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](https://nrn.readthedocs.io) and Python is required for this model. For help downloading and using NEURON models, see [https://modeldb.science/NEURON_Dwnldguide](https://modeldb.science/NEURON_Dwnldguide) 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 ```