Noble Ventricular Cell Model 1998 Penny Noble Oxford University
Model Status This version of the model has been curated and unit checked and is known to run in PCEnv, COR and Jsim. A PCEnv session file is also available for this model.
Model Structure The Noble98 (Noble et al. 1998) model of the guinea-pig ventricular cell was a development of the Noble91 (Noble et al. 1991) model and included representation of the components of IK, (IKr and IKs), the persistent sodium current and a dyadic space between the sarcolemma and the sarcoplasmic reticulum. In several important respects this model was a major improvement on the earlier model. However on rigorous testing for new applications problems associated with the calcium dynamics equations were found in the new model. The model demonstrated here is an attempt at 'correcting' the inability of Noble98 to reproduce a mechanism of initiation of Early After-Depolarizations (EADs), the voltage-dependence of calcium release from the sarcoplasmic reticulum (SR) and also to improve the shape of the calcium transient. model diagram Schematic diagram of the cell model.
i_Stim stim_amplitude time stim_start time stim_end time stim_start time stim_start stim_period stim_period stim_duration 0 time V 1 Cm i_Stim i_K1 i_to i_Kr i_Ks i_NaK i_Na i_b_Na i_p_Na i_Ca_L_Na_cyt i_Ca_L_Na_ds i_NaCa_cyt i_NaCa_ds i_Ca_L_Ca_cyt i_Ca_L_Ca_ds i_Ca_L_K_cyt i_Ca_L_K_ds i_b_Ca E_Na R T F Na_o Na_i E_K R T F K_o K_i E_Ks R T F K_o P_kna Na_o K_i P_kna Na_i E_Ca 0.5 R T F Ca_o Ca_i E_mh R T F Na_o 0.12 K_o Na_i 0.12 K_i i_K1 g_K1 K_o K_o K_mk1 V E_K 1 V E_K 10 F 1.25 R T i_Kr g_Kr1 xr1 g_Kr2 xr2 1 1 V 9 22.4 V E_K alpha_xr1 50 1 V 5 9 beta_xr1 0.05 V 20 15 time xr1 alpha_xr1 1 xr1 beta_xr1 xr1 alpha_xr2 50 1 V 5 9 beta_xr2 0.4 V 30 30 3 time xr2 alpha_xr2 1 xr2 beta_xr2 xr2 i_Ks g_Ks xs 2 V E_Ks alpha_xs 14 1 V 40 9 beta_xs 1 V 45 time xs alpha_xs 1 xs beta_xs xs i_Na g_Na m 3 h V E_mh E0_m V 41 alpha_m 2000 E0_m delta_m 200 E0_m 1 0.1 E0_m beta_m 8000 0.056 V 66 time m alpha_m 1 m beta_m m alpha_h 20 0.125 V 75 shift_h beta_h 2000 1 320 0.1 V 75 shift_h time h alpha_h 1 h beta_h h i_p_Na g_pna 1 1 V 52 8 V E_Na i_b_Na g_bna V E_Na i_Ca_L_Ca_cyt 1 FrICa 4 P_Ca_L d CaChoncyt V 50 F R T 1 V 50 F 2 R T Ca_i 100 F R T Ca_o V 50 F 2 R T i_Ca_L_K_cyt 1 FrICa P_CaK P_Ca_L d CaChoncyt V 50 F R T 1 V 50 F R T K_i 50 F R T K_o V 50 F R T i_Ca_L_Na_cyt 1 FrICa P_CaNa P_Ca_L d CaChoncyt V 50 F R T 1 V 50 F R T Na_i 50 F R T Na_o V 50 F R T i_Ca_L_Ca_ds FrICa 4 P_Ca_L d CaChonds V 50 F R T 1 V 50 F 2 R T Ca_i 100 F R T Ca_o V 50 F 2 R T i_Ca_L_K_ds FrICa P_CaK P_Ca_L d CaChonds V 50 F R T 1 V 50 F R T K_i 50 F R T K_o V 50 F R T i_Ca_L_Na_ds FrICa P_CaNa P_Ca_L d CaChonds V 50 F R T 1 V 50 F R T Na_i 50 F R T Na_o V 50 F R T i_Ca_L i_Ca_L_Ca_cyt i_Ca_L_K_cyt i_Ca_L_Na_cyt i_Ca_L_Ca_ds i_Ca_L_K_ds i_Ca_L_Na_ds E0_d V 24 5 alpha_d 120 E0_d 0.0001 30 E0_d 1 E0_d 4 beta_d 120 E0_d 0.0001 12 E0_d E0_d 10 1 time d speed_d alpha_d 1 d beta_d d E0_f V 34 alpha_f 25 E0_f delta_f 6.25 E0_f E0_f 4 1 beta_f 12 1 1 V 34 4 CaChoffcyt Ca_i KCaChoff Ca_i time f 120 1 f CaChoffcyt 1 f 1 CaChoffcyt speed_f beta_f alpha_f f CaChoncyt 1 f 1 CaChoffcyt CaChoffds Ca_ds Kmdsinact Ca_ds CaChonds 1 f 1 CaChoffds i_b_Ca g_bca V E_Ca i_to g_to g_tos s 1 g_tos r V E_K alpha_s 0.033 V 17 beta_s 33 1 0.125 V 10 time s alpha_s 1 s beta_s s time r 333 1 1 V 4 5 r i_NaK i_NaK_max K_o K_mK K_o Na_i K_mNa Na_i i_NaCa_cyt 1 FRiNaCa k_NaCa gamma n_NaCa 2 V F R T Na_i n_NaCa Ca_o gamma 1 n_NaCa 2 V F R T Na_o n_NaCa Ca_i 1 d_NaCa Ca_i Na_o n_NaCa Ca_o Na_i n_NaCa 1 Ca_i 0.0069 i_NaCa_ds FRiNaCa k_NaCa gamma n_NaCa 2 V F R T Na_i n_NaCa Ca_o gamma 1 n_NaCa 2 V F R T Na_o n_NaCa Ca_ds 1 d_NaCa Ca_ds Na_o n_NaCa Ca_o Na_i n_NaCa 1 Ca_ds 0.0069 i_NaCa i_NaCa_cyt i_NaCa_ds K_1 K_cyca K_xcs K_srca K_2 Ca_i Ca_up K_1 K_cyca K_xcs K_cyca i_up Ca_i K_2 alpha_up Ca_up K_1 K_2 beta_up i_trans 50 Ca_up Ca_rel VoltDep 0.08 V 40 CaiReg Ca_i Ca_i K_m_Ca_cyt CadsReg Ca_ds Ca_ds K_m_Ca_ds RegBindSite CaiReg 1 CaiReg CadsReg ActRate 0 VoltDep 90 RegBindSite 2 InactRate 60 500 RegBindSite 2 SpeedRel 5 V 50 1 PrecFrac 1 ActFrac ProdFrac time ActFrac PrecFrac SpeedRel ActRate ActFrac SpeedRel InactRate time ProdFrac ActFrac SpeedRel InactRate SpeedRel 1 ProdFrac i_rel ActFrac ActFrac 0.25 2 K_m_rel K_leak_rate Ca_rel time Na_i 1 1 V_i F i_Na i_p_Na i_b_Na 3 i_NaK 3 i_NaCa_cyt i_Ca_L_Na_cyt i_Ca_L_Na_ds time K_i 1 1 V_i F i_K1 i_Kr i_Ks i_Ca_L_K_cyt i_Ca_L_K_ds i_to 