/* * G-Protein Specificity In Synaptic Signalling * * Model Status * * This CellML model was written by the original model author and * is known to be completely correct. * * ValidateCellML confirms this model as valid CellML with consistent * units * * Model Structure * * A model of Ca2+ dynamics in mouse ventricular myocytes from * the C57BL/6 strain has been developed, based on experimental * data at the same temperature and under consistent experimental * conditions and protocols. * * Parameterisation of the NCX, SERCA and LCC formulations were * done sequentially. The model of NCX, based on the Luo and Rudy * 1994 formulation, was first fitted from the decay of the caffeine-induced * [Ca2+]i transient, which allowed us to infer the flux through * SERCA from the decay of the field-stimulated [Ca2+]i transient. * Frequency-dependence of the flux through SERCA was accounted * for using Hund and Rudy 2002 formulation of Ca2+/calmodulin * kinase II regulatory pathway, with parameters fitted to experimentally * measured SERCA flux at 0.5, 1 and 3Hz pacing frequencies. The * L-type Ca2+ channel model, with slight modifications to the * Hinch 2004 formulation, was fitted to data from voltage-clamp * experiments. All these component models were then incorporated * into the whole-cell AP model of Bondarenko et al., with parameters * of RyR adjusted to match the experimentally observed time-to-peak * of the [Ca2+]i transient at 3Hz, and parameters for the background * Ca2+ current and PMCA adjusted to match experimentally observed * diastolic [Ca2+]i levels. * * reaction diagram * * [[Image file: bondarenko_2004.png]] * * Schematic diagram of the Bondarenko 2004 model. * * Associated data * * Caffeine - Caffeine-induced Ca2+ transients from 18 individual * myocytes * * Each file contains the time course of caffeine-induced Ca2+ * transients from a myocyte. The traces were exported from IonOptix * for the duration of the caffeine application. * * Related parameter: Kncx * * Fitting process: 1. The decay of individual transients were * aligned and averaged. 2. The rate of decay of the average transient, * after taking into account of intracellular buffering, was used * to calculate Jncx. Jncx was then used to fit Kncx in the Luo * and Rudy 1994 model. * * 3Hz - Field-stimulated Ca2+ transients at 3Hz from 19 individual * myocytes * * Each file contains the time course of a Ca2+ transient, field * stimulated at 3Hz, from a myocyte. The time course was exported * from IonOptix for a duration of 1s starting from the first stimulus. * * Related parameter: Km, serca, Vserca at 3Hz * * Fitting process: 1. The individual transients were averaged. * The decay of the average transient, from 70ms after-peak until * the end of the period was analysed. 