Advertisement

Journal of Computational Neuroscience

, Volume 33, Issue 3, pp 515–531 | Cite as

Models of passive and active dendrite motoneuron pools and their differences in muscle force control

  • Leonardo Abdala EliasEmail author
  • Vitor Martins Chaud
  • André Fabio Kohn
Article

Abstract

Motoneuron (MN) dendrites may be changed from a passive to an active state by increasing the levels of spinal cord neuromodulators, which activate persistent inward currents (PICs). These exert a powerful influence on MN behavior and modify the motor control both in normal and pathological conditions. Motoneuronal PICs are believed to induce nonlinear phenomena such as the genesis of extra torque and torque hysteresis in response to percutaneous electrical stimulation or tendon vibration in humans. An existing large-scale neuromuscular simulator was expanded to include MN models that have a capability to change their dynamic behaviors depending on the neuromodulation level. The simulation results indicated that the variability (standard deviation) of a maintained force depended on the level of neuromodulatory activity. A force with lower variability was obtained when the motoneuronal network was under a strong influence of PICs, suggesting a functional role in postural and precision tasks. In an additional set of simulations when PICs were active in the dendrites of the MN models, the results successfully reproduced experimental results reported from humans. Extra torque was evoked by the self-sustained discharge of spinal MNs, whereas differences in recruitment and de-recruitment levels of the MNs were the main reason behind torque and electromyogram (EMG) hysteresis. Finally, simulations were also used to study the influence of inhibitory inputs on a MN pool that was under the effect of PICs. The results showed that inhibition was of great importance in the production of a phasic force, requiring a reduced co-contraction of agonist and antagonist muscles. These results show the richness of functionally relevant behaviors that can arise from a MN pool under the action of PICs.

Keywords

Bistability Nonlinearities in force control Electromyogram L-type calcium channel Persistent inward current Plateau potential 

Abbreviations

AD

Active dendrite

AHP

Afterhyperpolarization

BT

Basal torque

Ca++

Calcium

CV

Coefficient of variation

EMG

Electromyogram

EPSP

Excitatory post-synaptic potential

ET

Extra torque

IPSP

Inhibitory post-synaptic potential

K+

Potassium

LG

Lateral Gastrocnemius

MG

Medial Gastrocnemius

MN

Motoneuron

MT

Maximum torque

MU

Motor unit

Na+

Sodium

PD

Passive dendrite

PIC

Persistent inward current

SOL

Soleus muscle

TA

Tibialis anterior

TS

Triceps Surae

Notes

Acknowledgments

This work was funded by FAPESP (State of São Paulo Funding Agency) and CNPq (The National Council for Scientific and Technological Development). L.A. Elias and V.M. Chaud hold scholarships from FAPESP (#2009/15802-0) and CNPq (#132776/2011-1), respectively. The authors are grateful to Dr. F.H. Magalhães for his insights and valuable discussions.

Conflict of interest statement

The authors declare that there is no conflict of interest with any financial organization regarding the material discussed in this manuscript.

