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A new biological central pattern generator model and its relationship with the motor units

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Abstract

The central pattern generator (CPG) is a key neural-circuit component of the locomotion control system. Recently, numerous molecular and genetic approaches have been proposed for investigating the CPG mechanisms. The rhythm in the CPG locomotor circuits comes from the activity in the ipsilateral excitatory neurons whose output is controlled by inter-neuron inhibitory connections. Conventional models for simulating the CPG mechanism are complex Hodgkin-Huxley-type models. Inspired by biological investigations and the continuous-time Matsuoka model, we propose new integral-order and fractional-order CPG models, which consider time delays and synaptic interfaces. The phase diagrams exhibit limit cycles and periodic solutions, in agreement with the CPG biological characteristics. As well, the fractional-order model shows state transitions with order variations. In addition, we investigate the relationship between the CPG and the motor units through the construction of integral-order and fractional-order coupling models. Simulations of these coupling models show that the states generated by the three motor units are in accordance with the experimentally-obtained states in previous studies. The proposed models reveal that the CPG can regulate limb locomotion patterns through connection weights and synaptic interfaces. Moreover, in comparison to the integral-order models, the fractional-order ones appear to be more effective, and hence more suitable for describing the dynamics of the CPG biological system.

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References

  • Bannatyne BA, Hao ZZ, Dyer GMC et al (2020) Neurotransmitters and motoneuron contacts of multifunctional and behaviorally specialized turtle spinal cord interneurons. J Neurosci 40(3):2680–2694

    Article  Google Scholar 

  • Bikoff JB (2019) Interneuron diversity and function in the spinal motor system. Curr Opin Physio 8:36–43

    Article  Google Scholar 

  • Bisetto S, Wright MC, Nowak RA, et al. (2019) New insights into the lactate shuttle: role of MCT4 in the modulation of the exercise capacity. iScience 22: 507.

  • Chen L, Hao Y, Huang T et al (2020) Chaos in fractional-order discrete neural networks with application to image encryption. Neural Netw 125:174–184

    Article  Google Scholar 

  • Cole SR, Voytek B (2017) Brain oscillations and the importance of waveform shape. Trends Cogn Sci 21(2):137–149

    Article  Google Scholar 

  • Damm L, Varoqui D, De Cock VC et al (2020) Why do we move to the beat? a multi-scale approach, from physical principles to brain dynamics. Neurosci Biobehav Rev 112:553–584

    Article  Google Scholar 

  • Deska-Gauthier D, Zhang Y (2019) The functional diversity of spinal interneurons and locomotor control. Curr Opin Physio 8:99–108

    Article  Google Scholar 

  • Dominici N, Ivanenko YP, Cappellini G et al (2011) Locomotor primitives in newborn babies and their development. Science 334(6058):997–999

    Article  CAS  Google Scholar 

  • Falgairolle M, Puhl JG, Pujala A, et al. (2017). Motoneurons regulate the central pattern generator during drug-induced locomotor-like activity in the neonatal mouse. eLife 6: e26622.

  • Fiebelkorn IC, Kastner S (2019) A rhythmic theory of attention. Trends Cogn Sci 23(2):87–101

    Article  Google Scholar 

  • Fries P (2015) Rhythms for cognition: communication through coherence. Neuron 88:220–234

    Article  CAS  Google Scholar 

  • Ge MY, Lu LL, Xu Y et al (2020) Vibrational mono-bi/-resonance and wave propagation in FitzHugh-Nagumo neural systems under electromagnetic induction. Chaos Solitons Fractals 133:109645

    Article  Google Scholar 

  • He WM, Ahn CK, Xiang ZR (2020) Global fault-tolerant sampled-data control for large-scale switched time-delay nonlinear systems. IEEE Syst J 14(2):1549–1557

    Article  Google Scholar 

  • Ivanenko YP, Cappellini G, Dominici N et al (2005) Coordination of locomotion with voluntary movements in humans. J Neurosci 25(31):7238–7253

    Article  CAS  Google Scholar 

  • Kiehn O (2016) Decoding the organization of spinal circuits that control locomotion. Nat Rev Neurosci 17:224–238

    Article  CAS  Google Scholar 

  • Kumar D, Singh J, Baleanu D (2018) A new numerical algorithm for fractional Fitzhugh-Nagumo equation arising in transmission of nerve impulses. Nonlinear Dyn 91(1):307–317

    Article  Google Scholar 

  • Lacquaniti F, Ivanenko YP, Zago M (2012) Patterned control of human locomotion. J Physiol 590(10):2189–2199

    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(2):1120–1132

    Article  Google Scholar 

  • Lawton KJ, Perry WM, Yamaguchi A et al (2017) Motor neurons tune premotor activity in a vertebrate central pattern generator. J Neurosci 37(12):3264–3275

