/* * A Gradient Model Of Cardiac Pacemaker Myocytes * * Model Status * * This model is currently non-functional. * * Model Structure * * Electrical activity of the healthy mammalian heart is initiated * by an area of specialised pacemaker cells in the wall of the * heart, known as the sinoatrial node (SAN). These cells are spontaneously * active, demonstrating a slow depolarisation to threshold (pacemaker * potential) rather than a stable resting potential. Despite heterogeneity * amongst the cells of the SAN, the cells are able to synchronise * their firing rate and this in turn stimulates the contraction * of the atrial myocardium. Synchronisation is achieved by electronic * coupling between cells via gap junctions. * * To date, two potential theories have been put forward to explain * the observed spatial heterogeneity in the action potential characteristics * within the SAN: * * 1) The gradient model suggests that the heterogeneity arises * intrinsically from a spatial gradient in underlying cellular * electrophysiological properties; and * * 2) The mosaic model, which suggests that atrial myocytes are * peppered throughout the SAN region, increasing in density towards * the periphery. Action potential heterogeneity then arises due * to the electronic coupling between atrial and pacemaker myocytes, * and the differences between the relative density of the two * cell types with the SAN. * * In order to further investigate the source of the action potential * heterogeneity in the SAN, a mathematical model has been devloped * by Lovell et al. (see the figure below). Several mathematical * models of the SAN activity have been previously published, including: * * Demir et al. Sinoatrial Node Model, 1994; * * Modelling the Ion Currents Underlying Sinoatrial Node Pacemaker * Activity, Dokos et al., 1996; * * A Model of Sinoatrial Node Vagal Control, Dokos et al., 1996; * * Demir et al. Sinoatrial Node Model, 1999; * * Zhang et al. Sinoatrial Node Model, 2000; * * Boyett et al. Sinoatrial Node Model, 2001; * * Kurata et al. Improved Mathematical Model for the Primary Pacemaker * Cell, 2002. * * Although these models were able to recreate the generic action * potential waveforms from the SAN, none were able to represent * action potential waveforms from any specific SAN cell. This * limits the application of such models to analyse the factors * underlying action potential heterogeneity in coupled systems * of pacemaker cells, as well as elucidating specific ionic mechanisms * underlying action potential heterogeneity in the SAN. * * To meet these needs, Lovell et al. have devloped a generic single * cell ionic model of rabbit SAN cells, which is based on Markovian * state kinetics (all previously published SAN models are based * on a Hodgkin-Huxley mechanism). Parameters are fitted to this * model using a custom least squares optimisation approach. They * then propose a gradient model of the SAN by employing the same * optimisation approach to fit a smooth transition in ionic model * parameters to achieve a desired variation in AP characteristics. * * The model has been described here in CellML. It should be noted * that the initial parameters entered into this model are those * for the central SAN value. Peripheral SAN values and the interpolation * parameters are also provided in the original publication. * * The complete original paper reference is cited below: * * Progress in Biophysics and Molecular Biology, 85, 301-323. (Full * text (HTML) and PDF versions of the article are available to * subscribers on the Progress in Biophysics and Molecular Biology * website.) PubMed ID: 15142749 * * cell diagram * * [[Image file: lovell_2004.png]] * * A schematic diagram describing the ionic components of the SA * node mathematical model. */ import nsrunit; // Warning: unit conversion turned off due to unit errors in 28 equation(s) unit conversion off; unit first_order_rate_constant=1 second^(-1); unit third_order_rate_constant=1 meter^6*second^(-1)*mole^(-2); // unit millisecond predefined // unit millivolt predefined unit nanoS=1E-9 kilogram^(-1)*meter^(-2)*second^3*ampere^2; unit nanoF=1E-9 kilogram^(-1)*meter^(-2)*second^4*ampere^2; unit picoA=1E-12 ampere^1; unit picoA_per_millimolar=1E-12 meter^3*ampere^1*mole^(-1); // unit millimolar predefined unit joule_per_mole_kelvin=1 kilogram^1*meter^2*second^(-2)*kelvin^(-1)*mole^(-1); unit coulomb_per_mole=.001 second^(-1)*ampere^(-1)*mole^1; unit picol=1E-15 meter^3; math main { //Warning: the following variables were set 'extern' or given // an initial value of '0' because the model would otherwise be // underdetermined: L_type_calcium_current.I3, T_type_calcium_current.I2, // rapid_delayed_rectifying_potassium_current.I3, slow_delayed_rectifying_potassium_current.I2, // TTX_sensitive_sodium_current.I3, g_f_K, hyperpolarisation_activated_current.I2, // transient_outward_current.I3, Kb_K //Warning: the following variables had initial values which were // suppressed because the model would otherwise be overdetermined: // E_Ca_rev realDomain time second; time.min=0; extern time.max; extern time.delta; real Em(time) millivolt; when(time=time.min) Em=-6.395E1; real Cm nanoF; Cm=3.2E-2; real i_f(time) picoA; real i_Kr(time) picoA; real i_Ks(time) picoA; real i_bNa(time) picoA; real i_Na(time) picoA; real i_NaK(time) picoA; real i_NaCa(time) picoA; real i_to(time) picoA; real i_CaL(time) picoA; real i_CaT(time) picoA; real i_bK(time) picoA; real i_bCl(time) picoA; real E_Na(time) millivolt; real E_Cl(time) millivolt; real E_Ca_rev(time) millivolt; //Warning: CellML initial value suppressed to prevent overdetermining model. Original initial value: E_Ca_rev=4.972E1; real E_K(time) millivolt; real R joule_per_mole_kelvin; R=8.3144; real T kelvin; T=310.15; real F coulomb_per_mole; F=96485; real Nai(time) millimolar; when(time=time.min) Nai=8.004; real Nao(time) millimolar; when(time=time.min) Nao=1.400E2; real Cai(time) millimolar; when(time=time.min) Cai=1.275E-4; real Cao(time) millimolar; when(time=time.min) Cao=2.0; real Ki(time) millimolar; when(time=time.min) Ki=1.499E2; real Ko(time) millimolar; when(time=time.min) Ko=5.389; real Cli(time) millimolar; when(time=time.min) Cli=2.607E1; real Clo(time) millimolar; when(time=time.min) Clo=1.400E2; real g_CaL nanoS; g_CaL=1.604E2; real A_CaL(time) dimensionless; when(time=time.min) A_CaL=4.564E-4; real L_type_calcium_current.I1(time) dimensionless; when(time=time.min) L_type_calcium_current.I1=9.601E-1; real L_type_calcium_current.I2(time) dimensionless; when(time=time.min) L_type_calcium_current.I2=5.261E-3; real L_type_calcium_current.I3(time) dimensionless; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) L_type_calcium_current.I3=0; real L_type_calcium_current.alpha1(time) first_order_rate_constant; real L_type_calcium_current.alpha2(time) first_order_rate_constant; real L_type_calcium_current.alpha3 third_order_rate_constant; L_type_calcium_current.alpha3=1.395E5; real L_type_calcium_current.alpha4 first_order_rate_constant; L_type_calcium_current.alpha4=4.945; real L_type_calcium_current.beta1(time) first_order_rate_constant; real beta2(time) first_order_rate_constant; real L_type_calcium_current.beta3 first_order_rate_constant; L_type_calcium_current.beta3=7.648; real L_type_calcium_current.beta4 third_order_rate_constant; L_type_calcium_current.beta4=4.051E6; real L_type_calcium_current.alpha1_0 first_order_rate_constant; L_type_calcium_current.alpha1_0=1.115E2; real L_type_calcium_current.alpha1_infinity first_order_rate_constant; L_type_calcium_current.alpha1_infinity=2.451E3; real L_type_calcium_current.alpha1_E50 millivolt; L_type_calcium_current.alpha1_E50=-3.116E1; real L_type_calcium_current.alpha1_Eslope millivolt; L_type_calcium_current.alpha1_Eslope=8.815; real L_type_calcium_current.alpha2_0 first_order_rate_constant; L_type_calcium_current.alpha2_0=9.622E1; real L_type_calcium_current.alpha2_infinity first_order_rate_constant; L_type_calcium_current.alpha2_infinity=1.409E1; real L_type_calcium_current.alpha2_E50 millivolt; L_type_calcium_current.alpha2_E50=3.116; real L_type_calcium_current.alpha2_Eslope millivolt; L_type_calcium_current.alpha2_Eslope=5.936; real L_type_calcium_current.beta1_0 first_order_rate_constant; L_type_calcium_current.beta1_0=1.283E4; real L_type_calcium_current.beta1_infinity first_order_rate_constant; L_type_calcium_current.beta1_infinity=4.701E3; real L_type_calcium_current.beta1_E50 millivolt; L_type_calcium_current.beta1_E50=-2.448E1; real L_type_calcium_current.beta1_Eslope millivolt; L_type_calcium_current.beta1_Eslope=7.300; real beta2_0 first_order_rate_constant; beta2_0=1.950E-1; real beta2_infinity first_order_rate_constant; beta2_infinity=5.984E-2; real beta2_E50 millivolt; beta2_E50=5.934; real beta2_Eslope millivolt; beta2_Eslope=1.395E5; real g_CaT nanoS; g_CaT=6.816E2; real A_CaT(time) dimensionless; when(time=time.min) A_CaT=1.562E-5; real T_type_calcium_current.I1(time) dimensionless; when(time=time.min) T_type_calcium_current.I1=9.985E-1; real T_type_calcium_current.I2(time) dimensionless; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) T_type_calcium_current.I2=0; real T_type_calcium_current.alpha1(time) first_order_rate_constant; real T_type_calcium_current.alpha2(time) first_order_rate_constant; real T_type_calcium_current.alpha3(time) first_order_rate_constant; real T_type_calcium_current.beta1(time) first_order_rate_constant; real T_type_calcium_current.beta3(time) first_order_rate_constant; real T_type_calcium_current.alpha1_0 first_order_rate_constant; T_type_calcium_current.alpha1_0=0.0; real T_type_calcium_current.alpha1_infinity first_order_rate_constant; T_type_calcium_current.alpha1_infinity=1.203E3; real T_type_calcium_current.alpha1_E50 millivolt; T_type_calcium_current.alpha1_E50=-3.442E1; real T_type_calcium_current.alpha1_Eslope millivolt; T_type_calcium_current.alpha1_Eslope=6.143; real T_type_calcium_current.alpha2_0 first_order_rate_constant; T_type_calcium_current.alpha2_0=2.458E2; real T_type_calcium_current.alpha2_infinity first_order_rate_constant; T_type_calcium_current.alpha2_infinity=1.304E3; real T_type_calcium_current.alpha2_E50 millivolt; T_type_calcium_current.alpha2_E50=-1.978E1; real T_type_calcium_current.alpha2_Eslope millivolt; T_type_calcium_current.alpha2_Eslope=1.260E1; real T_type_calcium_current.alpha3_0 first_order_rate_constant; T_type_calcium_current.alpha3_0=1.003E-1; real T_type_calcium_current.alpha3_infinity first_order_rate_constant; T_type_calcium_current.alpha3_infinity=1.157E-2; real T_type_calcium_current.alpha3_E50 millivolt; T_type_calcium_current.alpha3_E50=6.079; real T_type_calcium_current.alpha3_Eslope millivolt; T_type_calcium_current.alpha3_Eslope=4.938E-1; real T_type_calcium_current.beta1_0 first_order_rate_constant; T_type_calcium_current.beta1_0=8.075E2; real T_type_calcium_current.beta1_infinity first_order_rate_constant; T_type_calcium_current.beta1_infinity=9.663; real T_type_calcium_current.beta1_E50 millivolt; T_type_calcium_current.beta1_E50=-3.025E1; real T_type_calcium_current.beta1_Eslope millivolt; T_type_calcium_current.beta1_Eslope=2.580E1; real T_type_calcium_current.beta3_0 first_order_rate_constant; T_type_calcium_current.beta3_0=1.914; real T_type_calcium_current.beta3_infinity first_order_rate_constant; T_type_calcium_current.beta3_infinity=4.490E2; real T_type_calcium_current.beta3_E50 millivolt; T_type_calcium_current.beta3_E50=-3.948E1; real T_type_calcium_current.beta3_Eslope millivolt; T_type_calcium_current.beta3_Eslope=1.295E1; real i_Kr_Na(time) picoA; real i_Kr_K(time) picoA; real g_Kr nanoS; g_Kr=4.714; real PKNa_r picoA_per_millimolar; PKNa_r=3.042E-2; real A_Kr(time) dimensionless; when(time=time.min) A_Kr=1.209E-1; real rapid_delayed_rectifying_potassium_current.I1(time) dimensionless; when(time=time.min) rapid_delayed_rectifying_potassium_current.I1=1.991E-3; real rapid_delayed_rectifying_potassium_current.I2(time) dimensionless; when(time=time.min) rapid_delayed_rectifying_potassium_current.I2=5.617E-2; real rapid_delayed_rectifying_potassium_current.I3(time) dimensionless; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) rapid_delayed_rectifying_potassium_current.I3=0; real rapid_delayed_rectifying_potassium_current.alpha1(time) first_order_rate_constant; real rapid_delayed_rectifying_potassium_current.alpha2(time) first_order_rate_constant; real rapid_delayed_rectifying_potassium_current.alpha3(time) first_order_rate_constant; real rapid_delayed_rectifying_potassium_current.alpha4(time) first_order_rate_constant; real