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]
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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 lumbar motor neuron alpha ACh cell;
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 lumbar motor neuron alpha ACh cell;
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RPCH_JNP17
FivecomptcMG
FivecompthTA
FivecompthTAlw
README.html
Gfluctdv.mod *
gh.mod
kdrRL.mod *
L_Ca_inact.mod *
mAHP.mod *
na3rp.mod *
naps.mod *
avrate.png
cc_command.hoc
fwave1s.txt
fwave2s.txt
init.hoc
init_5cmpt.hoc
makebiramp.hoc *
mosinit.hoc
pars2manyhocs.py *
SetConductances2.hoc *
twobirampsdel.hoc *
                            
TITLE naps		:modified to have slow inactivation described in Fleidervish and to make slope a global parameter

NEURON {
	SUFFIX naps
	USEION na READ ena WRITE ina
	RANGE  gbar, thegna, sh, ar,minf,sinf,taus
	GLOBAL mtau,vslope
}

PARAMETER {
	gbar = .0052085   	(mho/cm2)
	sh = 0  (mV)
	vslope=6.8   (mV)	:activation slope
	mtau = 1 (ms)
	ena		(mV)       :must be explicitly defined in hoc     
        a0s=0.001	(/ms)	
        b0s=0.0034	(/ms)
        asvh=-85	(mV) 
        bsvh=-17	(mV) 
        avs=30		(mV)
        bvs=10		(mV)
        ar=1		(1)		: 1=no inact., 0=max inact.
	celsius (degC)
	v 		(mV)
}


UNITS {
	(mA) = (milliamp)
	(mV) = (millivolt)
	(pS) = (picosiemens)
	(um) = (micron)
} 

ASSIGNED {
	ina 		(mA/cm2)
	thegna		(mho/cm2)
	minf 	
	sinf
	taus (ms)
}
 

STATE { m s }

UNITSOFF

BREAKPOINT {
    SOLVE states METHOD cnexp
	        		
	thegna =gbar*m*s       
	ina = thegna * (v - ena)
	} 

INITIAL {
	trates(v,ar,sh)
	m=minf  
	s=sinf
}

DERIVATIVE states {   
    	trates(v,ar,sh)
        s' = (sinf - s)/taus
	m' = (minf-m)/mtau
}

PROCEDURE trates(vm,a2,sh2) {  
        LOCAL   c 

	minf = (1/(1+exp(-(vm+52.3-sh2)/vslope)))      	
        taus = 1/(alps(vm)+bets(vm))
	c=alps(vm)*taus
        sinf = c+a2*(1-c)
 }




FUNCTION alps(v(mV)) {  
  alps = a0s*exp((asvh-v)/avs)
}

FUNCTION bets(v(mV)) {
  bets = b0s/(exp((bsvh-v)/bvs)+1)
}

UNITSON