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The Physics of the Mind and Brain Disorders pp 155–174Cite as

From Symmetry to Symmetry-Breaking in Locomotion

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Part of the book series: Springer Series in Cognitive and Neural Systems ((SSCNS,volume 11))

Abstract

The locomotor system is a hierarchical mechanism consisting of several functional components, including the decision mechanism, navigation map, locomotion command, central pattern generators and the EMG muscle activity patterns. In this chapter we discuss the role of symmetry/asymmetry and symmetry breaking of neural states during the emergence of locomotion and movement. We review recent results that show that inhibition plays a critical role in decision making, in the formation of grid cells and place cells for navigation, the locomotor command and central pattern generators. We employ the analogy with symmetry breaking in physical systems where at a bifurcation point on the phase diagram, infinitesimal perturbations result in a transition to a new global attractor state. This observation may have major implications for both understanding normal locomotion and therapeutics of spinal cord injury, as triggered by neuromodulatory/inhibitory causes.

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References

  • Anderson PW (1997) Basic notions of condensed matter physics. Addison-Wesley Reading, Boston

    Google Scholar 

  • Barbeau H, Rossignol S (1990) The effects of serotonergic drugs on the locomotor pattern and on cutaneous reflexes of the adult chronic spinal cat. Brain Res 514:55–67

    Article  CAS  Google Scholar 

  • Bras H, Jankowska E, Noga B, Skoog B (1990) Comparison of effects of various types of NA and 5-HT agonists on transmission from group II muscle afferents in the cat. Eur J Neurosci 2:1029–1039

    Article  Google Scholar 

  • Brocard F, Ryczko D, Fénelon K, Hatem R, Gonzales D, Auclair F, Dubuc R (2010) The transformation of a unilateral locomotor command into a symmetrical bilateral activation in the brainstem. J Neurosci 30:523–533

    Article  CAS  Google Scholar 

  • Buchanan JT, Grillner S (1991) 5-Hydroxytryptamine depresses reticulospinal excitatory postsynaptic potentials in motoneurons of the lamprey. Neurosci Lett 112:71–74

    Article  Google Scholar 

  • Chevalier G, Vacher S, Deniau JM (1984) Inhibitory nigral influence on tectospinal neurons, a possible implication of basal ganglia in orienting behavior. Exp Brain Res 53:320–326

    Article  CAS  Google Scholar 

  • Cocchi M, Minuto C, Tonello L, Gabrielli F, Bernroider G, Tuszynski JA, Cappello F, Rasenick M (2017) Linoleic acid: is this the key that unlocks the quantum brain? Insights linking broken symmetries in molecular biology, mood disorders and personalistic emergentism. BMC Neurosci 18:38

    Article  Google Scholar 

  • Cocchi M, Minuto C, Tonello L, Tuszynski JA (2015) Connection between the linoleic acid and psychopathology: a symmetry-breaking phenomenon in the brain? Open J Depress 4:41–52

    Article  Google Scholar 

  • Dean P, Redgrave P, Sahibzada N, Tsuji K (1986) Head and body movements produced by electrical stimulation of superior colliculus in rats: effects of interruption of crossed tectoreticulospinal pathway. Neuroscience 19:367–380

    Article  CAS  Google Scholar 

  • Deliagina TG, Beloozerova IN, Zelenin PV, Orlovsky GN (2008) Spinal and supraspinal postural networks. Brain Res Rev 57:212–221

    Article  CAS  Google Scholar 

  • Deliagina TG, Fagerstedt P (2000) Responses of reticulospinal neurons in intact lamprey to vestibular and visual inputs. J Neurophysiol 83:864–878

    Article  CAS  Google Scholar 

  • Deliagina TG, Grillner S, Orlovsky GN, Ullén F (1993) Visual input affects the response to roll in reticulospinal neurons of the lamprey. Exp Brain Res 95:421–428

