholar
  10. Buchanan, JT 1982Identification of interneurons with contralateral, caudal axons in the lamprey spinal cord: synaptic interactions and morphologyJ Neurophysiol47961975Google Scholar
  11. Buchanan, JT, Grillner, S, Cullheim, S, Risling, M 1989Identification of excitatory interneurons contributing to generation of locomotion in lamprey: structure, pharmacology, and functionJ Neurophysiol625969Google Scholar
  12. Christenson, J, Bongianni, F, Grillner, S, Hökfelt, T 1991Putative GABAergic input to axons of spinal interneurons and primary sensory neurons in the lamprey spinal cord as shown by intracellular Luzifer yellow and GABA immunohistochemistryBrain Res538313318Google Scholar
  13. Christenson, J, Shupliakov, O, Cullheim, S, Grillner, S 1993Possible morphological substrates for GABA-mediated presynaptic inhibition in the lamprey spinal cordJ Comp Neurol328463472Google Scholar
  14. Cina, C, Hochman, S 2000Diffuse distribution of sulphorhodamine-labeled neurons during serotonin-evoked locomotion in the neonatal rat thoracolumbal spinal cordJ Comp Neurol423590602Google Scholar
  15. Cohen, AH 1988Evolution of the vertebrate central pattern generator for locomotionCohen, AHRossignol, SGrillner, S eds. Neural control of rhythmic movements in vertebratesWileyNew York129166Google Scholar
  16. Collins, JJ 1995The redundant nature of locomotor optimization lawsJ Biomech28251267Google Scholar
  17. Devolve’I, , Bem, T, Cabelgruen, JM 1997Epaxial and limb muscle actitivty during swimming and terrestrial stepping in the adult newt, Pleurodeles waltlJ Neurophysiol78638650Google Scholar
  18. El, Manira A, Tegner, J, Grillner, S 1997Locomotor-related presynaptic modulation of primary afferents in lampreyEur J Neurosci9696705Google Scholar
  19. Farley, CT, Ko, TC 1997Mechanics of locomotion in lizardsJ Exp Biol20021772188Google Scholar
  20. Frolich, LM, Biewener, AA 1992Kinematic and electromyographic analysis of the functional role of the body axis during terrestrial and aquatic locomotion in the salamader Ambystoma tigrinumJ Exp Biol162107130Google Scholar
  21. Gans, C 1975Tetrapod limblessness: evolution and functional corrolariesAm Zool15455467Google Scholar
  22. Gerber, G, Zhong, J, Young, D, Randic, M 2000Group II and group III metabotropic glutamate receptor agonists depress synaptic transmission in the rat spinal cord dorsal hornNeuroscience100393406Google Scholar
  23. Gerhart, J, Kirschner, M 1997Cells, embryos and evolutionBlackwellOxfordGoogle Scholar
  24. Golomb, D, Amitai, Y 1997Propagating neuronal discharges in neocortical slices: computational and experimental studyJ Neurophysiol7811991211Google Scholar
  25. Golomb, D, Ermentrout, GB 1999Continous and lurching traveling pulses in neuronal networks with delay and spatially decaying connectivityProc Natl Acad Sci USA961348013485Google Scholar
  26. Golomb, D, Ermentrout, GB 2001Bistability in pulse propagation in networks of excitatory and inhibitory populationsPhys Rev Lett8641794182Google Scholar
  27. Golubitsky, M, Stewart, I, Buono, PL, Collins, JJ 1999Symmetry in locomotor central pattern generators and animal gaitsNature401693695CrossRefPubMedGoogle Scholar
  28. Gupta, A, Wang, Y, Markram, H 2000Organizing principles for a diversity of gabaergic interneurons and synapses in the neocortexScience287273279Google Scholar
  29. Gustafsson, JS, Birinyi, A, Crum, J, Ellisman, M, Brodin, L, Shupliakov, O 2002Ultrastructural organization of lamprey reticulospinal synapses in three dimensionsJ Comp Neurol450167182Google Scholar
  30. Hoppensteadt, FC, Izhikevich, EM 2002Canonical Neural ModelsArbib, MA eds. Brain Theory and Neural NetworksSecondThe MIT pressCambridge, MA181186Google Scholar
  31. Gutkin, BS, Ermentrout, GB 1998Dynamics of membrane excitability determine interspike interval variability: a link between spike generation mechanism and cortical spike train statisticsNeural Comput1910471065Google Scholar
  32. Ijspeert, AJ 2001A connectionist central pattern generator for the aquatic and terrestrial gaits of a simulated salamanderBiol Cybern84331348Google Scholar
  33. Izhikevich, E 2003Simple model of spiking neuronsIEEE Trans Neural Netw1415691572Google Scholar
  34. Kafkafi, N, Golani, I 1998A travelling wave of lateral movement coordinates both turning and forward walking un the ferretBiol Cybern78441453Google Scholar