rapid_delayed_rectifying_potassium_current.beta1(time) first_order_rate_constant; real rapid_delayed_rectifying_potassium_current.beta4(time) first_order_rate_constant; real rapid_delayed_rectifying_potassium_current.alpha1_0 first_order_rate_constant; rapid_delayed_rectifying_potassium_current.alpha1_0=2.924E-1; real rapid_delayed_rectifying_potassium_current.alpha1_infinity first_order_rate_constant; rapid_delayed_rectifying_potassium_current.alpha1_infinity=1.796; real rapid_delayed_rectifying_potassium_current.alpha1_E50 millivolt; rapid_delayed_rectifying_potassium_current.alpha1_E50=-2.821; real rapid_delayed_rectifying_potassium_current.alpha1_Eslope millivolt; rapid_delayed_rectifying_potassium_current.alpha1_Eslope=1.591E1; real rapid_delayed_rectifying_potassium_current.alpha2_0 first_order_rate_constant; rapid_delayed_rectifying_potassium_current.alpha2_0=8.011E-4; real rapid_delayed_rectifying_potassium_current.alpha2_infinity first_order_rate_constant; rapid_delayed_rectifying_potassium_current.alpha2_infinity=2.815E1; real rapid_delayed_rectifying_potassium_current.alpha2_E50 millivolt; rapid_delayed_rectifying_potassium_current.alpha2_E50=2.607E1; real rapid_delayed_rectifying_potassium_current.alpha2_Eslope millivolt; rapid_delayed_rectifying_potassium_current.alpha2_Eslope=4.849; real rapid_delayed_rectifying_potassium_current.alpha3_0 first_order_rate_constant; rapid_delayed_rectifying_potassium_current.alpha3_0=0.0; real rapid_delayed_rectifying_potassium_current.alpha3_infinity first_order_rate_constant; rapid_delayed_rectifying_potassium_current.alpha3_infinity=1.382E1; real rapid_delayed_rectifying_potassium_current.alpha3_E50 millivolt; rapid_delayed_rectifying_potassium_current.alpha3_E50=-1.706; real rapid_delayed_rectifying_potassium_current.alpha3_Eslope millivolt; rapid_delayed_rectifying_potassium_current.alpha3_Eslope=8.661; real rapid_delayed_rectifying_potassium_current.alpha4_0 first_order_rate_constant; rapid_delayed_rectifying_potassium_current.alpha4_0=8.526E1; real rapid_delayed_rectifying_potassium_current.alpha4_infinity first_order_rate_constant; rapid_delayed_rectifying_potassium_current.alpha4_infinity=5.840; real rapid_delayed_rectifying_potassium_current.alpha4_E50 millivolt; rapid_delayed_rectifying_potassium_current.alpha4_E50=1.663E1; real rapid_delayed_rectifying_potassium_current.alpha4_Eslope millivolt; rapid_delayed_rectifying_potassium_current.alpha4_Eslope=1.906E1; real rapid_delayed_rectifying_potassium_current.beta1_0 first_order_rate_constant; rapid_delayed_rectifying_potassium_current.beta1_0=1.161E-1; real rapid_delayed_rectifying_potassium_current.beta1_infinity first_order_rate_constant; rapid_delayed_rectifying_potassium_current.beta1_infinity=5.201E1; real rapid_delayed_rectifying_potassium_current.beta1_E50 millivolt; rapid_delayed_rectifying_potassium_current.beta1_E50=-6.477; real rapid_delayed_rectifying_potassium_current.beta1_Eslope millivolt; rapid_delayed_rectifying_potassium_current.beta1_Eslope=1.149E1; real rapid_delayed_rectifying_potassium_current.beta4_0 first_order_rate_constant; rapid_delayed_rectifying_potassium_current.beta4_0=5.728; real rapid_delayed_rectifying_potassium_current.beta4_infinity first_order_rate_constant; rapid_delayed_rectifying_potassium_current.beta4_infinity=5.372E2; real rapid_delayed_rectifying_potassium_current.beta4_E50 millivolt; rapid_delayed_rectifying_potassium_current.beta4_E50=4.594E1; real rapid_delayed_rectifying_potassium_current.beta4_Eslope millivolt; rapid_delayed_rectifying_potassium_current.beta4_Eslope=4.646; real i_Ks_Na(time) picoA; real i_Ks_K(time) picoA; real g_Ks nanoS; g_Ks=1.328E1; real PKNa_s picoA_per_millimolar; PKNa_s=3.053E-2; real A_Ks(time) dimensionless; when(time=time.min) A_Ks=5.049E-3; real slow_delayed_rectifying_potassium_current.I1(time) dimensionless; when(time=time.min) slow_delayed_rectifying_potassium_current.I1=9.921E-1; real slow_delayed_rectifying_potassium_current.I2(time) dimensionless; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) slow_delayed_rectifying_potassium_current.I2=0; real slow_delayed_rectifying_potassium_current.alpha1(time) first_order_rate_constant; real slow_delayed_rectifying_potassium_current.alpha2(time) first_order_rate_constant; real slow_delayed_rectifying_potassium_current.alpha3(time) first_order_rate_constant; real slow_delayed_rectifying_potassium_current.beta1(time) first_order_rate_constant; real slow_delayed_rectifying_potassium_current.beta3(time) first_order_rate_constant; real slow_delayed_rectifying_potassium_current.alpha1_0 first_order_rate_constant; slow_delayed_rectifying_potassium_current.alpha1_0=1.455; real slow_delayed_rectifying_potassium_current.alpha1_infinity first_order_rate_constant; slow_delayed_rectifying_potassium_current.alpha1_infinity=1.590E1; real slow_delayed_rectifying_potassium_current.alpha1_E50 millivolt; slow_delayed_rectifying_potassium_current.alpha1_E50=3.403E1; real slow_delayed_rectifying_potassium_current.alpha1_Eslope millivolt; slow_delayed_rectifying_potassium_current.alpha1_Eslope=9.464; real slow_delayed_rectifying_potassium_current.alpha2_0 first_order_rate_constant; slow_delayed_rectifying_potassium_current.alpha2_0=7.619E-1; real slow_delayed_rectifying_potassium_current.alpha2_infinity first_order_rate_constant; slow_delayed_rectifying_potassium_current.alpha2_infinity=7.207E-2; real slow_delayed_rectifying_potassium_current.alpha2_E50 millivolt; slow_delayed_rectifying_potassium_current.alpha2_E50=1.021E1; real slow_delayed_rectifying_potassium_current.alpha2_Eslope millivolt; slow_delayed_rectifying_potassium_current.alpha2_Eslope=2.584; real slow_delayed_rectifying_potassium_current.alpha3_0 first_order_rate_constant; slow_delayed_rectifying_potassium_current.alpha3_0=0.0; real slow_delayed_rectifying_potassium_current.alpha3_infinity first_order_rate_constant; slow_delayed_rectifying_potassium_current.alpha3_infinity=1.690E1; real slow_delayed_rectifying_potassium_current.alpha3_E50 millivolt; slow_delayed_rectifying_potassium_current.alpha3_E50=4.216E1; real slow_delayed_rectifying_potassium_current.alpha3_Eslope millivolt; slow_delayed_rectifying_potassium_current.alpha3_Eslope=8.481; real slow_delayed_rectifying_potassium_current.beta1_0 first_order_rate_constant; slow_delayed_rectifying_potassium_current.beta1_0=3.628E-3; real