Individual and collective properties of computationally efficient motoneuron models of types S and F with active dendrites Leonardo Abdala Elias n,1 , Andre ´ Fabio Kohn 1 Biomedical Engineering Laboratory, Escola Polite ´cnica, PTC, Universidade de S ~ ao Paulo, Avenida Prof. Luciano Gualberto, Travessa 3, 158, CEP 05508-900, S ~ ao Paulo, SP, Brazil article info Article history: Received 18 March 2012 Received in revised form 16 June 2012 Accepted 26 June 2012 Communicated by Demisn Battaglia Available online 28 August 2012 Keywords: Bistability L-type calcium channel Motor control Neuronal network Plateau potential Synaptic integration abstract The input–output properties of motoneurons (MNs) and motor units (MUs) may be modulated by different physiological variables, including neuromodulators released by presynaptic neurons from the brainstem. Monoamines, such as serotonin and norepinephrine, act on MNs mainly by activating dendritic L-type Ca þþ channels, generating a persistent inward current (PIC), which may change the input–output properties of the MU. If the firing properties of individual MNs and also the features of the force generated by the MUs can be changed, it follows that the descending monoaminergic systems may modulate the overall dynamics of motor control. The purpose of the present study is to investigate the effects of neuromodulation on the input–output properties of mathematically modeled type- specified MUs. Computationally efficient models are presented for S- and F-type mammalian MNs as well as a MN pool commanding muscle units of the Soleus muscle. The single models have a dendritic L-type Ca þþ channel, generating a PIC, along with somatic currents that are responsible for spike- generating mechanisms and the afterhyperpolarization. The S-type active-dendrite (AD) MN model resulted highly excitable and discharged in a self-sustained manner after an excitatory input (bistability). An inhibitory activity turned off this self-sustained discharge. In addition, this low- threshold MN model showed a significant reduction in interspike interval (ISI) variability in comparison with an equivalent passive-dendrite (PD) MN model discharging at a similar mean rate. The frequency response gain from presynaptic spike train rate modulation to output spike train modulation had a clear valley from about 1–10 Hz for the S-type AD MN model, whereas the PD model showed a gain increase instead. On the other hand, the frequency responses of PD and AD F-type models were similarly shaped, with the AD model having a higher gain at high frequencies. These results suggest that in motor behaviors where steady or low frequency activity is required, such as posture, PICs would aid low-threshold MNs to respond with regular spikes, reducing output variability, and would attenuate the effects of high-frequency input disturbances, helping maintain system steadiness. At the same time, high-threshold MNs being more responsive to high-frequency disturbances would contribute with the necessary activity to correct for postural deviations from a desired position. Simulation results from the neuromuscular model have shown that the PIC activation profoundly affects muscle force generation, with the neuromodulatory activity acting in the adjustment of the motor output. Both individual and collective results presented here expand the understanding of the versatility of monoaminergic neuromodulation in adjusting both the MN input–output coding and the control of force generation. & 2012 Elsevier B.V. All rights reserved. 1. Introduction During normal motor behavior or in reduced preparations of decerebrate unanesthetized cats, the activity of monoaminergic pathways descending from the brainstem has a powerful effect on intrinsic membrane properties of motoneurons (MNs) in the spinal cord [1,2]. Voltage-gated ionic channels, typically low- threshold non-inactivating L-type Ca þþ channels located at den- dritic regions [3], are activated by neuromodulators (e.g., serotonin and norepinephrine), resulting in a persistent inward current (PIC) that reaches the soma [4–6]. In this condition, complex behaviors, such as bistability and plateau potentials, may emerge Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/neucom Neurocomputing 0925-2312/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.neucom.2012.06.038 Abbreviations: AD, active dendrite; AHP, afterhyperpolarization; Ca þþ , calcium; EMG, electromyogram; EPSP, excitatory post-synaptic potential; IPSP, inhibitory post-synaptic potential; ISI, interspike interval; K þ , potassium; MG, medial gastrocnemius muscle; MN, motoneuron; MU, muscle unit; Na þ , sodium; PD, passive dendrite; PIC, persistent inward current; SOL, soleus muscle. n Corresponding author. Tel.: þ55 11 3091 5541; fax: þ55 11 3091 5718. E-mail addresses: leoabdala@leb.usp.br, ee.leoabdala@gmail.com (L.A. Elias). 1 Both authors contributed equally to this work. Neurocomputing 99 (2013) 521–533