2. Jncx was inferred from * previously fitted NCX model, and the difference between the * total Ca2+ flux and Jncx was taken as the net SR Ca2+ uptake * Jup. 3 A small SR leak (0.0082+ through SERCA Jserca = Jup+ * Jleak 4. Jserca was used to fit the Km,serca and Vserca at 3Hz. * * 1Hz - Field-stimulated Ca2+ transients at 1Hz from 7 individual * myocytes * * Each file contains the time course of a Ca2+ transient, field * stimulated at 1Hz, from a myocyte. * * Related parameter: Estimated Vserca at 1Hz * * 1. The derivation of Jserca at 1Hz is similar to above. 2. Jserca * was used to constrain Vserca at 1Hz * * 0.5Hz - Field-stimulated Ca2+ transients at 0.5Hz from 7 individual * myocytes * * Each file contains the time course of a Ca2+ transient, field * stimulated at 0.5Hz, from a myocyte * * Related parameter: Estimated Vserca at 0.5Hz * * 1. The derivation of Jserca at 0.5Hz is similar to above. 2. * Jserca was used to constrain Vserca at 0.5Hz * * Ica - Time courses of transmembrane currents from 5 individual * myocytes. * * Each file contains the time course of experimentally measured * L-type Ca2+ current from one myocyte, measured in nA. * * PCaL, * * Fitting process: 1. The time course of transmembrane currents * individual myocytes were averaged for each test potential between * -20 and 20mV (-20, -10, 0, 10, 20mV). 2. Averaged currents were * converted into current densities by division by cell membrane * capacitance (138.66pF). 3. Simulated sum of late K+ currents, * from the Bondarenko et al 2004 formulation, for test potentials * -20, -10, 0, 10, 20mV were subtracted from the decay phase of * each current. 4. The decay of the current at each test potential, * after correcting for late K+ currents, was fitted to a single * exponential function, giving a time constant of decay tau value. * 5. The IV relation and tau values at each test potential were * used to fit the model of LCC. * * Ica/IV.xls - Experimentally measured current-voltage relation * for the L-type Ca2+ current * * Average current-voltage curve. * * Related parameter: PCaL, * * Fitting process: as for Ica */ import nsrunit; unit conversion on; // unit millisecond predefined unit per_millisecond=1E3 second^(-1); unit micromolar_per_millisecond=1 meter^(-3)*second^(-1)*mole^1; unit per_micromolar_millisecond=1E6 meter^3*second^(-1)*mole^(-1); unit micromolar3_per_millisecond=1E12 meter^9*second^(-1)*mole^(-3); unit micromolar4_per_millisecond=1E15 meter^12*second^(-1)*mole^(-4); // unit millivolt predefined unit per_millivolt=1E3 kilogram^(-1)*meter^(-2)*second^3*ampere^1; unit millivolt2=1E-6 kilogram^2*meter^4*second^(-6)*ampere^(-2); unit per_millivolt_millisecond=1E6 kilogram^(-1)*meter^(-2)*second^2*ampere^1; unit milliS_per_microF=1E3 second^(-1); unit picoF=1E-12 kilogram^(-1)*meter^(-2)*second^4*ampere^2; unit per_picoF=1E12 kilogram^1*meter^2*second^(-4)*ampere^(-2); unit microF_per_cm2=.01 kilogram^(-1)*meter^(-4)*second^4*ampere^2; unit picoA_per_picoF=1 kilogram^1*meter^2*second^(-4)*ampere^(-1); // unit micromolar predefined unit joule_per_mole_kelvin=1 kilogram^1*meter^2*second^(-2)*kelvin^(-1)*mole^(-1); unit coulomb_per_millimole=1E3 second^1*ampere^1*mole^(-1); unit cm2=1E-4 meter^2; // unit microlitre predefined math main { realDomain time millisecond; time.min=0; extern time.max; extern time.delta; real V(time) millivolt; when(time=time.min) V=-85.64004; real Cm microF_per_cm2; Cm=1; real Vmyo microlitre; Vmyo=2.2e-5; real VJSR microlitre; VJSR=1.022e-7; real VNSR microlitre; VNSR=1.786e-6; real Vss microlitre; Vss=1.264e-9; real Acap cm2; Acap=0.00013866; real Ko micromolar; Ko=5400; real Nao micromolar; Nao=134000; real Cao micromolar; Cao=1400; real R joule_per_mole_kelvin; R=8.314; real T kelvin; T=308; real F coulomb_per_millimole; F=96.5; real i_CaL(time) picoA_per_picoF; real i_pCa(time) picoA_per_picoF; real i_NaCa(time) picoA_per_picoF; real i_Cab(time) picoA_per_picoF; real i_Na(time) picoA_per_picoF; real i_Nab(time) picoA_per_picoF; real i_NaK(time) picoA_per_picoF; real i_Kto_f(time) picoA_per_picoF; real i_Kto_s(time) picoA_per_picoF; real i_K1(time) picoA_per_picoF; real i_Ks(time) picoA_per_picoF; real i_Kur(time) picoA_per_picoF; real i_Kss(time) picoA_per_picoF; real i_ClCa(time) picoA_per_picoF; real i_Kr(time) picoA_per_picoF; real stim_offset millisecond; stim_offset=100; real stim_period millisecond; stim_period=333.3333333; real stim_duration millisecond; stim_duration=3; real stim_amplitude picoA_per_picoF; stim_amplitude=-15; real i_Stim(time) picoA_per_picoF; real past(time) millisecond; real Cai(time) micromolar; when(time=time.min) Cai=0.1040595; real Cass(time) micromolar; when(time=time.min) Cass=0.1043777; real CaJSR(time) micromolar; when(time=time.min) CaJSR=730.0589; real CaNSR(time) micromolar; when(time=time.min) CaNSR=841.106; real Bi(time) dimensionless; real Bss(time) dimensionless; real BJSR(time) dimensionless; real Bmax micromolar; Bmax=109; real CSQN_tot micromolar; CSQN_tot=15000; real Kd micromolar; Kd=0.6; real Km_CSQN micromolar; Km_CSQN=800; real J_leak(time) micromolar_per_millisecond; real J_rel(time) micromolar_per_millisecond; real J_serca(time) micromolar_per_millisecond; real J_tr(time) micromolar_per_millisecond; real J_xfer(time) micromolar_per_millisecond; real P_RyR(time) dimensionless; when(time=time.min) P_RyR=2.290355e-9; real v1 per_millisecond; v1=4.5; real tau_tr millisecond; tau_tr=20; real v2 per_millisecond; v2=1e-5; real tau_xfer millisecond; tau_xfer=8; real CaMKb(time) dimensionless; real CaMKt(time) dimensionless; when(time=time.min) CaMKt=0.08989079; real CaMKa(time) dimensionless; real on_rate per_millisecond; on_rate=0.05; real