Model Mathematics

Component: environment

Component: membrane

dd time V =- 1.0 Cm i_Na + i_Ca_L + i_Ca_T + i_Kr + i_Ks + i_K1 + i_Kp + i_NaCa + i_p_Ca + i_Na_b + i_Ca_b + i_NaK + i_ns_Ca + i_s + I_st

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: 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

Component: T_type_Ca_channel

i_Ca_T = g_Ca_T b 2.0 g V - E_Ca E_Ca = R T 2.0 F ln Cao Cai

Component: T_type_Ca_channel_b_gate

dd time b = b_infinity - b tau_b b_infinity = 1.0 1.0 +- V + 14.0 10.8 tau_b = 3.7 + 6.1 1.0 + 25.0 + V 4.5

Component: T_type_Ca_channel_g_gate

dd time g = g_infinity - g tau_g g_infinity = 1.0 1.0 + V + 60.0 5.6 tau_g = 12.0 if V > 0.0 -0.875 V + 12.0 otherwise

Component: rapid_time_dependent_potassium_current

g_Kr = 0.02614 Ko 5.4 E_Kr = R T F ln Ko Ki i_Kr = g_Kr Xr Rr V - E_Kr

Component: rapid_time_dependent_potassium_current_Xr_gate

dd time Xr = Xr_infinity - Xr tau_Xr Xr_infinity = 1.0 1.0 +- V + 21.5 7.5 tau_Xr = 1.0 0.00138 V + 14.2 1.0 - -0.123 V + 14.2 + 0.00061 V + 38.9 0.145 V + 38.9 - 1.0

Component: rapid_time_dependent_potassium_current_Rr_gate

Rr = 1.0 1.0 + V + 9.0 22.4

Component: slow_time_dependent_potassium_current

g_Ks = 0.057 + 0.19 1.0 + -7.2 + P_Ca 0.6 E_Ks = R T F ln Ko + P_NaK Nao Ki + P_NaK Nai P_Ca =-log10 Cai + 3.0 i_Ks = g_Ks Xs 2.0 V - E_Ks

Component: slow_time_dependent_potassium_current_Xs_gate

dd time Xs = Xs_infinity - Xs tau_Xs Xs_infinity = 1.0 1.0 +- V + -1.5 16.7 tau_Xs = 1.0 0.0000719 V + 30.0 1.0 - -0.148 V + 30.0 + 0.000131 V + 30.0 0.0687 V + 30.0 - 1.0

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 V + 5.476 - E_K1 12.45 + V - E_K1 + 594.31 16.2 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: stretch_activated_current

i_s = g_s V - E_s

Component: calcium_buffers_in_the_myoplasm

TRPN_buff = TRPN_max Cai Cai + K_mTRPN CMDN_buff = CMDN_max Cai Cai + K_mCMDN Ca_JSR_new = b1 2.0 + 4.0 c1 - b1 2.0 delta_Ca_JSR = Ca_JSR_old - Ca_JSR_new delta_Cai = Cai_old - Cai b1 = K_mCSQN - CSQN_max + CSQN_buff + delta_Ca_JSR + Ca_JSR_old c1 = K_mCSQN CSQN_buff + delta_Ca_JSR + Ca_JSR_old Cai = 2.0 3.0 b 2.0 - 3.0 c cosarccos 9.0 b c - 2.0 b 3.0 + 27.0 d 2.0 b 2.0 - 3.0 c 3.0 2.0 3.0 - b 3.0 b = CMDN_max + TRPN_max + K_mTRPN + K_mCMDN - Ca_total c = K_mCMDN K_mTRPN + TRPN_max K_mCMDN + CMDN_max K_mTRPN - Ca_total K_mTRPN + K_mCMDN d =- K_mTRPN K_mCMDN Ca_total Ca_total = TRPN_buff + CMDN_buff + delta_Cai + Cai_old

Component: calcium_fluxes_in_the_SR

i_rel = G_rel Ca_JSR_new - 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_new Ca_JSR_new + 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_new 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 Ki =- i_CaK + i_Kr + i_Ks + i_K1 + i_Kp + i_ns_K +- i_NaK 2.0 A_cap V_myo F dd time Ko = i_CaK + i_Kr + i_Ks + i_K1 + i_Kp + i_ns_K +- i_NaK 2.0 A_cap V_cleft F 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