Model Mathematics

Component: environment

Component: membrane

dd time V =- 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 C_sc

Component: fast_sodium_current

i_Na = g_Na m 3.0 h j V - E_Na E_Na = R T F ln Nao Nai

Component: fast_sodium_current_m_gate

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

Component: fast_sodium_current_h_gate

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

Component: fast_sodium_current_j_gate

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

Component: rapid_activating_delayed_rectifiyer_K_current

E_K = R T F ln Ko Ki i_Kr = g_Kr f_Ko R_V X_kr V - E_K f_Ko = Ko 4.0 R_V = 1.0 1.0 + 1.4945 0.0446 V

Component: rapid_activating_delayed_rectifiyer_K_current_X_kr_gate

dd time X_kr = K12 1.0 - X_kr - K12 X_kr K12 = -5.495 + 0.169 V K21 = -7.677 - 0.0128 V

Component: slow_activating_delayed_rectifiyer_K_current

i_Ks = g_Ks X_ks 2.0 V - E_Ks E_Ks = R T F ln Ko + 0.01833 Nao Ki + 0.01833 Nai

Component: slow_activating_delayed_rectifiyer_K_current_X_ks_gate

dd time X_ks = X_ks_infinity - X_ks tau_X_ks X_ks_infinity = 1.0 1.0 +- V - 24.7 13.6 tau_X_ks = 1.0 0.0000719 V - 10.0 1.0 - -0.148 V - 10.0 + 0.000131 V - 10.0 0.0687 V - 10.0 - 1.0

Component: transient_outward_potassium_current

i_to1 = i_Kv4_3 + i_Kv1_4

Component: Kv4_3_current

i_Kv4_3 = g_Kv4_3 P_open V - E_K P_open = P_O + P_OI dd time P_C0 = alpha_i P_CI0 + beta_a P_C1 - beta_i + 4.0 alpha_a P_C0 dd time P_C1 = alpha_i b1 P_CI1 + 4.0 alpha_a P_C0 + 2.0 beta_a P_C2 - f1 beta_i + beta_a + 3.0 alpha_a P_C1 dd time P_C2 = alpha_i b2 P_CI2 + 3.0 alpha_a P_C1 + 3.0 beta_a P_C3 - f2 beta_i + 2.0 beta_a + 2.0 alpha_a P_C2 dd time P_C3 = alpha_i b3 P_CI3 + 2.0 alpha_a P_C2 + 4.0 beta_a P_O - f3 beta_i + 3.0 beta_a + alpha_a P_C3 dd time P_O = alpha_a P_C3 + alpha_i b4 P_OI - f4 beta_i + 4.0 beta_a P_O dd time P_CI0 = beta_i P_C0 + beta_a f1 P_C1 - alpha_i + b1 4.0 alpha_a P_CI0 dd time P_CI1 = f1 2.0 beta_a f2 P_CI2 + b1 4.0 alpha_a P_CI0 + f1 beta_i P_C1 - b2 3.0 alpha_a b1 + alpha_i b1 + beta_a f1 P_CI1 dd time P_CI2 = f2 3.0 beta_a f3 P_CI3 + b2 3.0 alpha_a b1 P_CI1 + f2 beta_i P_C2 - b3 2.0 alpha_a b2 + alpha_i b2 + f1 2.0 beta_a f2 P_CI2 dd time P_CI3 = f3 4.0 beta_a f4 P_OI + b3 2.0 alpha_a b2 P_CI2 + f3 beta_i P_C3 - b4 alpha_a b3 + alpha_i b3 + f2 3.0 beta_a f3 P_CI3 dd time P_OI = b4 alpha_a b3 P_CI3 + f4 beta_i P_O - alpha_i b4 + f3 4.0 beta_a f4 P_OI alpha_a = alpha_a0 a_a beta_a = beta_a0 - b_a alpha_i = alpha_i0 - a_i beta_i = beta_i0 b_i

