Model Mathematics

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Component: environment

Component: membrane

\frac{d}{d time} (V) = (- (\frac{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 = \frac{R T}{F} \ln (\frac{Nao}{Nai})

Component: fast_sodium_current_m_gate

alpha_m = \frac{0.32 (V + 47.13)}{1.0 - (ⅇ^{(-0.1) (V + 47.13)})} beta_m = 0.08 ⅇ^{\frac{- V}{11.0}} \frac{d}{d time} (m) = alpha_m (1.0 - m) - (beta_m m)

Component: fast_sodium_current_h_gate

alpha_h = \{\begin{matrix} 0.135 ⅇ^{\frac{80.0 + V}{-6.8}} if V < -40.0 \\ 0.0 otherwise \end{matrix} beta_h = \{\begin{matrix} 3.56 ⅇ^{0.079 V} + 31.0E5 ⅇ^{0.35 V} if V < -40.0 \\ \frac{1.0}{0.13 (1.0 + ⅇ^{\frac{- (V + 10.66)}{11.1}})} otherwise \end{matrix} \frac{d}{d time} (h) = alpha_h (1.0 - h) - (beta_h h)

Component: fast_sodium_current_j_gate

alpha_j = \{\begin{matrix} ((-127140.0) ⅇ^{0.2444 V} - (0.00003474 ⅇ^{(-0.04391) V})) \frac{V + 37.78}{1.0 + ⅇ^{0.311 (V + 79.23)}} if V < -40.0 \\ 0.0 otherwise \end{matrix} beta_j = \{\begin{matrix} \frac{0.1212 ⅇ^{(-0.01052) V}}{1.0 + ⅇ^{(-0.1378) (V + 40.14)}} if V < -40.0 \\ \frac{0.3 ⅇ^{(-0.0000002535) V}}{1.0 + ⅇ^{(-0.1) (V + 32.0)}} otherwise \end{matrix} \frac{d}{d 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 = \frac{R T}{2.0 F} \ln (\frac{Cao}{Cai})

Component: slow_calcium_current_d_gate

alpha_d = \frac{14.98}{16.68 {(2.0 π)}^{0.5} ⅇ^{\frac{- ({(\frac{V - 22.36}{16.68})}^{2.0})}{2.0}}} beta_d = 0.1471 - (\frac{5.3}{14.93 {(2.0 π)}^{0.5} ⅇ^{\frac{- ({(\frac{V - 6.27}{14.93})}^{2.0})}{2.0}}}) \frac{d}{d time} (d) = alpha_d (1.0 - d) - (beta_d d)

Component: slow_calcium_current_f_gate

alpha_f = \frac{6.87E-3}{1.0 + ⅇ^{\frac{6.1546 - V}{-6.12}}} beta_f = \frac{0.069 ⅇ^{(-0.11) (V + 9.825) + 0.011}}{1.0 + ⅇ^{(-0.278) (V + 9.825)} - (5.75E-4)} \frac{d}{d time} (f) = alpha_f (1.0 - f) - (beta_f f)

Component: slow_calcium_current_f_Ca_gate

f_Ca = \frac{1.0}{1.0 + \frac{Cai}{Km_Ca}}

Component: transient_outward_current

i_to = g_to_max r t (V - E_to) E_to = \frac{R T}{F} \ln (\frac{0.043 Nao + Ko}{0.043 Nai + Ki})

Component: transient_outward_current_r_gate

\frac{d}{d time} (r) = alpha_r (1.0 - r) - (beta_r r) F1_beta_r_e = 0.00006 V alpha_r = \frac{F1_alpha_r}{F2_alpha_r} F1_alpha_r = F1_alpha_r_a ⅇ^{F1_alpha_r_b (V + F1_alpha_r_c) + F1_alpha_r_d} + F1_alpha_r_e F2_alpha_r = F2_alpha_r_a ⅇ^{F2_alpha_r_b (V + F2_alpha_r_c) + F2_alpha_r_d} + F2_alpha_r_e beta_r = \frac{F1_beta_r}{F2_beta_r} F1_beta_r = F1_beta_r_a ⅇ^{F1_beta_r_b (V + F1_beta_r_c) + F1_beta_r_d} + F1_beta_r_e F2_beta_r = F2_beta_r_a ⅇ^{F2_beta_r_b (V + F2_beta_r_c) + F2_beta_r_d} + F2_beta_r_e

