# Modified from FF_Single_Cell.ode # Two compartment model based on Maxim's code # Last change: 14th September 2005 by ff # modif: spring 2006 by mb # Fall 2009 by GPK # Winter-Spring 2012-2013 by Anatoly ######################################################################################################## # Parameters & Constants # input current to the dendrite par I=0 # AMPA synapse, mS/cm^2, gE is twice small par gE=0 par alphaE1=0.185, alphaE2=0.185 par VAMPA=0 # delay between gE and gI par tD=0 par # GABA-A synapse, mS/cm^2, gI is twice small par gI=0 par alphaI1=5, alphaI2=0.120 # par VGABA=-70 # Cl, Cl0 is assumed to be constant, 130 mM, around KCC2(+) point par Cli=3.46 par Clo=130 par HCO3o=26 par HCO3i=16 ############# ion concentrations ################ par kCL=100 # K par Ki=150 par Ko=4 par kK=10 # in the original model = 25 par Vbolz=22 # ratio of volume of extracellular compartment to the surface area par d=0.15 # volume of an extracellular compartment # Na par Nao=130, Nai=20 par kNa=10 par e0=26.6393 par E_l=-61, Cm=0.75 number kappa=10000,S_Soma=0.000001,S_Dend=0.000165, A=0, F=96489 ##### conductances ###### par G_Na=3450.0, G_Kv=200.0 par G_lD=0.01 par G_NaD=1.1 par G_NapD=3.5 par G_HVA=0.0195, E_Ca=140, TauCa=800, DCa=0.85 par G_KCa=2.5 par G_Km=0.01 # G_kl=0.044 in non-rescaled model par G_kl=0.044 par G_Nal=0.02 par gg_kl=0.042, gg_Nal=0.0198 ###### pumps parameters ####### microA/cm^2 par Koalpha=3.5, Naialpha=20 par Imaxsoma=25, Imaxdend=25 par Kothsoma=15, Kothdend=15 par koff=0.0008 par K1n=1.0, Bmax=500 ##### KCC2 pump model ##### #### Doyon et al, 2011 parameters #### par Vhalf=40 par Ikcc2=2 ############################### Algebraic equations ############################## ## Stimulus generation # if a!=b K(a,b)=a*b/(a-b)*((a/b)^(b/(b-a))-(a/b)^(a/(b-a))) # if a=b Ke(a,b)=b*exp(-1) # par ts=500 # par dts=500 # global 1 t-ts { ts=ts+dts } # delta functions deltaE=1/0.05*( heav(t-300)*heav(300+0.05-t) +heav(t-600)*heav(600+0.05-t) +heav(t-900)*heav(900+0.05-t) +heav(t-1200)*heav(1200+0.05-t) +heav(t-1500)*heav(1500+0.05-t) +heav(t-1800)*heav(1800+0.05-t) +heav(t-2100)*heav(2100+0.05-t)) # +heav(t-2400)*heav(2400+0.05-t) +heav(t-2700)*heav(2700+0.05-t) +heav(t-3000)*heav(3000+0.05-t) ) deltaI=1/0.05*( heav(t-tD-300)*heav(300+0.05-t+tD) +heav(t-td-600)*heav(600+0.05-t+td) +heav(t-td-900)*heav(900+0.05-t+td) +heav(t-td-1200)*heav(1200+0.05-t+td) +heav(t-td-1500)*heav(1500+0.05-t+td) +heav(t-td-1800)*heav(1800+0.05-t+td) +heav(t-td-2100)*heav(2100+0.05-t+td)) #+heav(t-td-2400)*heav(2400+0.05-t+td) +heav(t-td-2700)*heav(2700+0.05-t+td) +heav(t-td-3000)*heav(3000+0.05-t+td) ) dINE/dt=INNE