  35. Kaske, A, Winberg, G, Coster, J 2003Emergence of coherent traveling waves controlling quadruped gaits in a two dimensional spinal cord modelBiol Cybern882032Google Scholar
  36. Kistler, WM 2000Stability properties of solitary waves and periodic wave trains in a two-dimensional network of spiking neuronsPhys Rev E6288348837Google Scholar
  37. Kopel, N, Ermentrout, GB 1986Symmetry and phase locking in chains of weakly coupled oscillatorsCommun Pure Appl Math39623660Google Scholar
  38. Kotaleski, JH, Grillner, S, Lansner, A 1999Neural mechanisms potentially contributing to the intersegmental phase lag in lampreyBiol Cybern81317330Google Scholar
  39. Li, WC, Perrins, R, Walford, A, Roberts, A 2002The neuronal targets for GABAergic reticulospinal inhibition that stops swimming in hatchling frog tadpolesJ Comp Physiol A Neuroethol Sens Neural Behav Physiol1892937Google Scholar
  40. Li, Y, Burke, RE 2002Developmental changes in short-term synaptic depression in the neonatal mouse spinal cordJ Neurophysiol8832183231Google Scholar
  41. Maass, W, Natschläger, T 2002Real-time computing without stable states: a new framework for neural computation based on perturbationsNeural Comput1425312560Google Scholar
  42. MacLean, JN, Schmidt, BJ 2001Voltage-sensitivity of motoneuron NMDA receptor channels is modulated by serotonin in the neonatal rat spinal cordJ Neurophysiol8611311138Google Scholar
  43. Markram, H, Wang, Y, Tsodyks, M 1998Differential signalling via the same axon of neocortical pyramidal neuronsProc Natl Acad Sci USA9553235328Google Scholar
  44. Matsushimi, T, Grillner, S 1990Intersegmental coordination of undulatory movements – a “trailing oscillator” hypothesisNeuroreport15465Google Scholar
  45. Natschläger, T, Maass, W 2001Computing the optimally fitted spike train for a synapseNeural Comput1323772394Google Scholar
  46. O’Donovan, M, Ho, S, Yee, W 1994Calcium imaging of rhythmic network activity in the developing spinal cord of the chick embryoJ Neurosci1463546369Google Scholar
  47. Orlovsky, GN, Deliagina, TG, Grillner, S 1999Neuronal control of locomotionOxford University PressOxfordGoogle Scholar
  48. Osan, R, Ermentrout, B 2001Two dimensional synaptically generated traveling waves in a theta-neuron neural networkNeurocomputing38–40789795Google Scholar
  49. Osan, R, Ermentrout, B 2002The evolution of synaptically generated waves in one- and two-dimensional domainsPhysica D163217235Google Scholar
  50. Puskar, Z, Antal, M 1997Localisation of last-order premotor interneurons in the lumbar spinal cord of ratsJ Comp Neurol389377389Google Scholar
  51. Rexed, B 1952The cytoarchitectonic organization of the spinal cord in the catJ Comp Neurol96415496Google Scholar
  52. Rinzel, J, Terman, D, Wang, XJ, Ermentrout,  1998Propagating activity patterns in large-scale inhibitory neuronal networksScience27913511355Google Scholar
  53. Ritter, D 1992Lateral bending during lizard locomotionJ Exp Biol173110Google Scholar
  54. Ritter, D 1996Axial muscle function during lizard locomotionJ Exp Biol19924992510Google Scholar
  55. Roberts, A, Soffe, SR, Wolf, ES, Yoshida, M, Zhao, FY 1998Central circuits controlling locomotion in young tadpolesAnn NY Acad Sci8601934Google Scholar
  56. Roos, PJ 1964Lateral bending in newt locomotionProc Ned Acad Wetten C67223232Google Scholar
  57. Tanabe, M, Kaneko, T 1996Paired pulse facilitation of GABAergic IPSCs in ventral horn neurons in neonatal rat spinal cordBrain Res716101106Google Scholar
  58. Tyson, JJ 1994What evertone should know about the Belousov–Zhabotinsky reactionLect Notes Biomath100569587Google Scholar
  59. Wallen, P, Shupliakov, O, Hill, RH 1993Origin of phasic synaptic inhibition in myotomal motoneurons during fictive locomotion in lampreyExp Brain Res96194202Google Scholar
  60. Wheatley, M, Edamura, M, Stein, RB 1992A comparison of intact and in-vitro locomotion in an adult amphibianExp Brain Res88609614Google Scholar
  61. Yakovenko, S, Mushawar, V, VanderHorst, V, Holstege, G, Prochazka, A 2002Spatiotemporal activation of lumbosacral motoneurons in the locomotor step cycleJ Neurophys8715421553Google Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Institute for Theoretical Computer ScienceTechnische Universität GrazGrazAustria
  2. 2.KölnGermany

Personalised recommendations