Component: Kv1_4_current

i_Kv1_4 = i_Kv1_4_K + i_Kv1_4_Na i_Kv1_4_K = P_Kv1_4 C_sc F 2.0 V R T P_open Ki - Ko - V F R T 1.0 -- V F R T i_Kv1_4_Na = alpha P_Kv1_4 C_sc F 2.0 V R T P_open Ki - Ko - V F R T 1.0 -- V F R T P_open = P_O + P_OI dd time P_C0 = alpha_i P_CI0 + beta_a P_C1 - beta_i + 4.0 alpha_a P_C0 dd time P_C1 = alpha_i b1 P_CI1 + 4.0 alpha_a P_C0 + 2.0 beta_a P_C2 - f1 beta_i + beta_a + 3.0 alpha_a P_C1 dd time P_C2 = alpha_i b2 P_CI2 + 3.0 alpha_a P_C1 + 3.0 beta_a P_C3 - f2 beta_i + 2.0 beta_a + 2.0 alpha_a P_C2 dd time P_C3 = alpha_i b3 P_CI3 + 2.0 alpha_a P_C2 + 4.0 beta_a P_O - f3 beta_i + 3.0 beta_a + alpha_a P_C3 dd time P_O = alpha_a P_C3 + alpha_i b4 P_OI - f4 beta_i + 4.0 beta_a P_O dd time P_CI0 = beta_i P_C0 + beta_a f1 P_C1 - alpha_i + b1 4.0 alpha_a P_CI0 dd time P_CI1 = f1 2.0 beta_a f2 P_CI2 + b1 4.0 alpha_a P_CI0 + f1 beta_i P_C1 - b2 3.0 alpha_a b1 + alpha_i b1 + beta_a f1 P_CI1 dd time P_CI2 = f2 3.0 beta_a f3 P_CI3 + b2 3.0 alpha_a b1 P_CI1 + f2 beta_i P_C2 - b3 2.0 alpha_a b2 + alpha_i b2 + f1 2.0 beta_a f2 P_CI2 dd time P_CI3 = f3 4.0 beta_a f4 P_OI + b3 2.0 alpha_a b2 P_CI2 + f3 beta_i P_C3 - b4 alpha_a b3 + alpha_i b3 + f2 3.0 beta_a f3 P_CI3 dd time P_OI = b4 alpha_a b3 P_CI3 + f4 beta_i P_O - alpha_i b4 + f3 4.0 beta_a f4 P_OI alpha_a = alpha_a0 a_a beta_a = beta_a0 - b_a alpha_i = alpha_i0 - a_i beta_i = beta_i0 b_i

Component: time_independent_potassium_current

i_K1 = g_K1 K1_infinity_V Ko Ko + K_mK1 V - E_K

Component: time_independent_potassium_current_K1_gate

K1_infinity_V = 1.0 2.0 + 1.5 F R T V - E_K

Component: plateau_potassium_current

i_Kp = g_Kp Kp_V V - E_K

Component: plateau_potassium_current_Kp_gate

Kp_V = 1.0 1.0 + 7.488 - V 5.98

Component: Na_Ca_exchanger

i_NaCa = K_NaCa 5000.0 K_mNa 3.0 + Nao 3.0 1.0 K_mCa + Cao 1.0 1.0 + K_sat eta - 1.0 V F R T eta V F R T Nai 3.0 Cao - eta - 1.0 V F R T Nao 3.0 Cai

Component: sodium_potassium_pump

f_NaK = 1.0 1.0 + 0.1245 -0.1 V F R T + 0.0365 sigma - V F R T sigma = 1.0 7.0 Nao 67.3 - 1.0 i_NaK = I_NaK f_NaK 1.0 1.0 + K_mNai Nai 1.5 Ko Ko + K_mKo