2 i_NaK V_Cell 3.141592654 radius 1000 2 length 1000 V_i_ratio 1 V_e_ratio V_up_ratio V_rel_ratio V_i V_Cell V_i_ratio time Ca_i 1 2 1 V_i F i_Ca_L_Ca_cyt i_b_Ca 2 i_NaCa_cyt 2 i_NaCa_ds Ca_ds V_ds_ratio Kdecay i_rel V_rel_ratio V_i_ratio time Ca_Calmod time Ca_Trop i_up time Ca_ds 1 i_Ca_L_Ca_ds 2 1 V_ds_ratio V_i F Ca_ds Kdecay time Ca_up V_i_ratio V_up_ratio i_up i_trans time Ca_rel V_up_ratio V_rel_ratio i_trans i_rel time Ca_Calmod alpha_Calmod Ca_i Calmod Ca_Calmod beta_Calmod Ca_Calmod time Ca_Trop alpha_Trop Ca_i Trop Ca_Trop beta_Trop Ca_Trop fast sodium current inactivation variable calcium transfer flux from the network sarcoplasmic reticulum to the junctional sarcoplasmic reticulum sodium-calcium exchanger current in cytosol calcium reversal potential membrane potential volume ratio of domains product fraction calcium background current conductance L-type calcium channel potassium current in cytosol fast sodium current H-gate reversal potential concentration of calcium in release site fast sodium current inactivation variable membrane potential slow potassium current activation variable concentration of troponin rapid delayed rectifier potassium current inactivation variable rapid delayed rectifier potassium current inactivation variable membrane potential concentration of intracellular sodium concentration of calcium in domains regulatory calcium binding site rapid delayed rectifier potassium current activation variable absolute temperature concentration of intracellular sodium fast sodium current inactivation variable membrane potential calcium background current concentration of intracellular calcium calcium transfer flux from the network sarcoplasmic reticulum to the junctional sarcoplasmic reticulum absolute temperature concentration of calcium in uptake site slow delayed rectifier potassium current conductance concentration of extracellular sodium concentration of extracellular sodium transient outward current conductance membrane potential concentration of intracellular calcium L-type calcium channel potassium current in cytosol time-independent potassium current conductance concentration of extracellular calcium fast sodium current M-gate reversal potential concentration of intracellular calcium L-type calcium channel potassium current in cytosol transient outward current activation variable volume ratio of uptake site fast sodium current H-gate reversal potential transient outward current maximum L-type calcium channel calcium current conductance L-type calcium channel sodium current in cytosol membrane potential L-type calcium channel sodium current in cytosol L-type calcium channel potassium current in domains membrane potential sodium-potassium pump fast sodium current L-type calcium channel activation variable half-saturation constant of calcium-bound L-type calcium channel calcium transfer flux from the network sarcoplasmic reticulum to the junctional sarcoplasmic reticulum sodium reversal potential concentration of extracellular sodium volume ratio of cytosol L-type calcium channel calcium current in cytosol fast sodium current conductance transient outward current concentration of calmodulin calcium half-saturation constant of inactivated L-type calcium channel in domains L-type calcium channel sodium current in domains persistent sodium current conductance rapid delayed rectifier potassium current transient outward current absolute temperature concentration of extracellular potassium fast sodium current H-gate reversal potential fast sodium current conductance concentration of extracellular potassium time-independent potassium current concentration of extracellular potassium slow delayed rectifier potassium current half-saturation constant of calcium binding to cytosolic enzymes concentration of calcium in domains sodium background current L-type calcium current F-gate reversal potential L-type calcium channel calcium current in domains membrane potential precursor fraction maximum L-type calcium channel calcium current conductance product fraction half-saturation constant of calcium-bound L-type calcium channel concentration of extracellular potassium concentration of extracellular potassium sodium-potassium pump fraction of channels inactivated by voltage-dependent process in cytosol sodium-calcium exchanger current in domains regulatory domains calcium concentration of calcium in release site saturation potential of fast sodium current activation gate activator fraction