# Model Mathematics

### Component: membrane

$dd time V =- i_Na + i_K1 + i_to + i_Kur_d + i_Kr + i_Ks + i_Ca + i_Cl_Ca + i_p_Ca + i_NaCa + i_NaK + i_B_Na + i_B_Ca + i_B_Cl + i_stim Cm$

### Component: fast_sodium_current

$i_Na = g_Na ⁢ m 3.0 ⁢ h ⁢ j ⁢ V - E_Na E_Na = R ⁢ T F ⁢ln⁡ Na_o Na_i$

### Component: fast_sodium_current_m_gate

$alpha_m = 0.32 ⁢ V + 47.13 1.0 -ⅇ -0.1 ⁢ V + 47.13 beta_m = 0.08 ⁢ⅇ V -11.0 dd time m = alpha_m ⁢ 1.0 - m - beta_m ⁢ m$

### Component: fast_sodium_current_h_gate

$alpha_h = 0.135 ⁢ⅇ V + 80.0 -6.8 if V < -40.0 0.0 otherwise beta_h = 3.56 ⁢ⅇ 0.079 ⁢ V + 310000.0 ⁢ⅇ 0.35 ⁢ V if V < -40.0 1.0 0.13 ⁢ 1.0 +ⅇ V + 10.66 -11.1 otherwisedd time h = alpha_h ⁢ 1.0 - h - beta_h ⁢ h$

### Component: fast_sodium_current_j_gate

$alpha_j = -127140.0 ⁢ⅇ 0.2444 ⁢ V - 0.00003474 ⁢ⅇ -0.04391 ⁢ V 1.0 +ⅇ 0.311 ⁢ V + 79.23 ⁢ V + 37.78 if V < -40.0 0.0 otherwise beta_j = 0.1212 ⁢ⅇ -0.01052 ⁢ V 1.0 +ⅇ -0.1378 ⁢ V + 40.14 if V < -40.0 0.3 ⁢ⅇ -0.0000002535 ⁢ V 1.0 +ⅇ -0.1 ⁢ V + 32.0 otherwisedd time j = alpha_j ⁢ 1.0 - j - beta_j ⁢ j$

### Component: time_independent_potassium_current

$i_K1 = g_K1 ⁢ V - E_K 1.0 +ⅇ 0.07 ⁢ V + 80.0 E_K = R ⁢ T F ⁢ln⁡ K_o K_i$

### Component: transient_outward_K_current

$i_to = g_to ⁢ oa 3.0 ⁢ oi ⁢ V - E_K$

### Component: transient_outward_K_current_oa_gate

$dd time oa = oa_infinity - oa tau_oa alpha_oa = 0.65 ⁢ⅇ V + 18.0 -8.5 +ⅇ V - 16.0 -59.0 -1.0 beta_oa = 1.2 ⁢ 2.2 +ⅇ V + 75.0 18.0 -1.0 tau_oa = alpha_oa + beta_oa -1.0 oa_infinity = 1.0 +ⅇ V + 0.5 -10.5 - 1.0 3.0$

### Component: transient_outward_K_current_oi_gate

$dd time oi = oi_infinity - oi tau_oi alpha_oi = 6.2 +ⅇ V + 105.2 9.85 -1.0 beta_oi = 7.54 +ⅇ V - 8.89 -12.87 -1.0 tau_oi = alpha_oi + beta_oi -1.0 oi_infinity = 1.0 +ⅇ V + 43.377 6.45 -1.0$

### Component: ultrarapid_delayed_rectifier_K_current

$i_Kur_d = g_Kur_d ⁢ ua 3.0 ⁢ ui ⁢ V - E_K g_Kur_d = 0.00855 + 0.0779 1.0 +ⅇ V + 11.0 -16.0$

### Component: ultrarapid_delayed_rectifier_K_current_ua_gate

$dd time ua = ua_infinity - ua tau_ua alpha_ua = 1.47 ⁢ⅇ V + 33.2 -30.63 +ⅇ V - 27.6 -30.65 -1.0 beta_ua = 0.42 ⁢ⅇ V + 26.64 2.49 +ⅇ V + 44.41 20.36 -1.0 tau_ua = alpha_ua + beta_ua -1.0 ua_infinity = 1.0 +ⅇ V + 2.81 -9.49 - 1.0 3.0$

