This is the python and NEURON code associated with the paper:
Upchurch CM, Knowlton CK, Chamberland S Canavier CC, Persistent Interruption in Parvalbumin Positive Inhibitory Interneurons: Biophysical and Mathematical Mechanisms
This model entry was contributed by C Canavier. The freely available NEURON simulation enivronment from nrn.readthedocs.io and Python is required for this model.
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Bifurcations were analyzed using Matcont
The equations for our model in Matcont are below
area=7916.813487046279*1e-8
Iapp=4.5e-7/area #change to 3.3e-7/area for bursting model
ek=-90
taun=(0.087+11.4/(1+exp((V+14.6)/8.6)))*(0.087+11.4/(1+exp(-(V-1.3)/18.7)))
ninf=1/(1+exp(-(V+12.4)/6.8))
minf=(1/(1+exp(-(V+22)/11.5)))
hinf=1/(1 + exp(-(V+58.3)/-6.7))
tauh = 0.5 + 14 / ( 1 + exp(-(V+60)/-12))
Ina=0.1125*M^3*H*(V-50)
minfa = (1/(1 + exp(-(V+41.4)/26.6)))^4
mtaua =0.5/(3^(1/10))
Ia=0.005*A*hslowest*(V-ek)
Ipas=0.00025*(V+65)
A'=(minfa-A)/mtaua
M'=(minf-M)/0.001
H'=(hinf-H)/tauh
V'=(Iapp-(Ina+Ipas+Ia+0.225*(V-ek)*(N^2)))*1000
N'=(ninf-N)/taun
For the model Via et al 2022
area=8143.766620952326*1e-8
Iapp=inject*1e-8/area
ipas=0.0001689986677404316*(v+77.7944307717461)
ina = 0.28767750461978714*m*m*m*h* (v - 50)
alpham = -((v-(-49.87866107497816)-1e-7)/4)/(exp(-(v-(-49.87866107497816)-1e-7)/4)-1)
betam = 0.1*exp(-v/13)
mtau = 1/(alpham+betam)
minf = alpham/(alpham+betam)
alphah = 0.012/exp(-v/-20)
betah = -0.2*(v-(-53.326527961625075))/(exp(-(v-(-53.326527961625075))/3.5)-1)
htau = 1/(alphah+betah)
hinf = alphah/(alphah+betah)
ikv1 = 0.0009233607616445254*a*a*a*a * (v - (-90))
alphaa = -(v-51.90844000870827)/(exp(-(v-51.90844000870827)/12)-1)
betaa = 0.02/exp(-v/-80)
ikv3 = 0.011065851407902236*n*n*n*n * (v - (-90))
alphan = -(v-10.179873677546377)/(exp(-(v-10.179873677546377)/12)-1)
betan = 0.001/exp(-v/(-8.5))
m'=(minf-m)/mtau
h'=(hinf-h)/htau
a' = alphaa*(1-a) - betaa*a
n' = alphan*(1-n) - betan*n
v' = (Iapp-(ikv1+ikv3+ina+ipas))*1000