Model Mathematics

Component: environment

Component: membrane

dd time V =- 1.0 Cm i_Na + i_Ca + i_to + i_Kr + i_Ks + i_K1 + i_NaCa + i_NaK + i_b_Na + i_b_Ca + 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 + 31.0E5 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: slow_calcium_current

i_Ca = g_Ca_max d f f_Ca V - E_Ca E_Ca = R T 2.0 F ln Cao Cai

Component: slow_calcium_current_d_gate

alpha_d = 14.98 16.68 2.0 π 0.5 - V - 22.36 16.68 2.0 2.0 beta_d = 0.1471 - 5.3 14.93 2.0 π 0.5 - V - 6.27 14.93 2.0 2.0 dd time d = alpha_d 1.0 - d - beta_d d

Component: slow_calcium_current_f_gate

alpha_f = 6.87E-3 1.0 + 6.1546 - V -6.12 beta_f = 0.069 -0.11 V + 9.825 + 0.011 1.0 + -0.278 V + 9.825 - 5.75E-4 dd time f = alpha_f 1.0 - f - beta_f f

Component: slow_calcium_current_f_Ca_gate

f_Ca = 1.0 1.0 + Cai Km_Ca

Component: transient_outward_current

i_to = g_to_max r t V - E_to E_to = R T F ln 0.043 Nao + Ko 0.043 Nai + Ki

Component: transient_outward_current_r_gate

dd time r = alpha_r 1.0 - r - beta_r r F1_beta_r_e = 0.00006 V alpha_r = F1_alpha_r F2_alpha_r F1_alpha_r = F1_alpha_r_a F1_alpha_r_b V + F1_alpha_r_c + F1_alpha_r_d + F1_alpha_r_e F2_alpha_r = F2_alpha_r_a F2_alpha_r_b V + F2_alpha_r_c + F2_alpha_r_d + F2_alpha_r_e beta_r = F1_beta_r F2_beta_r F1_beta_r = F1_beta_r_a F1_beta_r_b V + F1_beta_r_c + F1_beta_r_d + F1_beta_r_e F2_beta_r = F2_beta_r_a F2_beta_r_b V + F2_beta_r_c + F2_beta_r_d + F2_beta_r_e

Component: transient_outward_current_t_gate

dd time t = alpha_t 1.0 - t - beta_t t F1_alpha_t_e = 0.00007 V F1_beta_t_e = 0.0001215 V alpha_t = F1_alpha_t F2_alpha_t F1_alpha_t = F1_alpha_t_a F1_alpha_t_b V + F1_alpha_t_c + F1_alpha_t_d + F1_alpha_t_e F2_alpha_t = F2_alpha_t_a F2_alpha_t_b V + F2_alpha_t_c + F2_alpha_t_d + F2_alpha_t_e beta_t = F1_beta_t F2_beta_t F1_beta_t = F1_beta_t_a F1_beta_t_b V + F1_beta_t_c + F1_beta_t_d + F1_beta_t_e F2_beta_t = F2_beta_t_a F2_beta_t_b V + F2_beta_t_c + F2_beta_t_d + F2_beta_t_e

Component: slowly_activating_delayed_rectifier_potassium_current

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

Component: slowly_activating_delayed_rectifier_potassium_current_Xs_gate

dd time Xs = alpha_Xs 1.0 - Xs - beta_Xs Xs alpha_Xs = F1_alpha_Xs F2_alpha_Xs F1_alpha_Xs = F1_alpha_Xs_a F1_alpha_Xs_b V + F1_alpha_Xs_c + F1_alpha_Xs_d + F1_alpha_Xs_e F2_alpha_Xs = F2_alpha_Xs_a F2_alpha_Xs_b V + F2_alpha_Xs_c + F2_alpha_Xs_d + F2_alpha_Xs_e beta_Xs = F1_beta_Xs F2_beta_Xs F1_beta_Xs = F1_beta_Xs_a F1_beta_Xs_b V + F1_beta_Xs_c + F1_beta_Xs_d + F1_beta_Xs_e F2_beta_Xs = F2_beta_Xs_a F2_beta_Xs_b V + F2_beta_Xs_c + F2_beta_Xs_d + F2_beta_Xs_e

Component: rapidly_activating_delayed_rectifier_potassium_current

i_Kr = g_Kr_max 1.0 FCIKr Xr V - E_K E_K = R T F ln Ko Ki FCIKr = FCIKr_a FCIKr_b V + FCIKr_c + FCIKr_d + FCIKr_e

Component: rapidly_activating_delayed_rectifier_potassium_current_Xr_gate

dd time Xr = alpha_Xr 1.0 - Xr - beta_Xr Xr alpha_Xr = F1_alpha_Xr F2_alpha_Xr F1_alpha_Xr = F1_alpha_Xr_a F1_alpha_Xr_b V + F1_alpha_Xr_c + F1_alpha_Xr_d + F1_alpha_Xr_e F2_alpha_Xr = F2_alpha_Xr_a F2_alpha_Xr_b V + F2_alpha_Xr_c + F2_alpha_Xr_d + F2_alpha_Xr_e beta_Xr = F1_beta_Xr F2_beta_Xr F1_beta_Xr = F1_beta_Xr_a F1_beta_Xr_b V + F1_beta_Xr_c + F1_beta_Xr_d + F1_beta_Xr_e F2_beta_Xr = F2_beta_Xr_a F2_beta_Xr_b V + F2_beta_Xr_c + F2_beta_Xr_d + F2_beta_Xr_e

