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# Model Mathematics

### Component: membrane

$RTONF=R⁢TFi_Stim=stim_amplitudeiftime≥stim_start∧time≦stim_end∧time-stim_start-⌊time-stim_startstim_period⌋⁢stim_period≦stim_duration0otherwiseddtimeV=-i_Stim+i_K1+i_b_Na+i_b_Ca+i_b_K+i_NaK+i_NaCa+i_Na+i_siC_m$

### Component: fast_sodium_current

$E_mh=RTONF⁢ln⁡Na_o+0.12⁢K_cNa_i+0.12⁢K_ii_Na=g_Na⁢m3⁢h⁢V-E_mh$

### Component: fast_sodium_current_m_gate

$E0_m=V+41alpha_m=2000if|E0_m|

### Component: fast_sodium_current_h_gate

$alpha_h=20⁢ⅇ-0.125⁢V+75beta_h=20001+320⁢ⅇ-0.1⁢V+75ddtimeh=alpha_h⁢1-h-beta_h⁢h$

### Component: sodium_potassium_pump

$i_NaK=i_NaK_max⁢K_cK_mK+K_c⁢Na_iK_mNa+Na_i$

### Component: sodium_background_current

$E_Na=RTONF⁢ln⁡Na_oNa_ii_b_Na=g_b_Na⁢V-E_Na$

### Component: calcium_background_current

$E_Ca=0.5⁢RTONF⁢ln⁡Ca_oCa_ii_b_Ca=g_b_Ca⁢V-E_Ca$

### Component: Na_Ca_exchanger

$i_NaCa=k_NaCa⁢ⅇgamma⁢n_NaCa-2⁢VRTONF⁢Na_in_NaCa⁢Ca_o-ⅇgamma-1⁢n_NaCa-2⁢VRTONF⁢Na_on_NaCa⁢Ca_i1+d_NaCa⁢Ca_i⁢Na_on_NaCa+Ca_o⁢Na_in_NaCa⁢1+Ca_i0.0069$

### Component: potassium_background_current

$i_b_K=g_b_K⁢V-E_K$

### Component: time_independent_potassium_current

$E_K=RTONF⁢ln⁡K_cK_ii_K1=g_K1⁢K_cK_c+K_m_K1⁢V-E_K1+ⅇV-E_K-10⁢2RTONF$

### Component: second_inward_calcium_current

$i_si=i_siCa+i_siK+i_siNai_siCa=4⁢P_si⁢d⁢CaChon⁢V-50RTONF1-ⅇ-1⁢V-50⁢2RTONF⁢Ca_i⁢ⅇ100RTONF-Ca_o⁢ⅇ-2⁢V-50RTONFi_siK=0.002⁢P_si⁢d⁢CaChon⁢V-50RTONF1-ⅇ-1⁢V-50RTONF⁢K_i⁢ⅇ50RTONF-K_c⁢ⅇ-1⁢V-50RTONFi_siNa=0.01⁢P_si⁢d⁢CaChon⁢V-50RTONF1-ⅇ-1⁢V-50RTONF⁢Na_i⁢ⅇ50RTONF-Na_o⁢ⅇ-1⁢V-50RTONF$

### Component: second_inward_calcium_current_d_gate

$E0_d=V+24-5alpha_d=120if|E0_d|

### Component: second_inward_calcium_current_f_Ca_gate

$E0_f=V+34alpha_f_Ca=25if|E0_f|

### Component: sarcoplasmic_reticulum_calcium_pump

$K_1=K_cyca⁢K_xcsK_srcaK_2=Ca_i+Ca_up⁢K_1+K_cyca⁢K_xcs+K_cycai_up=Ca_iK_2⁢alpha_up-Ca_up⁢K_1K_2⁢beta_up$

### Component: calcium_release

$PrecFrac=1-ActFrac-ProdFracVoltDep=ⅇ0.08⁢V-40RegBindSite=Ca_iCa_i+0.00052ActRate=600⁢VoltDep+500⁢RegBindSiteInactRate=60+500⁢RegBindSiteddtimeActFrac=PrecFrac⁢ActRate-ActFrac⁢InactRateddtimeProdFrac=ActFrac⁢InactRate-0.6⁢ProdFraci_rel=ActFracActFrac+0.252⁢K_m_rel+K_leak_rate⁢Ca_rel$

### Component: calcium_translocation

$i_trans=Ca_up-Ca_rel⁢alpha_tr$

### Component: intracellular_sodium_concentration

$ddtimeNa_i=-11⁢V_i⁢F⁢i_Na+i_b_Na+i_NaK⁢3+i_NaCa⁢3+i_siNa$

### Component: extracellular_calcium_concentration

$ddtimeCa_o=Cab-Ca_o⁢K_diff-1⁢i_siCa+i_NaCa+i_b_Ca2⁢1⁢Ve⁢F$

### Component: intracellular_potassium_concentration

$ddtimeK_i=-11⁢V_i⁢F⁢i_K1+i_siK+i_b_K-2⁢i_NaK$

### Component: intracellular_calcium_concentration

$V_Cell=3.141592654⁢radius2⁢lengthV_i_ratio=1-V_e_ratio-V_up_ratio-V_rel_ratioV_i=V_Cell⁢V_i_ratioVe=V_Cell⁢V_e_ratioddtimeCa_i=-12⁢1⁢V_i⁢F⁢i_siCa+i_b_Ca-2⁢i_NaCa+i_rel⁢V_rel_ratioV_i_ratio-dCaCalmoddt-dCaTropdt-i_upddtimeCa_up=V_i_ratioV_up_ratio⁢i_up-i_transddtimeCa_rel=V_up_ratioV_rel_ratio⁢i_trans-i_relddtimeCa_Calmod=alpha_Calmod⁢Ca_i⁢Calmod-Ca_Calmod-beta_Calmod⁢Ca_CalmodddtimeCa_Trop=alpha_Trop⁢Ca_i⁢Trop-Ca_Trop-beta_Trop⁢Ca_TropdCaCalmoddt=alpha_Calmod⁢Ca_i⁢Calmod-Ca_Calmod-beta_Calmod⁢Ca_CalmoddCaTropdt=alpha_Trop⁢Ca_i⁢Trop-Ca_Trop-beta_Trop⁢Ca_Trop$
Model Curation
• Curation Status
• JSim
• COR
• OpenCell
Source
Derived from workspace Hilgemann, Noble, 1987 at changeset 93edae1e1d06.