off_rate per_millisecond; off_rate=0.00068; real vmup(time) micromolar_per_millisecond; real Km_up micromolar; Km_up=0.412; real i_CaL_max picoA_per_picoF; i_CaL_max=4; real P_O1(time) dimensionless; when(time=time.min) P_O1=0.003825599; real P_O2(time) dimensionless; when(time=time.min) P_O2=1.835831e-8; real vmup_init micromolar_per_millisecond; vmup_init=0.3158; real P_ryr_const1 per_millisecond; P_ryr_const1=-0.09; real P_ryr_const2 per_millisecond; P_ryr_const2=-0.225; real P_C1(time) dimensionless; real P_C2(time) dimensionless; when(time=time.min) P_C2=0.3797679; real k_plus_a micromolar4_per_millisecond; k_plus_a=0.006075; real k_minus_a per_millisecond; k_minus_a=0.07125; real k_plus_b micromolar3_per_millisecond; k_plus_b=0.00405; real k_minus_b per_millisecond; k_minus_b=0.965; real k_plus_c per_millisecond; k_plus_c=0.009; real k_minus_c per_millisecond; k_minus_c=0.0008; // Var below replaced by constant in model eqns to satisfy unit correction // real m dimensionless; // m=3; // Var below replaced by constant in model eqns to satisfy unit correction // real n dimensionless; // n=4; real P_CaL per_millisecond; P_CaL=19.1078; real O(time) dimensionless; when(time=time.min) O=4.373318e-6; real C(time) dimensionless; real I(time) dimensionless; when(time=time.min) I=0.009171979; real y_gate(time) dimensionless; when(time=time.min) y_gate=0.8876797; real y_gate_inf(time) dimensionless; real y_gate_tau(time) millisecond; real alpha_p(time) per_millisecond; real alpha_m per_millisecond; real epsilon_p(time) per_micromolar_millisecond; real epsilon_m(time) per_millisecond; real V_L millivolt; V_L=-2; real delta_V_L millivolt; delta_V_L=7.0671; real t_L millisecond; t_L=1.1683; real phi_L dimensionless; phi_L=1.6411; real a dimensionless; a=0.07; real b dimensionless; b=14; real tau_L millisecond; tau_L=972.9715; real K_L micromolar; K_L=0.0964; real expVL(time) dimensionless; real FVRT(time) dimensionless; real FVRT_Ca(time) dimensionless; real const5 millivolt; const5=6.6755; real i_pCa_max picoA_per_picoF; i_pCa_max=0.9; real Km_pCa micromolar; Km_pCa=0.4; real J_pCa(time) micromolar_per_millisecond; real J_ncx(time) micromolar_per_millisecond; real k_NaCa picoA_per_picoF; k_NaCa=772.8991; real K_mNa micromolar; K_mNa=86500; real K_mCa micromolar; K_mCa=1380; real k_sat dimensionless; k_sat=0.1; real eta dimensionless; eta=0.35; real Nai(time) micromolar; when(time=time.min) Nai=16522.45; real g_Cab milliS_per_microF; g_Cab=0.00088; real E_CaN(time) millivolt; real J_Cab(time) micromolar_per_millisecond; real E_Na(time) millivolt; real g_Na milliS_per_microF; g_Na=13; real O_Na(time) dimensionless; when(time=time.min) O_Na=2.639399e-7; real C_Na1(time) dimensionless; when(time=time.min) C_Na1=0.0001581035; real C_Na2(time) dimensionless; when(time=time.min) C_Na2=0.01702105; real