    Article  CAS  Google Scholar 

  • Deliagina TG, Orlovsky GN, Grillner S, Wallén P (1992a) Vestibular control of swimming in lamprey. 2. Characteristics of spatial sensitivity of reticulospinal neurons. Exp Brain Res 90:489–498

    Article  CAS  Google Scholar 

  • Deliagina TG, Orlovsky GN, Grillner S, Wallén P (1992b) Vestibular control of swimming in lamprey. 3. Activity of vestibular afferents. Convergence of vestibular inputs on reticulospinal neurons. Exp Brain Res 90:499–507

    Article  CAS  Google Scholar 

  • Deliagina TG, Pavlova EL (2002) Modifications of vestibular responses of individual reticulospinal neurons in the lamprey caused by a unilateral labyrinthectomy. J Neurophysiol 87:1–14

    Article  CAS  Google Scholar 

  • Deliagina TG, Zelenin PV, Fagerstedt P, Grillner S, Orlovsky GN (2000) Activity of reticulospinal neurons during locomotion in the freely behaving lamprey. J Neurophysiol 83:853–863

    Article  CAS  Google Scholar 

  • Fagerstedt P, Orlovsky GN, Deliagina TG, Grillner S, Ullén F (2001) Lateral turns in the lamprey. II. Activity of reticulospinal neurons during the generation of fictive turns. J Neurophysiol 86:2257–2265

    Article  CAS  Google Scholar 

  • Fagerstedt P, Ullén F (2001) Lateral turns in the lamprey. I. Patterns of motoneuron activity. J Neurophysiol 86:2246–2256

    Article  CAS  Google Scholar 

  • Fuhs MC, Touretzky DS (2006) A spin glass model of path integration in rat medial entorhinal cortex. J Neurosci 26:4266–4276

    Article  CAS  Google Scholar 

  • Furigo IC, De Oliveira WF, De Oliveira AR, Colmoli E, Baldo MVC, Mota-Ortiz SR, Canteras NS (2010) The role of the superior colliculus in predatory hunting. Neurosci 165:1–15

    Article  CAS  Google Scholar 

  • Garcia-Rill E, Skinner RD (1987a) The mesencephalic locomotor region. I. Activation of a medullary projection site. Brain Res 411:1–12

    Article  CAS  Google Scholar 

  • Garcia-Rill E, Skinner RD (1987b) The mesencephalic locomotor region. II. Projections to reticulospinal neurons. Brain Res 411:13–20

    Article  CAS  Google Scholar 

  • Garcia-Rill E, Skinner RD, Gilmore SA (1981) Pallidal projections to the mesencephalic locomotor region (MLR) in the cat. Am J Anat 161:311–321

    Article  CAS  Google Scholar 

  • Garcia-Rill E, Skinner RD, Gilmore SA, Owings R (1983a) Connections of the mesencephalic locomotor region (MLR) II. Afferents and efferents. Brain Res Bull 10:63–71

    Article  CAS  Google Scholar 

  • Garcia-Rill E, Skinner RD, Jackson MB, Smith MM (1983b) Connections of the mesencephalic locomotor region (MLR) I. Substantia nigra afferents. Brain Res Bull 10:57–62

    Article  CAS  Google Scholar 

  • Graham Brown TG (1914) On the fundamental activity of the nervous centres: together with an analysis of the conditioning of rhythmic activity in progression, and a theory of the evolution of function in the nervous system. J Physiol (Lond) 48:18–41

    Article  Google Scholar 

  • Grillner S (1981) Control of locomotion in bipeds, tetrapods, and fish. In: Brookhart JM, Mountcastle VB (eds) Handbook of physiology – the nervous system II. American Physiological Society, Bethesda, pp 1179–1236

    Google Scholar 

  • Grillner S, Wallén P, Saitoh K, Kozlov A, Robertson B (2008) Neural bases of goal-directed locomotion in vertebrates - an overview. Brain Res Rev 57:2–12

    Google Scholar 

  • Grillner S, Zangger P (1975) How detailed is the central pattern generation for locomotion? Brain Res 88:367–371

