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 lumbar motor neuron alpha 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 cell;
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L_Ca_inact.mod *
mAHP.mod *
na3rp.mod *
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 COMMENT
 
 mAHP.mod
 
 Calcium-dependent potassium channel responsible for mAHP in motoneurons
 Simplified calcium channel that provides Ca for the KCa conductance is included
 	
 ENDCOMMENT

 NEURON {
 	SUFFIX mAHP
 	USEION k READ ek WRITE ik
 	USEION ca READ eca WRITE ica
 	RANGE n, gkcamax,gcamax,ik,cai,ica,depth,taur
 	GLOBAL fKCa, bKCa, caix
 }

 
 UNITS {
 	(mA) = (milliamp)
 	(mV) = (millivolt)
 	(S) = (siemens)
 	(um) = (micron)
 	(molar) = (1/liter)			: moles do not appear in units
 	(mM)	= (millimolar)
 	(msM)	= (ms mM)
 	FARADAY = (faraday) (coulomb)
 } 
 
 PARAMETER {
 	gkcamax = 0.03   	(S/cm2)	
	gcamax = 3e-5		(S/cm2)
	mvhalfca = -30		(mV)
	mslpca = 4 		(mV)
	mtauca = 1		(ms)	
 	caix = 2	
  	cainf=0.0001		(mM)
 	depth	= .1		(um)		: depth of shell
 	taur	= 20		(ms)		: rate of calcium removal
								
  	fKCa   = 0.1		: max act rate  
 	bKCa   = 0.1		: max deact rate 
 
 	celsius		(degC)
 } 
 
 
 ASSIGNED {
 	ik 		(mA/cm2)
 	v 		(mV)
	ica 		(mA/cm2)
 	ek		(mV)
	eca		(mV)
 	ninf
 	ntau 		(ms)
	minfca	
	drive_channel
 }
  
 
 STATE {
 mca 
 n 
 cai (mM)
}
 
 INITIAL { 
	cai=cainf
 	rates(cai)
	mcarate(v)
 	n = ninf
	mca=minfca
 }
 
 BREAKPOINT {
         SOLVE states METHOD cnexp
	ica = gcamax*mca*(v - eca)
 	ik =  gkcamax *n* (v - ek)
 } 
 

DERIVATIVE states { 
	 
 	drive_channel =  - (10000) * ica/ (2 * FARADAY * depth)
 	if (drive_channel <= 0.) { drive_channel = 0. }	: cannot pump inward
 	cai' = drive_channel + (cainf-cai)/taur

         rates(cai)    
         n' = (ninf-n)/ntau
         mcarate(v)    
         mca' = (minfca-mca)/mtauca
}
PROCEDURE rates(cai(mM)) {  LOCAL a,b
							UNITSOFF
         a = fKCa * (1e3*(cai  -cainf))^caix		: rate constant depends on cai in uM
         b = bKCa
         ntau = 1/(a+b)
         ninf = a*ntau
					UNITSON
 }

PROCEDURE mcarate(v (mV)) {
	TABLE minfca
	DEPEND mvhalfca,mslpca 
	FROM -100 TO 100 WITH 200
	
	minfca = 1/(1+exp(-(v-mvhalfca)/mslpca))
}

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