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

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Accession:152292
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.
Reference:
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;
Gene(s):
Transmitter(s):
Simulation Environment: XPP;
Model Concept(s): Bursting;
Implementer(s): Rubin, Jonathan E [jonrubin at pitt.edu]; Park, Choongseok [cpark at ncat.edu];
Search NeuronDB for information about:  AMPA; IP3; I Na,p; I K; I CAN; I Sodium;
## Set file for OneCellTwoOsc.ode on Thu Jan 16 20:15:34 2014
8   Number of equations and auxiliaries
20   Number of parameters
# Numerical stuff
1    nout
40    nullcline mesh
8   Qual RK
10000  total
0.1  DeltaT
0  T0
0  Transient
500001  Bound
1e-12  DtMin
1  DtMax
0.001  Tolerance
0.001  Abs. Tolerance
0  Max Delay
100   Eigenvector iterates
0.001  Eigenvector tolerance
0.001  Newton tolerance
0  Poincare plane
1e-05  Boundary value tolerance
1e-05  Boundary value epsilon
20   Boundary value iterates
0   Poincare None
1   Poincare variable
1   Poincare sign
0   Stop on Section
0   Delay flag
10000  Current time
10000  Last Time
1   MyStart
1   INFLAG
# Delays
-50  
0.004  
0.33  
0.03  
0.93  
# Bndry conds
0
0
0
0
0
# Old ICs
-49.42172818719667  V
0.006018887841041419  N
0.3993173817399912  H
0.0247530791180861  C
0.941723602876669  L
# Ending  ICs
-49.62249385170052  V
0.005732605363421063  N
0.3976212815079196  H
0.0247530791180861  C
0.941723602876669  L
# Parameters
21  Cms
0  I_aps
11.2  gk
28  gna
2.5  gnap
2.3  gl
0.74  Kcan
0.97  ncan
0.7  gcan
0.9  I
1.25  Ct
2.5e-05  fi
31000  P
1  Ki
0.4  Ka
400  Ve
0.2  Ke
0.005  A
0.4  Kd
0.185  sigma
# Graphics
0.7071097251469876  rm
-0.4999999999826661  rm
0.4999958366025516  rm
0.7071038372138505  rm
0.5000041633974482  rm
-0.4999999999826661  rm
0  rm
0.7071038372138505  rm
0.7071097251469876  rm
0    
1    
2    
1    
0    
0    
1    
2    
1    
0    
0    
1    
2    
1    
0    
0    
1    
2    
1    
0    
0    
1    
2    
1    
0    
0    
1    
2    
1    
0    
0    
1    
2    
1    
0    
0    
1    
2    
1    
0    
0    
1    
2    
1    
0    
0    
1    
2    
1    
0    
-1000   
1000   
0    
0   3DFlag
1   Timeflag
0   Colorflag
0   Type
1  color scale
0   minscale
10000   xmax
0   xmin
10   ymax
-60   ymin
12   zmax
-12   zmin
5000   
0.0002   
-25   
0.02857142857142857   
0   
0.08333333333333333   
45   Theta
45   Phi
0    xshft
0    yshft
0    zshft
0   xlo
-60   ylo
0   
-60   
10000   xhi
10   yhi
10000   
10   
# Transpose variables etc
V
2   n columns
1   n rows
1   row skip
1   col skip
1   row 0
# Coupling stuff for H funs
0
0
0
0
0
# Array plot stuff

1   NCols
0   Row 1
50   NRows
8   RowSkip
0  Zmin
1  Zmax
# Torus information 
0    Torus flag 1=ON
6.283185307179586  Torus period
# Range information
Cms
-1   eq-range stab col
0   shoot flag 1=on
10   eq-range steps
0  eq_range low
1  eq_range high
V
V
20   Range steps
0   Cycle color 1=on
1   Reset data 1=on
1   Use old I.C.s 1=yes
0  Par1 low
0  Par2 low
1  Par1 high
1  Par2 high
Cms
0   BVP side
0   color cycle flag 1=on
10   BVP range steps
0  BVP range low
1  BVP range high
RHS etc ...
dV/dT=(-I_K-I_NA-I_NAP-I_L-I_APS-I_CAN)/CMS
dN/dT=(NINF-N)/TAUN
dH/dT=(HINF-H)/TAUH
dC/dT=FI*(J_ER_IN-J_ER_OUT)
dL/dT=A*(KD-(C+KD)*L)
CE=CE
ICAN=I_CAN
INAPS=I_NAP

where ...
MINF = 1/(1+EXP((V-VM) /SM))    
NINF = 1/(1+EXP((V-VN) /SN))   
MINFP = 1/(1+EXP((V-VMP)/SMP))   
HINF = 1/(1+EXP((V-VH) /SH))   
TAUN = TAUNB/COSH((V-VN)/(2*SN))   
TAUH = TAUHB/COSH((V-VH)/(2*SH))   
I_NA = GNA*MINF^3*(1-N)*(V-VNA)   
I_K = GK*N^4*(V-VK)   
I_NAP = GNAP*MINFP*H*(V-VNA)   
I_L = GL*(V-VLEAKS)   
CANINF = 1/(1+(KCAN/C)^NCAN)   
I_CAN = GCAN*CANINF*(V-VNA)   
J_ER_IN = (LL + P*( (I*C*L)/( (I+KI)*(C+KA) ) )^3 )*(CE - C)   
J_ER_OUT = VE*C^2/(KE^2+C^2)   
CE =  (CT - C)/SIGMA   

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