/* * Model study of ATP and ADP buffering, transport of Ca(2+) and * Mg(2+), and regulation of ion pumps in ventricular myocyte * * Model Status * * This CellML model runs in both COR and OpenCell to recreate * the published results. The units have been checked and they * are consistent. We thank the original model author Anushka Michailova * for providing us with the MATLAB code for this model. Please * note when running a simultaion the step size has to be smaller * than 0.005 seconds. * * Model Structure * * ABSTRACT: We extended the model of the ventricular myocyte by * Winslow et al. (Circ. Res 1999, 84:571-586) by incorporating * equations for Ca(2+) and Mg(2+) buffering and transport by ATP * and ADP and equations for MgATP regulation of ion transporters * (Na(+)-K(+) pump, sarcolemmal and sarcoplasmic Ca(2+) pumps). * The results indicate that, under normal conditions, Ca(2+) binding * by low-affinity ATP and diffusion of CaATP may affect the amplitude * and time course of intracellular Ca(2+) signals. The model also * suggests that a fall in ATP/ADP ratio significantly reduces * sarcoplasmic Ca(2+) content, increases diastolic Ca(2+), lowers * systolic Ca(2+), increases Ca(2+) influx through L-type channels, * and decreases the efficiency of the Na(+)/Ca(2+) exchanger in * extruding Ca(2+) during periodic voltage-clamp stimulation. * The analysis suggests that the most important reason for these * changes during metabolic inhibition is the down-regulation of * the sarcoplasmic Ca(2+)-ATPase pump by reduced diastolic MgATP * levels. High Ca(2+) concentrations developed near the membrane * might have a greater influence on Mg(2+), ATP, and ADP concentrations * than that of the lower Ca(2+) concentrations in the bulk myoplasm. * The model predictions are in general agreement with experimental * observations measured under normal and pathological conditions. * * The original paper reference is cited below: * * Model study of ATP and ADP buffering, transport of Ca(2+) and * Mg(2+), and regulation of ion pumps in ventricular myocyte, * Anushka Michailova and Andrew McCulloch, 2001, Biophysical Journal, * 81, 614-629. PubMed ID: 11463611 * * cell diagram * * [[Image file: michailova_mcculloch_2001.png]] * * Schematic diagram of the mechanisms involved in the model. */ import nsrunit; unit conversion on; unit per_second=1 second^(-1); unit second_per_millisecond=1E3 dimensionless; // unit millivolt predefined unit per_millivolt=1E3 kilogram^(-1)*meter^(-2)*second^3*ampere^1; unit per_millivolt_second=1E3 kilogram^(-1)*meter^(-2)*second^2*ampere^1; unit milliS_per_microF=1E3 second^(-1); unit microF_per_cm2=.01 kilogram^(-1)*meter^(-4)*second^4*ampere^2; unit microA_per_microF=1 kilogram^1*meter^2*second^(-4)*ampere^(-1); unit