    Article  CAS  Google Scholar 

  • Guertin P, Angel MJ, Perreault M-C, McCrea DA (1995) Ankle extensor group I afferents excite extensors throughout the hindlimb during MLR-evoked fictive locomotion in the cat. J Physiol (Lond) 487:197–209

    Article  CAS  Google Scholar 

  • Hafting T, Fyhn M, Molden S, Moser M-B, Moser EI (2005) Microstructure of a spatial map in the entorhinal cortex. Nature 436:801–806

    Article  CAS  Google Scholar 

  • Harris-Warrick RM (1988) Chemical modulation of central pattern generators. In: Cohen AH, Rossignol S, Grillner S (eds) Neural control of rhythmic movements in vertebrates. Wiley, New York, pp 285–332

    Google Scholar 

  • Hikosaka O, Takikawa Y, Kawagoe R (2000) Role of the basal ganglia in the control of purposive saccadic eye movements. Physiol Rev 80:953–978

    Article  CAS  Google Scholar 

  • Hikosaka O, Wurtz RH (1983) Visual and oculomotor functions of monkey substantia nigra pars reticulata. IV. Relation of substantia nigra to superior colliculus. J Neurophysiol 49:1285–1301

    Article  CAS  Google Scholar 

  • Hohenberg PC, Halperin BI (1977) Theory of dynamic critical phenomena. Rev Modern Phys 49(3):435–479

    Article  CAS  Google Scholar 

  • Hohenberg PC, Krekhov AP (2015) An introduction to the Ginzburg–Landau theory of phase transitions and nonequilibrium patterns. Phys Rep 572:1–42

    Article  Google Scholar 

  • Holstege G, Kuypers HGJM (1982) The anatomy of the brain stem pathways to the spinal cord in a cat. A labelled amino acid tracing study. Prog Brain Res 57:145–175

    Article  CAS  Google Scholar 

  • Hounsgaard J, Hultborn H, Jespersen B, Kiehn O (1988) Bistability of α-motoneurones in the decerebrate cat and in the acute spinal cat after intravenous 5-hydroxytryptophan. J Physiol (Lond) 405:345–367

    Article  Google Scholar 

  • Huang S (2016) Where to go: breaking the symmetry in cell motility. PLoS Biol 14(5):e1002463

    Google Scholar 

  • Iles JF, Coles SK (1991) Effects of loading on muscle activity during locomotion in rat. In: Armstrong DM, Bush BMH (eds) Locomotor neural mechanisms in arthropods and vertebrates. Manchester University Press, Manchester/New York, pp 196–201

    Google Scholar 

  • Iles JF, Nicolopoulos-Stournaras S (1996) Fictive locomotion in the adult decerebrate rat. Exp Brain Res 109:393–398

    Article  CAS  Google Scholar 

  • Jankowska E, Jukes MGM, Lund S, Lundberg A (1967a) The effect of DOPA on the spinal cord: V. Reciprocal organization of pathways transmitting excitatory action to alpha motoneurones of flexors and extensors. Acta Physiol Scand 70:369–388

    Article  CAS  Google Scholar 

  • Jankowska E, Jukes MGM, Lund S, Lundberg A (1967b) The effect of DOPA on the spinal cord. VI. Half-centre organization of interneurons transmitting effects from the flexor reflex afferents. Acta Physiol Scand 70:389–402

    Article  CAS  Google Scholar 

  • Jankowska E, Noga BR (1990) Contralaterally projecting lamina VIII interneurons in middle lumbar segments in the cat. Brain Res 535:327–330

    Article  CAS  Google Scholar 

  • Jensen O, Mosekilde E, Borckmans P, Dewel G (1996) Computer simulation of turing structures in the chloride-iodide-malonic acid system. Phys Scr 53:243–251

    Article  CAS  Google Scholar 

  • Jilkine A, Edelstein-Keshet L (2011) A comparison of mathematical models for polarization of single Eukaryotic cells in response to guided cues. PLoS Comput Biol 7(4):e1001121

