The activity phase of postsynaptic neurons (Bose et al 2004)

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Accession:45513
We show, in a simplified network consisting of an oscillator inhibiting a follower neuron, how the interaction between synaptic depression and a transient potassium current in the follower neuron determines the activity phase of this neuron. We derive a mathematical expression to determine at what phase of the oscillation the follower neuron becomes active. This expression can be used to understand which parameters determine the phase of activity of the follower as the frequency of the oscillator is changed. See paper for more.
Reference:
1 . Bose A, Manor Y, Nadim F (2004) The activity phase of postsynaptic neurons in a simplified rhythmic network. J Comput Neurosci 17:245-61 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network;
Brain Region(s)/Organism: Stomatogastric ganglion;
Cell Type(s): Abstract Morris-Lecar neuron;
Channel(s): I A;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: XPP; MATLAB;
Model Concept(s): Activity Patterns; Bursting; Temporal Pattern Generation; Oscillations; Simplified Models;
Implementer(s): Nadim, Farzan [Farzan at andromeda.Rutgers.edu]; Bose, Amitabha [bose at njit.edu]; Lewis, Timothy [tlewis at cns.nyu.edu];
Search NeuronDB for information about:  I A;
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activityphase
readme.txt
DBdep+A.ode
DBdep+A.ode.set
DBjcns1.m
DBjcns2.m
DBjcns3.m
                            
## Set file for newdep+A.ode on Tue Jun  8 16:23:00 2004
11   Number of equations and auxiliaries
20   Number of parameters
# Numerical stuff
1    nout
200    nullcline mesh
9   Stiff
5000  total
1  DeltaT
0  T0
0  Transient
10000  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
5000  Current time
5000  Last Time
0   MyStart
1   INFLAG
# Delays
0.0
0.0
1  
0.0
0.0
0.0
0.0
0.0
# Bndry conds
0
0
0
0
0
0
0
0
# Old ICs
-45.58413083089855  VF
0.002323725319354741  WF
0.3288899159330281  HA
0.2692778015660057  D
0.3641973436473382  S
199.4999999999526  Y
560.6297679549228  TF
0  PERIOD
# Ending  ICs
-45.57977198419412  VF
0.002323749093931422  WF
0.3288888033418859  HA
0.2692544539181648  D
0.3641029018879464  S
199.4999999999569  Y
560.6230312878373  TF
0  PERIOD
# Parameters
75  ipost
15  v5
10  k
4  ga
-6  vma
0.5  kma
4  ginh
-7  vha
0.1  kha
500  tauhlo
15  tauhhi
700  tauhmed
40  tauwflo
10  tauwfhi
600  taua
5  taub
300  tauk
1  c1
20  TA
800  per
# Graphics
0.7071097251469876  rm
-0.4999999999826661  rm
0.4999958366025516  rm
0.7071038372138505  rm
0.5000041633974484  rm
-0.4999999999826661  rm
0  rm
0.7071038372138505  rm
0.7071097251469876  rm
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1    
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1    
2    
1    
0    
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3750   
0.0008   
-21.97285   
0.02126431221113761   
0   
0.08333333333333333   
45   Theta
45   Phi
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0    yshft
0    zshft
2500   xlo
-69   ylo
-60   
-0.125   
5000   xhi
25.0543   yhi
60   
0.6   
# Transpose variables etc
VF
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
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
ipost
-1   eq-range stab col
0   shoot flag 1=on
10   eq-range steps
0  eq_range low
1  eq_range high
VF
VF
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
ipost
0   BVP side
0   color cycle flag 1=on
10   BVP range steps
0  BVP range low
1  BVP range high
RHS etc ...
dVF/dT=(IPOST-GCA*MINF(VF)*(VF-VCA)-GK*WF*(VF-VK)-GA*MAINF(VF)*HA*(VF-VK)-GL*(VF-VL)-GINH*S*(VF-VSYN))/C1
dWF/dT=(WFINF(VF)-WF)/TAUW(VF)
dHA/dT=(HAINF(VF)-HA)/TAUHA(VF)
dD/dT=(1-D)*HEAV(VTHETA-V)/TAUA-D*HEAV(V-VTHETA)/TAUB
dS/dT=-S*(HEAV(VTHETA-V)/TAUK+HEAV(V-VTHETA)*SDECAYUP)
dY/dT=1
dTF/dT=0
dPERIOD/dT=0
PHASE=TF/PER
V=V
WINDOW=HEAV(VF-VHA)-HEAV(VF-VMA-K)

where ...
V = -50+50*HEAV(TA-MOD(T,PER))   
V1 = -1.2   
V2 = 18   
V3 = 0   
V4 = 5   
GK = 8   
GL = 2   
GCA = 4   
VK = -84   
VL = -60   
VCA = 120   
C = 40   
VSYN = -80   
VTHETA = -25   
SDECAYUP = 0   

User-defined functions:
MINF(V) = .5*(1+TANH((V-V1)/V2))  
WINF(V) = .5*(1+TANH((V-V3)/V4))  
WFINF(V) = .5*(1+TANH((V-V5)/V4))  
TAUW(V) = TAUWFLO+(TAUWFHI-TAUWFLO)*WINF(V)  
HAINF(V) = 1/(1+EXP((V-VHA)/KHA))  
MAINF(V) = 1/(1+EXP(-(V-VMA)/KMA))  
TAUHA(V) = TAUHHI+(TAUHLO-TAUHHI)*HAINF(V) + (TAUHMED-TAUHHI)*(HEAV(V-VHA) - HEAV(V-VMA-K))  

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