### Component: ultrarapid_delayed_rectifier_K_current_ui_gate

$dd time ui = ui_infinity - ui tau_ui alpha_ui = 21.0 +ⅇ V - 185.0 -28.0 -1.0 beta_ui =ⅇ V - 158.0 16.0 tau_ui = alpha_ui + beta_ui -1.0 ui_infinity = 1.0 +ⅇ V - 99.45 27.48 -1.0$

### Component: rapid_delayed_rectifier_K_current

$i_Kr = g_Kr ⁢ xr ⁢ 0.07 + 0.58 1.0 +ⅇ V + 15.0 22.4 ⁢ V - E_K$

### Component: rapid_delayed_rectifier_K_current_xr_gate

$dd time xr = xr_infinity - xr tau_xr alpha_xr = 0.04 ⁢ V - 248.0 1.0 -ⅇ V - 248.0 -28.0 beta_xr = 0.028 ⁢ V + 163.0 ⅇ V + 163.0 21.0 - 1.0 tau_xr = alpha_xr + beta_xr -1.0 xr_infinity = 1.0 +ⅇ V + 7.654 -5.377 -1.0$

### Component: slow_delayed_rectifier_K_current

$i_Ks = g_Ks ⁢ xs 2.0 ⁢ V - E_K$

### Component: slow_delayed_rectifier_K_current_xs_gate

$dd time xs = xs_infinity - xs tau_xs alpha_xs = 0.00001 ⁢ V + 28.5 1.0 -ⅇ V + 28.5 -115.0 beta_xs = 0.00023 ⁢ V + 28.5 ⅇ V + 28.5 3.3 - 1.0 tau_xs = alpha_xs + beta_xs -1.0 xs_infinity = 1.0 +ⅇ V - 13.0 -12.0 -0.5$

### Component: sarcolemmal_Ca_current

$i_Ca = g_Ca ⁢ d ⁢ f ⁢ f_Ca ⁢ V - 65.0$

### Component: sarcolemmal_Ca_current_d_gate

$dd time d = d_infinity - d tau_d d_infinity = 1.0 +ⅇ V + 10.0 -6.0 -1.0 tau_d = 1.0 -ⅇ V + 10.0 -6.24 0.035 ⁢ V + 10.0 ⁢ 1.0 +ⅇ V + 10.0 6.24$

### Component: sarcolemmal_Ca_current_f_gate

$dd time f = f_infinity - f tau_f f_infinity = 1.0 +ⅇ V + 24.6 6.2 -1.0 tau_f = 400.0 ⁢ 1.0 + 4.5 ⁢ⅇ -0.0007 ⁢ V - 9.0 2.0 -1.0$

### Component: sarcolemmal_Ca_current_f_Ca_gate

$dd time f_Ca = f_Ca_infinity - f_Ca tau_f_Ca f_Ca_infinity = 0.29 + 0.8 ⁢ 1.0 +ⅇ Ca_i - 0.00012 0.00006 -1.0$

### Component: Ca_activated_Cl_current

$i_Cl_Ca = g_Cl_Ca ⁢ q_Ca ⁢ V - E_Cl E_Cl = R ⁢ T F ⁢ln⁡ Cl_o Cl_i$

### Component: Ca_activated_Cl_current_q_Ca_gate

$q_Ca_infinity = 1.0 - 1.0 + Fn 0.00000000011 3.0 -1.0$

### Component: Na_Cl_cotransporter

$CT_NaCl = g_CT ⁢ delta_CT_n E_Na - E_Cl + delta_CT_n$

### Component: sodium_potassium_pump

$i_NaK = i_NaK_max ⁢ f_NaK ⁢ 1.0 1.0 + Km_Na_i Na_i 1.5 ⁢ K_o K_o + Km_K_o f_NaK = 1.0 + 0.1245 ⁢ⅇ -0.1 ⁢ F ⁢ V R ⁢ T + 0.0365 ⁢ sigma ⁢ⅇ- F ⁢ V R ⁢ T -1.0 sigma = 1.0 7.0 ⁢ⅇ Na_o 67.3 - 1.0$

### Component: Na_Ca_exchanger_current

$i_NaCa = I_NaCa_max ⁢ⅇ 0.35 ⁢ F ⁢ V R ⁢ T ⁢ Na_i 3.0 ⁢ Ca_o -ⅇ -0.65 ⁢ F ⁢ V R ⁢ T ⁢ Na_o 3.0 ⁢ Ca_i K_mNa 3.0 + Na_o 3.0 ⁢ K_mCa + Ca_o ⁢ 1.0 + K_sat ⁢ⅇ -0.65 ⁢ V ⁢ F R ⁢ T$