Component: transient_outward_current_t_gate

\frac{d}{d 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 = \frac{F1_alpha_t}{F2_alpha_t} F1_alpha_t = F1_alpha_t_a ⅇ^{F1_alpha_t_b (V + F1_alpha_t_c) + F1_alpha_t_d} + F1_alpha_t_e F2_alpha_t = F2_alpha_t_a ⅇ^{F2_alpha_t_b (V + F2_alpha_t_c) + F2_alpha_t_d} + F2_alpha_t_e beta_t = \frac{F1_beta_t}{F2_beta_t} F1_beta_t = F1_beta_t_a ⅇ^{F1_beta_t_b (V + F1_beta_t_c) + F1_beta_t_d} + F1_beta_t_e F2_beta_t = F2_beta_t_a ⅇ^{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 = \frac{R T}{F} \frac{\ln (0.01833 Nao + Ko)}{\ln (0.01833 Nai + Ki)}

Component: slowly_activating_delayed_rectifier_potassium_current_Xs_gate

\frac{d}{d time} (Xs) = alpha_Xs (1.0 - Xs) - (beta_Xs Xs) alpha_Xs = \frac{F1_alpha_Xs}{F2_alpha_Xs} F1_alpha_Xs = F1_alpha_Xs_a ⅇ^{F1_alpha_Xs_b (V + F1_alpha_Xs_c) + F1_alpha_Xs_d} + F1_alpha_Xs_e F2_alpha_Xs = F2_alpha_Xs_a ⅇ^{F2_alpha_Xs_b (V + F2_alpha_Xs_c) + F2_alpha_Xs_d} + F2_alpha_Xs_e beta_Xs = \frac{F1_beta_Xs}{F2_beta_Xs} F1_beta_Xs = F1_beta_Xs_a ⅇ^{F1_beta_Xs_b (V + F1_beta_Xs_c) + F1_beta_Xs_d} + F1_beta_Xs_e F2_beta_Xs = F2_beta_Xs_a ⅇ^{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 \frac{1.0}{FCIKr} Xr (V - E_K) E_K = \frac{R T}{F} \ln (\frac{Ko}{Ki}) FCIKr = FCIKr_a ⅇ^{FCIKr_b (V + FCIKr_c) + FCIKr_d} + FCIKr_e

Component: rapidly_activating_delayed_rectifier_potassium_current_Xr_gate

\frac{d}{d time} (Xr) = alpha_Xr (1.0 - Xr) - (beta_Xr Xr) alpha_Xr = \frac{F1_alpha_Xr}{F2_alpha_Xr} F1_alpha_Xr = F1_alpha_Xr_a ⅇ^{F1_alpha_Xr_b (V + F1_alpha_Xr_c) + F1_alpha_Xr_d} + F1_alpha_Xr_e F2_alpha_Xr = F2_alpha_Xr_a ⅇ^{F2_alpha_Xr_b (V + F2_alpha_Xr_c) + F2_alpha_Xr_d} + F2_alpha_Xr_e beta_Xr = \frac{F1_beta_Xr}{F2_beta_Xr} F1_beta_Xr = F1_beta_Xr_a ⅇ^{F1_beta_Xr_b (V + F1_beta_Xr_c) + F1_beta_Xr_d} + F1_beta_Xr_e F2_beta_Xr = F2_beta_Xr_a ⅇ^{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 \frac{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 = \frac{F1_alpha_K1}{F2_alpha_K1} F1_alpha_K1 = F1_alpha_K1_a ⅇ^{F1_alpha_K1_b (V + F1_alpha_K1_c) + F1_alpha_K1_d} + F1_alpha_K1_e F2_alpha_K1 = F2_alpha_K1_a ⅇ^{F2_alpha_K1_b (V + F2_alpha_K1_c) + F2_alpha_K1_d} + F2_alpha_K1_e beta_K1 = \frac{F1_beta_K1 + F2_beta_K1}{F3_beta_K1} F1_beta_K1 = F1_beta_K1_a ⅇ^{F1_beta_K1_b (V + F1_beta_K1_c) + F1_beta_K1_d} + F1_beta_K1_e F2_beta_K1 = F2_beta_K1_a ⅇ^{F2_beta_K1_b (V + F2_beta_K1_c) + F2_beta_K1_d} + F2_beta_K1_e F3_beta_K1 = F3_beta_K1_a ⅇ^{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 = \frac{1.0}{1.0 + 0.1245 ⅇ^{(-0.1) \frac{V F}{R T}} + 0.0365 sigma ⅇ^{\frac{(- V) F}{R T}}} sigma = \frac{1.0}{7.0} (ⅇ^{\frac{Nao}{67.3}} - 1.0) i_NaK = I_NaK f_NaK \frac{1.0}{(1.0 + {(\frac{K_mNai}{Nai})}^{1.5}) \frac{Ko}{Ko + K_mKo}}