nA_microA=.001 dimensionless; // unit millimolar predefined unit millimolar_per_second=1 meter^(-3)*second^(-1)*mole^1; unit per_millimolar_second=1 meter^3*second^(-1)*mole^(-1); unit millimolar3_per_second=1 meter^9*second^(-1)*mole^(-3); unit millimolar4_per_second=1 meter^12*second^(-1)*mole^(-4); 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 cm_per_second=.01 meter^1*second^(-1); unit cm_per_farad_second=.01 kilogram^1*meter^3*second^(-5)*ampere^(-2); unit cm2=1E-4 meter^2; // unit microlitre predefined math main { realDomain time second; time.min=0; extern time.max; extern time.delta; real V(time) millivolt; when(time=time.min) V=-96.1638; real R joule_per_mole_kelvin; R=8.314472; real T kelvin; T=310; real F coulomb_per_millimole; F=96.4853415; real C_sc microF_per_cm2; C_sc=0.001; real i_Stim(time) microA_per_microF; real i_Na(time) microA_per_microF; real i_Ca(time) microA_per_microF; real i_Ca_K(time) microA_per_microF; real i_Kr(time) microA_per_microF; real i_Ks(time) microA_per_microF; real i_to1(time) microA_per_microF; real i_K1(time) microA_per_microF; real i_Kp(time) microA_per_microF; real i_NaCa(time) microA_per_microF; real i_NaK(time) microA_per_microF; real i_p_Ca(time) microA_per_microF; real i_Ca_b(time) microA_per_microF; real i_Na_b(time) microA_per_microF; real stim_start second; stim_start=0.1; real stim_end second; stim_end=100000000; real stim_period second; stim_period=1; real stim_duration second; stim_duration=0.0005; real stim_amplitude microA_per_microF; stim_amplitude=-100.0; real E_Na(time) millivolt; real g_Na milliS_per_microF; g_Na=12.8; real Na_o millimolar; Na_o=138; real Na_i(time) millimolar; when(time=time.min) Na_i=10; real fast_sodium_current.m(time) dimensionless; when(time=time.min) fast_sodium_current.m=0.0328302; real h(time) dimensionless; when(time=time.min) h=0.988354; real j(time) dimensionless; when(time=time.min) j=0.99254; real alpha_m(time) per_second; real beta_m(time) per_second; real E0_m(time) millivolt; real alpha_h(time) per_second; real beta_h(time) per_second; real alpha_j(time) per_second; real beta_j(time) per_second; real E_K(time) millivolt; real g_Kr milliS_per_microF; g_Kr=0.0034; real f_K_o dimensionless; real R_V(time) dimensionless; real K_o millimolar; K_o=4; real K_i(time) millimolar; when(time=time.min) K_i=159.48; real X_kr(time) dimensionless; when(time=time.min) X_kr=0.51; real K12(time) dimensionless; real K21(time) dimensionless; real X_kr_inf(time) dimensionless; real tau_X_kr(time) second; real tau_factor dimensionless; tau_factor=1; real g_Ks milliS_per_microF; g_Ks=0.0027134; real E_Ks(time) millivolt; real X_ks(time) dimensionless; when(time=time.min) X_ks=0.264; real tau_X_ks(time) second; real