PreBotzinger Complex inspiratory neuron with NaP and CAN currents (Park and Rubin 2013)

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We have built on earlier models to develop a single-compartment Hodgkin-Huxley type model incorporating NaP and CAN currents, both of which can play important roles in bursting of inspiratory neurons in the PreBotzinger Complex of the mammalian respiratory brain stem. The model tracks the evolution of membrane potential, related (in)activation variables, calcium concentration, and available fraction of IP3 channels. The model can produce several types of bursting, presented and analyzed from a dynamical systems perspective in our paper.
1 . Park C, Rubin JE (2013) Cooperation of intrinsic bursting and calcium oscillations underlying activity patterns of model pre-Bötzinger complex neurons. J Comput Neurosci 34:345-66 [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): Respiratory column neuron; PreBotzinger complex neuron;
Channel(s): I Na,p; I K; I CAN; I Sodium;
Gap Junctions:
Receptor(s): AMPA; IP3;
Simulation Environment: XPP;
Model Concept(s): Bursting;
Implementer(s): Rubin, Jonathan E [jonrubin at]; Park, Choongseok [cpark at];
Search NeuronDB for information about:  AMPA; IP3; I Na,p; I K; I CAN; I Sodium;
# default: gnap=2,gcan=0.7,I=1 (SD-Burst)

# AUGUST 2010
# cell is combination of  Nap and CaN burster (Can closed-cell model with ER in dendrtes) 
# NaP burster is from from Butera, 1999; setting gcan=0 reproduce Butera 1999 model
# Frequency of Ca oscillations controlled by either Catot or I (larger values - faster bursting)

# units: V = mV; Cm = pF; g = uS

minf=1/(1+exp((v-vm) /sm)) 
ninf=1/(1+exp((v-vn) /sn))
hinf=1/(1+exp((v-vh) /sh))


I_l =gl*(v-vleaks)

# Equations for CaN current
caninf =1/(1+(Kcan/C)^ncan)

#Fluxes in and out of ER
# l is fraction of open IP3 channels
J_ER_in=(LL + P*( (I*C*l)/( (I+Ki)*(C+Ka) ) )^3 )*(Ce - C)
Ce = (Ct - C)/sigma

# Equations
v'= (-I_k - I_na-I_nap-I_l-I_aps-I_can)/Cms
n'= (ninf-n)/taun
h'= (hinf-h)/tauh
C' = fi*( J_ER_in- J_ER_out)
l' = A*( Kd - (C + Kd)*l )

# Auxilary variables
aux Ce=Ce
aux ican=I_can
aux inaps=I_nap

#Initial conditions


# Voltage parameters
par Cms=21, I_aps=0
num vna=50,vk=-85, vleaks=-58 
num vm=-34,vn=-29, vmp=-40, vh=-48
num sm=-5, sn=-4,  smp=-6,  sh=5
num taunb=10,  tauhb=10000, 
par gk=11.2, gna=28, gnap=2,gl=2.3

# Ca parameters
par Kcan=0.74, ncan=0.97,gcan=0.7
par I=1
par Ct=1.25
par fi=0.000025
num LL=0.37
par P=31000
par Ki=1.0
par Ka=0.4
par Ve=400
par Ke=0.2
par A=0.005 
par Kd=0.4
par sigma=0.185

@ dt=0.1,total=10000,meth=qualrk,xp=t,yp=v
@ xlo=0,xhi=10000,ylo=-60,yhi=10.,bound=500001,maxstor=5000001


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