#-- Attractor # Modeling Interactions Between Electrical Activity and # Second Messenger Cascades in Aplysia Neuron R15 # Yu et al. 2004, J. Neurophysiol. 91: 2297-2311 # Units: millivolts, milliseconds, nanoamps, microsiemens, # nanofarads, millimoles init V=-38.8468481124207656 init m=0.0196696802720699 init h=0.9963480051353911 init n=0.0504328903497288 init d=0.0000026145195067 init s=0.6584423516466250 init l=0.4382633433755155 init Ca=0.0003 init f=0.9910842262233112 init b=0.0342094859934714 init CaM=0.008 init CaCaM=0.0024 init Ca2CaM=0.00072 init Ca3CaM=0.0000864 init Ca4CaM=0.0000104 #init V=-53.11036793426285 #init m=0.01354547030760796 #init h=0.9999686638933726 #init d=6.126186943402957e-008 #init f=0.9997459538411338 #init s=0.2318420535504265 #init b=2.542904603595237e-006 #init n=0.01934984486453077 #init l=0.8439639705855201 init msyn2=0 init msyn=0 #init Ca=0.0002581366654826358 init cAMP=0.001 #--Parameters-- #--Stimulus Current p Astim1=0 p Astim2=0 p Ibias=0 p ts1=0 p te1=0 p ts2=0 p te2=0 p tclamp=200000 #--Conductances p gna=38 p gca=17 p gk=70 p gns=0.2 p gsi=0.65 p gr=0.18 p gl=0.075 p gsyn=1.0 #--Scaling Constants p Knaca=0.01 p Dnaca=0.01 p Icapmean=7 p Inakmean=5.9 p Dca=0.000150 p Dsicamp=0.00035 #p Dsicamp=0.000842 p Drcamp=0.0004 #p Drcamp=0.0009 p Ksicamp=0.0042 p KsiDA=5.5 p Krcamp=0.001 p Krmod=1.5 p KmodHT=1.2 p KmodCa=1.1 p KmodPDE=0.8 p lamda=0.6 p alpha=0.45 #--Synaptic Input Parameters p zeta=25 p tau=0.5 #--Reversal Potentials p Ena=54 p Eca=65 p Ek=-77 p Ens=-22 p El=10.3 p Esyn=-25 #--Michalis-Menten Constants p Kmsi=0.000025 p Kmcap=0.001 p Kmns=0.000150 p Kpca=0.000350 p Kpna=5.46 p Kpk=0.621 p Kca=0.0005 p KDa=0.2 p KHT=0.006 p Kpde=0.003 #--Reaction Rate Constants #(mM/ms) #p C0=0.000 #p D0=0.001 #p VmaxC=0.0005 #p VmaxD=0.002 #p VmaxHT=0.001 #p VmaxCa=0.0009 p Vadc=0.0000006 p Vpde=0.0000024 # from Tarra param k1f=2300, k1b=2.4, k2f=2300, k2b=2.4, k3f=160000, k3b=405, k4f=160000, k4b=405 #(mM) p kCh=0.0000968 p kCl=0.075 p kD=0.0000968 #--Cell Properties and Concentrations p Cm=17.5 p Vol=4 p Bi=0.10125 p Na0=500 p Na=50 p K0=10 p Ca0=10 p DA=0 p HT=0 #--Physical Constants p Rgas=8314 p Temp=295 p Fc=96500 p ku=100 p kr=0.238 p gamma=0.5 p r=4 p nn=4 p Z=2 p hill=1 #--Time stuff p y=0 p x=10000 p puff=0.001 p hyper=1000 p cdelay=0 p kclamp=0.1 #--Overall Equation-- Istim1=if (t<ts1 | t>=te1) then (0) else (Astim1) Istim2=if (t<ts2 | t>=te2) then (0) else (Astim2) Vnorm=-(Ina(m,h,V)+Ica(Ca,d,f,V)+Isi(cAMP,s,V,Ca)+Ins(b,V,Ca)+Ik(n,l,V)+Ir(cAMP,V)+Il(V)+Inaca(V,Ca)+Inak(V)+Icap(Ca)-Istim1-Istim2+Isyn(V)-Ibias)/Cm #Vclamp=-kclamp*(V + 75) #V'=0 #V'=if(t>(x+cdelay))then(Vclamp)else(Vnorm) V'=Vnorm #-- Format for most currents #Tm(V)=1/(Am(V) + Bm(V)) #m'=(minf(V)-m)/Tm(V) #--Inward Currents-- m'=(1/(1+exp((-10.23-V)/10))-m)/(1/(0.4*(V+6)/(1-exp((-V-6)/4.09)) + 10.75*exp((-28-V)/4.01))) h'=(1/(1+exp((V+22)/3))-h)/(1/(0.112*exp((-30-V)/10) + 0.23/(exp((9.65-V)/23.9)+1))) Ina(m,h,V)=gna*m*m*m*h*(V-Ena) #-- d'=(1/(1+exp((10-V)/3.8))-d)/(1/(0.0063*(V+10.81)/(1-exp((-10.81-V)/5.03)) + 0.01*exp((25-V)/10))) f'=(1/(1+exp((V+20)/4))-f)/(1/(0.00325*exp((10-V)/7.57) + 0.029/(exp((20.29-V)/5.4) + 1))) Ica(Ca,d,f,V)=gca*(1/(1+exp((Ca-Kca)/Dca)))*d*d*f*(V-Eca) #-- s'=(1/(1+exp((-40-V)/11.5))-s)/(1/(0.0014*(V-54)/(1-exp((-V+54)/12.63)) + 0.00013*exp((-11.32-V)/16.8))) Isi(cAMP,s,V,Ca)=gsi*(KDa/(DA+KDa)*(1+KsiDA/(1+exp((-cAMP+Ksicamp)/Dsicamp))))*s*(V-Eca)*(Kmsi/(Kmsi+Ca)) #-- b'=((1/(1+exp((-15-V)/3)))-b)/(500*(0.8/(1+exp((10+V)/3))+0.2)) Ins(b,V,Ca)=gns*b*(V-Ens)*(Ca/(Ca+Kmns)) #-- Il(V)=gl*(V-El) #--Outward Currents-- n'=(1/(1+exp((3.65-V)/14.46))-n)/(1/(0.0035*(V+17)/(1-exp((-V-17)/3)) + 0.04*exp((-28-V)/10))) l'=(1/(1+exp((32.5+V)/12.7))-l)/(2000*(0.9/(1+exp((28+V)/3))+0.10)) Ik(n,l,V)=gk*n*n*n*n*l*(V-Ek) #-- Ir(cAMP,V)=gr*(1+Krmod/(1+exp((-cAMP+Krcamp)/Drcamp)))*(V-Ek+5.66)/(1+exp((V-Ek-15.3)*Z*Fc/Rgas/Temp)) a EyeR=Ir(cAMP,V) #--Synaptic Current-- msyn2'=(-msyn-2*zeta*tau*msyn)/tau*tau msyn'=msyn2 Isyn(V)=gsyn*msyn*(V-Esyn) #--Pumps and Exchangers-- Icap(Ca)=Icapmean*(Ca/(Ca+Kmcap)) Inak(V)=Inakmean*(Na/(Na+Kpna)*K0/(K0+Kpk)*1.5/(1.5+exp((-V-60)/40))) Inaca(V,Ca)=Knaca*(exp((r-2)*gamma*(V*Fc/Rgas/Temp))*Ca0*Na**r-exp((r-2)*(gamma-1)*(V*Fc/Rgas/Temp))*Ca*Na0**r)/(1+Dnaca*(Ca*Na0**r+Ca0*Na**r)) #--Internal calcium concentration-- Oc'=ku*Ca*(1-Oc)-kr*Oc CaM'(CaM, CaCaM) = k1b*CaCaM - k1f*Ca*CaM CaCaM'(CaM, CaCaM, Ca2CaM) = k1f*Ca*CaM - k1b*CaCaM + k2b*Ca2CaM - k2f*Ca*CaCaM Ca2CaM'(CaCaM, Ca2CaM, Ca3CaM) = k2f*Ca*CaCaM - k2b*Ca2CaM + k3b*Ca3CaM - k3f*Ca*Ca2CaM Ca3CaM'(Ca2CaM, Ca3CaM, Ca4CaM) = k3f*Ca*Ca2CaM - k3b*Ca3CaM + k4b*Ca4CaM - k4f*Ca3CaM*Ca Ca4CaM'(Ca3CaM, Ca4CaM) = k4f*Ca*Ca3CaM - k4b*Ca4CaM xy=(k1f*Ca*CaM - k1b*CaCaM + k2b*Ca2CaM - k2f*Ca*CaCaM) + 2*(k2f*Ca*CaCaM - k2b*Ca2CaM + k3b*Ca3CaM - k3f*Ca*Ca2CaM) + 3*(k3f*Ca*Ca2CaM - k3b*Ca3CaM + k4b*Ca4CaM - k4f*Ca3CaM*Ca) + 4*(k4f*Ca*Ca3CaM - k4b*Ca4CaM) Ca'=(Inaca(V,Ca)-Isi(cAMP,s,V,Ca)-Ica(Ca,d,f,V)-Icap(Ca)-0.197*((V-Eca)/(V-Ens))*Ins(b,V,Ca))/(2*Vol*Fc)- xy - nn*Bi*(ku*Ca*(1-Oc)-kr*Oc) #--Internal cAMP concentration-- Ca34CaM=Ca3CaM+Ca4CaM Cycpos(Ca34CaM)=Ca34CaM**hill/(Ca34CaM**hill + kCh**hill) Cycneg(Ca)=kCl**hill/(Ca**hill + kCl**hill) Cycht=HT/(HT + KHT) CYCa(Ca34CaM)=Vadc*(alpha + KmodHT*Cycht + KmodCa*Cycpos(Ca34CaM)*Cycneg(Ca34CaM)) PDEa(Ca34CaM)=Vpde*(lamda + KmodPDE*Ca34CaM**hill/(Ca34CaM**hill + kD**hill)) #cAMP'=CYCa(Ca34CaM)-PDEa(Ca34CaM)*cAMP/(cAMP+Kpde) cAMP'=if(t>tclamp)then(0)else(CYCa(Ca34CaM)-PDEa(Ca34CaM)*cAMP/(cAMP+Kpde)) @ TOTAL=80000,dt=0.2 @ METHOD=cvode,BOUND=1e7,TOL=0.00001,ATOL=0.0000001,MAXSTOR=4000000 d