X_ks_infinity(time) dimensionless; real g_to1 milliS_per_microF; g_to1=0.23815; real X_to1(time) dimensionless; when(time=time.min) X_to1=2.63; real Y_to1(time) dimensionless; when(time=time.min) Y_to1=0.99; real alpha_X_to1(time) per_second; real beta_X_to1(time) per_second; real alpha_Y_to1(time) per_second; real beta_Y_to1(time) per_second; real g_K1 milliS_per_microF; g_K1=2.8; real K_mK1 millimolar; K_mK1=13; real K1_infinity_V(time) dimensionless; real g_Kp milliS_per_microF; g_Kp=0.002216; real Kp_V(time) dimensionless; real K_mCa millimolar; K_mCa=1.38; real K_mNa millimolar; K_mNa=87.5; real K_NaCa microA_per_microF; K_NaCa=0.3; real K_sat dimensionless; K_sat=0.2; real eta dimensionless; eta=0.35; real Ca_i(time) millimolar; when(time=time.min) Ca_i=8.464E-5; real Ca_o millimolar; Ca_o=2; real i_NaK_winslow(time) microA_per_microF; real I_NaK microA_per_microF; I_NaK=0.693; real f_NaK(time) dimensionless; real K_mNa_i millimolar; K_mNa_i=10; real K_mK_o millimolar; K_mK_o=1.5; real sigma dimensionless; real MgATP_i(time) millimolar; when(time=time.min) MgATP_i=6.4395; real MgATP_i0 millimolar; MgATP_i0=2.888; real i_p_Ca_winslow(time) microA_per_microF; real K_mpCa millimolar; K_mpCa=0.00005; real I_pCa microA_per_microF; I_pCa=0.05; real g_Cab milliS_per_microF; g_Cab=0.0003842; real E_Ca(time) millivolt; real g_Nab milliS_per_microF; g_Nab=0.0031; real P_Ca cm_per_second; P_Ca=3.125e-4; real P_K cm_per_second; P_K=5.79e-7; real p_prime_k(time) cm_per_second; real i_Ca_half microA_per_microF; i_Ca_half=-0.265; real i_Ca_max(time) microA_per_microF; real O(time) dimensionless; when(time=time.min) O=9.84546e-21; real O_Ca(time) dimensionless; when(time=time.min) O_Ca=0; real alpha(time) per_second; real beta(time) per_second; real gamma(time) per_second; real alpha_a(time) per_second; real beta_b(time) per_second; real a dimensionless; a=2; real b dimensionless; b=2; real g per_second; g=2000; real f per_second; f=300; real gprime per_second; gprime=7000; real fprime per_second; fprime=7; real omega per_second; omega=10; real C0(time) dimensionless; when(time=time.min) C0=0.997208; real C1(time) dimensionless; when(time=time.min) C1=6.38897e-5; real C2(time) dimensionless; when(time=time.min) C2=1.535e-9; real C3(time) dimensionless; when(time=time.min) C3=1.63909e-14; real C4(time) dimensionless; when(time=time.min) C4=6.56337e-20; real C_Ca0(time) dimensionless; when(time=time.min) C_Ca0=0.00272826; real C_Ca1(time) dimensionless; when(time=time.min) C_Ca1=6.99215e-7; real C_Ca2(time) dimensionless; when(time=time.min) C_Ca2=6.71989e-11; real C_Ca3(time) dimensionless; when(time=time.min) C_Ca3=2.87031e-15; real C_Ca4(time) dimensionless; when(time=time.min) C_Ca4=4.59752e-20; real