C_Na3(time) dimensionless; real I1_Na(time) dimensionless; when(time=time.min) I1_Na=0.00001799179; real I2_Na(time) dimensionless; when(time=time.min) I2_Na=0.000005460299; real IF_Na(time) dimensionless; when(time=time.min) IF_Na=0.0000556206; real IC_Na2(time) dimensionless; when(time=time.min) IC_Na2=0.005985434; real IC_Na3(time) dimensionless; when(time=time.min) IC_Na3=0.2543133; real alpha_Na11(time) per_millisecond; real beta_Na11(time) per_millisecond; real alpha_Na12(time) per_millisecond; real beta_Na12(time) per_millisecond; real alpha_Na13(time) per_millisecond; real beta_Na13(time) per_millisecond; real alpha_Na3(time) per_millisecond; real beta_Na3(time) per_millisecond; real alpha_Na2(time) per_millisecond; real beta_Na2(time) per_millisecond; real alpha_Na4(time) per_millisecond; real beta_Na4(time) per_millisecond; real alpha_Na5(time) per_millisecond; real beta_Na5(time) per_millisecond; real Ki(time) micromolar; when(time=time.min) Ki=141474; real g_Nab milliS_per_microF; g_Nab=0.0026; real E_K(time) millivolt; real g_Kto_f milliS_per_microF; g_Kto_f=0.4067; real ato_f(time) dimensionless; when(time=time.min) ato_f=0.001937245; real ito_f(time) dimensionless; when(time=time.min) ito_f=0.9999985; real alpha_a(time) per_millisecond; real beta_a(time) per_millisecond; real fast_transient_outward_K_I.alpha_i(time) per_millisecond; real fast_transient_outward_K_I.beta_i(time) per_millisecond; real ass(time) dimensionless; real iss(time) dimensionless; real g_Kto_s milliS_per_microF; g_Kto_s=0; real ato_s(time) dimensionless; when(time=time.min) ato_s=0.02000568; real ito_s(time) dimensionless; when(time=time.min) ito_s=0.9308568; real tau_ta_s(time) millisecond; real tau_ti_s(time) millisecond; real g_K1 milliS_per_microF; g_K1=0.2938; real g_Ks milliS_per_microF; g_Ks=0.00575; real nKs(time) dimensionless; when(time=time.min) nKs=0.002206261; real alpha_n(time) per_millisecond; real beta_n(time) per_millisecond; real g_Kur milliS_per_microF; g_Kur=0.16; real aur(time) dimensionless; when(time=time.min) aur=0.02000568; real iur(time) dimensionless; when(time=time.min) iur=0.9822006; real tau_aur(time) millisecond; real tau_iur(time) millisecond; real g_Kss milliS_per_microF; g_Kss=0.05; real aKss(time) dimensionless; when(time=time.min) aKss=0.8883113; real iKss(time) dimensionless; when(time=time.min) iKss=1; real tau_Kss(time) millisecond; real g_Kr milliS_per_microF; g_Kr=0.078; real O_K(time) dimensionless; when(time=time.min) O_K=0.0004858865; real C_K1(time) dimensionless; when(time=time.min) C_K1=0.0007799137; real C_K2(time) dimensionless; when(time=time.min) C_K2=0.0005301217; real C_K0(time) dimensionless; real I_K(time) dimensionless; when(time=time.min) I_K=0.00007519518; real alpha_a0(time) per_millisecond; real beta_a0(time) per_millisecond; real kb per_millisecond; kb=0.036778; real kf per_millisecond; kf=0.023761; real alpha_a1(time) per_millisecond; real beta_a1(time) per_millisecond; real rapid_delayed_rectifier_K_I.alpha_i(time) per_millisecond; real rapid_delayed_rectifier_K_I.beta_i(time) per_millisecond; real i_NaK_max picoA_per_picoF; i_NaK_max=1.66; real Km_Nai micromolar; Km_Nai=21000; real Km_Ko micromolar; Km_Ko=1500; real f_NaK(time) dimensionless; real sigma dimensionless; real g_ClCa milliS_per_microF; g_ClCa=10; real O_ClCa(time) dimensionless; real E_Cl millivolt; E_Cl=-40; real Km_Cl micromolar; Km_Cl=10; // // past=(floor(time/stim_period)*stim_period); i_Stim=(if (((time-past)>=stim_offset) and ((time-past)<=(stim_offset+stim_duration))) stim_amplitude else (0 picoA_per_picoF)); V:time=((-1)*(i_CaL+i_pCa+i_NaCa+i_Cab+i_Na+i_Nab+i_NaK+i_Kto_f+i_Kto_s+i_K1+i_Ks+i_Kur+i_Kss+i_Kr+i_ClCa+i_Stim)); // Cai:time=(Bi*(J_leak+J_xfer-(i_Cab+i_pCa-2*i_NaCa)*Acap*Cm/(2*Vmyo*F)-J_serca)); Cass:time=(Bss*(J_rel*VJSR/Vss-(J_xfer*Vmyo/Vss+i_CaL*Acap*Cm/(2*Vss*F)))); CaJSR:time=(BJSR*(J_tr-J_rel)); CaNSR:time=((J_serca-J_leak)*Vmyo/VNSR-J_tr*VJSR/VNSR); Bi=((1+Bmax*Kd/(Kd+Cai)^2)^((-1)*1)); Bss=((1+Bmax*Kd/(Kd+Cass)^2)^((-1)*1)); BJSR=((1+CSQN_tot*Km_CSQN/(Km_CSQN+CaJSR)^2)^((-1)*1)); // J_rel=(v1*(P_O1+P_O2)*(CaJSR-Cass)*P_RyR); J_tr=((CaNSR-CaJSR)/tau_tr); J_xfer=((Cass-Cai)/tau_xfer); J_leak=(v2*(CaNSR-Cai)); CaMKb=(.05*(1-CaMKt)*1/(1+(.7 micromolar)/Cass)); CaMKt:time=(on_rate*CaMKb*(CaMKb+CaMKt)-off_rate*CaMKt); CaMKa=(CaMKb+CaMKt); vmup=((3.1512*CaMKa^2.2062/(.1588^2.2062+CaMKa^2.2062)+1)*vmup_init); J_serca=(vmup*Cai^2/(Km_up^2+Cai^2)); P_RyR:time=(P_ryr_const1*P_RyR+P_ryr_const2*i_CaL/i_CaL_max*exp((-1)*(V-(5 millivolt))^2/(648 millivolt2))); // P_O1:time=(k_plus_a*Cass^4*P_C1+k_minus_b*P_O2+k_minus_c*P_C2-(k_minus_a*P_O1+k_plus_b*Cass^3*P_O1+k_plus_c*P_O1)); P_C1=(1-(P_C2+P_O1+P_O2)); P_O2:time=(k_plus_b*Cass^3*P_O1-k_minus_b*P_O2); P_C2:time=(k_plus_c*P_O1-k_minus_c*P_C2); // FVRT=(F*V/(R*T)); FVRT_Ca=(2*FVRT); expVL=exp((V-V_L)/delta_V_L); alpha_p=(expVL/(t_L*(expVL+1))); alpha_m=(phi_L/t_L); epsilon_p=((expVL+a)/(tau_L*K_L*(expVL+1))); epsilon_m=(b*(expVL+a)/(tau_L*(b*expVL+a))); y_gate_inf=(1/(1+exp((V+(16.6577 millivolt))/const5))+.1/(1+exp(((-1)*V+(40 millivolt))/(6 millivolt)))); y_gate_tau=((20 millisecond)+(600 millisecond)/(1+exp((V+(30 millivolt))/(9.6 millivolt)))); C=(1-O-I); O:time=(alpha_p*C-alpha_m*O); I:time=(epsilon_p*Cass*C-epsilon_m*I); y_gate:time=((y_gate_inf-y_gate)/y_gate_tau); i_CaL=(if (abs(FVRT_Ca)>1E-5) (-1)*P_CaL*2*Vss*F/(Acap*Cm)*O*y_gate*FVRT_Ca/(1-exp((-1)*FVRT_Ca))*(Cao*exp((-1)*FVRT_Ca)-Cass) else (-1)*P_CaL*2*Vss*F/(Acap*Cm)*O*y_gate*1E-5/(1-exp((-1)*1E-5))*(Cao*exp((-1)*1E-5)-Cass)); // i_pCa=(i_pCa_max*Cai^2/(Km_pCa^2+Cai^2)); J_pCa=((-1)*i_pCa*Acap*Cm/(2*Vmyo*F)); // i_NaCa=(k_NaCa*1/(K_mNa^3+Nao^3)*1/(K_mCa+Cao)*1/(1+k_sat*exp((eta-1)*V*F/(R*T)))*(exp(eta*V*F/(R*T))*Nai^3*Cao-exp((eta-1)*V*F/(R*T))*Nao^3*Cai)); J_ncx=(i_NaCa*Acap*Cm/(Vmyo*F)); // i_Cab=(g_Cab*(V-E_CaN)); E_CaN=(R*T/(2*F)*ln(Cao/Cai)); J_Cab=((-1)*i_Cab*Acap*Cm/(2*Vmyo*F)); // Nai:time=((-1)*(i_Na+i_Nab+3*i_NaK+3*i_NaCa)*Acap*Cm/(Vmyo*F)); // i_Na=(g_Na*O_Na*(V-E_Na)); E_Na=(R*T/F*ln((.9*Nao+.1*Ko)/(.9*Nai+.1*Ki))); C_Na3=(1-(O_Na+C_Na1+C_Na2+IF_Na+I1_Na+I2_Na+IC_Na2+IC_Na3)); C_Na2:time=(alpha_Na11*C_Na3+beta_Na12*C_Na1+alpha_Na3*IC_Na2-(beta_Na11*C_Na2+alpha_Na12*C_Na2+beta_Na3*C_Na2)); C_Na1:time=(alpha_Na12*C_Na2+beta_Na13*O_Na+alpha_Na3*IF_Na-(beta_Na12*C_Na1+alpha_Na13*C_Na1+beta_Na3*C_Na1)); O_Na:time=(alpha_Na13*C_Na1+beta_Na2*IF_Na-(beta_Na13*O_Na+alpha_Na2*O_Na)); IF_Na:time=(alpha_Na2*O_Na+beta_Na3*C_Na1+beta_Na4*I1_Na+alpha_Na12*IC_Na2-(beta_Na2*IF_Na+alpha_Na3*IF_Na+alpha_Na4*IF_Na+beta_Na12*IF_Na)); I1_Na:time=(alpha_Na4*IF_Na+beta_Na5*I2_Na-(beta_Na4*I1_Na+alpha_Na5*I1_Na)); I2_Na:time=(alpha_Na5*I1_Na-beta_Na5*I2_Na); IC_Na2:time=(alpha_Na11*IC_Na3+beta_Na12*IF_Na+beta_Na3*IC_Na2-(beta_Na11*IC_Na2+alpha_Na12*IC_Na2+alpha_Na3*IC_Na2)); IC_Na3:time=(beta_Na11*IC_Na2+beta_Na3*C_Na3-(alpha_Na11*IC_Na3+alpha_Na3*IC_Na3)); alpha_Na11=((3.802 per_millisecond)/(.1027*exp((-1)*(V+(2.5 millivolt))/(17 millivolt))+.2*exp((-1)*(V+(2.5 millivolt))/(150 millivolt)))); alpha_Na12=((3.802 per_millisecond)/(.1027*exp((-1)*(V+(2.5 millivolt))/(15 millivolt))+.23*exp((-1)*(V+(2.5 millivolt))/(150 millivolt)))); alpha_Na13=((3.802 per_millisecond)/(.1027*exp((-1)*(V+(2.5 millivolt))/(12 millivolt))+.25*exp((-1)*(V+(2.5 millivolt))/(150 millivolt)))); beta_Na11=((.1917 per_millisecond)*exp((-1)*(V+(2.5 millivolt))/(20.3 millivolt))); beta_Na12=((.2 per_millisecond)*exp((-1)*(V-(2.5 millivolt))/(20.3 millivolt))); beta_Na13=((.22 per_millisecond)*exp((-1)*(V-(7.5 millivolt))/(20.3 millivolt))); alpha_Na3=((7E-7 per_millisecond)*exp((-1)*(V+(7 millivolt))/(7.7 millivolt))); beta_Na3=((.0084 per_millisecond)+(2E-5 per_millivolt_millisecond)*(V+(7 millivolt))); alpha_Na2=((1 per_millisecond)/(.188495*exp((-1)*(V+(7 millivolt))/(16.6 millivolt))+.393956)); beta_Na2=(alpha_Na13*alpha_Na2*alpha_Na3/(beta_Na13*beta_Na3)); alpha_Na4=(alpha_Na2/1E3); beta_Na4=alpha_Na3; alpha_Na5=(alpha_Na2/95000); beta_Na5=(alpha_Na3/50); // i_Nab=(g_Nab*(V-E_Na)); // Ki:time=((-1)*(i_Stim+i_Kto_f+i_Kto_s+i_K1+i_Ks+i_Kss+i_Kur+i_Kr-2*i_NaK)*Acap*Cm/(Vmyo*F)); // i_Kto_f=(g_Kto_f*ato_f^3*ito_f*(V-E_K)); E_K=(R*T/F*ln(Ko/Ki)); ato_f:time=(alpha_a*(1-ato_f)-beta_a*ato_f); ito_f:time=(fast_transient_outward_K_I.alpha_i*(1-ito_f)-fast_transient_outward_K_I.beta_i*ito_f); alpha_a=((.18064 per_millisecond)*exp((.03577 per_millivolt)*(V+(30 millivolt)))); beta_a=((.3956 per_millisecond)*exp((-1)*(.06237 