# RANDOM, SPARSELY CONNECTED NETWORK 4/10/02 # Produces "episodic" rhythm with somewhat irregular # firing within each episode. # Used to generate Figure 3 in J. Neuro. paper. # There are 10 STN and GPe cells. # Each STN cell receives input from two GPe cells chosen at random. # Each GPe cell receives input from one STN cell. # There is all to all coupling among the GPe cells. ######## STN Parameters ####### p vl=-60,vna=55.,vk=-80.,thetam=30,sigmam=15 p gl=2.25,gna=37.5,gk=45,tn=1.,th=0.05 p gahp=9.,gca=.5,vca=140.,k1=15.,eps=5e-05 p kca=22.5,thetas=39.,sigmas=8.,xp=1.,i=0. p thetah=-39,sigmah=3.1,thetan=-32.,sigman=-8. p taun0=1,taun1=100.,thn=80.,sigmant=26. p tauh0=1,tauh1=500,thh=57.,sigmaht=3.,phi=.75 p thetaa=-63.,sigmaa=-7.8,gt=.5,phir=.5 p thetar=-67,sigmar=2.,taur0=7.1,taur1=17.5,thr=-68,sigmart=2.2 ############################## #these parameters are not needed p eps1=.01 p root1=-60,root2=-40,root3=-10,root4=-35,add=0.6 p scale=10000.,gd=1.0 ############################### p alpha=5,beta=1.,ab=-30. p gGtoS=2.5,vGtoS=-100 p thetab=.25,sigmab=-.07 ####### GPe Parameters ####### p gnag=120.,gkg=30.,gahpg=30.,gtg=.5,gcag=.15,glg=.1 p vnag=55.,vkg=-80.,vcag=120.,vlg=-55. p thag=-57.,sigag=2.,thsg=-35.,sigsg=2. p thrg=-70.,sigrg=-2.,taurg=30. p thmg=-37.,sigmg=10. p thng=-50.,signg=14. p taun0g=.05,taun1g=.27,thngt=-40,sng=-12 p thhg=-58,sighg=-12 p tauh0g=.05,tauh1g=.27,thhgt=-40,shg=-12 p k1g=30.,kcag=20.,epsg=0.0001 p phig=1.,phing=.05,phihg=.05 p iapp=-1.2,gGtoG=0.0,vGtoG=-100. p gStoG=0.016,vStoG=0,alphag=2,betag=.08,abg=-20 ####### STN Functions ####### sinf(v)=1./(1.+exp(-(v+thetas)/sigmas)) minf(v)=1./(1.+exp(-(v+thetam)/sigmam)) hinf(v)=1./(1.+exp((v-thetah)/sigmah)) ninf(v)=1./(1.+exp((v-thetan)/sigman)) taun(v)=taun0+taun1/(1+exp((v+thn)/sigmant)) tauh(v)=tauh0+tauh1/(1+exp((v+thh)/sigmaht)) rinf(v)=1/(1+exp((v-thetar)/sigmar)) taur(v)=taur0+taur1/(1+exp((v+thr)/sigmart)) ainf(v)=1/(1+exp((v-thetaa)/sigmaa)) binf(r)=1/(1+exp((r-thetab)/sigmab))-1/(1+exp(-thetab/sigmab)) ####### GPe Functions ####### ainfg(v)=1/(1+exp(-(v-thag)/sigag)) sinfg(v)=1/(1+exp(-(v-thsg)/sigsg)) rinfg(v)=1/(1+exp(-(v-thrg)/sigrg)) minfg(v)=1./(1.+exp(-(v-thmg)/sigmg)) ninfg(v)=1./(1.+exp(-(v-thng)/signg)) taung(v)=taun0g+taun1g/(1+exp(-(v-thngt)/sng)) hinfg(v)=1./(1.