    Article  CAS  Google Scholar 

  • Juvin L, Simmers J, Morin D (2007) Locomotor rhythmogenesis in the isolated rat spinal cord: a phase-coupled set of symmetrical flexion-extension oscillators. J Physiol (Lond) 583(1):115–128

    Article  CAS  Google Scholar 

  • Kausz M (1991) Arrangement of neurons in the medullary reticular formation and raphe nuclei projecting to thoracic, lumbar and sacral segments of the spinal cord in the cat. Anat Embryol 183:151–163

    Article  CAS  Google Scholar 

  • Kiehn O, Kjærulff O (1996) Spatiotemporal characteristics of 5-HT and dopamine-induced rhythmic hindlimb activity in the in vitro neonatal rat. J Neurophysiol 75:1472–1482

    Article  CAS  Google Scholar 

  • Kittel C (1971) Introduction to solid state physics, 4th edn. Wiley, New York

    Google Scholar 

  • Kjaerulff O, Kiehn O (1997) Crossed rhythmic synaptic input to motoneurons during selective activation of the contralateral spinal locomotor network. J Neurosci 17:9433–9447

    Article  CAS  Google Scholar 

  • Kravitz AV, Freeze BS, Parker PR, Kay K, Thwin MT, Deisseroth K, Kreitzer AC (2010) Regulation of parkinsonian motor behaviours by optogenetic control of basal ganglia circuitry. Nature 466:622–626

    Article  CAS  Google Scholar 

  • Kremer E, Lev-Tov A (1997) Localization of the spinal network associated with generation of hindlimb locomotion in the neonatal rat and organization of its transverse coupling system. J Neurophysiol 77:1155–1170

    Article  CAS  Google Scholar 

  • Kriellaars DJ, Brownstone RM, Noga BR, Jordan LM (1994) Mechanical entrainment of fictive locomotion in the decerebrate cat. J Neurophysiol 71:2074–2086

    Article  CAS  Google Scholar 

  • Kubicki M, McCarley R, Li R, Bowerman B (2010) Symmetry breaking in biology. Cold Spring Harb Perspect Biol 2(3):a003475. doi:10.1101/cshperspect.a003475

    Article  CAS  Google Scholar 

  • Lafreniere-Roula M, McCrea DA (2005) Deletions of rhythmic motoneuron activity during fictive locomotion and scratch provide clues to the organization of the mammalian central pattern generator. J Neurophysiol 94:1120–1132

    Article  Google Scholar 

  • Li R, Bowerman B (2010) Symmetry breaking in biology. Cold Spring Harb Perspect Biol 2(3):a003475. https://doi.org/10.1101/cshperspect.a003475

    Article  CAS  Google Scholar 

  • Lundberg A (1981) Half-centres revisited. In: Szentagothai J, Palkovits M, Hamori J (eds) Regulatory functions of the CNS. Motion and organization principles. Advances in physiological sciences vol. 1. Pergamon Press, Akademiai Kiado, Budapest, pp 155–167

    Google Scholar 

  • McCrea DA, Rybak IA (2007) Modeling the mammalian locomotor CPG: insights from mistakes and perturbations. Prog Brain Res 165:235–253

    Article  Google Scholar 

  • McCrea DA, Rybak IA (2008) Organization of mammalian locomotor rhythm and pattern generation. Brain Res Rev 57:134–146

    Article  Google Scholar 

  • McNaughton BL, Battaglia FP, Jensen O, Moser EI, Moser MB (2006) Path integration and the neural basis of the ‘cognitive map’. Nat Rev Neurosci 7(8):663–678

    Article  CAS  Google Scholar 

  • Mergner T, Becker W (2003) A modeling approach to the human spatial orientation system. Ann N Y Acad Sci 1004:303–315

    Article  CAS  Google Scholar 

  • Merrywest SD, McDearmid JR, Kjaerulff O, Kiehn O, Sillar KT (2003) Mechanisms underlying the noradrenergic modulation of longitudinal coordination during swimming in Xenopus laevis tadpoles. Eur J Neurosci 17:1013–1022