sodium-calcium exchanger current in domains calcium half-saturation constant for calcium release from domains membrane potential concentration of intracellular potassium calcium half-saturation constant for calcium release from cytosol transient outward current conductance fast sodium current activation variable slow potassium current activation variable calcium background current conductance concentration of intracellular calcium concentration of extracellular calcium volume ratio of release site L-type calcium channel calcium current in domains cytosolic volume maximum sodium-calcium exchanger current concentration of intracellular calcium rapid delayed rectifier potassium current conductance half-saturation constant of calcium-bound L-type calcium channel L-type calcium channel activation variable sodium background current conductance fast sodium current membrane potential fast sodium current H-gate reversal potential concentration of calcium in domains concentration of intracellular sodium sodium-calcium exchanger current in cytosol cell radius persistent sodium current fast sodium current slow potassium current activation variable concentration of calcium in domains calcium half-saturation constant of inactivated L-type calcium channel in domains slow potassium current reversal potential sodium-calcium exchanger current in domains maximum L-type calcium channel sodium current conductance rapid delayed rectifier potassium current activation variable sodium-potassium pump sodium half-saturation constant for sodium-potassium pump potassium reversal potential calcium half-saturation constant for time-independent potassium current fraction of channels inactivated by voltage-dependent process in cytosol transient outward current inactivation variable absolute temperature fast sodium current activation variable concentration of calcium in domains cytosolic volume rapid delayed rectifier potassium current activation variable half-saturation constant of calcium-bound L-type calcium channel sodium-calcium exchanger current in cytosol fraction of channels with calcium-bound regulatory site in domains transient outward current L-type calcium current F-gate reversal potential concentration of intracellular calcium rapid delayed rectifier potassium current conductance L-type calcium channel potassium current in domains membrane potential concentration of extracellular sodium rapid delayed rectifier potassium current inactivation variable sodium reversal potential concentration of extracellular calcium rapid delayed rectifier potassium current activation variable membrane potential volume ratio of uptake site concentration of calcium in domains L-type calcium channel sodium current in cytosol sodium-potassium pump concentration of extracellular calcium regulatory domains calcium concentration of intracellular potassium membrane potential concentration of extracellular calcium membrane potential concentration of calcium in uptake site calcium flux into sarcoplasmic reticulum through SERCA pumps cytosolic volume concentration of intracellular sodium concentration of calcium in uptake site calcium flux into sarcoplasmic reticulum through SERCA pumps sodium reversal potential L-type calcium channel sodium current in cytosol L-type calcium channel calcium current in cytosol concentration of intracellular calcium concentration of troponin transient outward current absolute temperature membrane potential transient outward current activation variable voltage dependence of calcium release sodium-calcium exchanger current in domains rapid delayed rectifier potassium current volume ratio of domains fraction of channels inactivated by voltage-dependent process in domains L-type calcium channel activation variable L-type calcium current D-gate reversal potential concentration of intracellular potassium sodium-calcium exchanger current in cytosol membrane potential precursor fraction calcium background current rapid delayed rectifier potassium current conductance transient outward current activation variable calcium half-saturation constant of inactivated L-type calcium channel in domains calcium transfer flux from the network sarcoplasmic reticulum to the junctional sarcoplasmic reticulum concentration of extracellular potassium L-type calcium channel calcium current in domains calcium flux out of sarcoplasmic reticulum through ryanodine receptors rapid delayed rectifier potassium current conductance fast sodium current inactivation variable