References

  1. Bennett, D. J., Hultborn, H., Fedirchuk, B., & Gorassini, M. (1998). Synaptic activation of plateaus in hindlimb motoneurons of decerebrate cats. Journal of Neurophysiology, 80(4), 2023–2037.PubMedGoogle Scholar
  2. Bergquist, A. J., Clair, J. M., & Collins, D. F. (2011). Motor unit recruitment when neuromuscular electrical stimulation is applied over a nerve trunk compared with a muscle belly: triceps surae. Journal of Applied Physiology, 110(3), 627–637.PubMedCrossRefGoogle Scholar
  3. Binder, M. D. (2002). Integration of synaptic and intrinsic dendritic currents in cat spinal motoneurons. Brain Research Reviews, 40(1–3), 1–8.PubMedCrossRefGoogle Scholar
  4. Binder, M. D., & Powers, R. K. (1999). Synaptic integration in spinal motoneurones. Journal of Physiology, Paris, 93(1–2), 71–79.PubMedCrossRefGoogle Scholar
  5. Cisi, R. R. L., & Kohn, A. F. (2008). Simulation system of spinal cord motor nuclei and associated nerves and muscles, in a Web-based architecture. Journal of Computational Neuroscience, 25(3), 520–542. doi: 10.1007/s10827-008-0092-8.PubMedCrossRefGoogle Scholar
  6. Collins, D. F. (2007). Central contributions to contractions evoked by tetanic neuromuscular electrical stimulation. Exercise and Sport Sciences Reviews, 35(3), 102–109. doi: 10.1097/jes.0b013e3180a0321b.PubMedCrossRefGoogle Scholar
  7. Collins, D. F., Bergquist, A. J. (2011). “Extra torque” during electrically evoked contractions in humans. J Neurosci eLetters. Available via http://www.jneurosci.org/content/31/15/5579.long#responses. Accessed 01 August 2011.
  8. Collins, D. F., Burke, D., & Gandevia, S. C. (2001). Large involuntary forces consistent with plateau-like behavior of human motoneurons. Journal of Neuroscience, 21(11), 4059–4065.PubMedGoogle Scholar
  9. Collins, D. F., Burke, D., & Gandevia, S. C. (2002). Sustained contractions produced by plateau-like behaviour in human motoneurones. J Physiol-London, 538(1), 289–301.PubMedCrossRefGoogle Scholar
  10. Dean, J. C., Yates, L. M., & Collins, D. F. (2007). Turning on the central contribution to contractions evoked by neuromuscular electrical stimulation. Journal of Applied Physiology, 103(1), 170–176. doi: 10.1152/japplphysiol.01361.2006.PubMedCrossRefGoogle Scholar
  11. Destexhe, A. (1997). Conductance-based integrate-and-fire models. Neural Computation, 9(3), 503–514.PubMedCrossRefGoogle Scholar
  12. Destexhe, A., Mainen, Z. F., & Sejnowski, T. J. (1994). An efficient method for computing synaptic conductances based on a kinetic-model of receptor-binding. Neural Computation, 6(1), 14–18.CrossRefGoogle Scholar
  13. ElBasiouny, S. M., Schuster, J. E., & Heckman, C. J. (2010). Persistent inward currents in spinal motoneurons: Important for normal function but potentially harmful after spinal cord injury and in amyotrophic lateral sclerosis. Clinical Neurophysiology, 121(10), 1669–1679. doi: 10.1016/j.clinph.2009.12.041.PubMedCrossRefGoogle Scholar
  14. Elias, L. A., Kohn, A. F. (2010). Single neuron and network models in force control. In: 9th Neural Coding Workshop, Limassol, Cyprus, pp 31–32.Google Scholar
  15. Finkel, A. S., & Redman, S. J. (1983). The synaptic current evoked in cat spinal motoneurones by impulses in single group-1a axons. J Physiol-London, 342, 615–632.PubMedGoogle Scholar
  16. Fleshman, J. W., Segev, I., & Burke, R. E. (1988). Electrotonic architecture of type-identified alpha-motoneurons in the cat spinal-cord. Journal of Neurophysiology, 60(1), 60–85.PubMedGoogle Scholar
  17. Frigon, A., Thompson, C. K., Johnson, M. D., Manuel, M., Hornby, T. G., & Heckman, C. J. (2011). Extra forces evoked during electrical stimulation of the muscle or its nerve are generated and modulated by a length-dependent intrinsic property of muscle in humans and cats. Journal of Neuroscience, 31(15), 5579–5588. doi: 10.1523/JNEUROSCI.6641-10.2011.PubMedCrossRefGoogle Scholar
  18. Fuglevand, A. J., Winter, D. A., & Patla, A. E. (1993). Models of recruitment and rate coding organization in motor-unit pools. Journal of Neurophysiology, 70(6), 2470–2488.PubMedGoogle Scholar
  19. Fuglevand, A. J., Dutoit, A. P., Johns, R. K., & Keen, D. A. (2006). Evaluation of plateau-potential-mediated ‘warm up’ in human motor units. J Physiol-London, 571(Pt 3), 683–693.PubMedCrossRefGoogle Scholar
  20. Gorassini, M. A., Bennett, D. J., & Yang, J. F. (1998). Self-sustained firing of human motor units. Neuroscience Letters, 247(1), 13–16.PubMedCrossRefGoogle Scholar
  21. Heckman, C. J. (1994). Computer-simulations of the effects of different synaptic input systems on the steady-state input-output structure of the motoneuron pool. Journal of Neurophysiology, 71(5), 1727–1739.PubMedGoogle Scholar
  22. Heckman, C. J., & Lee, R. H. (1999). Synaptic integration in bistable motoneurons. Peripheral and Spinal Mechanisms in the Neural Control of Movement, 123, 49–56.CrossRefGoogle Scholar
  23. Heckman, C. J., Gorassini, M. A., & Bennett, D. J. (2005). Persistent inward currents in motoneuron dendrites: implications for motor output. Muscle & Nerve, 31(2), 135–156. doi: 10.1002/Mus.20261.CrossRefGoogle Scholar
  24. Heckman, C. J., Mottram, C., Quinlan, K., Theiss, R., & Schuster, J. (2009). Motoneuron excitability: The importance of neuromodulatory inputs. Clinical Neurophysiology, 120(12), 2040–2054. doi: 10.1016/j.clinph.2009.08.009.PubMedCrossRefGoogle Scholar
  25. Hounsgaard, J., Hultborn, H., Jespersen, B., & Kiehn, O. (1988). Bistability of alpha-motoneurones in the decerebrate cat and in the acute spinal cat after intravenous 5-hydroxytryptophan. J Physiol-London, 405, 345–367.PubMedGoogle Scholar
  26. Hyngstrom, A. S., Johnson, M. D., Miller, J. F., & Heckman, C. J. (2007). Intrinsic electrical properties of spinal motoneurons vary with joint angle. Nature Neuroscience, 10(3), 363–369. doi: 10.1038/Nn1852.PubMedCrossRefGoogle Scholar
  27. Hyngstrom, A. S., Johnson, M. D., & Heckman, C. J. (2008). Summation of excitatory and inhibitory synaptic inputs by motoneurons with highly active dendrites. Journal of Neurophysiology, 99(4), 1643–1652. doi: 10.1152/jn.01253.2007.PubMedCrossRefGoogle Scholar
  28. Jacobs, B. L., & Fornal, C. A. (1997). Serotonin and motor activity. Current Opinion in Neurobiology, 7(6), 820–825.PubMedCrossRefGoogle Scholar
  29. Jacobs, B. L., Martin-Cora, F. J., & Fornal, C. A. (2002). Activity of medullary serotonergic neurons in freely moving animals. Brain Research Reviews, 40(1–3), 45–52.PubMedCrossRefGoogle Scholar
  30. Johnson, M. D., & Heckman, C. J. (2010). Interactions between focused synaptic inputs and diffuse neuromodulation in the spinal cord. Ann Ny Acad Sci, 1198, 35–41. doi: 10.1111/j.1749-6632.2010.05430.x.PubMedCrossRefGoogle Scholar
  31. Kiehn, O., & Eken, T. (1998). Functional role of plateau potentials in vertebrate motor neurons. Current Opinion in Neurobiology, 8(6), 746–752.PubMedCrossRefGoogle Scholar
  32. Klakowicz, P. M., Baldwin, E. R. L., & Collins, D. F. (2006). Contribution of M-waves and H-reflexes to contractions evoked by tetanic nerve stimulation in humans. Journal of Neurophysiology, 96(3), 1293–1302. doi: 10.1152/jn.00765.2005.PubMedCrossRefGoogle Scholar
  33. Kuo, J. J., Lee, R. H., Johnson, M. D., Heckman, H. M., & Heckman, C. J. (2003). Active dendritic integration of inhibitory synaptic inputs in vivo. Journal of Neurophysiology, 90(6), 3617–3624. doi: 10.1152/jn.00521.2003.PubMedCrossRefGoogle Scholar
  34. Lee, R. H., & Heckman, C. J. (1996). Influence of voltage-sensitive dendritic conductances on bistable firing and effective synaptic current in cat spinal motoneurons in vivo. Journal of Neurophysiology, 76(3), 2107–2110.PubMedGoogle Scholar
  35. Lee, R. H., & Heckman, C. J. (1998a). Bistability in spinal motoneurons in vivo: Systematic variations in persistent inward currents. Journal of Neurophysiology, 80(2), 583–593.PubMedGoogle Scholar
  36. Lee, R. H., & Heckman, C. J. (1998b). Bistability in spinal motoneurons in vivo: systematic variations in rhythmic firing patterns. Journal of Neurophysiology, 80(2), 572–582.PubMedGoogle Scholar
  37. Lee, R. H., & Heckman, C. J. (1999). Paradoxical effect of QX-314 on persistent inward currents and bistable behavior in spinal motoneurons in vivo. Journal of Neurophysiology, 82(5), 2518–2527.PubMedGoogle Scholar
  38. Lee, R. H., & Heckman, C. J. (2000). Adjustable amplification of synaptic input in the dendrites of spinal motoneurons in vivo. Journal of Neuroscience, 20(17), 6734–6740.PubMedGoogle Scholar
  39. Li, Y. R., Gorassini, M. A., & Bennett, D. J. (2004). Role of persistent sodium and calcium currents in motoneuron firing and spasticity in chronic spinal rats. Journal of Neurophysiology, 91(2), 767–783. doi: 10.1152/jn.00788.2003.PubMedCrossRefGoogle Scholar
  40. Lloyd, D. P. (1949). Post-tetanic potentiation of response in monosynaptic reflex pathways of the spinal cord. Journal of General Physiology, 33(2), 147–170.PubMedCrossRefGoogle Scholar
  41. Lytton, W. W. (1996). Optimizing synaptic conductance calculation for network simulations. Neural Computation, 8(3), 501–509.PubMedCrossRefGoogle Scholar
  42. Magalhaes, F. H., & Kohn, A. F. (2010). Vibration-induced extra torque during electrically-evoked contractions of the human calf muscles. Journal of Neuroengineering and Rehabilitation, 7, 26. doi: 10.1186/1743-0003-7-26.PubMedCrossRefGoogle Scholar
  43. Menegaldo, L. L., de Toledo, F. A., & Weber, H. I. (2004). Moment arms and musculotendon lengths estimation for a three-dimensional lower-limb model. Journal of Biomechanics, 37(9), 1447–1453. doi: 10.1016/j.jbiomech.2003.12.017.PubMedCrossRefGoogle Scholar
  44. Nickolls, P., Collins, D. F., Gorman, R. B., Burke, D., & Gandevia, S. C. (2004). Forces consistent with plateau-like behaviour of spinal neurons evoked in patients with spinal cord injuries. Brain, 127, 660–670. doi: 10.1093/Brain/Awh073.PubMedCrossRefGoogle Scholar
  45. Schwindt, P. C., & Crill, W. E. (1980a). Properties of a persistent inward current in normal and TEA-injected moto-neurons. Journal of Neurophysiology, 43(6), 1700–1724.PubMedGoogle Scholar
  46. Schwindt, P. C., & Crill, W. E. (1980b). Role of a persistent inward current in moto-neuron bursting during spinal seizures. Journal of Neurophysiology, 43(5), 1296–1318.PubMedGoogle Scholar
  47. Stuart, G. J., & Redman, S. J. (1990). Voltage dependence of Ia reciprocal inhibitory currents in cat spinal motoneurons. J Physiol-London, 420, 111–125.PubMedGoogle Scholar
  48. Taylor, A. M., & Enoka, R. M. (2004). Quantification of the factors that influence discharge correlation in model motor neurons. Journal of Neurophysiology, 91(2), 796–814. doi: 10.1152/jn.00802.2003.PubMedCrossRefGoogle Scholar
  49. Williams, E. R., & Baker, S. N. (2009). Circuits generating corticomuscular coherence investigated using a biophysically based computational model. I. Descending systems. J Neurophysiol, 101(1), 31–41. doi: 10.1152/jn.90362.2008.PubMedCrossRefGoogle Scholar
  50. Zengel, J. E., Reid, S. A., Sypert, G. W., & Munson, J. B. (1985). Membrane electrical-properties and prediction of motor-unit type of medial gastrocnemius motoneurons in the cat. Journal of Neurophysiology, 53(5), 1323–1344.PubMedGoogle Scholar
  51. Zhou, P., & Rymer, W. Z. (2004). MUAP number estimates in surface EMG: template-matching methods and their performance boundaries. Ann Biom Eng, 32(7), 1007–1015.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Leonardo Abdala Elias
    • 1
    Email author
  • Vitor Martins Chaud
    • 1
  • André Fabio Kohn
    • 1
  1. 1.Biomedical Engineering Laboratory, Escola Politécnica, PTC, Universidade de São Paulo, Av. Prof. Luciano GualbertoSão PauloBrazil

Personalised recommendations