    Article  Google Scholar 

  • Miller DM, DeMayo WM, Bourdages GH, Wittman SR, Yates BJ, McCall AA (2017) Neurons in the pontomedullary reticular formation receive convergin inpts from the hindlimb and labyrinth. Exp Brain Res 235:1195–1207

    Article  Google Scholar 

  • Mnyukh Y (2012) Ferromagnetic state and phase transitions. Am J Cond Mat Phys 2(5):109–115

    Google Scholar 

  • Mullins D (2009) Symmetry breaking in biology. Cold Spring Harb Perspect Biol 2:a003392

    Google Scholar 

  • Munro E, Bowerman B (2009) Cellular symmetry breaking during C. elegans development. Cold Spring Harb Perspect Biol 1:a003400

    Article  Google Scholar 

  • Murray JD (1989) Mathematical biology. Springer, Heidelberg

    Book  Google Scholar 

  • Noga BR, Fortier PA, Kriellaars DJ, Dai X, Detillieux GR, Jordan LM (1995) Field potential mapping of neurons in the lumbar spinal cord activated following stimulation of the mesencephalic locomotor region. J Neurosci 15:2203–2217

    Article  CAS  Google Scholar 

  • Noga BR, Johnson DMG, Riesgo MI, Pinzon A (2009) Locomotor-activated neurons of the cat. I. Serotonergic innervation and co-localization of 5-HT7, 5-HT2A and 5-HT1A receptors in the thoraco-lumbar spinal cord. J Neurophysiol 102:1560–1576. PMID: 19571190 937

    Article  CAS  Google Scholar 

  • Noga BR, Johnson DMG, Riesgo MI, Pinzon A (2011) Locomotor-activated neurons of the cat. II. Noradrenergic innervation and co-localization of NAα1A and NAα2B receptors in the thoraco-lumbar spinal cord. J Neurophysiol 105:1835–1849

    Google Scholar 

  • Noga BR, Kettler J, Jordan LM (1988) Locomotion produced in mesencephalic cats by injections of putative transmitter substances and antagonists into the medial reticular formation and the pontomedullary locomotor strip. J Neurosci 8:2074–2086

    Article  CAS  Google Scholar 

  • Noga BR, Kriellaars DJ, Brownstone RM, Jordan LM (2003) Mechanism for activation of locomotor centers in the spinal cord by stimulation of the mesencephalic locomotor region. J Neurophysiol 90:1464–1478. doi:10.1152/jn.00034.2003

    Article  Google Scholar 

  • Noga BR, Kriellaars DJ, Jordan LM (1991) The effect of selective brainstem or spinal cord lesions on treadmill locomotion evoked by stimulation of the mesencephalic or pontomedullary locomotor regions. J Neurosci 11:1691–1700

    Article  CAS  Google Scholar 

  • Noga BR, Opris I (2017) The hierarchical circuit for executive control of movement. (Chapter 5). In: Opris I, Casanova MF Physics of the mind and brain disorders: integrated neural circuits supporting the emergence of mind. Springer Series in Cognitive and Neural Systems, New York, NY. ISBN 978-3-319-29674-6

    Google Scholar 

  • O’Keefe J (1976) Place units in the hippocampus of the freely moving rat. Exp Neurol 51:78–109

    Article  Google Scholar 

  • Opris I (2013) Inter-laminar microcircuits across the neocortex: repair and augmentation. Front Syst Neurosci 7:80

    Article  Google Scholar 

  • Opris I, Casanova MF (2014) Prefrontal cortical minicolumn: from executive control to disrupted cognitive processing. Brain 137(7):1863–1875. doi:10.1093/brain/awt359

    Article  Google Scholar 

  • Opris I, Fuqua JL, Huettl PF, Gerhardt GA, Berger TW, Hampson RE et al (2012b) Closing the loop in primate prefrontal cortex: inter-laminar processing. Front Neural Circ 6:88