sodium-calcium exchanger current in domains calcium reversal potential concentration of calcium in release site membrane potential rapid delayed rectifier potassium current shift potential of fast sodium current inactivation gate L-type calcium channel calcium current in domains transient outward current inactivation variable potassium reversal potential membrane potential persistent sodium current calcium background current slow delayed rectifier potassium current fast sodium current M-gate reversal potential calcium background current fast sodium current concentration of extracellular calcium time-independent potassium current slow potassium current reversal potential cell length L-type calcium channel activation variable sodium background current fast sodium current activation variable L-type calcium current D-gate reversal potential membrane potential L-type calcium channel sodium current in domains membrane capacitance L-type calcium channel calcium current in cytosol fast sodium current activation variable volume ratio of endoplasmic reticulum maximum L-type calcium channel potassium current conductance rapid delayed rectifier potassium current inactivation variable membrane potential cytosolic volume L-type calcium channel inactivation variable membrane potential concentration of intracellular calcium absolute temperature membrane potential absolute temperature concentration of intracellular calcium slow potassium current reversal potential concentration of calcium in uptake site fraction of channels inactivated by voltage-dependent process in cytosol concentration of intracellular sodium cell length cytosolic volume fraction of channels with calcium-bound regulatory site in cytosol L-type calcium channel calcium current in domains concentration of calcium in uptake site rapid delayed rectifier potassium current sodium background current rapid delayed rectifier potassium current L-type calcium channel potassium current in domains L-type calcium channel calcium current in cytosol maximum sodium-potassium pump current L-type calcium channel inactivation variable total L-type calcium channel current concentration of intracellular potassium L-type calcium channel potassium current in cytosol concentration of calcium-bound troponin fraction of channels inactivated by voltage-dependent process in domains concentration of extracellular sodium L-type calcium channel potassium current in domains concentration of extracellular sodium L-type calcium channel sodium current in cytosol concentration of calmodulin potassium reversal potential shift potential of fast sodium current inactivation gate time-independent potassium current fraction of channels inactivated by voltage-dependent process in domains concentration of extracellular potassium concentration of intracellular sodium concentration of calcium-bound troponin concentration of intracellular sodium fraction of channels inactivated by voltage-dependent process in cytosol sodium-calcium exchanger current in cytosol cooperativity parameter of sodium-calcium exchanger absolute temperature calcium flux out of sarcoplasmic reticulum through ryanodine receptors time-independent potassium current slow delayed rectifier potassium current concentration of intracellular potassium L-type calcium channel sodium current in domains sodium-calcium exchanger current in cytosol rate of calcium transfer between cytosol and sarcoplasmic reticulum membrane potential concentration of intracellular calcium membrane potential concentration of intracellular sodium absolute temperature sodium-calcium exchanger current in domains membrane potential maximum L-type calcium channel sodium current conductance calcium flux out of sarcoplasmic reticulum through ryanodine receptors membrane potential regulatory calcium binding site potassium reversal potential concentration of calcium in domains concentration of intracellular calcium membrane potential persistent sodium current concentration of calcium in domains sodium-calcium exchanger current in cytosol L-type calcium channel potassium current in domains concentration of intracellular calcium total L-type calcium channel current L-type calcium channel sodium current in domains concentration of calcium in uptake site concentration of calcium-bound calmodulin L-type calcium channel potassium current in cytosol transient outward current activation variable cell radius concentration of calcium in release site sodium background current sodium