dINNE/dt=alphaE1*alphaE2*(deltaE*(1-INE)/Ke(alphaE1,alphaE2)-INE-(1/alphaE1+1/alphaE2)*INNE) dINI/dt=INNI dINNI/dt=alphaI1*alphaI2*(deltaI*(1-INI)/K(alphaI1,alphaI2)-INI-(1/alphaI1+1/alphaI2)*INNI) ### Dendritic Compartment ### ####### iNaD ###### iNaD(m_iNaD,h_iNaD,VD) = 2.9529 * G_NaD * m_iNaD * m_iNaD * m_iNaD * h_iNaD * (VD - eNad) am_iNaD=0.182*(VD-10+35)/(1-exp(-(VD-10+35)/9)) bm_iNaD=0.124*(-VD+10-35)/(1-exp(-(-VD+10-35)/9)) ah_iNaD=0.024*(VD-10+50)/(1-exp(-(VD-10+50)/5)) bh_iNaD=0.0091*(-VD+10-75)/(1-exp(-(-VD+10-75)/5)) tau_mD = (1/(am_iNaD+bm_iNaD))/2.9529 tau_hD = (1/(ah_iNaD+bh_iNaD))/2.9529 minf_newD = am_iNaD/(am_iNaD+bm_iNaD) hinf_newD = 1/(1+exp((VD-10+65)/6.2)) dm_iNaD/dt= -(m_iNaD - minf_newD)/tau_mD dh_iNaD/dt = -(h_iNaD - hinf_newD)/tau_hD ####### iNapD ###### iNapD(m_iNapD,VD) = G_NapD * m_iNapD * (VD - eNad) minfiNapD(VD) = 0.02/(1 + exp(-(VD+42)/5)) dm_iNapD/dt = -(m_iNapD - minfiNapD(VD))/0.1992 ####### IHVA ###### iHVA(m_iHVA,h_iHVA,VD) = 2.9529* G_HVA * m_iHVA*m_iHVA*h_iHVA * (VD - E_Ca) am_iHVA(VD) = 0.055*(-27 - VD)/(exp((-27-VD)/3.8) - 1) bm_iHVA(VD) = 0.94*exp((-75-VD)/17) tauHVAm = 1/((am_iHVA(VD)+bm_iHVA(VD))*2.9529) infHVAm = am_iHVA(VD)/(am_iHVA(VD)+bm_iHVA(VD)) ah_iHVA(VD) = 0.000457*exp((-13-VD)/50) bh_iHVA(VD) = 0.0065/(exp((-VD-15)/28) + 1) tauHVAh = 1/((ah_iHVA(VD)+bh_iHVA(VD))*2.9529) infHVAh = ah_iHVA(VD)/(ah_iHVA(VD)+bh_iHVA(VD)) dm_iHVA/dt = -(m_iHVA-infHVAm)/tauHVAm dh_iHVA/dt = -(h_iHVA-infHVAh)/tauHVAh ####### iKCa ###### iKCa(m_iKCa,VD) = G_KCa*m_iKCa*m_iKCa*(VD - eKd) minf_iKCa(cai) = (48*cai*cai/0.03)/(48*cai*cai/0.03 + 1) taum_iKCa(cai) = (1/(0.03*(48*cai*cai/0.03 + 1)))/4.6555 dm_iKCa/dt = -(1/taum_iKCa(cai))*(m_iKCa - minf_iKCa(cai)) ####### Ca2+ dynamics ###### dcai/dt = -5.1819e-5*iHVA(m_iHVA,h_iHVA,VD)/DCa + (0.00024-cai)/TauCa ####### iKm ###### iKm(m_iKm,VD) = 2.9529 * G_Km * m_iKm * (VD - eKd) am_iKm(VD) = 0.001 * (VD + 30) / (1 - exp(-(VD + 30)/9)) bm_iKm(VD) = -0.001 * (VD + 30) / (1 - exp((VD + 30)/9)) tauKmm = 1/((am_iKm(VD)+bm_iKm(VD))*2.9529) infKmm = am_iKm(VD)/(am_iKm(VD)+bm_iKm(VD)) dm_iKm/dt = -(m_iKm-infKmm)/tauKmm ## Dendrite equations, inject conductances to the dendrite iDendrite(VD)=I-gE*INE*(VD-VAMPA) -gI*INI*(VD-VGABA) -G_lD*(VD-eLKd) -G_kl*(VD-eKd) -G_Nal*(VD-eNad)-INapump(Imaxdend,Ko,Nai) -Ikpump(Imaxdend,Ko,Nai) -iNapD(m_iNapD,VD) -iKCa(m_iKCa,VD) -iHVA(m_iHVA,h_iHVA,VD) -iNaD(m_iNaD,h_iNaD,VD) -iKm(m_iKm,VD) # -iKm(m_iKm,VD) ## Soma equations input current to dendrite, current is injected to the soma VSOMA(VD,m_iNa,h_iNa,m_iKv)=(VD + (kappa*S_Soma * g2_SOMA(m_iNa,h_iNa,m_iKv)))/(1+kappa*S_Soma*g1_SOMA(m_iNa,h_iNa,m_iKv)) # inject conductances to the dendrite g1_SOMA(m_iNa,h_iNa,m_iKv)=gg_kl+gg_Nal+(2.9529*G_Na*m_iNa*m_iNa*m_iNa*h_iNa)+(2.9529*G_Kv*m_iKv) g2_SOMA(m_iNa,h_iNa,m_iKv)= (gg_kl*eKs) +gg_Nal*eNas+(2.9529*G_Na*m_iNa*m_iNa*m_iNa*h_iNa*eNas)+(2.9529*G_Kv*m_iKv*eKs) -INapump(Imaxsoma,Ko,Nai) -Ikpump(Imaxsoma,Ko,Nai) # Reversal potentials # somatic and dendritic reversal potentials are the same eKs=e0*log(Ko/Ki) eKd=e0*log(Ko/Ki) eNas=e0*log(Nao/Nai) eNad=e0*log(Nao/Nai) # Chloride leak and VGABA eLKs=e0*log(Cli/Clo) eLKd=e0*log(Cli/Clo) VGABA=e0*log((4*Cli+HCO3i)/(4*Clo+HCO3o)) ####################################################################################################### #### Na K pump, buffer pump ## Ap(Ko,Nai)=(1/((1+(Koalpha/Ko))*(1+(Koalpha/Ko))))*(1/((1+(Naialpha/Nai))*(1+(Naialpha/Nai))*(1+(Naialpha/Nai)))) Ikpump(Imax,Ko,Nai)=-2*Imax*Ap(Ko,Nai) INapump(Imax,Ko,Nai)=3*Imax*Ap(Ko,Nai) ######################################################################################################## ############################### Axo-somatic compartment ############################## ###### K channel ###### approximation is changed a_iKv=0.02*(VSOMA(VD,m_iNa,h_iNa,m_iKv)-Vbolz)/(1-exp(-(VSOMA(VD,m_iNa,h_iNa,m_iKv)-Vbolz)/9)) b_iKv=-0.002*(VSOMA(VD,m_iNa,h_iNa,m_iKv)-Vbolz)/(1-exp((VSOMA(VD,m_iNa,h_iNa,m_iKv)-Vbolz)/9)) tauKvm=1/((a_iKv+b_iKv)*2.9529) infKvm=a_iKv/(a_iKv+b_iKv) dm_iKv/dt=-(m_iKv-infKvm)/tauKvm iKv(m_iKv)=2.9529*G_Kv * m_iKv * (VSOMA(VD,m_iNa,h_iNa,m_iKv) - eKs) # is a themperature coefficient, phi ####### Na Channel - m and h variables ###### am_iNa=0.182*(VSOMA(VD,m_iNa,h_iNa,m_iKv)-10+35)/(1-exp(-(VSOMA(VD,m_iNa,h_iNa,m_iKv)-10+35)/9)) bm_iNa=0.124*(-VSOMA(VD,m_iNa,h_iNa,m_iKv)+10-35)/(1-exp(-(-VSOMA(VD,m_iNa,h_iNa,m_iKv)+10-35)/9)) ah_iNa=0.024*(VSOMA(VD,m_iNa,h_iNa,m_iKv)-10+50)/(1-exp(-(VSOMA(VD,m_iNa,h_iNa,m_iKv)-10+50)/5)) bh_iNa=0.0091*(-VSOMA(VD,m_iNa,h_iNa,m_iKv)+10-75)/(1-exp(-(-VSOMA(VD,m_iNa,h_iNa,m_iKv)+10-75)/5)) tau_m=(1/(am_iNa+bm_iNa))/2.9529 tau_h=(1/(ah_iNa+bh_iNa))/2.9529 m_inf_new=am_iNa/(am_iNa+bm_iNa) h_inf_new=1/(1+exp((VSOMA(VD,m_iNa,h_iNa,m_iKv)-10+65)/6.2)) dm_iNa/dt=-(m_iNa-m_inf_new)/tau_m dh_iNa/dt=-(h_iNa-h_inf_new)/tau_h iNa(m_iNa,h_iNa)=2.9529 *G_Na * m_iNa * m_iNa * m_iNa * h_iNa * (VSOMA(VD,m_iNa,h_iNa,m_iKv) - eNas) ####### Extracellular K+ & Intracelluar Na ###### # SigIkints = gg_kl*(VSOMA(VD,m_iNa,h_iNa,m_iKv)-eKs) +G_kl*(VD-eKd) +iKCa(m_iKCa,VD) +iKm(m_iKm,VD) +iKv(m_iKv)/200 # SigINaints = gg_Nal*(VSOMA(VD,m_iNa,h_iNa,m_iKv)-eNas) +G_Nal*(VD-eNad) +iNaD(m_iNaD,h_iNaD,VD) +iNapD(m_iNapD,VD) +(iNa(m_iNa,h_iNa)/200) # approximately 0.4 mM Cli increase after one stimulation (see Jedlichka model) # SigCl = G_lD*(VD-eLKd) +gI*INI*(VD-VGABA) # dNai/dt=-kNa/F*(SigINaints+INapump(Imaxsoma,Ko,Nai)) # dNao/dt=kNa/F/d*(SigINaints+INapump(Imaxsoma,Ko,Nai)) # par eps=0, k_inf=4 # Ko accumulation with KCC2 extrusion included # dKi/dt=-kK/F*(SigIkints+Ikpump(Imaxsoma,Ko,Nai)) # dKo/dt=kK/F/d*(SigIkints +Ikpump(Imaxsoma,Ko,Nai) +Ikpump(Imaxdend,Ko,Nai) -Ikcc2*(eKs-eLKs)/((eKs-eLKs)+Vhalf) ) +Glia(Ko,Bs) # kon(Ko,Koth)=koff/(1+exp((Ko-Koth)/(-1.15))) # Glia(Ko,Bs)=koff*(Bmax-Bs)/K1n -kon(Ko,Kothsoma)/K1n*Bs*Ko # dBs/dt=koff*(Bmax-Bs) -kon(Ko,Kothsoma)*Bs*Ko # KCC2-dependent extrusion, # dCli/dt=kCL/F*(SigCl + Ikcc2*(eKs-eLKs)/((eKs-eLKs)+Vhalf) ) ###### Integration ###### dVD/dt =(1/Cm)*(iDendrite(VD)+(VSOMA(VD,m_iNa,h_iNa,m_iKv)-VD)/(kappa*S_Dend)) aux VS=VSOMA(VD,m_iNa,h_iNa,m_iKv) ########## Initial conditions ########### # initial conditions at equilibrium init VD=-63.2216, m_iKv=0, m_iNa=0.0204, h_iNa=0.7918 # dendrite currents init M_INAD=0.00, H_INAD=0.91 init M_INAPD=0.00 init M_IHVA=0.00, H_IHVA=0.00, CAI=0.00 init M_IKCA=0.00 init CAI=0.00 init M_IKM=0.01 init INE=0, INNE=0, INI=0, INNI=0 # init Ko=3.4565 # init Ki=130 # init Bs=500 # init Nai=20 # init Nao=130 # init Cli=5.4220 # init Clo=130 @ MAXSTOR=10000000,TOTAL=1000,XP=T,YP=VS @ BOUND=10000000000000000,DT=0.05,METH=Euler,XHI=20,XLO=0,YLO=0,YHI=20 # @ dsmax=0.5, parmin=0.1, parmax=30, dsmin=0.0001, ntst=100, ds=0.001 done