Model Mathematics

Component: environment

Component: membrane

dd time V =- 1.0 Cm i_Na + i_Ca_L + i_K + i_K1 + i_Kp + i_NaCa + i_p_Ca + i_Na_b + i_Ca_b + i_NaK + i_ns_Ca + i_to + I_st

Component: transient_outward_potassium_current

i_to = g_to z 3.0 y R_to V - E_K R_to = V 100.0

Component: transient_outward_potassium_current_z_gate

dd time z = alpha_z 1.0 - z - beta_z z alpha_z = 10.0 V - 40.0 25.0 1.0 + V - 40.0 25.0 beta_z = 10.0 - V + 90.0 25.0 1.0 +- V + 90.0 25.0

Component: transient_outward_potassium_current_y_gate

dd time y = alpha_y 1.0 - y - beta_y y alpha_y = 0.015 1.0 + V + 60.0 5.0 beta_y = 0.1 V + 25.0 5.0 1.0 + V + 25.0 5.0

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 otherwisedd 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 otherwisedd time j = alpha_j 1.0 - j - beta_j j

Component: L_type_Ca_channel

i_CaCa = d f f_Ca I_CaCa i_CaNa = d f f_Ca I_CaNa i_CaK = d f f_Ca I_CaK I_CaCa = P_Ca 2.0 2.0 V F 2.0 R T gamma_Cai Cai 2.0 V F R T - gamma_Cao Cao 2.0 V F R T - 1.0 I_CaNa = P_Na 1.0 2.0 V F 2.0 R T gamma_Nai Nai 1.0 V F R T - gamma_Nao Nao 1.0 V F R T - 1.0 I_CaK = P_K 1.0 2.0 V F 2.0 R T gamma_Ki Ki 1.0 V F R T - gamma_Ko Ko 1.0 V F R T - 1.0 i_Ca_L = i_CaCa + i_CaK + i_CaNa

Component: L_type_Ca_channel_d_gate

alpha_d = d_infinity tau_d d_infinity = 1.0 1.0 +- V + 10.0 6.24 tau_d = d_infinity 1.0 -- V + 10.0 6.24 0.035 V + 10.0 beta_d = 1.0 - d_infinity tau_d dd time d = alpha_d 1.0 - d - beta_d d

Component: L_type_Ca_channel_f_gate

alpha_f = f_infinity tau_f f_infinity = 1.0 1.0 + V + 35.06 8.6 + 0.6 1.0 + 50.0 - V 20.0 tau_f = 1.0 0.0197 - 0.0337 V + 10.0 2.0 + 0.02 beta_f = 1.0 - f_infinity tau_f dd time f = alpha_f 1.0 - f - beta_f f

Component: L_type_Ca_channel_f_Ca_gate

f_Ca = 1.0 1.0 + Cai Km_Ca 2.0

Component: time_dependent_potassium_current

g_K = 0.282 Ko 5.4 E_K = R T F ln Ko + PR_NaK Nao Ki + PR_NaK Nai i_K = g_K X 2.0 Xi 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 - 56.26 32.1

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 + 5.476 - E_K1 + 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: sarcolemmal_calcium_pump

i_p_Ca = I_pCa Cai K_mpCa + Cai

Component: sodium_background_current

E_NaN = E_Na i_Na_b = g_Nab V - E_NaN

Component: calcium_background_current

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

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 = P_ns_Ca 1.0 2.0 V F 2.0 R T gamma_Nai Nai 1.0 V F R T - gamma_Nao Nao 1.0 V F R T - 1.0 I_ns_K = P_ns_Ca 1.0 2.0 V F 2.0 R T gamma_Ki Ki 1.0 V F R T - gamma_Ko Ko 1.0 V F R T - 1.0

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: calcium_buffers_in_the_myoplasm

Tn_buff = Tn_max Cai Cai + K_mTn CMDN_buff = CMDN_max Cai Cai + K_mCMDN

Component: calcium_fluxes_in_the_SR

i_rel = G_rel Ca_JSR - Cai G_rel = G_rel_max delta_Ca_i2 - delta_Ca_ith K_mrel + delta_Ca_i2 - delta_Ca_ith 1.0 -- t tau_on - t tau_off if calcium_overload = 0.0 G_rel_max 1.0 -- t tau_on - t tau_off otherwise G_rel_max = 0.0 if delta_Ca_i2 < delta_Ca_ith 60.0 otherwiseif calcium_overload = 0.0 0.0 if CSQN_buff < CSQN_th 4.0 otherwiseotherwise CSQN_buff = CSQN_max Ca_JSR Ca_JSR + K_mCSQN i_up = I_up Cai Cai + K_mup i_leak = K_leak Ca_NSR K_leak = I_up Ca_NSR_max i_tr = Ca_NSR - Ca_JSR tau_tr

Component: ionic_concentrations

dd time Nai =- i_Na + i_CaNa + i_Na_b + i_ns_Na + i_NaCa 3.0 + i_NaK 3.0 A_cap V_myo F dd time Cai = i_CaCa + i_p_Ca + i_Ca_b - i_NaCa A_cap 2.0 V_myo F + i_rel V_JSR V_myo + i_leak - i_up V_NSR V_myo dd time Ki =- i_CaK + i_K + i_K1 + i_Kp + i_ns_K +- i_NaK 2.0 A_cap V_myo F dd time Ko = i_CaK + i_K + i_K1 + i_Kp + i_ns_K +- i_NaK 2.0 A_cap V_cleft F dd time Ca_JSR =- i_rel - i_tr V_NSR V_JSR dd time Ca_NSR =- i_leak + i_tr - i_up dd time Ca_foot =- i_CaCa A_cap 2.0 V_myo F R_A_V