    Article  CAS  Google Scholar 

  • Lin L, Zheng L, Chen Y et al (2018) Anomalous diffusion in comb model with fractional dual-phase-lag constitutive relation. Comput Math Appl 76(2):245–256

    Article  Google Scholar 

  • Lu Q (2015) Coupling relationship between the central pattern generator and the cerebral cortex with time delay. Cogn Neurodyn 9:423–436

    Article  Google Scholar 

  • Lu Q (2019) Relationship between the nonlinear oscillator and the motor cortex. IEEE Access 7:44525–44535

    Article  Google Scholar 

  • Lu Q (2020) Dynamics and coupling of fractional-order models of the motor cortex and central pattern generators. J Neural Eng 17:036021

    Article  Google Scholar 

  • Lu Q, Tian J (2014) Synchronization and stochastic resonance of the small-world neural networks based on the CPG. Cogn Neurodyn 8(3):217–226

    Article  Google Scholar 

  • Lu Q, Li W, Tian J et al (2015) Effects on hypothalamus when CPG is fed back to basal ganglia based on KIV model. Cogn Neurodyn 9(1):85–92

    Article  Google Scholar 

  • Lundstrom BN, Higgs MH, Spain WJ et al (2008) Fractional differentiation by neocortical pyramidal neurons. Nat Neurosci 11:1335–1342

    Article  CAS  Google Scholar 

  • Matsuoka K (2011) Analysis of a neural oscillator. Biol Cybern 104:297–304

    Article  Google Scholar 

  • McCrea DA, Rybak IA (2008) Organization of mammalian locomotor rhythm and pattern generation. Brain Res Rev 57(1):134–146

    Article  Google Scholar 

  • Moran-Rivard L, Kagawa T, Saueressig H et al (2001) Evx1 is a postmitotic determinant of v0 interneuron identity in the spinal cord. Neuron 29(2):385–399

    Article  CAS  Google Scholar 

  • Nassour J, Henaff P, Benouezdou F et al (2014) Multi-layered multi-pattern CPG for adaptive locomotion of humanoid robots. Biol Cybern 108:291–303

    Article  Google Scholar 

  • Qiao Y, Yan H, Duan L et al (2020) Finite-time synchronization of fractional-order gene regulatory networks with time delay. Neural Netw 126:1–10

    Article  Google Scholar 

  • Roberts A, Li WC, Soffe SR (2012) A functional scaffold of CNS neurons for the vertebrates: the developing Xenopus laevis spinal cord. Dev Neurobiol 72(4):575–584

    Article  CAS  Google Scholar 

  • Rybak IA, Shevtsova NA, Lafreniere-Roula M et al (2006) Modelling spinal circuitry involved in locomotor pattern generation: insights from deletions during fictive locomotion. J Physiol 577:617–639

    Article  CAS  Google Scholar 

  • Shevtsova NA, Talpalar AE, Markin SN et al (2015) Organization of left-right coordination of neuronal activity in the mammalian spinal cord: insights from computational modelling. J Physiol Lond 593(11):2403–2426

    Article  CAS  Google Scholar 

  • Teka WW, Upadhyay RK, Mondal A (2017) Fractional-order leaky integrate-and-fire model with long-term memory and power law dynamics. Neural Netw 93:110–125

    Article  Google Scholar 

  • Yan CG, Yang Z, Colcombe SJ et al (2017) Concordance among indices of intrinsic brain function: Insights from inter-individual variation and temporal dynamics. Sci Bull 62(23):1572–1584

    Article  Google Scholar 

  • Yang Z, Zhang D, Rocha MV et al (2017) Prescription of rhythmic patterns for legged locomotion. Neural Comput Appl 28(11):3587–3601

    Article  Google Scholar 

  • Zhong G, Chen L, Jiao Z et al (2018) Locomotion control and gait planning of a novel hexapod robot using biomimetic neurons. IEEE Trans Control Syst Technol 26(2):624–636

    Article  Google Scholar 

  • Zhou Y, Yamamoto M, Engel JD (2000) GATA2 is required for the generation of V2 interneurons. Development 127(17):3829–3838

    Article  CAS  Google Scholar 

Download references

Acknowledgements

This work was supported by the Key Research and Development Project of Shandong Province in China under Grant 2019GGX101062, and Shandong Provincial Natural Science Foundation, China under Grant ZR2020MF156.

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Authors and Affiliations

  1. College of Medical Information Engineering, Shandong First Medical University & Shandong Academy of Medical Sciences, Taian, 271000, China

    Qiang Lu, Xiaoyan Wang & Juan Tian

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  1. Qiang Lu
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  2. Xiaoyan Wang
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  3. Juan Tian
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Correspondence to Qiang Lu.

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Lu, Q., Wang, X. & Tian, J. A new biological central pattern generator model and its relationship with the motor units. Cogn Neurodyn 16, 135–147 (2022). https://doi.org/10.1007/s11571-021-09710-0

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