+exp(-(v-thhg)/sighg)) tauhg(v)=tauh0g+tauh1g/(1+exp(-(v-thhgt)/shg)) ####### STN Currents ####### il(v)=gl*(v-vl) ina(v,h)=gna*(minf(v))^3*h*(v-vna) ik(v,n)=gk*n^4*(v-vk) iahp(v,ca)=gahp*(v-vk)*ca/(ca+k1) ica(v)=gca*((sinf(v))^2)*(v-vca) it(v,r)=gt*(ainf(v)**3)*(binf(r)^2)*(v-vca) ############################# #The choice of T-current is a bit unusual. #Here we use binf(r) instead of just r. #This gives a more acurrate rebound. ############################# isyn1=gGtoS*(sg10+sg2)*(v1-vGtoS) isyn2=gGtoS*(sg7+sg9)*(v2-vGtoS) isyn3=gGtoS*(sg4+sg6)*(v3-vGtoS) isyn4=gGtoS*(sg5+sg3)*(v4-vGtoS) isyn5=gGtoS*(sg1+sg8)*(v5-vGtoS) isyn6=gGtoS*(sg2+sg9)*(v6-vGtoS) isyn7=gGtoS*(sg5+sg6)*(v7-vGtoS) isyn8=gGtoS*(sg1+sg7)*(v8-vGtoS) isyn9=gGtoS*(sg4+sg10)*(v9-vGtoS) isyn10=gGtoS*(sg3+sg8)*(v10-vGtoS) ####### GPe Currents ####### itg(vg,rg)=gtg*(ainfg(vg)^3)*rg*(vg-vcag) inag(vg,hg)=gnag*(minfg(vg)^3)*hg*(vg-vnag) ikg(vg,ng)=gkg*(ng^4)*(vg-vkg) iahpg(vg,cag)=gahpg*(vg-vkg)*cag/(cag+k1g) icag(vg)=gcag*((sinfg(vg))^2)*(vg-vcag) ilg(vg)=glg*(vg-vlg) isyng1=gStoG*s1*(vg1-vStoG) isyng2=gStoG*s2*(vg2-vStoG) isyng3=gStoG*s3*(vg3-vStoG) isyng4=gStoG*s4*(vg4-vStoG) isyng5=gStoG*s5*(vg5-vStoG) isyng6=gStoG*s6*(vg6-vStoG) isyng7=gStoG*s7*(vg7-vStoG) isyng8=gStoG*s8*(vg8-vStoG) isyng9=gStoG*s9*(vg9-vStoG) isyng10=gStoG*s10*(vg10-vStoG) stot=sg1+sg2+sg3+sg4+sg5+sg6+sg7+sg8+sg9+sg10 isyngg(vg,sg)=gGtoG*stot*(vg-vGtoG) ####### STN Equations ####### v[1..10]'=-(il(v[j])+ina(v[j],h[j])+ik(v[j],n[j])+iahp(v[j],ca[j])+ica(v[j])+it(v[j],r[j]))-isyn[j] h[1..10]'=phi*( hinf(v[j])-h[j] )/tauh(v[j]) n[1..10]'=phi*( ninf(v[j])-n[j] )/taun(v[j]) r[1..10]'=phir*(rinf(v[j])-r[j])/taur(v[j]) ca[1..10]'=phi*eps*(-ica(v[j])-it(v[j],r[j]) - kca*ca[j]) s[1..10]'=alpha*(1-s[j])*sinf(v[j]+ab)-beta*s[j] ####### GPe Equations ####### vg[1..10]'= -(itg(vg[j],rg[j])+inag(vg[j],hg[j])+ikg(vg[j],ng[j])+iahpg(vg[j],cag[j])+icag(vg[j])+ilg(vg[j])) +iapp -isyngg(vg[j],stot)-isyng[j] ng[1..10]'= phing*(ninfg(vg[j])-ng[j])/taung(vg[j]) hg[1..10]'= phihg*(hinfg(vg[j])-hg[j])/tauhg(vg[j]) rg[1..10]'= phig*(rinfg(vg[j])-rg[j])/taurg cag[1..10]'=epsg*(-icag(vg[j])-itg(vg[j],rg[j]) - kcag*cag[j]) sg[1..10]'=alphag*(1-sg[j])*sinfg(vg[j]+abg)-betag*sg[j] @ dt=.2,total=999,meth=qualrk,xp=t,yp=v5,xlo=0,xhi=1000,ylo=-80,yhi=20.,bound=5000 done