Component: sarcolemmal_calcium_pump

i_p_Ca = I_pCa Cai K_mpCa + Cai

Component: calcium_background_current

E_Ca = R T 2.0 F ln Cao Cai i_Ca_b = g_Cab V - E_Ca

Component: sodium_background_current

i_Na_b = g_Nab V - E_Na

Component: L_type_Ca_current

i_Ca = i_Ca_max y O + O_Ca i_Ca_K = p_k C_sc y O + O_Ca V F 2.0 R T Ki V F R T - Ko V F R T - 1.0 p_k = P_K 1.0 + i_Ca_max i_Ca_half i_Ca_max = P_Ca C_sc 4.0 V F 2.0 R T 0.001 2.0 V F R T - 0.341 Cao 2.0 V F R T - 1.0 alpha = 0.4 V + 2.0 10.0 beta = 0.05 - V + 2.0 13.0 alpha_a = alpha a beta_b = beta b gamma = 0.10375 Ca_ss dd time C0 = beta C1 + omega C_Ca0 - 4.0 alpha + gamma C0 dd time C1 = 4.0 alpha C0 + 2.0 beta C2 + omega b C_Ca1 - beta + 3.0 alpha + gamma a C1 dd time C2 = 3.0 alpha C1 + 3.0 beta C3 + omega b 2.0 C_Ca2 - beta 2.0 + 2.0 alpha + gamma a 2.0 C2 dd time C3 = 2.0 alpha C2 + 4.0 beta C4 + omega b 3.0 C_Ca3 - beta 3.0 + alpha + gamma a 3.0 C3 dd time C4 = alpha C3 + g O + omega b 4.0 C_Ca4 - beta 4.0 + f + gamma a 4.0 C4 dd time O = f C4 - g O dd time C_Ca0 = beta_b C_Ca1 + gamma C_Ca0 - 4.0 alpha_a + omega C_Ca0 dd time C_Ca1 = 4.0 alpha_a C_Ca0 + 2.0 beta_b C_Ca2 + gamma a C1 - beta_b + 3.0 alpha_a + omega b C_Ca1 dd time C_Ca2 = 3.0 alpha_a C_Ca1 + 3.0 beta_b C_Ca3 + gamma a 2.0 C2 - beta_b 2.0 + 2.0 alpha_a + omega b 2.0 C_Ca2 dd time C_Ca3 = 2.0 alpha_a C_Ca2 + 4.0 beta_b C_Ca4 + gamma a 3.0 C3 - beta_b 3.0 + alpha_a + omega b 3.0 C_Ca3 dd time C_Ca4 = alpha_a C_Ca3 + g_ O_Ca + gamma a 4.0 C4 - beta_b 4.0 + f_ + omega b 4.0 C_Ca4 dd time O_Ca = f_ C_Ca4 - g_ O_Ca

Component: L_type_Ca_current_y_gate

dd time y = y_infinity - y tau_y y_infinity = 0.8 1.0 + V + 12.5 5.0 + 0.2 tau_y = 20.0 + 600.0 1.0 + V + 20.0 9.5

Component: RyR_channel

dd time P_C1 =- k_a_plus Ca_ss n P_C1 + k_a_minus P_O1 dd time P_O1 = k_a_plus Ca_ss n P_C1 - k_a_minus P_O1 + k_b_plus Ca_ss m P_O1 + k_c_plus P_O1 + k_b_minus P_O2 + k_c_minus P_C2 dd time P_O2 = k_b_plus Ca_ss m P_O1 - k_b_minus P_O2 dd time P_C2 = k_c_plus P_O1 - k_c_minus P_C2 J_rel = v1 P_O1 + P_O2 Ca_JSR - Ca_ss

Component: SERCA2a_pump

J_up = K_SR Vmaxf fb - Vmaxr rb 1.0 + fb + rb fb = Cai K_fb N_fb rb = Ca_NSR K_rb N_rb

Component: intracellular_Ca_fluxes

J_tr = Ca_NSR - Ca_JSR tau_tr J_xfer = Ca_ss - Cai tau_xfer J_trpn = J_HTRPNCa + J_LTRPNCa J_HTRPNCa =dd time HTRPNCa dd time HTRPNCa = k_htrpn_plus Cai HTRPN_tot - HTRPNCa - k_htrpn_minus HTRPNCa J_LTRPNCa =dd time LTRPNCa dd time LTRPNCa = k_ltrpn_plus Cai LTRPN_tot - LTRPNCa - k_ltrpn_minus LTRPNCa

Component: intracellular_ion_concentrations

dd time Cai = beta_i J_xfer - J_up + J_trpn + i_Ca_b - 2.0 i_NaCa + i_p_Ca A_cap C_sc 2.0 V_myo F dd time Nai =- i_Na + i_Na_b + i_NaCa 3.0 + i_NaK 3.0 A_cap C_sc V_myo F dd time Ki =- i_Ca_K + i_Kr + i_Ks + i_K1 + i_Kp + i_to1 + i_NaK -2.0 A_cap C_sc V_myo F beta_i = 1.0 1.0 + CMDN_tot K_mCMDN K_mCMDN + Cai 2.0 beta_SS = 1.0 1.0 + CMDN_tot K_mCMDN K_mCMDN + Ca_ss 2.0 beta_JSR = 1.0 1.0 + CSQN_tot K_mCSQN K_mCSQN + Ca_JSR 2.0 dd time Ca_ss = beta_SS J_rel V_JSR V_SS - J_xfer V_myo V_SS - i_Ca A_cap C_sc 2.0 V_SS F dd time Ca_JSR = beta_JSR J_tr - J_rel dd time Ca_NSR = J_up V_myo V_NSR - J_tr V_JSR V_NSR

Component: standard_ionic_concentrations