    Google Scholar 

  • Opris I, Hampson RE, Gerhardt GA, Berger TW, Deadwyler SA (2012a) Columnar processing in primate pFC: evidence for executive control microcircuits. J Cogn Neurosci 24:2334–2347

    Article  Google Scholar 

  • Opris I, Hampson RE, Stanford TR, Gerhardt GA, Deadwyler SA (2011) Neural activity in frontal cortical cell layers: evidence for columnar sensorimotor processing. J Cogn Neurosci 23:1507–1521

    Article  Google Scholar 

  • Opris I, Santos LM, Song D, Gerhardt GA, Berger TW, Hampson RE et al (2013) Prefrontal cortical microcircuits bind perception to executive control. Sci Rep 3:2285

    Article  Google Scholar 

  • Orlovsky GN (1969) Electrical activity in the brainstem and descending pathways in guided locomotion. Fiziol Zh (SSSR) 55:437–444

    Google Scholar 

  • Orlovsky GN (1970a) Connexions of the reticulo-spinal neurons with the “locomotor sections” of the brainstem. Biophysics 15:178–186

    Google Scholar 

  • Orlovsky GN (1970b) Work of the reticulospinal neurons during locomotion. Biophysics 15:761–771

    Google Scholar 

  • Pavlova EL, Popova LB, Orlovsky GN, Deliagina TF (2004) Vestibular compensation in lampreys: restoration of symmetry in reticulospinal commands. J Exp Biol 207:4595–5603

    Article  Google Scholar 

  • Perreault M-C, Angel MJ, Guertin P, McCrea DA (1995) Effects of stimulation of hindlimb flexor group II muscle afferents during fictive locomotion. J Physiol 487:211–220

    Article  CAS  Google Scholar 

  • Perreault M-C, Drew T, Rossignol S (1993) Activity of medullary reticulospinal neurons during fictive locomotion. J Neurophysiol 69:2232–2247

    Article  CAS  Google Scholar 

  • Peterson BW, Abzug C (1975) Properties of projections from vestibular nuclei to medial reticular formation in the cat. J Neurophysiol 38:1421–1435

    Article  CAS  Google Scholar 

  • Roseberry TK, Lee AM, Lalive AL, Wilbrecht L, Bonci A, Kreitzer AC (2016) Cell-type-specific control of brainstem locomotor circuits by basal ganglia. Cell 164:526–537

    Article  CAS  Google Scholar 

  • Rybak IA, Stecina K, Shevtsova NA, McCrea DA (2006) Modelling spinal circuitry involved in locomotor pattern generation: insights from the effects of afferent stimulation. J Physiol 577:641–658

    Article  CAS  Google Scholar 

  • Shadlen MN, Newsome WT (1998) The variable discharge of cortical neurons: implications for connectivity, computation, and information coding. J Neurosci 18:3870–3896

    Article  CAS  Google Scholar 

  • Spardy LE, Markin SN, Shevtsova NA, Prilutsky BI, Rybak IA, Rubin JE (2011b) A dynamical systems analysis of afferent control in a neuromechanical model of locomotion: I. Rhythm generation. J Neural Eng 8:065003

    Article  Google Scholar 

  • Spardy LE, Markin SN, Shevtsova NA, Prilutsky BI, Rybak IA, Rubin JE (2011a) A dynamical systems analysis of afferent control in a neuromechanical model of locomotion: II. Phase asymmetry. J Neural Eng 8:065004

    Article  Google Scholar 

  • Stecina K, Quevedo J, McCrea DA (2005) Parallel reflex pathways from flexor muscle afferents evoking resetting and flexion-enhancement during fictive locomotion in the cat. J Physiol 569:275–290

    Article  CAS  Google Scholar 

  • Steeves JD, Jordan LM (1980) Localization of a descending pathway in the spinal cord which is necessary for controlled treadmill locomotion. Neurosci Lett 20(283):288

    Google Scholar 

  • Steeves JD, Jordan LM (1984) Autoradiographic demonstration of the projections from the mesencephalic locomotor region. Brain Res 307:263–276