per_millivolt)*(V+(30 millivolt)))); fast_transient_outward_K_I.alpha_i=((1.52E-4 per_millisecond)*exp((-1)*(V+(13.5 millivolt))/(7 millivolt))/(.0067083*exp((-1)*(V+(33.5 millivolt))/(7 millivolt))+1)); fast_transient_outward_K_I.beta_i=((9.5E-4 per_millisecond)*exp((V+(33.5 millivolt))/(7 millivolt))/(.051335*exp((V+(33.5 millivolt))/(7 millivolt))+1)); // i_Kto_s=(g_Kto_s*ato_s*ito_s*(V-E_K)); ato_s:time=((ass-ato_s)/tau_ta_s); ito_s:time=((iss-ito_s)/tau_ti_s); ass=(1/(1+exp((-1)*(V+(22.5 millivolt))/(7.7 millivolt)))); iss=(1/(1+exp((V+(45.2 millivolt))/(5.7 millivolt)))); tau_ta_s=((.493 millisecond)*exp((-1)*(.0629 per_millivolt)*V)+(2.058 millisecond)); tau_ti_s=((270 millisecond)+(1050 millisecond)/(1+exp((V+(45.2 millivolt))/(5.7 millivolt)))); // i_K1=(g_K1*Ko/(Ko+(210 micromolar))*(V-E_K)/(1+exp((.0896 per_millivolt)*(V-E_K)))); // i_Ks=(g_Ks*nKs^2*(V-E_K)); nKs:time=(alpha_n*(1-nKs)-beta_n*nKs); alpha_n=((4.81333E-6 per_millivolt_millisecond)*(V+(26.5 millivolt))/(1-exp((-1)*(.128 per_millivolt)*(V+(26.5 millivolt))))); beta_n=((9.53333E-5 per_millisecond)*exp((-1)*(.038 per_millivolt)*(V+(26.5 millivolt)))); // i_Kur=(g_Kur*aur*iur*(V-E_K)); aur:time=((ass-aur)/tau_aur); iur:time=((iss-iur)/tau_iur); tau_aur=((.493 millisecond)*exp((-1)*(.0629 per_millivolt)*V)+(2.058 millisecond)); tau_iur=((1200 millisecond)-(170 millisecond)/(1+exp((V+(45.2 millivolt))/(5.7 millivolt)))); // i_Kss=(g_Kss*aKss*iKss*(V-E_K)); aKss:time=((ass-aKss)/tau_Kss); iKss:time=(0 per_millisecond); tau_Kss=((39.3 millisecond)*exp((-1)*(.0862 per_millivolt)*V)+(13.17 millisecond)); // i_Kr=(g_Kr*O_K*(V-R*T/F*ln((.98*Ko+.02*Nao)/(.98*Ki+.02*Nai)))); C_K0=(1-(C_K1+C_K2+O_K+I_K)); C_K2:time=(kf*C_K1+beta_a1*O_K-(kb*C_K2+alpha_a1*C_K2)); C_K1:time=(alpha_a0*C_K0+kb*C_K2-(beta_a0*C_K1+kf*C_K1)); O_K:time=(alpha_a1*C_K2+rapid_delayed_rectifier_K_I.beta_i*I_K-(beta_a1*O_K+rapid_delayed_rectifier_K_I.alpha_i*O_K)); I_K:time=(rapid_delayed_rectifier_K_I.alpha_i*O_K-rapid_delayed_rectifier_K_I.beta_i*I_K); alpha_a0=((.022348 per_millisecond)*exp((.01176 per_millivolt)*V)); beta_a0=((.047002 per_millisecond)*exp((-1)*(.0631 per_millivolt)*V)); alpha_a1=((.013733 per_millisecond)*exp((.038198 per_millivolt)*V)); beta_a1=((6.89E-5 per_millisecond)*exp((-1)*(.04178 per_millivolt)*V)); rapid_delayed_rectifier_K_I.alpha_i=((.090821 per_millisecond)*exp((.023391 per_millivolt)*(V+(5 millivolt)))); rapid_delayed_rectifier_K_I.beta_i=((.006497 per_millisecond)*exp((-1)*(.03268 per_millivolt)*(V+(5 millivolt)))); // i_NaK=(i_NaK_max*f_NaK*1/(1+(Km_Nai/Nai)^1.5)*Ko/(Ko+Km_Ko)); f_NaK=(1/(1+.1245*exp((-1)*.1*V*F/(R*T))+.0365*sigma*exp((-1)*V*F/(R*T)))); sigma=(1/7*(exp(Nao/(67300 micromolar))-1)); // i_ClCa=(g_ClCa*O_ClCa*Cai/(Cai+Km_Cl)*(V-E_Cl)); O_ClCa=(.2/(1+exp((-1)*(V-(46.7 millivolt))/(7.8 millivolt)))); // // // }