Model Mathematics

Component: cell

Component: wal_environment

I_T = 1000 1 vS - vT R_a dd time vS =- I_ionic_s + I_T C_m dd time vT =- I_ionic_t - I_T gam C_m I_ionic_s = I_Cl + I_IR + I_DR + I_Na + I_NaK +- I_HH I_ionic_t = I_Cl_t + I_IR_t + I_DR_t + I_Na_t + I_NaK_t dd time K_i =- f_T I_IR_t + I_DR_t + I_K_rest +- 2 I_NaK_t 1000 1 FF tsi - I_IR + I_DR + I_K_rest + -2 I_NaK 1000 1 FF tsi2 dd time K_t = I_IR_t + I_DR_t + I_K_rest +- 2 I_NaK_t 1000 1 FF tsi - K_t - K_e tau_K dd time K_e = I_IR + I_DR + I_K_rest +- 2 I_NaK 1000 1 FF tsi3 + K_t - K_e tau_K2 dd time Na_i =- f_T I_Na_t + I_Na_rest + 3 I_NaK_t 1000 1 FF tsi - I_Na + I_Na_rest + 3 I_NaK 1000 1 FF tsi2 dd time Na_t = I_Na_t + I_Na_rest + 3 I_NaK_t 1000 1 FF tsi - Na_t - Na_e tau_Na dd time Na_e = I_Na + I_Na_rest + 3 I_NaK 1000 1 FF tsi3 + Na_t - Na_e tau_Na2 E_K = RR TT FF ln K_e K_i E_K_t = RR TT FF ln K_t K_i Cl_i = 156.5 5 +- FF E_K RR TT Cl_o = 156.5 - 5 Cl_i Cl_i_t = 156.5 5 +- FF E_K_t RR TT Cl_o_t = 156.5 - 5 Cl_i_t J_K = vS K_i - K_e -1 FF vS RR TT 1 - -1 FF vS RR TT J_K_t = vT K_i - K_t -1 FF vT RR TT 1 - -1 FF vT RR TT I_HH = 150 if time 0 time < 0.5 150 if time 50 time < 50.5 150 if time 100 time < 100.5 150 if time 150 time < 150.5 150 if time 200 time < 200.5 150 if time 250 time < 250.5 150 if time 300 time < 300.5 150 if time 350 time < 350.5 150 if time 400 time < 400.5 0 otherwise

Component: sarco_Cl_channel

a = 1 1 + vS - V_a A_a J_Cl = vS Cl_i - Cl_o FF vS RR TT 1 - FF vS RR TT g_Cl = g_Cl_bar a 4 I_Cl = g_Cl J_Cl 45

Component: sarco_IR_channel

K_R = K_e - del E_K FF RR TT g_IR_bar = G_K K_R 2 K_K + K_R 2 y = 1 - 1 + K_S 1 + K_R 2 K_K S_i 2 2 1 - del vS FF RR TT -1 g_IR = g_IR_bar y I_IR = g_IR 1 if J_K > 0 0 otherwise J_K 50

Component: sarco_DR_channel

alpha_n = alpha_n_bar vS - V_n 1 -- vS - V_n K_alpha_n beta_n = beta_n_bar - vS - V_n K_beta_n h_K_inf = 1 1 + vS - V_h_K_inf A_h_K_inf tau_h_K = 1000 - vS + 40 25.75 dd time n = alpha_n 1 - n - beta_n n dd time h_K = h_K_inf - h_K tau_h_K g_DR = g_K_bar n 4 h_K I_DR = g_DR J_K 50

Component: sarco_Na_channel

alpha_h = alpha_h_bar - vS - V_h K_alpha_h beta_h = beta_h_bar 1 +- vS - V_h K_beta_h alpha_m = alpha_m_bar vS - V_m 1 -- vS - V_m K_alpha_m beta_m = beta_m_bar - vS - V_m K_beta_m S_inf = 1 1 + vS - V_S_inf A_S_inf tau_S = 8571 0.2 + 5.65 vS + V_tau 100 2 J_Na = vS Na_i - Na_e -1 FF vS RR TT 1 - -1 FF vS RR TT dd time m = alpha_m 1 - m - beta_m m dd time h = alpha_h 1 - h - beta_h h dd time S = S_inf - S tau_S g_Na = g_Na_bar m 3 h S I_Na = g_Na J_Na 75