    Article  CAS  Google Scholar 

  • Swindale NV (1980) A model for the formation of ocular dominance stripes. Proc R Soc Lond B Biol Sci 208:243–264

    Article  CAS  Google Scholar 

  • Takakusaki K (2017) Functional neuroanatomy for posture and gait control. J Mov Disord 10:1–17

    Article  Google Scholar 

  • Tohyama M, Sakai K, Salvert D, Touret M, Jouvet M (1979) Spinal projections from the lower brain stem in the cat as demonstrated by the horseradish peroxidase technique. I. Origins of the reticulospinal tracts and their funicular trajectories. Brain Res 173:383–403

    Article  CAS  Google Scholar 

  • Turing AM (1953) The chemical basis of morphogenesis. Phil Trans R Soc B 237:37–72. Reprinted in Bull Math Biol 52, 153–197 (1990)

    Google Scholar 

  • Van der Gucht J, Sykes C (2009) Physical model of cellular symmetry breaking. Cold Spring Harb Perspect Biol 1:a001909

    Google Scholar 

  • Wang X-J (2002) Probabilistic decision making by slow reverberation in cortical circuits. Neuron 36:955–968

    Article  CAS  Google Scholar 

  • Wang XJ (2012) Neural dynamics and circuit mechanisms of decision-making. Curr Opin Neurobiol 22:1039–1046

    Article  Google Scholar 

  • Wannier T, Deliagina TG, Orlovsky GN, Grillner S (1998) Differential effects of the reticulospinal system on locomotion in lamprey. J Neurophysiol 80:103–112

    Article  CAS  Google Scholar 

  • Whelan P, Bonnot A, O’Donovan MJ (2000) Properties of rhythmic activity generated by the isolated spinal cord of the neonatal mouse. J Neurophysiol 84:2821–2933

    Article  CAS  Google Scholar 

  • Wilson KG, Kogut J (1974) The renormalization group and the ϵ expansion. Phys Rep 12:75–199

    Article  Google Scholar 

  • Wimmer K, Nykamp DQ, Constantinidis C, Compte A (2014) Bump attractor dynamics in prefrontal cortex explains behavioral precision in spatial working memory. Nat Neurosci 17:431–439

    Article  CAS  Google Scholar 

  • Yakovenko S, McCrea DA, Stecina K, Prochazka A (2005) Control of locomotor cycle durations. J Neurophysiol 94:1057–1065

    Article  CAS  Google Scholar 

  • Yamaguchi T (1987) Monopodal fictive locomotion evoked by cervical cord stimulation in decerebrate cats. Neurosci Lett 74(69):74

    Google Scholar 

  • Yoshimura M, Furue H (2006) Mechanisms for the anti-nociceptive actions of the descending noradrenergic and serotonergic systems in the spinal cord. J Pharmacol Sci 101:107–117

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Miami Project to Cure Paralysis, Department of Neurological Surgery, Miller School of Medicine, University of Miami, Miami, FL, USA

    Brian R. Noga & Ioan Opris

  2. Department of Veterinary Medicine, University of Agronomical Sciences and Veterinary Medicine, Bucharest, Romania

    Ioan Opris

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  1. Brian R. Noga
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Correspondence to Brian R. Noga .

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Editors and Affiliations

  1. Miami Project to Cure Paralysis, Department of Neurological Surgery, Miller School of Medicine, University of Miami, Miami, FL, USA

    Ioan Opris

  2. Greenville Health System, University of South Carolina, School of Medicine Greenville, Greenville, SC, USA

    Manuel F. Casanova

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Noga, B.R., Opris, I. (2017). From Symmetry to Symmetry-Breaking in Locomotion. In: Opris, I., Casanova, M.F. (eds) The Physics of the Mind and Brain Disorders. Springer Series in Cognitive and Neural Systems, vol 11. Springer, Cham. https://doi.org/10.1007/978-3-319-29674-6_7

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