Motoneuron pool input-output function (Powers & Heckman 2017)

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Accession:239582
"Although motoneurons have often been considered to be fairly linear transducers of synaptic input, recent evidence suggests that strong persistent inward currents (PICs) in motoneurons allow neuromodulatory and inhibitory synaptic inputs to induce large nonlinearities in the relation between the level of excitatory input and motor output. To try to estimate the possible extent of this nonlinearity, we developed a pool of model motoneurons designed to replicate the characteristics of motoneuron input-output properties measured in medial gastrocnemius motoneurons in the decerebrate cat with voltage- clamp and current-clamp techniques. We drove the model pool with a range of synaptic inputs consisting of various mixtures of excitation, inhibition, and neuromodulation. We then looked at the relation between excitatory drive and total pool output. Our results revealed that the PICs not only enhance gain but also induce a strong nonlinearity in the relation between the average firing rate of the motoneuron pool and the level of excitatory input. The relation between the total simulated force output and input was somewhat more linear because of higher force outputs in later-recruited units. ..."
Reference:
1 . Powers RK, Heckman CJ (2017) Synaptic control of the shape of the motoneuron pool input-output function. J Neurophysiol 117:1171-1184 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell;
Brain Region(s)/Organism:
Cell Type(s): Spinal cord L motor neuron alpha;
Channel(s):
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: NEURON;
Model Concept(s):
Implementer(s): Powers, Randy [rkpowers at u.washington.edu];
Search NeuronDB for information about:  Spinal cord L motor neuron alpha;
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TITLE Motoneuron L-type Calcium channels
:
: The parameters for this current come from V. Booth et al. J Neurophysiol 78:3371-3385, 1997
: Iterative equations
: Modified by RP to provide calcium to a separate pool (caL)and to have adjustable equilibrium
: potential vca


NEURON {
	SUFFIX L_Ca_inact
	USEION caL READ ecaL WRITE icaL VALENCE 2
	RANGE gcabar,icaL,m_inf,m,h
	GLOBAL vca,theta_m,kappa_m,theta_h,kappa_h
}


UNITS {
	(mA) = (milliamp)
	(mV) = (millivolt)
}

PARAMETER {
	gcabar  = 0.0003  (mho/cm2)
	ecaL		(mV)	: eca can't be set here, only in hoc
:	celcius = 36	(degC)
	dt		(ms)
	tau_m	= 20	(ms)
	v		(mV)
        vca=80		(mV)
	theta_m = -30   (mV)
	kappa_m = -6	(-mV)
	tau_h	= 1500	(ms)
	theta_h = 14   (mV)
	kappa_h = 4	(-mV)
}

STATE {
	m
	h
}

ASSIGNED {
	icaL		(mA/cm2)
	m_inf
	h_inf
	tadj
}

BREAKPOINT {
	SOLVE states METHOD cnexp
	icaL = gcabar * m *h* (v - vca)  :I have tried this as m*m also
}

DERIVATIVE states {
	evaluate_fct(v)
	m' = (m_inf - m) / tau_m
	h' = (h_inf - h) / tau_h
}

UNITSOFF
INITIAL {

:
:  Q10 was assumed to be 3 for both currents
:
:	tadj = 3.0 ^ ((celsius-36)/ 10 )

	evaluate_fct(v)
	m = m_inf
	h = h_inf
}

PROCEDURE evaluate_fct(v(mV)) {

	m_inf = 1 / (1 + (Exp((v - theta_m)/ kappa_m))): / tadj
	h_inf = 1 / (1 + (Exp((v - theta_h)/ kappa_h))): / tadj

}

FUNCTION vtrap(x,y) {
	if (fabs(x/y) < 1e-6) {
		vtrap = y*(1 - x/y/2)
	}else{
		vtrap = x/(Exp(x/y)-1)
	}
}

FUNCTION Exp(x) {
	if (x < -100) {
		Exp = 0
	}else{
		Exp = exp(x)
	}
} 


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