######### PARAMETERs # PARAMETERS - Applied Current p IApp = 0 # PARAMETERS - Conductances p gKDR = 100 p gK = 29 p gKATP = 6 p gBK = 80 p gCaPQ = 5 p gCaL = 19 p gCaT = 5 p gL = 0.1 p gNaP = 33 p gNaF = 100 p gNaL = 1 p gHCN = 5 p gKCa = 11 ######### ODEs # ODE - VOLTAGE dV/dt = - ( ICa(hCaL,mCaT,hCaT,V) + IKV(mK,mKDR,V) + IKC(mBK,hBK,Ca,V) + INa(hNaF,V) + ILK(V) + IHCN(mHCN,V) - IApp )/C # ODE - ACTIVATION VARIABLEs dhCaL/dt = ( hCaLI(V) - hCaL ) / hCaLT dmCaT/dt = ( mCaTI(V) - mCaT ) / mCaTT(V) dhCaT/dt = ( hCaTI(V) - hCaT ) / hCaTT(V) dmK/dt = ( mKI(V) - mK ) / mKT dmKDR/dt = ( mKDRI(V) - mKDR ) / mKDRT(V) dmBK/dt = ( mBKI(V) - mBK ) / mBKT dhBK/dt = ( hBKI(V) - hBK ) / hBKT dhNaF/dt = ( hNaFI(V) - hNaF ) / hNaFT(V) dmHCN/dt = ( mHCNI(V) - mHCN ) / mHCNT # ODE - CALCIUM DYNAMICs dCa/dt = -f * (a*(ICa(hCaL,mCaT,hCaT,V)) + k*Ca) ######### CURRENTS # CURRENTS - VOLTAGE DEPENDENT IKDR(m,V) = gKDR * m * 1 * ( V - EK ) IK(m,V) = gK * m^4 * 1 * ( V - EK ) IBK(m,h,V) = gBK * m * h * ( V - EK ) ICaPQ(V) = gCaPQ * mCaPQI(V) * 1 * ( V - ECa ) ICaL(h,V) = gCaL * mCaLI(V) * h * ( V - ECa ) ICaT(m,h,V) = gCaT * m * h * ( V - ECa ) INaF(h,V) = gNaF * mNaFI(V)^3 * h * ( V - ENa ) INaP(V) = gNaP * mNaPI(V)^3 * 1 * ( V - ENa ) IHCN(m,V) = gHCN * m * 1 * ( V - EHCN ) IKCa(c,V) = gKCa * mKCaI(c) * 1 * ( V - EK ) # CURRENTS - LEAKAGE IL(V) = gL * 1 * 1 * ( V - EL ) INaL(V) = gNaL * 1 * 1 * ( V - ENaL ) IKATP(V) = gKATP * 1 * 1 * ( V - EK ) # OVERALL ICa(hCaL,mCaT,hCaT,V) = ICaT(mCaT,hCaT,V) + ICaL(hCaL,V) + ICaPQ(V) IKV(mK,mKDR,V) = IK(mK,V) + IKDR(mKDR,V) IKC(mBK,hBK,Ca,V) = IBK(mBK,hBK,V) + IKCa(Ca,V) INa(hNaF,V) = INaF(hNaF,V) + INaP(V) ILK(V) = IL(V) + IKATP(V) + INaL(V) ######### ION CHANNEL DYNAMICS # ICaT ----------------------------------------------- num vmCaT = -40, smCaT = 9 num vhCaT = -93, shCaT = -10 num TmCaT = 7, TmCaT0 = 0.4, vmCaT1 = -120, smCaT1 = 240, vmCaT2 = -40, smCaT2 = -10 num ThCaT = 500, ThCaT0 = 8 , vhCaT1 = -93 , shCaT1 = 10 , vhCaT2 = -93, shCaT2 = -10 mCaTI(V) = 1/(1 + exp(-(V-vmCaT)/smCaT)) hCaTI(V) = 1/(1 + exp(-(V-vhCaT)/shCaT)) mCaTT(V) = TmCaT0 + TmCaT/(exp(-(V-vmCaT1)/smCaT1) + exp(-(V-vmCaT2)/smCaT2)) hCaTT(V) = ThCaT0 + ThCaT/(exp(-(V-vhCaT1)/shCaT1) + exp(-(V-vhCaT2)/shCaT2)) # ICaL ------------------------------------------------ num vmCaL = -38, smCaL = 6 num vhCaL = -42, shCaL = -4 num hCaLT = 20 mCaLI(V) = 1/(1 + exp(-(V-vmCaL)/smCaL)) hCaLI(V) = 1/(1 + exp(-(V-vhCaL)/shCaL)) # ICaPQ ------------------------------------------------ num vmCaPQ = -22, smCaPQ = 8 mCaPQI(V) = 1/(1 + exp(-(V-vmCaPQ)/smCaPQ)) # IK ------------------------------------------------- num vmK = -55, smK = 15 num mKT = 2 mKI(V) = 1/(1 + exp(-(V - vmK)/smK)) # IKDR ------------------------------------------------ num vmKDR = -11, smKDR = 8 num TmKDR = 13, vmKDR1 = -100, vmKDR2 = 50, smKDR1 = -39, smKDR2 = 65 mKDRI(V) = 1/(1 + exp(-(V-vmKDR)/smKDR)) mKDRT(V) = TmKDR/(exp(-(V-vmKDR1)/smKDR1) + exp(-(V-vmKDR2)/smKDR2)) # IBK ------------------------------------------------- num mBKT = 2 num dhBK = 0.0025, KCa = 0.67, ghBK = 0.002 num hBKT = 5 mBKI(V) = mCaPQI(V) hBKI(V) = ghBK/(mCaPQI(V)*dhBK*KCa*abs(V-ECa) + ghBK) # INaP ------------------------------------------------ num vmNaP = -50, smNaP = 15 mNaPI(V) = 1/(1 + exp(-(V - vmNaP)/smNaP)) # INaF ------------------------------------------------ num vmNaF = -35, smNaF = 7 num vhNaF = -77, shNaF = -9 num ThNaF = 13 , vhNaF1 = -70, vhNaF2 = -54, shNaF1 = -15, shNaF2 = 44 mNaFI(V) = 1/(1 + exp(-(V-vmNaF)/smNaF)) hNaFI(V) = 1/(1 + exp(-(V-vhNaF)/shNaF)) hNaFT(V) = ThNaF/(exp(-(V-vhNaF1)/shNaF1) + exp(-(V-vhNaF2)/shNaF2)) # IHCN ------------------------------------------------ num vmHCN = -90, smHCN = -15 num mHCNT = 30 mHCNI(V) = 1/(1 + exp(-(V-vmHCN)/smHCN)) # IKCa ------------------------------------------------ num nKCa = 2 num kKCa = 0.4 mKCaI(Ca) = (Ca^nKCa) / ( Ca^nKCa + kKCa^nKCa ) ######### HIDDEN PAMETERs - ELECTROPHYSIOLOGY # CAPACITANCE p C = 10 # NERNST POTENTIALs p ECa = 60 p EK = -85 p EL = -40 p ENAL = 0 p ENa = 50 p EHCN = -20 # CALCIUM DYNAMICs p f = 0.05 p k = 0.3 p a = 0.003 ######### SETTNGS # VISUALIZATION @ MULTIWIN=1 @ SIMPLOT=0 @ NPLOT=1 @ XP=t @ YP=V @ XLO=2500 @ XHI=3000 @ YLO=-90 @ YHI=10 # AUTO @ NTST=30 @ NPR=10000 @ NMAX=10000 @ DS=1e-3 @ DSMAX=1 @ DSMIN=1e-3 @ NORMMIN=0 @ NORMMAX=Inf @ PARMIN=-300 @ PARMAX=1000 @ AUTOVAR=V @ AUTOXMIN=-300 @ AUTOYMIN=-90 @ AUTOXMAX=1000 @ AUTOYMAX=20 # INTEGRATION @ TRANS=0 @ TOTAL=6000 @ BOUND=1e50 @ DT=0.01 @ TOL=1e-9 @ ATOLER=1e-9 @ METHOD=Q done