slow_delayed_rectifying_potassium_current.beta1_infinity first_order_rate_constant; slow_delayed_rectifying_potassium_current.beta1_infinity=4.191; real slow_delayed_rectifying_potassium_current.beta1_E50 millivolt; slow_delayed_rectifying_potassium_current.beta1_E50=2.231E1; real slow_delayed_rectifying_potassium_current.beta1_Eslope millivolt; slow_delayed_rectifying_potassium_current.beta1_Eslope=1.063E1; real slow_delayed_rectifying_potassium_current.beta3_0 first_order_rate_constant; slow_delayed_rectifying_potassium_current.beta3_0=1.772; real slow_delayed_rectifying_potassium_current.beta3_infinity first_order_rate_constant; slow_delayed_rectifying_potassium_current.beta3_infinity=4.141E-1; real slow_delayed_rectifying_potassium_current.beta3_E50 millivolt; slow_delayed_rectifying_potassium_current.beta3_E50=9.822; real slow_delayed_rectifying_potassium_current.beta3_Eslope millivolt; slow_delayed_rectifying_potassium_current.beta3_Eslope=1.280E1; real g_Na nanoS; g_Na=2.889; real A_Na(time) dimensionless; when(time=time.min) A_Na=5.586E-4; real TTX_sensitive_sodium_current.I1(time) dimensionless; when(time=time.min) TTX_sensitive_sodium_current.I1=3.750E-1; real TTX_sensitive_sodium_current.I2(time) dimensionless; when(time=time.min) TTX_sensitive_sodium_current.I2=1.039E-1; real TTX_sensitive_sodium_current.I3(time) dimensionless; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) TTX_sensitive_sodium_current.I3=0; real TTX_sensitive_sodium_current.alpha1(time) first_order_rate_constant; real TTX_sensitive_sodium_current.alpha2(time) first_order_rate_constant; real TTX_sensitive_sodium_current.alpha3(time) first_order_rate_constant; real TTX_sensitive_sodium_current.alpha4(time) first_order_rate_constant; real TTX_sensitive_sodium_current.beta1(time) first_order_rate_constant; real TTX_sensitive_sodium_current.beta4(time) first_order_rate_constant; real TTX_sensitive_sodium_current.alpha1_0 first_order_rate_constant; TTX_sensitive_sodium_current.alpha1_0=1.022E-31; real TTX_sensitive_sodium_current.alpha1_infinity first_order_rate_constant; TTX_sensitive_sodium_current.alpha1_infinity=4.355E5; real TTX_sensitive_sodium_current.alpha1_E50 millivolt; TTX_sensitive_sodium_current.alpha1_E50=-3.808E1; real TTX_sensitive_sodium_current.alpha1_Eslope millivolt; TTX_sensitive_sodium_current.alpha1_Eslope=4.402; real TTX_sensitive_sodium_current.alpha2_0 first_order_rate_constant; TTX_sensitive_sodium_current.alpha2_0=2.950E1; real TTX_sensitive_sodium_current.alpha2_infinity first_order_rate_constant; TTX_sensitive_sodium_current.alpha2_infinity=1.710E2; real TTX_sensitive_sodium_current.alpha2_E50 millivolt; TTX_sensitive_sodium_current.alpha2_E50=-1.841E1; real TTX_sensitive_sodium_current.alpha2_Eslope millivolt; TTX_sensitive_sodium_current.alpha2_Eslope=1.661E1; real TTX_sensitive_sodium_current.alpha3_0 first_order_rate_constant; TTX_sensitive_sodium_current.alpha3_0=0.0; real TTX_sensitive_sodium_current.alpha3_infinity first_order_rate_constant; TTX_sensitive_sodium_current.alpha3_infinity=2.031; real TTX_sensitive_sodium_current.alpha3_E50 millivolt; TTX_sensitive_sodium_current.alpha3_E50=-3.004E1; real TTX_sensitive_sodium_current.alpha3_Eslope millivolt; TTX_sensitive_sodium_current.alpha3_Eslope=1.275E-1; real TTX_sensitive_sodium_current.alpha4_0 first_order_rate_constant; TTX_sensitive_sodium_current.alpha4_0=6.000E1; real TTX_sensitive_sodium_current.alpha4_infinity first_order_rate_constant; TTX_sensitive_sodium_current.alpha4_infinity=0.0; real TTX_sensitive_sodium_current.alpha4_E50 millivolt; TTX_sensitive_sodium_current.alpha4_E50=-5.556E1; real TTX_sensitive_sodium_current.alpha4_Eslope millivolt; TTX_sensitive_sodium_current.alpha4_Eslope=4.849; real TTX_sensitive_sodium_current.beta1_0 first_order_rate_constant; TTX_sensitive_sodium_current.beta1_0=1.133E6; real TTX_sensitive_sodium_current.beta1_infinity first_order_rate_constant; TTX_sensitive_sodium_current.beta1_infinity=4.104E5; real TTX_sensitive_sodium_current.beta1_E50 millivolt; TTX_sensitive_sodium_current.beta1_E50=-2.239; real TTX_sensitive_sodium_current.beta1_Eslope millivolt; TTX_sensitive_sodium_current.beta1_Eslope=1.651; real TTX_sensitive_sodium_current.beta4_0 first_order_rate_constant; TTX_sensitive_sodium_current.beta4_0=1.831E-4; real TTX_sensitive_sodium_current.beta4_infinity first_order_rate_constant; TTX_sensitive_sodium_current.beta4_infinity=1.904E3; real TTX_sensitive_sodium_current.beta4_E50 millivolt; TTX_sensitive_sodium_current.beta4_E50=1.821E1; real TTX_sensitive_sodium_current.beta4_Eslope millivolt; TTX_sensitive_sodium_current.beta4_Eslope=1.466E1; real kNaCa picoA; kNaCa=2.249E3; real x1(time) dimensionless; real x2(time) dimensionless; real x3(time) dimensionless; real x4(time) dimensionless; real k41(time) dimensionless; real k34(time) dimensionless; real k23(time) dimensionless; real k21(time) dimensionless; real k32(time) dimensionless; real k43(time) dimensionless; real k12(time) dimensionless; real k14(time) dimensionless; real Qci dimensionless; Qci=1.421E-1; real Qn dimensionless; Qn=2.650E-1; real Qco dimensionless; Qco=0.0; real K3ni millimolar; K3ni=2.490E1; real Kci millimolar; Kci=6.510E-3; real K1ni millimolar; K1ni=3.938E2; real K2ni millimolar; K2ni=2.286; real Kcni millimolar; Kcni=2.568E1; real K3no millimolar; K3no=6.325; real K1no millimolar; K1no=2.200E3; real K2no millimolar; K2no=7.639E2; real Kco millimolar; Kco=3.299; real D1(time) dimensionless; real D2(time) dimensionless; real i_fNa(time) picoA; real i_fK(time) picoA; real P_f_K dimensionless; P_f_K=1.162; real g_f_Na nanoS; g_f_Na=5.031E2; extern real g_f_K nanoS; real A_f(time) dimensionless; when(time=time.min) A_f=3.716E-4; real Km_f millimolar; Km_f=1.030E1; real hyperpolarisation_activated_current.I1(time) dimensionless; when(time=time.min) hyperpolarisation_activated_current.I1=9.972E-1; real hyperpolarisation_activated_current.I2(time) dimensionless; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) hyperpolarisation_activated_current.I2=0; real hyperpolarisation_activated_current.alpha1(time) first_order_rate_constant; real hyperpolarisation_activated_current.alpha2(time) first_order_rate_constant; real hyperpolarisation_activated_current.alpha3(time) first_order_rate_constant; real