Model Mathematics

Component: environment

Component: cell_geometry

Component: membrane

dd time V = -1.0 Cm i_Na + i_Ca + i_Ca_K + i_K + i_K1 + i_Kp + i_NaCa + i_NaK + i_ns_Ca + i_p_Ca + i_Ca_b + i_Na_b

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: time_dependent_potassium_current

g_K = 0.1128 Ko 5.4 E_K = R T F ln Ko + PNa_K Nao Ki + PNa_K Nai i_K = g_K Xi X 2.0 V - E_K

Component: time_dependent_potassium_current_X_gate

alpha_X = 0.0000719 V + 30.0 1.0 - -0.148 V + 30.0 beta_X = 0.000131 V + 30.0 -1.0 + 0.0687 V + 30.0 dd time X = alpha_X 1.0 - X - beta_X X

Component: time_dependent_potassium_current_Xi_gate

Xi = 1.0 1.0 + V - 40.0 40.0

Component: time_independent_potassium_current

g_K1 = 0.75 Ko 5.4 E_K1 = R T F ln Ko Ki i_K1 = g_K1 K1_infinity V - E_K1

Component: time_independent_potassium_current_K1_gate

alpha_K1 = 1.02 1.0 + 0.2385 V - E_K1 + 59.215 beta_K1 = 0.49124 0.08032 V - E_K1 + 5.476 + 0.06175 V - E_K1 - 594.31 1.0 + -0.5143 V - E_K1 + 4.753 K1_infinity = alpha_K1 alpha_K1 + beta_K1

Component: plateau_potassium_current

E_Kp = E_K1 Kp = 1.0 1.0 + 7.488 - V 5.98 i_Kp = g_Kp Kp V - E_Kp

Component: Na_Ca_exchanger

i_NaCa = k_NaCa 1.0 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: non_specific_calcium_activated_current

i_ns_Na = I_ns_Na 1.0 1.0 + K_m_ns_Ca Cai 3.0 i_ns_K = I_ns_K 1.0 1.0 + K_m_ns_Ca Cai 3.0 i_ns_Ca = i_ns_Na + i_ns_K I_ns_Na = Pns_Na V F 2.0 R T 0.75 Nai V F R T - 0.75 Nao V F R T - 1.0 I_ns_K = Pns_K V F 2.0 R T 0.75 Ki V F R T - 0.75 Ko V F R T - 1.0

Component: sarcolemmal_calcium_pump

i_p_Ca = I_pCa Cai K_mpCa + Cai

Component: calcium_background_current

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

Component: sodium_background_current

E_NaN = E_Na i_Na_b = g_Nab V - E_NaN

Component: L_type_Ca_channel

i_Ca = i_Ca_max y O + O_Ca i_Ca_max = P_Ca 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 i_Ca_K = p_k 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 alpha = 0.4 V + 12.0 10.0 beta = 0.05 - V + 12.0 13.0 alpha_a = alpha a beta_b = beta b gamma = 0.5625 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_channel_y_gate

dd time y = y_infinity - y tau_y y_infinity = 1.0 1.0 + V + 55.0 7.5 + 0.1 1.0 +- V + 21.0 6.0 tau_y = 20.0 + 600.0 1.0 + V + 30.0 9.5

Component: RyR_channel_states

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

Component: SERCA_pump

J_up = Vmax_f fb - Vmax_r rb 1.0 + fb + rb fb = Cai k_fb n_fb rb = Ca_NSR k_rb n_rb

Component: intracellular_Ca_fluxes

J_rel = v1 P_O1 + P_O2 Ca_JSR - Ca_SS J_tr = Ca_NSR - Ca_JSR tau_tr J_xfer = Ca_SS - Cai tau_xfer J_trpn = k_htrpn_plus Cai HTRPN_tot - HTRPNCa - k_htrpn_minus HTRPNCa + k_ltrpn_plus Cai LTRPN_tot - LTRPNCa - k_ltrpn_minus LTRPNCa

Component: intracellular_ionic_concentrations

betai = 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 Cai = betai - J_xfer + J_up + J_trpn + i_Ca_b +- 2.0 i_NaCa + i_p_Ca A_cap 2.0 V_myo F dd time Ca_SS = beta_SS J_rel V_JSR V_SS - J_xfer V_myo V_SS - i_Ca A_cap 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 dd time Nai =- i_Na + i_Na_b + i_ns_Na + i_NaCa 3.0 + i_NaK 3.0 A_cap V_myo F dd time Ki =- i_Ca_K + i_K + i_K1 + i_Kp + i_ns_K +- i_NaK 2.0 A_cap V_myo F

Component: troponin

dd time HTRPNCa = k_htrpn_plus Cai HTRPN_tot - HTRPNCa - k_htrpn_minus HTRPNCa dd time LTRPNCa = k_ltrpn_plus Cai LTRPN_tot - LTRPNCa - k_ltrpn_minus LTRPNCa 0.333 + 0.667 1.0 - Force_norm

Component: tropomyosin_cross_bridges

f_01 = 3.0 f_XB f_12 = 10.0 f_XB f_23 = 7.0 f_XB g_01_SL = 1.0 g_XB_SL g_12_SL = 2.0 g_XB_SL g_23_SL = 3.0 g_XB_SL g_XB_SL = g_XB 1.0 + 1.0 - SL_norm 1.6 SL_norm = SL - 1.7 0.7 k_trop_np = k_trop_pn LTRPNCa LTRPN_tot K_trop_half N_trop N_trop = 3.5 + 2.5 SL_norm K_trop_half = 1.0 + K_trop_Ca 1.7 - 0.9 SL_norm -1.0 K_trop_Ca = k_ltrpn_minus k_ltrpn_plus dd time N0 = k_trop_pn P0 - k_trop_np N0 + g_01_SL N1 dd time P0 =- k_trop_pn + f_01 P0 + k_trop_np N0 + g_01_SL P1 dd time P1 =- k_trop_pn + f_12 + g_01_SL P1 + k_trop_np N1 + k_trop_np N1 + f_01 P0 + g_12_SL P2 dd time P2 =- f_23 + g_12_SL P2 + f_12 P1 + g_23_SL P3 dd time P3 =- g_23_SL P3 + f_23 P2

Component: force_computation

Force = zeta Force_norm Force_norm = phi_SL P1 + N1 + 2.0 P2 + 3.0 P3 Force_max Force_max = P1_max + 2.0 P2_max + 3.0 P3_max phi_SL = SL - 0.6 1.4 if SL < 2.0 SL > 1.7 1.0 if SL < 2.2 SL > 2.0 3.6 - SL 1.4 if SL < 2.3 SL > 2.2 P1_max = f_01 2.0 g_XB 3.0 g_XB g_XB 2.0 g_XB 3.0 g_XB + f_01 2.0 g_XB 3.0 g_XB + f_01 f_12 3.0 g_XB + f_01 f_12 f_23 P2_max = f_01 f_12 3.0 g_XB g_XB 2.0 g_XB 3.0 g_XB + f_01 2.0 g_XB 3.0 g_XB + f_01 f_12 3.0 g_XB + f_01 f_12 f_23 P3_max = f_01 f_12 f_23 g_XB 2.0 g_XB 3.0 g_XB + f_01 2.0 g_XB 3.0 g_XB + f_01 f_12 3.0 g_XB + f_01 f_12 f_23