CA1 pyramidal cell: I_NaP and I_M contributions to somatic bursting (Golomb et al 2006)

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Accession:66268
To study the mechanisms of bursting, we have constructed a conductance-based, one-compartment model of CA1 pyramidal neurons. In this neuron model, reduced [Ca2+]o is simulated by negatively shifting the activation curve of the persistent Na+ current (INaP), as indicated by recent experimental results. The neuron model accounts, with different parameter sets, for the diversity of firing patterns observed experimentally in both zero and normal [Ca2+]o. Increasing INaP in the neuron model induces bursting and increases the number of spikes within a burst, but is neither necessary nor sufficient for bursting. We show, using fast-slow analysis and bifurcation theory, that the M-type K+ current (IM) allows bursting by shifting neuronal behavior between a silent and a tonically-active state, provided the kinetics of the spike generating currents are sufficiently, though not extremely, fast. We suggest that bursting in CA1 pyramidal cells can be explained by a single compartment *square bursting* mechanism with one slow variable, the activation of IM. See paper for more and details.
Reference:
1 . Golomb D, Yue C, Yaari Y (2006) Contribution of persistent Na+ current and M-type K+ current to somatic bursting in CA1 pyramidal cells: combined experimental and modeling study. J Neurophysiol 96:1912-26 [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): Hippocampus CA1 pyramidal GLU cell;
Channel(s): I Na,p; I Na,t; I A; I K; I M;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: XPP;
Model Concept(s): Bursting; Bifurcation;
Implementer(s): Golomb, David [golomb at bgu.ac.il];
Search NeuronDB for information about:  Hippocampus CA1 pyramidal GLU cell; I Na,p; I Na,t; I A; I K; I M;
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ca1_model_db
README.HTML
casup.pdf
nca.ode
ncaScreenShot.jpg
zca.ode
zcaScreenShot.jpg
                            
# Excitatory cortical neurons, normal [Ca].
#
number Cm=1.0
number pms=3,pns=4
number VNa=55.0,t_tauh=-40.5,t_taun=-27.0
number thetaa=-50.0,sigmaa=20.0,thetab=-80.0,sigmab=-6.0,tauBs=15.0
number thetam=-30.0,sigmam=9.5,sigmah=-7.0,sigman=10.0,sigmaz=5.0
number VCa=120
number thetar=-20.0,sigmar=10.0,thetac=-30,sigmac=7
number pwrc=1,pwrq=4
# 
p gNa=35.0,gKdr=6.0,gL=0.05,Iapp=1.0
p gA=1.4,gNaP=0.2,gZ=1.0
p thetaz=-39.0,tauZs=75.0
p phi=10.0, thetah=-45.0
p thetan=-35.0,thetap=-41.0,sigmap=3.0
p VK=-90.0,VL=-70.0
p gCa=0.08,gKCa=10.0,gKAHP=5
p tauRs=1.0,aq=2,ac=6,tauq=450,tauCa=13,uuCa=0.13,tauKc=2
#
GAMMAF(VV,theta,sigma)=1.0/(1.0+exp(-(VV-theta)/sigma))
ZFUNC(AA,CA,zz)=1/(1+(AA^zz/CA^zz))
#
VVs'=(-gL*(VVs-VL)-INa-INaP-IKdr-IA-Iz-ICa-IKC-IAHP+Iappx)/Cm
hhs'=phi*(GAMMAF(VVs,thetah,sigmah)-hhs)/(1.0+7.5*GAMMAF(VVs,t_tauh,-6.0))
nns'=phi*(GAMMAF(VVs,thetan,sigman)-nns)/(1.0+5.0*GAMMAF(VVs,t_taun,-15.0))
bbs'=(GAMMAF(VVs,thetab,sigmab)-bbs)/tauBs
zzs'=(GAMMAF(VVs,thetaz,sigmaz)-zzs)/tauZs
rrs'=(GAMMAF(VVs,thetar,sigmar)-rrs)/tauRs
ccs'=(GAMMAF(VVs,thetac,sigmac)-ccs)/tauKc
qqs'=(ZFUNC(aq,Ca,pwrq)-qqs)/tauq
Ca'=-uuCa*ICa-Ca/tauCa
#
Iappx=Iapp
#if(t<=3.0)then(Iapp)else(0.0)
Minfs=GAMMAF(VVs,thetam,sigmam)
Pinfs=GAMMAF(VVs,thetap,sigmap)
Ainfs=GAMMAF(VVs,thetaa,sigmaa)
mKCa=ZFUNC(ac,Ca,pwrc)
#
INa=gNa*(Minfs^pms)*hhs*(VVs-VNa)
INaP=gNaP*Pinfs*(VVs-VNa)
IKdr=gKdr*(nns^pns)*(VVs-VK)
IA=gA*Ainfs^3*bbs*(VVs-VK)
Iz=gZ*zzs*(VVs-VK)
ICa=gCa*rrs^2*(VVs-VCa)
IKC=gKCa*mKCa*ccs*(VVs-VK)
IAHP=gKAHP*qqs*(VVs-VK) 
#
VVs(0)=-71.962
hhs(0)=0.979199
nns(0)=0.0242166
bbs(0)=0.207565
zzs(0)=0.0013689
Ca[0]=0.000787
rrs(0)=0.005507
ccs(0)=0.002486
qqs(0)=0.0
#
@ MAXSTOR=800000
@ BACK=Black
@ XP=T
@ YP=VVs
@ AXES=2
@ TOTAL=500.0
@ DT=0.05
@ NJMP=1
@ T0=0.0
@ TRANS=0.0
@ NMESH=40
@ METH=rungekutta
@ DTMIN=0.001
@ DTMAX=1.0
@ TOLER=0.00001
@ BOUND=10000.0
@ DELAY=0
@ XLO=0.0, XHI=500.0, YLO=-90.0, YHI=30.0
@ NTST=50,NMAX=2000,NPR=50
@ DS=0.02,DSMIN=0.001,DSMAX=0.5
@ PARMIN=-10,PARMAX=50,NORMMIN=0.0,NORMMAX=10000.0
@ AUTOVAR=VVs1,AUTOXMIN=-10.0,AUTOXMAX=50.0,AUTOYMIN=-90.0,AUTOYMAX=50.0
done