HH_syndep_100.ode

# network of 100 HH (reduced) cells with heterogeneous input current (Ii)
# all to all coupling with synaptic depression
#
# From Tabak, Mascagni, Bertram. J Neurophysiol, 103:2208-2221, 2010.
#


# cellular parameters
p i0=-10. deli=15
p vna=115  vk=-12  vl=10.6  gnabar=36  gkbar=12  gl=0.1
p h0=0.8 

# synaptic parameters
p taus=10 tauf=1
p gsyn=3.6 vsyn=70 
p alphad=0.0015 betad=0.12
p Vthresh=40 kv=1

# create a table of applied currents Ii
table iapp % 100 0 99 i0+t*deli/99

# rate constants and steady state activation function for Na+ and K+ currents
am(v)=.1*(25-v)/(exp(.1*(25-v))-1)
bm(v)=4.0*exp(-v/18)
minf(v)=am(v)/(am(v)+bm(v))
bn(v)=.125*exp(-v/80)
an(v)=.01*(10-v)/(exp(.1*(10-v))-1.0)

# synaptic activation
fsyn(V) = 1./(1+exp((Vthresh-V)/kv))

# differential equations
# v[i] membrane potential of cell i
# n[i] activation of K+ conductance for cell i
# a[i] synaptic drive from cell i
# s[i] synaptic recovery for terminals from cell i
v[0..99]'= -gl*(v[j]-vl) - gnabar*minf(v[j])^3*(h0-n[j])*(v[j]-vna) -gkbar*n[j]^4*(v[j]-vk) -gsyn*(atot-a[j]*s[j]/100)*(v[j]-vsyn) + iapp([j])
n[0..99]'=an(v[j])-(an(v[j])+bn(v[j]))*n[j]
a[0..99]'=fsyn(v[j])*(1-a[j])/tauf - a[j]/taus
s[0..99]'=alphad*(1-s[j])-betad*fsyn(v[j])*s[j]

# synaptic drive to all cells
atot=sum(0,99)of(shift(s0,i')*shift(a0,i'))/100

# auxiliary variables for output
aux ave=sum(0,99)of(shift(a0,i'))/100
aux stot=sum(0,99)of(shift(s0,i'))/100

# only output these variables when running in silent mode
only t ave stot

# initial conditions
init v[0..99]=0 n[j]=0 a[j]=0.01 s[j]=.25

# simulation options
@ total=8000, bounds=100000 back=white maxstor=2200000 yp=ave
@ dt=0.01 njmp=10 xlo=0 xhi=8000 ylo=0 yhi=0.9 nplot=2 yp2=stot
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