Component: sarco_NaK_channel

sig = 1 7 Na_e 67.3 - 1 f1 = 1 + 0.12 -0.1 vS FF RR TT + 0.04 sig - vS FF RR TT -1 I_NaK_bar = FF J_NaK_bar 1 + K_m_K K_e 2 1 + K_m_Na Na_i 3 I_NaK = I_NaK_bar f1

Component: t_Cl_channel

a_t = 1 1 + vT - V_a A_a J_Cl_t = vT Cl_i_t - Cl_o_t FF vT RR TT 1 - FF vT RR TT g_Cl_t = g_Cl_bar a_t 4 I_Cl_t = eta_Cl g_Cl_t J_Cl_t 45

Component: t_IR_channel

K_R_t = K_t - del E_K_t FF RR TT g_IR_bar_t = G_K K_R_t 2 K_K + K_R_t 2 y_t = 1 - 1 + K_S 1 + K_R_t 2 K_K S_i 2 2 1 - del vT FF RR TT -1 g_IR_t = g_IR_bar_t y_t I_IR_t = eta_IR g_IR_t J_K_t 50

Component: t_DR_channel

alpha_n_t = alpha_n_bar vT - V_n 1 -- vT - V_n K_alpha_n beta_n_t = beta_n_bar - vT - V_n K_beta_n h_K_inf_t = 1 1 + vT - V_h_K_inf A_h_K_inf tau_h_K_t = 1 - vT + 40 25.75 dd time n_t = alpha_n_t 1 - n_t - beta_n_t n_t dd time h_K_t = h_K_inf_t - h_K_t tau_h_K_t g_DR_t = g_K_bar n_t 4 h_K_t I_DR_t = eta_DR g_DR_t J_K_t 50

Component: t_Na_channel

alpha_h_t = alpha_h_bar - vT - V_h K_alpha_h beta_h_t = beta_h_bar 1 +- vT - V_h K_beta_h alpha_m_t = alpha_m_bar vT - V_m 1 -- vT - V_m K_alpha_m beta_m_t = beta_m_bar - vT - V_m K_beta_m S_inf_t = 1 1 + vT - V_S_inf A_S_inf tau_S_t = 8571 0.2 + 5.65 vT + V_tau 100 2 J_Na_t = vT Na_i - Na_t -1 FF vT RR TT 1 - -1 FF vT RR TT dd time m_t = alpha_m_t 1 - m_t - beta_m_t m_t dd time h_t = alpha_h_t 1 - h_t - beta_h_t h_t dd time S_t = S_inf_t - S_t tau_S_t g_Na_t = g_Na_bar m_t 3 h_t S_t I_Na_t = eta_Na g_Na_t J_Na_t 75

Component: t_NaK_channel

sig_t = 1 7 Na_t 67.3 - 1 f1_t = 1 + 0.12 -0.1 vT FF RR TT + 0.04 sig_t - vT FF RR TT -1 I_NaK_bar_t = FF J_NaK_bar 1 + K_m_K K_t 2 1 + K_m_Na Na_i 3 I_NaK_t = eta_NaK I_NaK_bar_t f1_t

Component: sternrios

k_C = 0.5 alpha1 vT - Vbar 8 K k_Cm = 0.5 alpha1 Vbar - vT 8 K dd time C_0 =- k_L C_0 + k_Lm O_0 + -4 k_C C_0 + k_Cm C_1 dd time O_0 = k_L C_0 +- k_Lm O_0 + -4 k_C O_0 f + f k_Cm O_1 dd time C_1 = 4 k_C C_0 +- k_Cm C_1 +- k_L C_1 f + f k_Lm O_1 + -3 k_C C_1 + 2 k_Cm C_2 dd time O_1 = k_L C_1 f +- k_Lm f O_1 + 4 k_C O_0 f +- f k_Cm O_1 + -3 k_C O_1 f + 2 f k_Cm O_2 dd time C_2 = 3 k_C C_1 + -2 k_Cm C_2 +- k_L C_2 f 2 + f 2 k_Lm O_2 + -2 k_C C_2 + 3 k_Cm C_3 dd time O_2 = 3 k_C O_1 f + -2 f k_Cm O_2 + k_L C_2 f 2 +- k_Lm f 2 O_2 + -2 k_C O_2 f + 3 f k_Cm O_3 dd time C_3 = 2 k_C C_2 + -3 k_Cm C_3 +- k_L C_3 f 3 + k_Lm f 3 O_3 +- k_C C_3 + 4 k_Cm C_4 dd time O_3 = k_L C_3 f 3 +- k_Lm f 3 O_3 + 2 k_C O_2 f + -3 k_Cm f O_3 +- k_C O_3 f + 4 f k_Cm O_4 dd time C_4 = k_C C_3 + -4 k_Cm C_4 +- k_L C_4 f 4 + k_Lm f 4 O_4 dd time O_4 = k_C O_3 f + -4 f k_Cm O_4 + k_L C_4 f 4 +- k_Lm f 4 O_4