Ca_ss(time) millimolar; when(time=time.min) Ca_ss=1.315E-4; real y(time) dimensionless; when(time=time.min) y=0.798; real y_infinity(time) dimensionless; real tau_y(time) second; real J_rel(time) millimolar_per_second; real v1 per_second; v1=1800; real k_a_plus millimolar4_per_second; k_a_plus=1.215e13; real k_a_minus per_second; k_a_minus=576; real k_b_plus millimolar3_per_second; k_b_plus=4.05e9; real k_b_minus per_second; k_b_minus=1930; real k_c_plus per_second; k_c_plus=100; real k_c_minus per_second; k_c_minus=0.8; real P_O1(time) dimensionless; when(time=time.min) P_O1=0; real P_O2(time) dimensionless; when(time=time.min) P_O2=0; real P_C1(time) dimensionless; when(time=time.min) P_C1=0.47; real P_C2(time) dimensionless; when(time=time.min) P_C2=0.53; // Var below replaced by constant in model eqns to satisfy unit correction // real n dimensionless; // n=4; // Var below replaced by constant in model eqns to satisfy unit correction // real RyR_channel.m dimensionless; // RyR_channel.m=3; real Ca_JSR(time) millimolar; when(time=time.min) Ca_JSR=0.2616; real J_up(time) millimolar_per_second; real J_up_winslow(time) millimolar_per_second; real K_fb millimolar; K_fb=0.000168; real K_rb millimolar; K_rb=3.29; real fb(time) dimensionless; real rb(time) dimensionless; real Vmaxf millimolar_per_second; Vmaxf=0.0813; real Vmaxr millimolar_per_second; Vmaxr=0.318; real K_SR dimensionless; K_SR=1; real N_fb dimensionless; N_fb=1.2; real N_rb dimensionless; N_rb=1; real Ca_NSR(time) millimolar; when(time=time.min) Ca_NSR=0.2620; real J_tr(time) millimolar_per_second; real J_xfer(time) millimolar_per_second; real J_trpn(time) millimolar_per_second; real tau_tr second; tau_tr=0.0005747; real tau_xfer second; tau_xfer=0.0267; real HTRPNCa(time) millimolar; when(time=time.min) HTRPNCa=0.98; real LTRPNCa(time) millimolar; when(time=time.min) LTRPNCa=0.078; real J_HTRPNCa(time) millimolar_per_second; real J_LTRPNCa(time) millimolar_per_second; real HTRPN_tot dimensionless; HTRPN_tot=0.14; real LTRPN_tot dimensionless; LTRPN_tot=0.07; real k_htrpn_plus per_millimolar_second; k_htrpn_plus=20000; real k_htrpn_minus per_second; k_htrpn_minus=0.066; real k_ltrpn_plus per_millimolar_second; k_ltrpn_plus=40000; real k_ltrpn_minus per_second; k_ltrpn_minus=40; real A_cap cm2; A_cap=0.0001534; real intracellular_ion_concentrations.V_myo microlitre; intracellular_ion_concentrations.V_myo=0.00002584; real V_JSR microlitre; V_JSR=0.00000016; real V_NSR microlitre; V_NSR=0.0000021; real intracellular_ion_concentrations.V_ss microlitre; intracellular_ion_concentrations.V_ss=0.0000000012; real K_mCMDN millimolar; K_mCMDN=0.00238; real K_mEGTA millimolar; K_mEGTA=0.00015; real K_mCSQN millimolar; K_mCSQN=0.8; real CMDN_tot millimolar; CMDN_tot=0.05; real