% HVCRA_BD.ode % A model for the adult HVC_RA neuron. Iap is a parameter, facilitating % its use as a bifurcation parameter. % initial conditions v(0)=-77 n(0)=0 h(0)=1 hp(0)=1 e(0)=1 z(0)=0 rT(0)=1 Cai(0)=0.05 rf(0)=0.2 rs(0)=0.2 % applied current parameters par Iap=0 % conductances par gL=7,gNap=1,gCaL=1,gNa=300,gK=500,gA=5,gM=32,gCaT=1,gSK=32,gH=1.6 % fraction of h-current that is fast par kr=0.95 % Nernst potentials num VK=-90 num VNa=50 num VH=-43 par VL=-77 % capacitance par C=58 % time constants num WtauH=1 num tauNbar=15 num tauZ=75 num tauHpbar=1000 num tauE=20 num tauR0=200 num tauR1=87.5 % shape parameters num sigmaM=-10,sigmaN=-7,sigmaAT=-6,sigmaMp=-6,sigmaHp=6,sigmaA=-10,sigmaE=5 num sigmaZ=5,sigmaS=-8.6,sigmaBT=-0.1,sigmaRT=2,sigmaRRT=2.2,sigmaRf=6.4 num sigmaRs=6.4 num thetaM=-35,thetaZ=-45,thetaN=-30,thetaE=-60,thetaAT=-59,thetaRs=-87.7 num thetaMp=-40,thetaHp=-48,thetaA=-20,thetaS=-13,thetaBT=0.4 num thetaRT=-67,thetaRRT=68,thetaRf=-87.7 % other parameters num Ca_ex=2.5,RTF=26.7,ks=0.4,f=0.01,eps=0.0015,kCa=0.3,bCa=0.05,prf=100 % Leak current iL = gL*(V-VL) % K+ Current (iK) ninf = 1./(1+exp((V-thetaN)/sigmaN)) tauN = tauNbar/cosh((V-thetaN)/(2*sigmaN)) iK = gK*(n^4)*(V-VK) % Na+ Current (iNa) minf = 1/(1+exp((V-thetaM)/sigmaM)) alphah = 0.128*exp(-(V+50)/18) betah = 4/(1+exp(-(V+27)/5)) hinf = alphah/(alphah+betah) tauH = (1.2)/(alphah+betah) iNa = gNa*(minf^3)*h*(V-VNa) % Nap+ current (iNap) mpinf = 1/(1+exp((V-thetaMp)/sigmaMp)) hpinf = 1/(1+exp((V-thetaHp)/sigmaHp)) tauHp = tauHpbar/cosh((V-thetaHp)/(2*sigmaHp)) iNap = gNap*mpinf*hp*(V-VNa) % A+ Current (iA) ainf = 1/(1+exp((V-thetaA)/sigmaA)) einf = 1/(1+exp((V-thetaE)/sigmaE)) iA = gA*ainf*e*(V-VK) % M+ Current (iM) zinf = 1/(1+exp(-(V-thetaZ)/sigmaZ)) iM = gM*z*(V-VK) % High-threshold L-type Ca 2+ Current (iCaL) sinf = 1/(1+exp((V-thetaS)/sigmaS)) iCaL = gCaL*(sinf^2)*V*(Ca_ex/(1-exp((2*V)/RTF))) % Low-threshold T-type Ca 2+ current (iCaT) aTinf = 1/(1+exp((V-thetaAT)/sigmaAT)) bTinf = 1/(1+exp((rT-thetaBT)/sigmaBT))-1/(1+exp(-thetaBT/sigmaBT)) rTinf = 1/(1+exp((V-thetaRT)/sigmaRT)) tauRT = (tauR0 + tauR1/(1+exp((V-thetaRRT)/sigmaRRT))) iCaT = gCaT*(aTinf^3)*(bTinf^3)*V*(Ca_ex/(1-exp((2*V)/RTF))) % Ca2+ dependent K+ current (iSK) kinf = (Cai^2)/(Cai^2 + ks^2) iSK = gSK*kinf*(V-VK) % Hyperpolarization-activated inward Current (iH) rfinf = 1/(1+exp((V-thetaRf)/sigmaRf)) rsinf = 1/(1+exp((V-thetaRs)/sigmaRs)) tauRf = prf/(-7.4*(V+70)/(exp(-(V+70)/0.8)-1)+65*exp(-(V+56)/23)) tauRs = exp((V+289.71)/33.3) iH = gH*(kr*rf+(1-kr)*rs)*(V-VH) % differential equations v' = -(iL+iK+iNa+iNap+iA+iM+iCaL+iCaT+iSK+iH-Iap)/C n' = (ninf-n)/tauN h' = (hinf-h)/tauH hp' = (hpinf-hp)/tauHp e' = (einf-e)/tauE z' = (zinf-z)/tauZ rT' = (rTinf-rT)/tauRT Cai' = -f*(eps*(iCaL + iCaT)+ kCa*(Cai-bCa)) rf' = (rfinf-rf)/tauRf rs' = (rsinf-rs)/tauRs % XPP parameters @ maxstor=120000 @ total=1200, dt=0.05, bounds=1000000 @ method=Runge-Kutta, toler=0.0000001, dtmin=0.000001, dtmax=1 @ xlo=0, xhi=1200, ylo=-120, yhi=20 % AUTO parameters @ Nmax=5000, NPr=5000, Dsmax=5 aux iH=iH aux iSK=iSK aux iCaT=iCaT aux iCaL=iCaL aux iM=iM aux iA=iA aux iNap=iNap aux iNa=iNa aux iK=iK aux iL=iL aux Iap=Iap done