Component: inward_rectifier_potassium_current

i_K1 = g_K1_max alpha_K1 alpha_K1 + beta_K1 V - E_K + Vs

Component: inward_rectifier_potassium_current_K1_gate

F2_alpha_K1_c = 206.0 - E_K F2_beta_K1_c = -16.0 - E_K F1_beta_K1_c = 94.0 - E_K F3_beta_K1_c = 4.0 - E_K alpha_K1 = F1_alpha_K1 F2_alpha_K1 F1_alpha_K1 = F1_alpha_K1_a F1_alpha_K1_b V + F1_alpha_K1_c + F1_alpha_K1_d + F1_alpha_K1_e F2_alpha_K1 = F2_alpha_K1_a F2_alpha_K1_b V + F2_alpha_K1_c + F2_alpha_K1_d + F2_alpha_K1_e beta_K1 = F1_beta_K1 + F2_beta_K1 F3_beta_K1 F1_beta_K1 = F1_beta_K1_a F1_beta_K1_b V + F1_beta_K1_c + F1_beta_K1_d + F1_beta_K1_e F2_beta_K1 = F2_beta_K1_a F2_beta_K1_b V + F2_beta_K1_c + F2_beta_K1_d + F2_beta_K1_e F3_beta_K1 = F3_beta_K1_a F3_beta_K1_b V + F3_beta_K1_c + F3_beta_K1_d + F3_beta_K1_e

Component: calcium_background_current

i_b_Ca = g_b_Ca_max V - E_Ca

Component: sodium_background_current

i_b_Na = g_b_Na_max V - E_Na

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: 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: CICR_of_JSR

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 -- time tau_on - time tau_off if calcium_overload = 0.0 G_rel_max Ca_JSR - Cai 1.0 -- time tau_on - time tau_off otherwise

Component: Ca_uptake_of_NSR

i_up = I_up Cai Cai + K_mup

Component: Ca_leakage_of_NSR

i_leak = K_leak Ca_NSR

Component: translocation_of_Ca_from_NSR_to_JSR

i_tr = Ca_NSR - Ca_JSR tau_tr

Component: calcium_buffers_in_the_myoplasm

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

Component: calcium_buffers_in_the_JSR

CSQN_buff = CSQN_max Ca_JSR Ca_JSR + K_mCSQN

Component: ionic_concentrations

dd time Nai =- i_Na + i_b_Na + i_NaCa 3.0 + i_NaK 3.0 A_cap V_myo F dd time Cai = i_Ca + i_b_Ca - 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_to + i_Kr + i_K1 + i_Ks +- i_NaK 2.0 A_cap V_myo F dd time Ko = i_to + i_Kr + i_K1 + i_Ks +- 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_Ca A_cap 2.0 V_myo F R_A_V

Component: ATP

Component: T

Component: TCa

timeTCa= kon 1.0 + S_A_M + lamda TCa_lamda Cai T - koff TCa

Component: TMoff

Component: TMon

timeTMon= kmon TCa 1.0 + TMoncoop + lamda TMon TMonpow TMoff - kmoff TMon

Component: M_ATP

timeM_ATP= t2 + t14 - t3

Component: M_ADP_Pi

timeM_ADP_Pi= t3 + t13 - t4

Component: A_M__ADP_Pi

timeA_M__ADP_Pi= t4 - t5

Component: A_M_ADP_Pi

timeA_M_ADP_Pi= t5 - t6 + t13

Component: A_M__ADP

timeA_M__ADP= t6 - t7 + t11

Component: A_M_ADP

timeA_M_ADP= t7 - t8 + t10

Component: A_M

timeA_M= t8 - t9 + t1

Component: A__M_ATP

timeA__M_ATP= t1 - t2

Component: M

timeM= t9 + t12 - t14

Component: M_ADP

timeM_ADP= t10 + t11 - t12

Component: S_A_M

S_A_M= A_M_ADP_Pi + A_M__ADP + A_M_ADP + A_M

Component: t1

t1= k1 ATP A_M - k_1 A__M_ATP

Component: t2

t2= k2 1.0 + v_factor v_detach A__M_ATP

Component: t3

t3= k3 M_ATP - k_3 M_ADP_Pi

Component: t4

t4= k4 M_ADP_Pi - k_4 1.0 + v_factor v_detach A_M__ADP_Pi

Component: t5

t5= k5 TMon k5_lamda lamda + 0.4 1.0 + k5_xb S_A_M 2.0 A_M__ADP_Pi - k_5 A_M_ADP_Pi

Component: t6

t6= k6 A_M_ADP_Pi - k_6 A_M__ADP

Component: t7

t7= k7 A_M__ADP k7_base - k7_lamda lamda + v 1.0 + k7_force F

Component: t8

t8= k8 A_M_ADP - k_8 A_M

Component: t9

t9= k9 v_factor A_M

Component: t10

t10= k10 v_factor A_M_ADP

Component: t11

t11= k11 v_factor A_M__ADP

Component: t12

t12= k12 M_ADP

Component: t13

t13= k13 v_factor A_M_ADP_Pi

Component: t14

t14= k14 ATP M

Component: v_factor

v_factor= v Nv v Nv + v50 Nv

Component: F

F= Fmax Cai nh Cai nh + Ca50 nh

Component: parameters