EGTA_tot millimolar; EGTA_tot=0; real CSQN_tot millimolar; CSQN_tot=15; real beta_i(time) dimensionless; real beta_SS(time) dimensionless; real beta_JSR(time) dimensionless; real k_plus_CaATP per_millimolar_second; k_plus_CaATP=225000.0; real k_minus_CaATP per_second; k_minus_CaATP=45000.0; real k_plus_CaADP per_millimolar_second; k_plus_CaADP=125000.0; real k_minus_CaADP per_second; k_minus_CaADP=193500; real CaADP_i(time) millimolar; when(time=time.min) CaADP_i=0.11E-6; real CaADP_ss(time) millimolar; when(time=time.min) CaADP_ss=0.13E-6; real CaATP_ss(time) millimolar; when(time=time.min) CaATP_ss=0.25E-3; real ATP_i(time) millimolar; real ADP_i(time) millimolar; real ADP_ss(time) millimolar; real ATP_ss(time) millimolar; real CaATP_i(time) millimolar; when(time=time.min) CaATP_i=0.237E-3; real Mg_ss(time) millimolar; when(time=time.min) Mg_ss=1.0; real Mg_i(time) millimolar; when(time=time.min) Mg_i=1.0; real MgADP_i(time) millimolar; when(time=time.min) MgADP_i=0.298E-2; real MgADP_ss(time) millimolar; when(time=time.min) MgADP_ss=0.298E-2; real MgATP_ss(time) millimolar; when(time=time.min) MgATP_ss=6.4395; real ATP_tot millimolar; ATP_tot=7.0; real k_plus_MgATP per_millimolar_second; k_plus_MgATP=125000.0; real k_minus_MgATP per_second; k_minus_MgATP=10875.0; real Jxfer_CaATP(time) millimolar_per_second; real Jxfer_MgATP(time) millimolar_per_second; real Jxfer_Mg(time) millimolar_per_second; real tau_xfer_CaATP second; tau_xfer_CaATP=0.0534; real tau_xfer_MgATP second; tau_xfer_MgATP=0.0534; real tau_xfer_Mg second; tau_xfer_Mg=0.0267; real ADP_tot millimolar; ADP_tot=0.005; real k_plus_MgADP per_millimolar_second; k_plus_MgADP=125000.0; real k_minus_MgADP per_second; k_minus_MgADP=84500.0; real Jxfer_CaADP(time) millimolar_per_second; real Jxfer_MgADP(time) millimolar_per_second; real tau_xfer_CaADP second; tau_xfer_CaADP=0.0534; real tau_xfer_MgADP second; tau_xfer_MgADP=0.0534; real Ca_and_Mg_buffering_by_ATP.V_myo microlitre; Ca_and_Mg_buffering_by_ATP.V_myo=0.00002584; real Ca_and_Mg_buffering_by_ATP.V_ss microlitre; Ca_and_Mg_buffering_by_ATP.V_ss=0.0000000012; // // i_Stim=(if (((time>=stim_start) and (time<=stim_end)) and ((time-stim_start-floor((time-stim_start)/stim_period)*stim_period)<=stim_duration)) stim_amplitude else (0 microA_per_microF)); V:time=((-1)*(1 microF_per_cm2)*(1 nA_microA)*(i_Na+i_Ca+i_Ca_K+i_Kr+i_Ks+i_to1+i_K1+i_Kp+i_NaCa+i_NaK+i_p_Ca+i_Na_b+i_Ca_b+i_Stim)/C_sc); // E_Na=(R*T/F*ln(Na_o/Na_i)); i_Na=(g_Na*fast_sodium_current.m^3*h*j*(V-E_Na)); // E0_m=(V+(47.13 millivolt)); alpha_m=(if (abs(E0_m)<(1E-5 millivolt)) (320 per_second)/(.1-(.005 per_millivolt)*E0_m) else (320 per_millivolt_second)*E0_m/(1-exp((-1)*(.1 per_millivolt)*E0_m))); beta_m=((80 per_second)*exp((-1)*V/(11 