half-saturation constant for sodium-potassium pump calcium half-saturation constant for calcium release from domains rate of calcium transfer between cytosol and sarcoplasmic reticulum membrane potential membrane potential concentration of extracellular calcium concentration of intracellular sodium half-saturation constant of calcium binding to cytosolic enzymes concentration of intracellular potassium concentration of intracellular sodium concentration of extracellular potassium sodium background current sodium background current calcium flux out of sarcoplasmic reticulum through ryanodine receptors membrane potential calcium half-saturation constant of inactivated L-type calcium channel in domains concentration of extracellular potassium time-independent potassium current conductance sodium reversal potential concentration of calcium in domains fraction of channels inactivated by voltage-dependent process in domains potassium reversal potential sodium-calcium exchanger current transient outward current inactivation variable L-type calcium channel calcium current in domains sodium reversal potential saturation potential of fast sodium current activation gate volume ratio of endoplasmic reticulum slow potassium current reversal potential membrane potential cytosolic volume L-type calcium channel potassium current in domains concentration of intracellular calcium activator fraction sodium-potassium pump concentration of intracellular sodium membrane potential calcium reversal potential concentration of extracellular potassium calcium background current slow delayed rectifier potassium current slow delayed rectifier potassium current concentration of calcium in release site potassium half-saturation constant for sodium-potassium pump time-independent potassium current sodium reversal potential membrane capacitance L-type calcium channel calcium current in cytosol concentration of calcium in release site transient outward current inactivation variable rapid delayed rectifier potassium current maximum L-type calcium channel potassium current conductance membrane potential persistent sodium current slow delayed rectifier potassium current conductance L-type calcium channel sodium current in cytosol calcium half-saturation constant for calcium release from cytosol calcium flux into sarcoplasmic reticulum through SERCA pumps membrane potential volume ratio of cytosol membrane potential concentration of calcium in domains transient outward current half-saturation constant of calcium binding to sarcoplasmic reticulum enzymes transient outward current conductance calcium background current L-type calcium channel sodium current in domains persistent sodium current conductance membrane potential fraction of channels with calcium-bound regulatory site in domains transient outward current conductance potassium reversal potential membrane potential sodium-calcium exchanger current in cytosol cell volume sodium-calcium exchanger current voltage dependence of calcium release fraction of channels with calcium-bound regulatory site in cytosol volume ratio of release site concentration of calcium-bound calmodulin half-saturation constant of calcium binding to sarcoplasmic reticulum enzymes absolute temperature fast sodium current fast sodium current regulatory intracellular calcium sodium-potassium pump membrane potential regulatory intracellular calcium slow potassium current activation variable sodium-potassium pump cooperativity parameter of sodium-calcium exchanger concentration of intracellular sodium persistent sodium current time-independent potassium current calcium half-saturation constant for time-independent potassium current sodium background current conductance L-type calcium channel potassium current in cytosol potassium half-saturation constant for sodium-potassium pump cell volume potassium reversal potential concentration of extracellular sodium membrane potential membrane potential calcium reversal potential membrane potential sodium-potassium pump concentration of extracellular sodium concentration of extracellular calcium maximum sodium-calcium exchanger current membrane potential persistent sodium current maximum sodium-potassium pump current L-type calcium channel sodium current in domains potassium reversal potential slow delayed rectifier potassium current calcium flux into sarcoplasmic reticulum through SERCA pumps concentration of intracellular calcium L-type calcium channel calcium current in cytosol