Simulations of motor unit discharge patterns (Powers et al. 2011)

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Accession:143671
" ... To estimate the potential contributions of PIC (Persistent Inward Current) activation and synaptic input patterns to motor unit discharge patterns, we examined the responses of a set of cable motoneuron models to different patterns of excitatory and inhibitory inputs. The models were first tuned to approximate the current- and voltage-clamp responses of low- and medium-threshold spinal motoneurons studied in decerebrate cats and then driven with different patterns of excitatory and inhibitory inputs. The responses of the models to excitatory inputs reproduced a number of features of human motor unit discharge. However, the pattern of rate modulation was strongly influenced by the temporal and spatial pattern of concurrent inhibitory inputs. Thus, even though PIC activation is likely to exert a strong influence on firing rate modulation, PIC activation in combination with different patterns of excitatory and inhibitory synaptic inputs can produce a wide variety of motor unit discharge patterns."
Reference:
1 . Powers RK, Elbasiouny SM, Rymer WZ, Heckman CJ (2012) Contribution of Intrinsic Properties and Synaptic Inputs to Motoneuron Discharge Patterns: A Simulation Study. J Neurophysiol 107(3):808-23 [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): Activity Patterns; Bursting; Action Potentials;
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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PowersEtAl2012
code
Gfluctdv.mod *
ghchan.mod *
kca2.mod *
kdrRL.mod *
L_Ca.mod *
mAHP.mod *
na3rp.mod *
naps.mod *
synss.mod
ana_FI.hoc
ana_G.hoc
ana_passive.hoc
ana_vc.hoc
ana_vc_synss.hoc
AP_AHP.ses
FIgraph.hoc
FRcablepas.hoc
FRmnrampcc.ses
FRmnrampvc_synss.ses
FRMotoneuronNaHH.hoc
gramp.ses
GUI_FR_analysis.hoc
inhibdist
makebiramp.hoc *
passive.ses
RecActive.hoc
re-init.hoc
SetConductances.hoc
test.hoc
twobirampsdel.hoc *
vramp
vrampdel
vrampdel.hoc
                            
TITLE na3rp
: Na current 
: modified from Jeff Magee. M.Migliore may97
: added sh to account for higher threshold M.Migliore, Apr.2002
: modified by RP to have slow inactivation given in Fleiderivsh et al.

NEURON {
	SUFFIX na3rp
	USEION na READ ena WRITE ina
	RANGE  gbar, ar, sh
	GLOBAL minf, hinf, mtau, htau, sinf, taus,qinf, thinf
}

PARAMETER {
	sh   = 8	(mV)
	gbar = 0.010   	(mho/cm2)	
								
	tha  =  -30	(mV)		: v 1/2 for act	
	qa   = 7.2	(mV)		: act slope (4.5)		
	Ra   = 0.4	(/ms)		: open (v)		
	Rb   = 0.124 	(/ms)		: close (v)		

	thi1  = -45	(mV)		: v 1/2 for inact 	
	thi2  = -45 	(mV)		: v 1/2 for inact 	
	qd   = 1.5	(mV)	        : inact tau slope
	qg   = 1.5      (mV)
	mmin=0.02	
	hmin=0.5			
	q10=2
	Rg   = 0.01 	(/ms)		: inact recov (v) 	
	Rd   = .03 	(/ms)		: inact (v)	
	qq   = 10        (mV)
	tq   = -55      (mV)

	thinf  = -50 	(mV)		: inact inf slope	
	qinf  = 4 	(mV)		: inact inf slope 

        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.
	ena		(mV)            : must be explicitly def. in hoc
	celsius
	v 		(mV)
}


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

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

STATE { m h s}

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

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


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

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

LOCAL mexp, hexp, sexp

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

PROCEDURE trates(vm,a2,sh2) {  
        LOCAL  a, b, c, qt
        qt=q10^((celsius-24)/10)
	a = trap0(vm,tha+sh2,Ra,qa)
	b = trap0(-vm,-tha-sh2,Rb,qa)
	mtau = 1/(a+b)/qt
        if (mtau<mmin) {mtau=mmin}
	minf = a/(a+b)

	a = trap0(vm,thi1+sh2,Rd,qd)
	b = trap0(-vm,-thi2-sh2,Rg,qg)
	htau =  1/(a+b)/qt
        if (htau<hmin) {htau=hmin}
	hinf = 1/(1+exp((vm-thinf-sh2)/qinf))
        taus = 1/(alps(vm)+bets(vm))
	c=alps(vm)*taus
        sinf = c+a2*(1-c)
}

FUNCTION trap0(v,th,a,q) {
	if (fabs(v-th) > 1e-6) {
	        trap0 = a * (v - th) / (1 - exp(-(v - th)/q))
	} else {
	        trap0 = a * q
 	}
}	

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