millivolt))); fast_sodium_current.m:time=(if (V>=((-1)*(90 millivolt))) alpha_m*(1-fast_sodium_current.m)-beta_m*fast_sodium_current.m else (0 per_second)); // alpha_h=(if (V<((-1)*(40 millivolt))) (135 per_second)*exp(((80 millivolt)+V)/((-1)*(6.8 millivolt))) else (0 per_second)); beta_h=(if (V<((-1)*(40 millivolt))) (3560 per_second)*exp((.079 per_millivolt)*V)+(3.1E5 per_second)*exp((.35 per_millivolt)*V) else 1E3/((.13 second)*(1+exp((V+(10.66 millivolt))/((-1)*(11.1 millivolt)))))); h:time=(alpha_h*(1-h)-beta_h*h); // alpha_j=(if (V<((-1)*(40 millivolt))) 1E3*((-1)*((127140 per_millivolt_second)*exp((.2444 per_millivolt)*V)+(3.474E-5 per_millivolt_second)*exp((-1)*(.04391 per_millivolt)*V)))*(V+(37.78 millivolt))/(1+exp((.311 per_millivolt)*(V+(79.23 millivolt)))) else (0 per_second)); beta_j=(if (V<((-1)*(40 millivolt))) (121.2 per_second)*exp((-1)*(.01052 per_millivolt)*V)/(1+exp((-1)*(.1378 per_millivolt)*(V+(40.14 millivolt)))) else (300 per_second)*exp((-1)*(2.535E-7 per_millivolt)*V)/(1+exp((-1)*(.1 per_millivolt)*(V+(32 millivolt))))); j:time=(alpha_j*(1-j)-beta_j*j); // E_K=(R*T/F*ln(K_o/K_i)); f_K_o=sqrt(K_o/(4 millimolar)); R_V=(1/(1+1.4945*exp((.0446 per_millivolt)*V))); i_Kr=(g_Kr*f_K_o*R_V*X_kr*(V-E_K)); // K12=exp((-1)*5.495+(.1691 per_millivolt)*V); K21=exp((-1)*7.677-(.0128 per_millivolt)*V); X_kr_inf=(K12/(K12+K21)); tau_X_kr=((.001 second)/(K12+K21)+tau_factor*(.027 second)); X_kr:time=((X_kr_inf-X_kr)/tau_X_kr); // E_Ks=(R*T/F*ln((K_o+.01833*Na_o)/(K_i+.01833*Na_i))); i_Ks=(g_Ks*X_ks^2*(V-E_Ks)); // X_ks_infinity=(1/(1+exp((-1)*(V-(24.7 millivolt))/(13.6 millivolt)))); tau_X_ks=((.001 second)/((7.19E-5 per_millivolt)*(V-(10 millivolt))/(1-exp((-1)*(.148 per_millivolt)*(V-(10 millivolt))))+(1.31E-4 per_millivolt)*(V-(10 millivolt))/(exp((.0687 per_millivolt)*(V-(10 millivolt)))-1))); X_ks:time=((X_ks_infinity-X_ks)/tau_X_ks); // i_to1=(g_to1*X_to1*Y_to1*(V-E_K)); // alpha_X_to1=((45.16 per_second)*exp((.03577 per_millivolt)*V)); beta_X_to1=((98.9 per_second)*exp((-1)*(.06237 per_millivolt)*V)); X_to1:time=(alpha_X_to1*(1-X_to1)-beta_X_to1*X_to1); // alpha_Y_to1=((5.415 per_second)*exp((-1)*(V+(33.5 millivolt))/(5 millivolt))/(1+.051335*exp((-1)*(V+(33.5 millivolt))/(5 millivolt)))); beta_Y_to1=((5.415 per_second)*exp((V+(33.5 millivolt))/(5 millivolt))/(1+.051335*exp((V+(33.5 millivolt))/(5 millivolt)))); Y_to1:time=(alpha_Y_to1*(1-Y_to1)-beta_Y_to1*Y_to1); // i_K1=(g_K1*K1_infinity_V*K_o/(K_o+K_mK1)*(V-E_K)); // K1_infinity_V=(1/(2+exp(1.5*F/(R*T)*(V-E_K)))); // i_Kp=(g_Kp*Kp_V*(V-E_K)); // Kp_V=(1/(1+exp(((7.488 millivolt)-V)/(5.98 millivolt)))); // i_NaCa=(K_NaCa*5E3/((K_mNa^3+Na_o^3)*(K_mCa+Ca_o)*(1+K_sat*exp((eta-1)*V*F/(R*T))))*(exp(eta*V*F/(R*T))*Na_i^3*Ca_o-exp((eta-1)*V*F/(R*T))*Na_o^3*Ca_i)); // f_NaK=(1/(1+.1245*exp((-1)*.1*V*F/(R*T))+.0365*sigma*exp((-1)*V*F/(R*T)))); sigma=(1/7*(exp(Na_o/(67.3 