Component: razumova

V_o = 0.95 L_x π R_R 2 V_1 = 0.01 V_o V_2 = 0.99 V_o V_SR = 0.05 L_x π R_R 2 V_SR1 = 0.01 V_SR V_SR2 = 0.99 V_SR T_0 = T_tot +- Ca_T_2 +- Ca_CaT2 +- D_0 +- D_1 +- D_2 +- A_1 +- A_2 dd time Ca_1 = i2 O_0 + O_1 + O_2 + O_3 + O_4 Ca_SR1 - Ca_1 V_1 - nu_SR Ca_1 Ca_1 + K_SR V_1 + L_e Ca_SR1 - Ca_1 V_1 +- tau_R Ca_1 - Ca_2 V_1 +- k_P_on Ca_1 P_tot +- Ca_P1 +- Mg_P1 +- k_P_off Ca_P1 +- k_CATP_on Ca_1 ATP1 +- k_CATP_off Ca_ATP1 dd time Ca_SR1 =- i2 O_0 + O_1 + O_2 + O_3 + O_4 Ca_SR1 - Ca_1 V_SR1 + nu_SR Ca_1 Ca_1 + K_SR V_SR1 +- L_e Ca_SR1 - Ca_1 V_SR1 +- tau_SR_R Ca_SR1 - Ca_SR2 V_SR1 +- k_Cs_on Ca_SR1 Cs_tot - Ca_Cs1 +- k_Cs_off Ca_Cs1 dd time Ca_2 =- nu_SR Ca_2 Ca_2 + K_SR V_2 + L_e Ca_SR2 +- Ca_2 V_2 + tau_R Ca_1 - Ca_2 V_2 +- k_T_on Ca_2 T_0 +- k_T_off Ca_T_2 + k_T_on Ca_2 Ca_T_2 +- k_T_off Ca_CaT2 + k_T_on Ca_2 D_0 +- k_T_off D_1 + k_T_on Ca_2 D_1 +- k_T_off D_2 +- k_P_on Ca_2 P_tot +- Ca_P2 +- Mg_P2 +- k_P_off Ca_P2 +- k_CATP_on Ca_2 ATP2 +- k_CATP_off Ca_ATP2 dd time Ca_SR2 = nu_SR Ca_2 Ca_2 + K_SR V_SR2 +- L_e Ca_SR2 +- Ca_2 V_SR2 + tau_SR_R Ca_SR1 +- Ca_SR2 V_SR2 +- k_Cs_on Ca_SR2 Cs_tot +- Ca_Cs2 +- k_Cs_off Ca_Cs2 - 1000 1 A_p P_SR 0.001 1 Ca_SR2 - PP 1 if P_SR 0.001 1 Ca_SR2 - PP > 0 0 otherwise 0.001 1 P_SR Ca_SR2 - B_p P_C_SR PP - P_SR 0.001 1 Ca_SR2 1 if PP - P_SR 0.001 1 Ca_SR2 > 0 0 otherwise dd time Ca_T_2 = k_T_on Ca_2 T_0 +- k_T_off Ca_T_2 +- k_T_on Ca_2 Ca_T_2 + k_T_off Ca_CaT2 +- k_0_on Ca_T_2 + k_0_off D_1 dd time Ca_P1 = k_P_on Ca_1 P_tot +- Ca_P1 +- Mg_P1 +- k_P_off Ca_P1 dd time Ca_P2 = k_P_on Ca_2 P_tot +- Ca_P2 +- Mg_P2 +- k_P_off Ca_P2 dd time Mg_P1 = k_Mg_on P_tot +- Ca_P1 +- Mg_P1 Mg1 +- k_Mg_off Mg_P1 dd time Mg_P2 = k_Mg_on P_tot +- Ca_P2 +- Mg_P2 Mg2 +- k_Mg_off Mg_P2 dd time Ca_Cs1 = k_Cs_on Ca_SR1 Cs_tot +- Ca_Cs1 +- k_Cs_off Ca_Cs1 dd time Ca_Cs2 = k_Cs_on Ca_SR2 Cs_tot +- Ca_Cs2 +- k_Cs_off