# Wang-Buzsaki neuron network with 50E-cells and 20I-cells with all-to-all # connectivity with heterogeneity with tonic input for 1 sec table Ir % 50 0 49 ran(1)*0.5 @ autoeval=0 wiener ze[0..49] wiener zi[0..19] # # Parameters used p gKLe=0.12, gNaL=0.017, gKLi=0.15 p gK=9.0, gNa=35.0 p ENa=55.0, EK=-90.0 p gei=0.6, gee=0.05, gie=0.6, gii=0.10 p sige=1.2,sigi=1.2 p phi=5.0 p Vsyni=-75,Vti=2,Vsi=5,alphai=5,betai=.1,tmaxi=1 p Vsyne=0,Vte=2,Vse=5,alphae=1.1,betae=.19,tmaxe=1 p Vlth=-25,Vshp=5 # # Tonic input description and parameters Iapp[0..49]=I0+I1*Ir([j]) p I0=2.5,I1=2 # aveVE=(sum(0,49)of(shift(Ve0,i')))/50 inputse=sum(0,49)of(shift(se0,i'))/50 inputsi=sum(0,19)of(shift(si0,i'))/20 # #ODEs for e-cells Ve[0..49]'=Iapp[j]-gKLe*(Ve[j]-EK)-gNaL*(Ve[j]-ENa)-gNa*(Minf(ve[j])^3)*he[j]*(Ve[j]-ENa)-gK*(ne[j]^4)*(Ve[j]-EK)-gie*inputsi*(Ve[j]-Vsyni)-gee*inputse*(Ve[j]-Vsyne)-ica(ve[j])-iahp(ca[j],ve[j])+sige*ze[j] he[0..49]'=phi*(Hinf(ve[j])-he[j])/tauH(ve[j]) ne[0..49]'=phi*(Ninf(ve[j])-ne[j])/tauN(ve[j]) se[0..49]'=alphae*ke(ve[j])*(1-se[j])-betae*se[j] # #ODEs for i-cells Vi[0..19]'=-gKLi*(Vi[j]-EK)-gNaL*(Vi[j]-ENa)-gNa*(Minf(vi[j])^3)*hi[j]*(Vi[j]-ENa)-gK*(ni[j]^4)*(Vi[j]-EK)-gei*inputse*(Vi[j]-Vsyne)-gii*inputsi*(Vi[j]-Vsyni)+sigi*zi[j] hi[0..19]'=phi*(Hinf(vi[j])-hi[j])/tauH(vi[j]) ni[0..19]'=phi*(Ninf(vi[j])-ni[j])/tauN(vi[j]) si[0..19]'=alphai*ki(vi[j])*(1-si[j])-betai*si[j] # ki(x)=tmaxi/(1+exp(-(x-vti)/vsi)) ke(y)=tmaxe/(1+exp(-(y-vte)/vse)) # # Spike frequency adaptation description with parameters # calcium mlinf(v)=1/(1+exp(-(v-vlth)/vshp)) ica(v)=gca*mlinf(v)*(v-eca) ca[0..49]'=(-alpha*ica(ve[j])-ca[j]/tauca) # k-ca iahp(ca,v)=gahp*(ca/(ca+kd))*(v-Ek) # corresponding parameters p kd=30, Eca=120 p alpha=.002, tauca=80, gca=1, gahp=3 # # alpham(v)=0.1*(V+35.0)/(1.0-exp(-(V+35.0)/10.0)) betam(v)=4.0*exp(-(V+60.0)/18.0) Minf(v)=alpham(v)/(alpham(v)+betam(v)) # alphah(v)= 0.07*exp(-(V+58.0)/20.0) betah(v)=1.0/(1.0+exp(-(V+28.0)/10.0)) Hinf(v)=alphah(v)/(alphah(v)+betah(v)) tauH(v)=1.0/(alphah(v)+betah(v)) # alphan(v)=0.01*(V+34.0)/(1.0-exp(-(V+34.0)/10.00)) betan(v)=0.125*exp(-(V+44.0)/80.0) Ninf(v)=alphan(v)/(alphan(v)+betan(v)) tauN(v)=1.0/(alphan(v)+betan(v)) # # Initial conditions init Ve[0..49]=-64 init he[0..49]=0.78 init ne[0..49]=0.09 init Vi[0..19]=-64 init hi[0..19]=0.78 init ni[0..19]=0.09 # # Creating some auxiliary variables aux aveSE=inputse auc aveSI=inputsi aux LFP=aveVE # # Numerics description @ XP=T @ YP=LFP @ autoeval=0 @ TOTAL=1400,trans=400 @ nOut=10 @ DT=0.01,bound=100000,maxstor=1000000 @ METH=euler @ TOLER=0.00001 @ XLO=0.0, XHI=30.0, YLO=-90.0, YHI=30.0 done