millimolar))-1)); i_NaK=(MgATP_i/MgATP_i0*i_NaK_winslow); i_NaK_winslow=(I_NaK*f_NaK/(1+(K_mNa_i/Na_i)^1.5)*K_o/(K_o+K_mK_o)); // i_p_Ca=(MgATP_i/MgATP_i0*i_p_Ca_winslow); i_p_Ca_winslow=(I_pCa*Ca_i/(K_mpCa+Ca_i)); // E_Ca=(R*T/(2*F)*ln(Ca_o/Ca_i)); i_Ca_b=(g_Cab*(V-E_Ca)); // i_Na_b=(g_Nab*(V-E_Na)); // i_Ca=(i_Ca_max*y*(O+O_Ca)); i_Ca_K=(p_prime_k/((1 microF_per_cm2)*(1 second_per_millisecond))*y*(O+O_Ca)*V*F^2/(R*T)*(K_i*exp(V*F/(R*T))-K_o)/(exp(V*F/(R*T))-1)); p_prime_k=(P_K/(1+i_Ca_max/i_Ca_half)); i_Ca_max=(P_Ca/((1 microF_per_cm2)*(1 second_per_millisecond))*4*V*F^2*1E3/(R*T)*((.001 millimolar)*exp(2*V*F/(R*T))-.341*Ca_o)/(exp(2*V*F/(R*T))-1)); alpha=((400 per_second)*exp((V+(2 millivolt))/(10 millivolt))); beta=((50 per_second)*exp((-1)*(V+(2 millivolt))/(13 millivolt))); alpha_a=(alpha*a); beta_b=(beta/b); gamma=((103.75 per_second)*Ca_ss/(1 millimolar)); C0:time=(beta*C1+omega*C_Ca0-(4*alpha+gamma)*C0); C1:time=(4*alpha*C0+2*beta*C2+omega/b*C_Ca1-(beta+3*alpha+gamma*a)*C1); C2:time=(3*alpha*C1+3*beta*C3+omega/b^2*C_Ca2-(beta*2+2*alpha+gamma*a^2)*C2); C3:time=(2*alpha*C2+4*beta*C4+omega/b^3*C_Ca3-(beta*3+alpha+gamma*a^3)*C3); C4:time=(alpha*C3+g*O+omega/b^4*C_Ca4-(beta*4+f+gamma*a^4)*C4); O:time=(f*C4-g*O); C_Ca0:time=(beta_b*C_Ca1+gamma*C0-(4*alpha_a+omega)*C_Ca0); C_Ca1:time=(4*alpha_a*C_Ca0+2*beta_b*C_Ca2+gamma*a*C1-(beta_b+3*alpha_a+omega/b)*C_Ca1); C_Ca2:time=(3*alpha_a*C_Ca1+3*beta_b*C_Ca3+gamma*a^2*C2-(beta_b*2+2*alpha_a+omega/b^2)*C_Ca2); C_Ca3:time=(2*alpha_a*C_Ca2+4*beta_b*C_Ca4+gamma*a^3*C3-(beta_b*3+alpha_a+omega/b^3)*C_Ca3); C_Ca4:time=(alpha_a*C_Ca3+gprime*O_Ca+gamma*a^4*C4-(beta_b*4+fprime+omega/b^4)*C_Ca4); O_Ca:time=(fprime*C_Ca4-gprime*O_Ca); // y_infinity=(.8/(1+exp((V+(12.5 millivolt))/(5 millivolt)))+.2); tau_y=(((20 second)+(600 second)/(1+exp((V+(20 millivolt))/(9.5 millivolt))))/1E3); y:time=((y_infinity-y)/tau_y); // P_C1:time=((-1)*k_a_plus*Ca_ss^4*P_C1+k_a_minus*P_O1); P_O1:time=(k_a_plus*Ca_ss^4*P_C1-(k_a_minus*P_O1+k_b_plus*Ca_ss^3*P_O1+k_c_plus*P_O1)+k_b_minus*P_O2+k_c_minus*P_C2); P_O2:time=(k_b_plus*Ca_ss^3*P_O1-k_b_minus*P_O2); P_C2:time=(k_c_plus*P_O1-k_c_minus*P_C2); J_rel=(v1*(P_O1+P_O2)*(Ca_JSR-Ca_ss)); // fb=((Ca_i/K_fb)^N_fb); rb=((Ca_NSR/K_rb)^N_rb); J_up=(MgATP_i/MgATP_i0*J_up_winslow); J_up_winslow=(K_SR*(Vmaxf*fb-Vmaxr*rb)/(1+fb+rb)); // J_tr=((Ca_NSR-Ca_JSR)/tau_tr); J_xfer=((Ca_ss-Ca_i)/tau_xfer); J_trpn=(HTRPN_tot*J_HTRPNCa+LTRPN_tot*J_LTRPNCa); J_HTRPNCa=(HTRPNCa:time); HTRPNCa:time=(k_htrpn_plus*Ca_i*((1 millimolar)-HTRPNCa)-k_htrpn_minus*HTRPNCa); J_LTRPNCa=(LTRPNCa:time); LTRPNCa:time=(k_ltrpn_plus*Ca_i*((1 