Ca_Cs2 dd time Ca_ATP1 = k_CATP_on Ca_1 ATP1 +- k_CATP_off Ca_ATP1 +- tau_ATP Ca_ATP1 +- Ca_ATP2 V_1 dd time Ca_ATP2 = k_CATP_on Ca_2 ATP2 +- k_CATP_off Ca_ATP2 + tau_ATP Ca_ATP1 +- Ca_ATP2 V_2 dd time Mg_ATP1 = k_MATP_on Mg1 ATP1 +- k_MATP_off Mg_ATP1 +- tau_ATP Mg_ATP1 +- Mg_ATP2 V_1 dd time Mg_ATP2 = k_MATP_on Mg2 ATP2 +- k_MATP_off Mg_ATP2 + tau_ATP Mg_ATP1 +- Mg_ATP2 V_2 dd time ATP1 =- k_CATP_on Ca_1 ATP1 +- k_CATP_off Ca_ATP1 +- k_MATP_on Mg1 ATP1 +- k_MATP_off Mg_ATP1 +- tau_ATP ATP1 +- ATP2 V_1 dd time ATP2 =- k_CATP_on Ca_2 ATP2 +- k_CATP_off Ca_ATP2 +- k_MATP_on Mg2 ATP2 +- k_MATP_off Mg_ATP2 + tau_ATP ATP1 +- ATP2 V_2 dd time Mg1 =- k_Mg_on P_tot +- Ca_P1 +- Mg_P1 Mg1 +- k_Mg_off Mg_P1 +- k_MATP_on Mg1 ATP1 +- k_MATP_off Mg_ATP1 +- tau_Mg Mg1 +- Mg2 V_1 dd time Mg2 =- k_Mg_on P_tot +- Ca_P2 +- Mg_P2 Mg2 +- k_Mg_off Mg_P2 +- k_MATP_on Mg2 ATP2 +- k_MATP_off Mg_ATP2 + tau_Mg Mg1 +- Mg2 V_2 dd time Ca_CaT2 = k_T_on Ca_2 Ca_T_2 +- k_T_off Ca_CaT2 +- k_Ca_on Ca_CaT2 + k_Ca_off D_2 dd time D_0 =- k_T_on Ca_2 D_0 + k_T_off D_1 + k_0_on T_0 +- k_0_off D_0 dd time D_1 = k_T_on Ca_2 D_0 +- k_T_off D_1 + k_0_on Ca_T_2 +- k_0_off D_1 +- k_T_on Ca_2 D_1 + k_T_off D_2 dd time D_2 = k_T_on Ca_2 D_1 +- k_T_off D_2 + k_Ca_on Ca_CaT2 +- k_Ca_off D_2 +- f_o D_2 + f_p A_1 + g_o A_2 dd time A_1 = f_o D_2 +- f_p A_1 + h_p A_2 +- h_o A_1 dd time A_2 =- h_p A_2 + h_o A_1 +- g_o A_2 dd time P = 0.001 1 h_o A_1 - h_p A_2 + -1 b_p P + -1 k_p P - P_SR V_2 dd time P_SR = k_p P - P_SR V_SR2 - 1 A_p P_SR 0.001 1 Ca_SR2 - PP 1 if P_SR 0.001 1 Ca_SR2 - PP > 0 0 otherwise 0.001 1 P_SR Ca_SR2 - B_p P_C_SR PP - P_SR 0.001 1 Ca_SR2 1 if PP - P_SR 0.001 1 Ca_SR2 > 0 0 otherwise dd time P_C_SR = 1 A_p P_SR 0.001 1 Ca_SR2 - PP 1 if P_SR 0.001 1 Ca_SR2 - PP > 0 0 otherwise 0.001 1 P_SR Ca_SR2 - B_p P_C_SR PP - P_SR 0.001 1 Ca_SR2 1 if PP - P_SR 0.001 1 Ca_SR2 > 0 0 otherwise