### Component: background_currents

$i_B_Na = g_B_Na ⁢ V - E_Na i_B_Ca = g_B_Ca ⁢ V - E_Ca i_B_K = g_B_K ⁢ V - E_K i_B_Cl = g_B_Cl ⁢ V - E_Cl E_Ca = R ⁢ T 2.0 ⁢ F ⁢ln⁡ Ca_o Ca_i$

### Component: Ca_pump_current

$i_p_Ca = i_p_Ca_max ⁢ Ca_i 0.0005 + Ca_i$

### Component: Ca_release_current_from_JSR

$i_rel = K_rel ⁢ u 2.0 ⁢ v ⁢ w ⁢ Ca_rel - Ca_i Fn = 1E-12 ⁢ V_rel ⁢ i_rel - 5E-13 ⁢ 1.0 2.0 ⁢ F ⁢ i_Ca - 1.0 5.0 ⁢ F ⁢ i_NaCa$

### Component: Ca_release_current_from_JSR_u_gate

$dd time u = u_infinity - u tau_u tau_u = 8.0 u_infinity = 1.0 +ⅇ Fn - 3.4175E-13 -13.67E-16 -1.0$

### Component: Ca_release_current_from_JSR_v_gate

$dd time v = v_infinity - v tau_v tau_v = 1.91 + 2.09 ⁢ 1.0 +ⅇ Fn - 3.4175E-13 -13.67E-16 -1.0 v_infinity = 1.0 - 1.0 +ⅇ Fn - 6.835E-14 -13.67E-16 -1.0$

### Component: Ca_release_current_from_JSR_w_gate

$dd time w = w_infinity - w tau_w tau_w = 6.0 - 6.0 ⁢ⅇ V - 7.9 -5.0 1.0 + 0.3 ⁢ⅇ V - 7.9 -5.0 ⁢ V - 7.9 w_infinity = 1.0 - 1.0 +ⅇ V - 40.0 -17.0 -1.0$

### Component: transfer_current_from_NSR_to_JSR

$i_tr = Ca_up - Ca_rel tau_tr$

### Component: Ca_uptake_current_by_the_NSR

$i_up = I_up_max 1.0 + K_up Ca_i$

### Component: Ca_leak_current_by_the_NSR

$i_up_leak = I_up_max ⁢ Ca_up Ca_up_max$

### Component: Ca_buffers

$Ca_CMDN = 200.0 ⁢ Ca_i ⁢ 1.0 - Ca_CMDN CMDN_max - 0.476 ⁢ Ca_CMDN CMDN_max J_Ca_CMDN =dd time Ca_CMDN Ca_TRPN = 78.4 ⁢ Ca_i ⁢ 1.0 - Ca_TRPN TRPN_max - 0.392 ⁢ Ca_TRPN TRPN_max J_Ca_TRPN =dd time Ca_TRPN Ca_CSQN = 0.48 ⁢ Ca_rel ⁢ 1.0 - Ca_CSQN CSQN_max - 0.4 ⁢ Ca_CSQN CSQN_max J_Ca_CSQN =dd time Ca_CSQN$

### Component: intracellular_ion_concentrations

$dd time Na_i = -3.0 ⁢ i_NaK - 3.0 ⁢ i_NaCa + i_B_Na + i_Na V_i ⁢ F dd time K_i = 2.0 ⁢ i_NaK - i_K1 + i_to + i_Kur_d + i_Kr + i_Ks + i_B_K V_i ⁢ F dd time Cl_i = i_Cl_Ca V_i ⁢ F dd time Ca_i = 2.0 ⁢ i_NaCa - i_p_Ca + i_Ca + i_B_Ca 2.0 ⁢ V_i ⁢ F + V_up ⁢ i_up_leak - i_up + i_rel ⁢ V_rel V_i - TRPN_max ⁢ J_Ca_TRPN + CMDN_max ⁢ J_Ca_CMDN dd time Ca_up = i_up - i_up_leak + i_tr ⁢ V_rel V_up dd time Ca_rel = i_tr - i_rel + 31.0 ⁢ J_Ca_CSQN$

### Component: standard_ionic_concentrations

Source
Derived from workspace Kneller, Ramirez, Chartier, Courtemanche, Nattel, 2002 at changeset 7815d0f5b1fa.
Collaboration
To begin collaborating on this work, please use your git client and issue this command: