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

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An Erratum to this article was published on 25 July 2012

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.

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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

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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.

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Authors and Affiliations

  1. Biomedical Engineering Laboratory, Escola Politécnica, PTC, Universidade de São Paulo, Av. Prof. Luciano Gualberto, trav. 3, 158,, São Paulo, SP, Brazil, CEP: 05508-900

    Leonardo Abdala Elias, Vitor Martins Chaud & André Fabio Kohn

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  1. Leonardo Abdala Elias
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  2. Vitor Martins Chaud
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Correspondence to Leonardo Abdala Elias.

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Action Editor: Eberhard Fetz

All authors contributed equally to this work.

Appendix: Geometric and electrotonic properties of the motoneuron pool

Appendix: Geometric and electrotonic properties of the motoneuron pool

The passive characteristics of each single MN model (see section 2.1.1) depended on the geometric and electrotonic properties of the cell (Equations A1 to A5), which were based on data from type-specified (i.e., S-, FR-, and FF-type) cat MNs (Fleshman et al. 1988; Zengel et al. 1985). In this study, the parameters varied linearly within each type of MNs (see Table 3), resulting in a piece-wise linear approximation of how these parameters vary along the whole pool. Figure 10 shows an example for the range of rheobase currents adopted in the SOL MN pool. All the parameters were made equal for the different motor nuclei (i.e., SOL, MG, LG, and TA) and the differences between them were only in the numbers of each MU type (Table 4).

$$ {g_c} = \frac{2}{{\frac{{{R_i}.{l_D}}}{{\pi .r_D^2}} + \frac{{{R_i}.{l_S}}}{{\pi .r_S^2}}}} $$
(A1)
$$ {g_{{lD}}} = \frac{{2.\pi .{r_D}.{l_D}}}{{{R_{{m,D}}}}} $$
(A2)
$$ {g_{{lS}}} = \frac{{2.\pi .{r_S}.{l_S}}}{{{R_{{m,S}}}}} $$
(A3)
$$ {C_D} = 2.\pi .{r_D}.{l_D}.{C_m} $$
(A4)
$$ {C_S} = 2.\pi .{r_S}.{l_S}.{C_m} $$
(A5)
Fig. 10
figure 10

Range of rheobase currents for the SOL MN pool. Within each MN type (the range is bounded by dots) the values varied linearly, resulting in a piece-wise linear variation along the pool

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Table 3 Range of values adopted for the geometric and electrotonic parameters of MN models
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Table 4 MU number adopted in each motor nucleus of the neuromuscular system
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Elias, L.A., Chaud, V.M. & Kohn, A.F. Models of passive and active dendrite motoneuron pools and their differences in muscle force control. J Comput Neurosci 33, 515–531 (2012). https://doi.org/10.1007/s10827-012-0398-4

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