millimolar)-LTRPNCa)-k_ltrpn_minus*LTRPNCa); // Ca_i:time=(beta_i*(J_xfer-(J_up+J_trpn)+(-1)*((i_p_Ca+i_Ca_b-2*i_NaCa)*(A_cap*C_sc/(2*intracellular_ion_concentrations.V_myo*F)))+(k_minus_CaATP*CaATP_i+k_minus_CaADP*CaADP_i-(k_plus_CaATP*Ca_i*ATP_i+k_plus_CaADP*Ca_i*ADP_i)))); Na_i:time=((-1)*0*(i_Na+i_Na_b+i_NaCa*3+i_NaK*3)*A_cap*(1 microF_per_cm2)/(intracellular_ion_concentrations.V_myo*F)); K_i:time=((-1)*0*(i_Ca_K+i_Kr+i_Ks+i_K1+i_Kp+i_to1+i_NaK*((-1)*2))*A_cap*(1 microF_per_cm2)/(intracellular_ion_concentrations.V_myo*F)); beta_i=(1/(1+CMDN_tot*K_mCMDN/(K_mCMDN+Ca_i)^2+EGTA_tot*K_mEGTA/(K_mEGTA+Ca_i)^2)); beta_SS=(1/(1+CMDN_tot*K_mCMDN/(K_mCMDN+Ca_ss)^2+EGTA_tot*K_mEGTA/(K_mEGTA+Ca_ss)^2)); beta_JSR=(1/(1+CSQN_tot*K_mCSQN/(K_mCSQN+Ca_JSR)^2)); Ca_ss:time=(beta_SS*(J_rel*V_JSR/intracellular_ion_concentrations.V_ss+k_minus_CaATP*CaATP_ss+k_minus_CaADP*CaADP_ss-(J_xfer*intracellular_ion_concentrations.V_myo/intracellular_ion_concentrations.V_ss+i_Ca*(A_cap*(1 microF_per_cm2)/(2*intracellular_ion_concentrations.V_ss*F))+k_plus_CaATP*Ca_ss*ATP_ss+k_plus_CaADP*Ca_ss*ADP_ss))); Ca_JSR:time=(beta_JSR*(J_tr-J_rel)); Ca_NSR:time=(J_up*intracellular_ion_concentrations.V_myo/V_NSR-J_tr*V_JSR/V_NSR); // ATP_ss=(ATP_tot-(CaATP_ss+MgATP_ss)); CaATP_ss:time=(k_plus_CaATP*Ca_ss*ATP_ss-(Jxfer_CaATP*(Ca_and_Mg_buffering_by_ATP.V_myo/Ca_and_Mg_buffering_by_ATP.V_ss)+k_minus_CaATP*CaATP_ss)); MgATP_ss:time=(k_plus_MgATP*Mg_ss*ATP_ss-(Jxfer_MgATP*(Ca_and_Mg_buffering_by_ATP.V_myo/Ca_and_Mg_buffering_by_ATP.V_ss)+k_minus_MgATP*MgATP_ss)); ATP_i=(ATP_tot-(CaATP_i+MgATP_i)); CaATP_i:time=(Jxfer_CaATP+k_plus_CaATP*Ca_i*ATP_i-k_minus_CaATP*CaATP_i); MgATP_i:time=(Jxfer_MgATP+k_plus_MgATP*Mg_i*ATP_i-k_minus_MgATP*MgATP_i); Jxfer_CaATP=((CaATP_ss-CaATP_i)/tau_xfer_CaATP); Jxfer_MgATP=((MgATP_ss-MgATP_i)/tau_xfer_MgATP); ADP_ss=(ADP_tot-(CaADP_ss+MgADP_ss)); CaADP_ss:time=(k_plus_CaADP*Ca_ss*ADP_ss-(Jxfer_CaADP*(Ca_and_Mg_buffering_by_ATP.V_myo/Ca_and_Mg_buffering_by_ATP.V_ss)+k_minus_CaADP*CaADP_ss)); MgADP_ss:time=(k_plus_MgADP*Mg_ss*ADP_ss-(Jxfer_MgADP*(Ca_and_Mg_buffering_by_ATP.V_myo/Ca_and_Mg_buffering_by_ATP.V_ss)+k_minus_MgADP*MgADP_ss)); ADP_i=(ADP_tot-(CaADP_i+MgADP_i)); CaADP_i:time=(Jxfer_CaADP+k_plus_CaADP*Ca_i*ADP_i-k_minus_CaADP*CaADP_i); MgADP_i:time=(Jxfer_MgADP+k_plus_MgADP*Mg_i*ADP_i-k_minus_MgADP*MgADP_i); Jxfer_CaADP=((CaADP_ss-CaADP_i)/tau_xfer_CaADP); Jxfer_MgADP=((MgADP_ss-MgADP_i)/tau_xfer_MgADP); Mg_ss:time=(k_minus_MgATP*MgATP_ss+k_minus_MgADP*MgADP_ss-(k_plus_MgATP*Mg_ss*ATP_ss+k_plus_MgADP*Mg_ss*ADP_ss+Jxfer_Mg*(Ca_and_Mg_buffering_by_ATP.V_myo/Ca_and_Mg_buffering_by_ATP.V_ss))); Mg_i:time=(Jxfer_Mg+k_minus_MgATP*MgATP_i+k_minus_MgADP*MgADP_i-(k_plus_MgATP*Mg_i*ATP_i+k_plus_MgADP*Mg_i*ADP_i)); Jxfer_Mg=((Mg_ss-Mg_i)/tau_xfer_Mg); // // }