hyperpolarisation_activated_current.beta1(time) first_order_rate_constant; real hyperpolarisation_activated_current.beta3(time) first_order_rate_constant; real hyperpolarisation_activated_current.alpha1_0 first_order_rate_constant; hyperpolarisation_activated_current.alpha1_0=1.244; real hyperpolarisation_activated_current.alpha1_infinity first_order_rate_constant; hyperpolarisation_activated_current.alpha1_infinity=2.157; real hyperpolarisation_activated_current.alpha1_E50 millivolt; hyperpolarisation_activated_current.alpha1_E50=-4.973E1; real hyperpolarisation_activated_current.alpha1_Eslope millivolt; hyperpolarisation_activated_current.alpha1_Eslope=9.458; real hyperpolarisation_activated_current.alpha2_0 first_order_rate_constant; hyperpolarisation_activated_current.alpha2_0=0.0; real hyperpolarisation_activated_current.alpha2_infinity first_order_rate_constant; hyperpolarisation_activated_current.alpha2_infinity=6.951; real hyperpolarisation_activated_current.alpha2_E50 millivolt; hyperpolarisation_activated_current.alpha2_E50=-6.658E1; real hyperpolarisation_activated_current.alpha2_Eslope millivolt; hyperpolarisation_activated_current.alpha2_Eslope=1.013E1; real hyperpolarisation_activated_current.alpha3_0 first_order_rate_constant; hyperpolarisation_activated_current.alpha3_0=5.826; real hyperpolarisation_activated_current.alpha3_infinity first_order_rate_constant; hyperpolarisation_activated_current.alpha3_infinity=0.0; real hyperpolarisation_activated_current.alpha3_E50 millivolt; hyperpolarisation_activated_current.alpha3_E50=-1.235E2; real hyperpolarisation_activated_current.alpha3_Eslope millivolt; hyperpolarisation_activated_current.alpha3_Eslope=1.036E1; real hyperpolarisation_activated_current.beta1_0 first_order_rate_constant; hyperpolarisation_activated_current.beta1_0=9.584E-3; real hyperpolarisation_activated_current.beta1_infinity first_order_rate_constant; hyperpolarisation_activated_current.beta1_infinity=2.619E1; real hyperpolarisation_activated_current.beta1_E50 millivolt; hyperpolarisation_activated_current.beta1_E50=-2.529E1; real hyperpolarisation_activated_current.beta1_Eslope millivolt; hyperpolarisation_activated_current.beta1_Eslope=6.206; real hyperpolarisation_activated_current.beta3_0 first_order_rate_constant; hyperpolarisation_activated_current.beta3_0=0.0; real hyperpolarisation_activated_current.beta3_infinity first_order_rate_constant; hyperpolarisation_activated_current.beta3_infinity=1.507E1; real hyperpolarisation_activated_current.beta3_E50 millivolt; hyperpolarisation_activated_current.beta3_E50=-7.443; real hyperpolarisation_activated_current.beta3_Eslope millivolt; hyperpolarisation_activated_current.beta3_Eslope=1.323E1; real Km_K millimolar; Km_K=4.0E1; real Km_Na millimolar; Km_Na=1.0; real Ip_max picoA; Ip_max=2.463E2; real g_to nanoS; g_to=2.818E-1; real A_to(time) dimensionless; when(time=time.min) A_to=1.220E-2; real transient_outward_current.I1(time) dimensionless; when(time=time.min) transient_outward_current.I1=6.310E-1; real transient_outward_current.I2(time) dimensionless; when(time=time.min) transient_outward_current.I2=2.697E-2; real transient_outward_current.I3(time) dimensionless; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) transient_outward_current.I3=0; real transient_outward_current.alpha1(time) first_order_rate_constant; real transient_outward_current.alpha2(time) first_order_rate_constant; real transient_outward_current.alpha3(time) first_order_rate_constant; real transient_outward_current.alpha4(time) first_order_rate_constant; real transient_outward_current.beta1(time) first_order_rate_constant; real transient_outward_current.beta4(time) first_order_rate_constant; real transient_outward_current.alpha1_0 first_order_rate_constant; transient_outward_current.alpha1_0=3.723; real transient_outward_current.alpha1_infinity first_order_rate_constant; transient_outward_current.alpha1_infinity=3.244E2; real transient_outward_current.alpha1_E50 millivolt; transient_outward_current.alpha1_E50=2.695E1; real transient_outward_current.alpha1_Eslope millivolt; transient_outward_current.alpha1_Eslope=1.808E1; real transient_outward_current.alpha2_0 first_order_rate_constant; transient_outward_current.alpha2_0=3.713E2; real transient_outward_current.alpha2_infinity first_order_rate_constant; transient_outward_current.alpha2_infinity=1.288E2; real transient_outward_current.alpha2_E50 millivolt; transient_outward_current.alpha2_E50=-9.952E1; real transient_outward_current.alpha2_Eslope millivolt; transient_outward_current.alpha2_Eslope=1.706E1; real transient_outward_current.alpha3_0 first_order_rate_constant; transient_outward_current.alpha3_0=4.309; real transient_outward_current.alpha3_infinity first_order_rate_constant; transient_outward_current.alpha3_infinity=3.371E1; real transient_outward_current.alpha3_E50 millivolt; transient_outward_current.alpha3_E50=1.886E1; real transient_outward_current.alpha3_Eslope millivolt; transient_outward_current.alpha3_Eslope=1.485E1; real transient_outward_current.alpha4_0 first_order_rate_constant; transient_outward_current.alpha4_0=1.167E2; real transient_outward_current.alpha4_infinity first_order_rate_constant; transient_outward_current.alpha4_infinity=1.997E2; real transient_outward_current.alpha4_E50 millivolt; transient_outward_current.alpha4_E50=-8.894E1; real transient_outward_current.alpha4_Eslope millivolt; transient_outward_current.alpha4_Eslope=8.432E1; real transient_outward_current.beta1_0 first_order_rate_constant; transient_outward_current.beta1_0=2.729E-2; real transient_outward_current.beta1_infinity first_order_rate_constant; transient_outward_current.beta1_infinity=1.451E2; real transient_outward_current.beta1_E50 millivolt; transient_outward_current.beta1_E50=-1.075E1; real transient_outward_current.beta1_Eslope millivolt; transient_outward_current.beta1_Eslope=5.012; real transient_outward_current.beta4_0 first_order_rate_constant; transient_outward_current.beta4_0=2.805E-1; real transient_outward_current.beta4_infinity first_order_rate_constant; transient_outward_current.beta4_infinity=7.776; real transient_outward_current.beta4_E50 millivolt; transient_outward_current.beta4_E50=-1.176E2; real transient_outward_current.beta4_Eslope millivolt; transient_outward_current.beta4_Eslope=1.032E2; real g_bCl nanoS; g_bCl=8.691E-2; extern real Kb_K dimensionless; real i_Ca_up(time) picoA; real i_Ca_rel(time) picoA; real i_Ca_tr(time) picoA; real Iup_max picoA; Iup_max=2.120E1; real Km_Caup millimolar; Km_Caup=5.000E-4; real Km_Carel millimolar; Km_Carel=1.000E-3; real tau_rel second; tau_rel=5.000E-3; real tau_tr second; tau_tr=4.000E-1; real Vrel picol; Vrel=1.5E-2; real Carel(time) millimolar; when(time=time.min) Carel=2.448E-1; real Caup(time) millimolar; when(time=time.min) Caup=1.035; real tau_b second; tau_b=1.0E-1; real Cab millimolar; Cab=2.0; real Clb millimolar; Clb=1.4E2; real Kb millimolar; Kb=5.4; real Nab millimolar; Nab=1.4E2; real Vi picol; Vi=2.5; real Vup picol; Vup=3.5E-2; real Ve picol; Ve=5.0E-1; // // Em:time=((-1)*(i_f+i_Kr+i_Ks+i_bNa+i_Na+i_NaK+i_NaCa+i_to+i_CaL+i_CaT+i_bK+i_bCl)/Cm); // E_Na=(R*T/F*ln(Nao/Nai)); E_Ca_rev=(R*T/(2*F)*ln(Cao/Cai)); E_Cl=(R*T/((-1)*F)*ln(Clo/Cli)); E_K=(R*T/F*ln(Ko/Ki)); // i_CaL=(g_CaL*A_CaL*(Em-E_Ca_rev)); A_CaL:time=(L_type_calcium_current.alpha1*L_type_calcium_current.I3+L_type_calcium_current.beta1*L_type_calcium_current.I1-(L_type_calcium_current.beta1+L_type_calcium_current.alpha2)*A_CaL); L_type_calcium_current.I1:time=(L_type_calcium_current.alpha2*A_CaL+L_type_calcium_current.beta3*L_type_calcium_current.I2-(beta2+L_type_calcium_current.alpha3+Cai^2)*L_type_calcium_current.I1); L_type_calcium_current.I2:time=(L_type_calcium_current.alpha3*Cai^2*L_type_calcium_current.I1+L_type_calcium_current.beta4*Cai^2*L_type_calcium_current.I3-(L_type_calcium_current.beta3+L_type_calcium_current.alpha4)*L_type_calcium_current.I2); L_type_calcium_current.I3:time=(L_type_calcium_current.beta1*A_CaL+L_type_calcium_current.alpha4*L_type_calcium_current.I2-(L_type_calcium_current.alpha1+L_type_calcium_current.beta4*Cai^2)*L_type_calcium_current.I3); L_type_calcium_current.alpha1=(L_type_calcium_current.alpha1_infinity+(L_type_calcium_current.alpha1_0-L_type_calcium_current.alpha1_infinity)/(1+exp((Em-L_type_calcium_current.alpha1_E50)/L_type_calcium_current.alpha1_Eslope))); L_type_calcium_current.beta1=(L_type_calcium_current.beta1_infinity+(L_type_calcium_current.beta1_0-L_type_calcium_current.beta1_infinity)/(1+exp((Em-L_type_calcium_current.beta1_E50)/L_type_calcium_current.beta1_Eslope))); L_type_calcium_current.alpha2=(L_type_calcium_current.alpha2_infinity+(L_type_calcium_current.alpha2_0-L_type_calcium_current.alpha2_infinity)/(1+exp((Em-L_type_calcium_current.alpha2_E50)/L_type_calcium_current.alpha2_Eslope))); beta2=(beta2_infinity+(beta2_0-beta2_infinity)/(1+exp((Em-beta2_E50)/beta2_Eslope))); // i_CaT=(g_CaT*A_CaT*(Em-E_Ca_rev)); A_CaT:time=(T_type_calcium_current.alpha1*T_type_calcium_current.I2-(T_type_calcium_current.beta1+T_type_calcium_current.alpha2)*A_CaT); T_type_calcium_current.I1:time=(T_type_calcium_current.alpha2*A_CaT+T_type_calcium_current.beta3*T_type_calcium_current.I2-T_type_calcium_current.alpha3*T_type_calcium_current.I1); T_type_calcium_current.I2:time=(T_type_calcium_current.alpha3*T_type_calcium_current.I1+T_type_calcium_current.beta1*A_CaT-(T_type_calcium_current.beta3+T_type_calcium_current.alpha1)*T_type_calcium_current.I2); T_type_calcium_current.alpha1=(T_type_calcium_current.alpha1_infinity+(T_type_calcium_current.alpha1_0-T_type_calcium_current.alpha1_infinity)/(1+exp((Em-T_type_calcium_current.alpha1_E50)/T_type_calcium_current.alpha1_Eslope))); T_type_calcium_current.beta1=(T_type_calcium_current.beta1_infinity+(T_type_calcium_current.beta1_0-T_type_calcium_current.beta1_infinity)/(1+exp((Em-T_type_calcium_current.beta1_E50)/T_type_calcium_current.beta1_Eslope))); T_type_calcium_current.alpha2=(T_type_calcium_current.alpha2_infinity+(T_type_calcium_current.alpha2_0-T_type_calcium_current.alpha2_infinity)/(1+exp((Em-T_type_calcium_current.alpha2_E50)/T_type_calcium_current.alpha2_Eslope))); T_type_calcium_current.alpha3=(T_type_calcium_current.alpha3_infinity+(T_type_calcium_current.alpha3_0-T_type_calcium_current.alpha3_infinity)/(1+exp((Em-T_type_calcium_current.alpha3_E50)/T_type_calcium_current.alpha3_Eslope))); T_type_calcium_current.beta3=(T_type_calcium_current.beta3_infinity+(T_type_calcium_current.beta3_0-T_type_calcium_current.beta3_infinity)/(1+exp((Em-T_type_calcium_current.beta3_E50)/T_type_calcium_current.beta3_Eslope))); // i_Kr=(i_Kr_Na+i_Kr_K); i_Kr_Na=(g_Kr*A_Kr*PKNa_r*(Em-E_Na)); i_Kr_K=(g_Kr*A_Kr*(Em-E_K)); A_Kr:time=(rapid_delayed_rectifying_potassium_current.alpha1*rapid_delayed_rectifying_potassium_current.I3-(rapid_delayed_rectifying_potassium_current.beta1+rapid_delayed_rectifying_potassium_current.alpha2)*A_Kr); rapid_delayed_rectifying_potassium_current.I1:time=(rapid_delayed_rectifying_potassium_current.alpha2*A_Kr-rapid_delayed_rectifying_potassium_current.alpha3*rapid_delayed_rectifying_potassium_current.I1); rapid_delayed_rectifying_potassium_current.I2:time=(rapid_delayed_rectifying_potassium_current.alpha3*rapid_delayed_rectifying_potassium_current.I1+rapid_delayed_rectifying_potassium_current.beta4*rapid_delayed_rectifying_potassium_current.I3-rapid_delayed_rectifying_potassium_current.alpha4*rapid_delayed_rectifying_potassium_current.I2); rapid_delayed_rectifying_potassium_current.I3:time=(rapid_delayed_rectifying_potassium_current.beta1*A_Kr+rapid_delayed_rectifying_potassium_current.alpha4*rapid_delayed_rectifying_potassium_current.I2-(rapid_delayed_rectifying_potassium_current.alpha1+rapid_delayed_rectifying_potassium_current.beta4)*rapid_delayed_rectifying_potassium_current.I3); rapid_delayed_rectifying_potassium_current.alpha1=(rapid_delayed_rectifying_potassium_current.alpha1_infinity+(rapid_delayed_rectifying_potassium_current.alpha1_0-rapid_delayed_rectifying_potassium_current.alpha1_infinity)/(1+exp((Em-rapid_delayed_rectifying_potassium_current.alpha1_E50)/rapid_delayed_rectifying_potassium_current.alpha1_Eslope))); rapid_delayed_rectifying_potassium_current.beta1=(rapid_delayed_rectifying_potassium_current.beta1_infinity+(rapid_delayed_rectifying_potassium_current.beta1_0-rapid_delayed_rectifying_potassium_current.beta1_infinity)/(1+exp((Em-rapid_delayed_rectifying_potassium_current.beta1_E50)/rapid_delayed_rectifying_potassium_current.beta1_Eslope))); rapid_delayed_rectifying_potassium_current.alpha2=(rapid_delayed_rectifying_potassium_current.alpha2_infinity+(rapid_delayed_rectifying_potassium_current.alpha2_0-rapid_delayed_rectifying_potassium_current.alpha2_infinity)/(1+exp((Em-rapid_delayed_rectifying_potassium_current.alpha2_E50)/rapid_delayed_rectifying_potassium_current.alpha2_Eslope))); rapid_delayed_rectifying_potassium_current.alpha3=(rapid_delayed_rectifying_potassium_current.alpha3_infinity+(rapid_delayed_rectifying_potassium_current.alpha3_0-rapid_delayed_rectifying_potassium_current.alpha3_infinity)/(1+exp((Em-rapid_delayed_rectifying_potassium_current.alpha3_E50)/rapid_delayed_rectifying_potassium_current.alpha3_Eslope))); rapid_delayed_rectifying_potassium_current.alpha4=(rapid_delayed_rectifying_potassium_current.alpha4_infinity+(rapid_delayed_rectifying_potassium_current.alpha4_0-rapid_delayed_rectifying_potassium_current.alpha4_infinity)/(1+exp((Em-rapid_delayed_rectifying_potassium_current.alpha4_E50)/rapid_delayed_rectifying_potassium_current.alpha4_Eslope))); rapid_delayed_rectifying_potassium_current.beta4=(rapid_delayed_rectifying_potassium_current.beta4_infinity+(rapid_delayed_rectifying_potassium_current.beta4_0-rapid_delayed_rectifying_potassium_current.beta4_infinity)/(1+exp((Em-rapid_delayed_rectifying_potassium_current.beta4_E50)/rapid_delayed_rectifying_potassium_current.beta4_Eslope))); // i_Ks=(i_Ks_Na+i_Ks_K); i_Ks_Na=(g_Ks*A_Ks*PKNa_s*(Em-E_Na)); i_Ks_K=(g_Ks*A_Ks*(Em-E_K)); A_Ks:time=(slow_delayed_rectifying_potassium_current.alpha1*slow_delayed_rectifying_potassium_current.I2-(slow_delayed_rectifying_potassium_current.beta1+slow_delayed_rectifying_potassium_current.alpha2)*A_Ks); slow_delayed_rectifying_potassium_current.I1:time=(slow_delayed_rectifying_potassium_current.alpha2*A_Ks+slow_delayed_rectifying_potassium_current.beta3*slow_delayed_rectifying_potassium_current.I2-slow_delayed_rectifying_potassium_current.alpha3*slow_delayed_rectifying_potassium_current.I1); slow_delayed_rectifying_potassium_current.I2:time=(slow_delayed_rectifying_potassium_current.alpha3*slow_delayed_rectifying_potassium_current.I1+slow_delayed_rectifying_potassium_current.beta1*A_Ks-(slow_delayed_rectifying_potassium_current.alpha1+slow_delayed_rectifying_potassium_current.beta3)*slow_delayed_rectifying_potassium_current.I2); slow_delayed_rectifying_potassium_current.alpha1=(slow_delayed_rectifying_potassium_current.alpha1_infinity+(slow_delayed_rectifying_potassium_current.alpha1_0-slow_delayed_rectifying_potassium_current.alpha1_infinity)/(1+exp((Em-slow_delayed_rectifying_potassium_current.alpha1_E50)/slow_delayed_rectifying_potassium_current.alpha1_Eslope))); slow_delayed_rectifying_potassium_current.beta1=(slow_delayed_rectifying_potassium_current.beta1_infinity+(slow_delayed_rectifying_potassium_current.beta1_0-slow_delayed_rectifying_potassium_current.beta1_infinity)/(1+exp((Em-slow_delayed_rectifying_potassium_current.beta1_E50)/slow_delayed_rectifying_potassium_current.beta1_Eslope))); slow_delayed_rectifying_potassium_current.alpha2=(slow_delayed_rectifying_potassium_current.alpha2_infinity+(slow_delayed_rectifying_potassium_current.alpha2_0-slow_delayed_rectifying_potassium_current.alpha2_infinity)/(1+exp((Em-slow_delayed_rectifying_potassium_current.alpha2_E50)/slow_delayed_rectifying_potassium_current.alpha2_Eslope))); slow_delayed_rectifying_potassium_current.alpha3=(slow_delayed_rectifying_potassium_current.alpha3_infinity+(slow_delayed_rectifying_potassium_current.alpha3_0-slow_delayed_rectifying_potassium_current.alpha3_infinity)/(1+exp((Em-slow_delayed_rectifying_potassium_current.alpha3_E50)/slow_delayed_rectifying_potassium_current.alpha3_Eslope))); slow_delayed_rectifying_potassium_current.beta3=(slow_delayed_rectifying_potassium_current.beta3_infinity+(slow_delayed_rectifying_potassium_current.beta3_0-slow_delayed_rectifying_potassium_current.beta3_infinity)/(1+exp((Em-slow_delayed_rectifying_potassium_current.beta3_E50)/slow_delayed_rectifying_potassium_current.beta3_Eslope))); // i_Na=(g_Na*A_Na*(Em-E_Na)); A_Na:time=(TTX_sensitive_sodium_current.alpha1*TTX_sensitive_sodium_current.I3-(TTX_sensitive_sodium_current.beta1+TTX_sensitive_sodium_current.alpha2)*A_Na); TTX_sensitive_sodium_current.I1:time=(TTX_sensitive_sodium_current.alpha2*A_Na-TTX_sensitive_sodium_current.alpha3*TTX_sensitive_sodium_current.I1); TTX_sensitive_sodium_current.I2:time=(TTX_sensitive_sodium_current.alpha3*TTX_sensitive_sodium_current.I1+TTX_sensitive_sodium_current.beta4*TTX_sensitive_sodium_current.I3-TTX_sensitive_sodium_current.alpha4*TTX_sensitive_sodium_current.I2); TTX_sensitive_sodium_current.I3:time=(TTX_sensitive_sodium_current.beta1*A_Na+TTX_sensitive_sodium_current.alpha4*TTX_sensitive_sodium_current.I2-(TTX_sensitive_sodium_current.alpha1+TTX_sensitive_sodium_current.beta4)*TTX_sensitive_sodium_current.I3); TTX_sensitive_sodium_current.alpha1=(TTX_sensitive_sodium_current.alpha1_infinity+(TTX_sensitive_sodium_current.alpha1_0-TTX_sensitive_sodium_current.alpha1_infinity)/(1+exp((Em-TTX_sensitive_sodium_current.alpha1_E50)/TTX_sensitive_sodium_current.alpha1_Eslope))); TTX_sensitive_sodium_current.beta1=(TTX_sensitive_sodium_current.beta1_infinity+(TTX_sensitive_sodium_current.beta1_0-TTX_sensitive_sodium_current.beta1_infinity)/(1+exp((Em-TTX_sensitive_sodium_current.beta1_E50)/TTX_sensitive_sodium_current.beta1_Eslope))); TTX_sensitive_sodium_current.alpha2=(TTX_sensitive_sodium_current.alpha2_infinity+(TTX_sensitive_sodium_current.alpha2_0-TTX_sensitive_sodium_current.alpha2_infinity)/(1+exp((Em-TTX_sensitive_sodium_current.alpha2_E50)/TTX_sensitive_sodium_current.alpha2_Eslope))); TTX_sensitive_sodium_current.alpha3=(TTX_sensitive_sodium_current.alpha3_infinity+(TTX_sensitive_sodium_current.alpha3_0-TTX_sensitive_sodium_current.alpha3_infinity)/(1+exp((Em-TTX_sensitive_sodium_current.alpha3_E50)/TTX_sensitive_sodium_current.alpha3_Eslope))); TTX_sensitive_sodium_current.alpha4=(TTX_sensitive_sodium_current.alpha4_infinity+(TTX_sensitive_sodium_current.alpha4_0-TTX_sensitive_sodium_current.alpha4_infinity)/(1+exp((Em-TTX_sensitive_sodium_current.alpha4_E50)/TTX_sensitive_sodium_current.alpha4_Eslope))); TTX_sensitive_sodium_current.beta4=(TTX_sensitive_sodium_current.beta4_infinity+(TTX_sensitive_sodium_current.beta4_0-TTX_sensitive_sodium_current.beta4_infinity)/(1+exp((Em-TTX_sensitive_sodium_current.beta4_E50)/TTX_sensitive_sodium_current.beta4_Eslope))); // i_NaCa=(kNaCa*((x2*k21-x1*k12)/(x1+x2+x3+x4))); x1=(k41*k34*(k23+k21)+k21*k32*(k43+k41)); x2=(k32*k43*(k14+k12)+k41*k12*(k34+k32)); x3=(k14*k43*(k23+k21)+k12*k23*(k43+k41)); x4=(k23*k34*(k14+k12)+k14*k21*(k34+k32)); k43=(Nai/(K3ni+Nai)); k12=(Cai*exp((-1)*(Em*Qci*F/(R*T)))/(Kci*D1)); k14=(Nai^2*(1+Nai/K3ni)*exp(Qn*Em*F/(2*R*T))/(K1ni*K2ni*D1)); k41=exp((-1)*(Em*Qn*F/(2*R*T))); D1=(1+Cai/Kci*(1+exp((-1)*(Em*Qci*F/(R*T))))*(Cai*Nai/(Kci*Kcni))+Nai/K1ni*(1+Nai/K2ni*(1+Nai/K3ni))); k34=(Nao/(K3no+Nao)); k21=(Cao/Kco*exp(Qco*Em*F/(R*T))/D2); k23=(Nao^2*(1+Nao/K3no)*exp((-1)*(Qn*Em*F/(2*R*T)))/(K1no*K2no*D2)); k32=exp(Qn*Em*F/(2*R*T)); D2=(1+Cao/Kco*(1+exp(Qco*Em*F/(R*T)))+Nao/K1no*(1+Nao/K2no)*(1+Nao/K3no)); // i_f=(i_fNa+i_fK); i_fNa=(A_f*(Ko^1.83/(Ko^1.83+Km_f^1.83))*g_f_Na*(Em-E_Na)); i_fK=(A_f*(Ko^1.83/(Ko^1.83+Km_f^1.83))*P_f_K*g_f_K*(Em-E_K)); A_f:time=(hyperpolarisation_activated_current.alpha1*hyperpolarisation_activated_current.I2-(hyperpolarisation_activated_current.beta1+hyperpolarisation_activated_current.alpha2)*A_f); hyperpolarisation_activated_current.I1:time=(hyperpolarisation_activated_current.alpha2*A_f+hyperpolarisation_activated_current.beta3*hyperpolarisation_activated_current.I2-hyperpolarisation_activated_current.alpha3*hyperpolarisation_activated_current.I1); hyperpolarisation_activated_current.I2:time=(hyperpolarisation_activated_current.alpha3*hyperpolarisation_activated_current.I1+hyperpolarisation_activated_current.beta1*A_f-(hyperpolarisation_activated_current.beta3+hyperpolarisation_activated_current.alpha1)*hyperpolarisation_activated_current.I2); hyperpolarisation_activated_current.alpha1=(hyperpolarisation_activated_current.alpha1_infinity+(hyperpolarisation_activated_current.alpha1_0-hyperpolarisation_activated_current.alpha1_infinity)/(1+exp((Em-hyperpolarisation_activated_current.alpha1_E50)/hyperpolarisation_activated_current.alpha1_Eslope))); hyperpolarisation_activated_current.beta1=(hyperpolarisation_activated_current.beta1_infinity+(hyperpolarisation_activated_current.beta1_0-hyperpolarisation_activated_current.beta1_infinity)/(1+exp((Em-hyperpolarisation_activated_current.beta1_E50)/hyperpolarisation_activated_current.beta1_Eslope))); hyperpolarisation_activated_current.alpha2=(hyperpolarisation_activated_current.alpha2_infinity+(hyperpolarisation_activated_current.alpha2_0-hyperpolarisation_activated_current.alpha2_infinity)/(1+exp((Em-hyperpolarisation_activated_current.alpha2_E50)/hyperpolarisation_activated_current.alpha2_Eslope))); hyperpolarisation_activated_current.alpha3=(hyperpolarisation_activated_current.alpha3_infinity+(hyperpolarisation_activated_current.alpha3_0-hyperpolarisation_activated_current.alpha3_infinity)/(1+exp((Em-hyperpolarisation_activated_current.alpha3_E50)/hyperpolarisation_activated_current.alpha3_Eslope))); hyperpolarisation_activated_current.beta3=(hyperpolarisation_activated_current.beta3_infinity+(hyperpolarisation_activated_current.beta3_0-hyperpolarisation_activated_current.beta3_infinity)/(1+exp((Em-hyperpolarisation_activated_current.beta3_E50)/hyperpolarisation_activated_current.beta3_Eslope))); // i_NaK=(Ip_max*(Nai/(Nai+Km_Na))*(Ko/(Ko+Km_K))*(1-((Em-(40 millivolt))/(211 millivolt))^2)); // i_to=(g_to*A_to*(Em-E_K)); A_to:time=(transient_outward_current.alpha1*transient_outward_current.I3-(transient_outward_current.beta1+transient_outward_current.alpha2)*A_to); transient_outward_current.I1:time=(transient_outward_current.alpha2*A_to-transient_outward_current.alpha3*transient_outward_current.I1); transient_outward_current.I2:time=(transient_outward_current.alpha3*transient_outward_current.I1+transient_outward_current.beta4*transient_outward_current.I3-transient_outward_current.alpha4*transient_outward_current.I2); transient_outward_current.I3:time=(transient_outward_current.beta1*A_to+transient_outward_current.alpha4*transient_outward_current.I2-(transient_outward_current.alpha1+transient_outward_current.beta4)*transient_outward_current.I3); transient_outward_current.alpha1=(transient_outward_current.alpha1_infinity+(transient_outward_current.alpha1_0-transient_outward_current.alpha1_infinity)/(1+exp((Em-transient_outward_current.alpha1_E50)/transient_outward_current.alpha1_Eslope))); transient_outward_current.beta1=(transient_outward_current.beta1_infinity+(transient_outward_current.beta1_0-transient_outward_current.beta1_infinity)/(1+exp((Em-transient_outward_current.beta1_E50)/transient_outward_current.beta1_Eslope))); transient_outward_current.alpha2=(transient_outward_current.alpha2_infinity+(transient_outward_current.alpha2_0-transient_outward_current.alpha2_infinity)/(1+exp((Em-transient_outward_current.alpha2_E50)/transient_outward_current.alpha2_Eslope))); transient_outward_current.alpha3=(transient_outward_current.alpha3_infinity+(transient_outward_current.alpha3_0-transient_outward_current.alpha3_infinity)/(1+exp((Em-transient_outward_current.alpha3_E50)/transient_outward_current.alpha3_Eslope))); transient_outward_current.alpha4=(transient_outward_current.alpha4_infinity+(transient_outward_current.alpha4_0-transient_outward_current.alpha4_infinity)/(1+exp((Em-transient_outward_current.alpha4_E50)/transient_outward_current.alpha4_Eslope))); transient_outward_current.beta4=(transient_outward_current.beta4_infinity+(transient_outward_current.beta4_0-transient_outward_current.beta4_infinity)/(1+exp((Em-transient_outward_current.beta4_E50)/transient_outward_current.beta4_Eslope))); // i_bNa=(g_Na*(Em-E_Na)); i_bK=(Kb_K*Ko^.41*(Ki-Ko*exp((-1)*(Em*F/(R*T))))); i_bCl=(g_bCl*(Em-E_Cl)); // i_Ca_up=(Iup_max*(1/(1+(Km_Caup/Cai)^2))); i_Ca_rel=(2*F*Vrel/tau_rel*Carel*(1/(1+(Km_Carel/Cai)^2))); i_Ca_tr=(2*F*Vrel/tau_tr*Caup); // Cai:time=((-1)*((i_CaL+i_CaT+i_Ca_up-(2*i_NaCa+i_Ca_rel))/(2*F*Vi))); Caup:time=((i_Ca_up-i_Ca_tr)/(2*F*Vup)); Carel:time=((i_Ca_tr-i_Ca_rel)/(2*F*Vrel)); Cao:time=((i_CaL+i_CaT-2*i_NaCa)/(2*F*Ve)+(Cab-Cao)/tau_b); Nai:time=((-1)*((i_Kr_Na+i_Ks_Na+i_Na+3*i_NaCa+i_bNa+i_fNa+3*i_NaK)/(F*Vi))); Nao:time=((i_Kr_Na+i_Ks_Na+i_Na+3*i_NaCa+i_bNa+i_fNa+3*i_NaK)/(F*Ve)+(Nab-Nao)/tau_b); Ki:time=((-1)*((i_Kr_K+i_Ks_K+i_bK+i_fK+i_to-2*i_NaK)/(F*Vi))); Ko:time=((i_Kr_K+i_Ks_K+i_bK+i_fK+i_to-2*i_NaK)/(F*Ve)+(Kb-Ko)/tau_b); Cli:time=(i_bCl/(F*Vi)); Clo:time=(i_bCl/(F*Ve)+(Clb-Clo)/tau_b); }