Component: Na_Ca_exchanger

i_NaCa = K_NaCa \frac{1.0}{{K_mNa}^{3.0} + {Nao}^{3.0}} \frac{1.0}{K_mCa + Cao} \frac{1.0}{1.0 + K_sat ⅇ^{(eta - 1.0) V \frac{F}{R T}}} (ⅇ^{eta V \frac{F}{R T}} {Nai}^{3.0} Cao - (ⅇ^{(eta - 1.0) V \frac{F}{R T}} {Nao}^{3.0} Cai))

Component: CICR_of_JSR

i_rel = G_rel (Ca_JSR - Cai) G_rel = \{\begin{matrix} G_rel_max \frac{delta_Ca_i2 - delta_Ca_ith}{K_mrel + delta_Ca_i2 - delta_Ca_ith} (1.0 - (ⅇ^{- (\frac{time}{tau_on})})) ⅇ^{\frac{- time}{tau_off}} if calcium_overload = 0.0 \\ G_rel_max (Ca_JSR - Cai) (1.0 - (ⅇ^{\frac{- time}{tau_on}})) ⅇ^{\frac{- time}{tau_off}} otherwise \end{matrix}

Component: Ca_uptake_of_NSR

i_up = I_up \frac{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 = \frac{Ca_NSR - Ca_JSR}{tau_tr}

Component: calcium_buffers_in_the_myoplasm

Tn_buff = Tn_max \frac{Cai}{Cai + K_mTn} CMDN_buff = CMDN_max \frac{Cai}{Cai + K_mCMDN}

Component: calcium_buffers_in_the_JSR

CSQN_buff = CSQN_max \frac{Ca_JSR}{Ca_JSR + K_mCSQN}

Component: ionic_concentrations

\frac{d}{d time} (Nai) = (- (i_Na + i_b_Na + i_NaCa 3.0 + i_NaK 3.0)) \frac{A_cap}{V_myo F} \frac{d}{d time} (Cai) = (i_Ca + i_b_Ca - i_NaCa) \frac{A_cap}{2.0 V_myo F} + i_rel \frac{V_JSR}{V_myo} + (i_leak - i_up) \frac{V_NSR}{V_myo} \frac{d}{d time} (Ki) = (- (i_to + i_Kr + i_K1 + i_Ks + (- (i_NaK 2.0)))) \frac{A_cap}{V_myo F} \frac{d}{d time} (Ko) = (i_to + i_Kr + i_K1 + i_Ks + (- (i_NaK 2.0))) \frac{A_cap}{V_cleft F} \frac{d}{d time} (Ca_JSR) = - (i_rel - (i_tr \frac{V_NSR}{V_JSR})) \frac{d}{d time} (Ca_NSR) = - (i_leak + i_tr - i_up) \frac{d}{d time} (Ca_foot) = (- i_Ca) \frac{A_cap}{2.0 V_myo F} R_A_V

Component: ATP

Component: T

Component: TCa

\frac{\partial}{\partial time} (TCa) = kon (1.0 + S_A_M + {lamda}^{TCa_lamda}) Cai T - (koff TCa)

Component: TMoff

Component: TMon

\frac{\partial}{\partial time} (TMon) = kmon TCa {(1.0 + (TMoncoop + lamda) TMon)}^{TMonpow} TMoff - (kmoff TMon)

Component: M_ATP

\frac{\partial}{\partial time} (M_ATP) = t2 + t14 - t3

Component: M_ADP_Pi

\frac{\partial}{\partial time} (M_ADP_Pi) = t3 + t13 - t4

Component: A_M__ADP_Pi

\frac{\partial}{\partial time} (A_M__ADP_Pi) = t4 - t5

Component: A_M_ADP_Pi

\frac{\partial}{\partial time} (A_M_ADP_Pi) = t5 - (t6 + t13)

Component: A_M__ADP

\frac{\partial}{\partial time} (A_M__ADP) = t6 - (t7 + t11)

Component: A_M_ADP

\frac{\partial}{\partial time} (A_M_ADP) = t7 - (t8 + t10)

Component: A_M

\frac{\partial}{\partial time} (A_M) = t8 - (t9 + t1)

Component: A__M_ATP

\frac{\partial}{\partial time} (A__M_ATP) = t1 - t2

Component: M

\frac{\partial}{\partial time} (M) = t9 + t12 - t14

Component: M_ADP

\frac{\partial}{\partial time} (M_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 \frac{(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 = \frac{v^{Nv}}{v^{Nv} + {v50}^{Nv}}

Component: F

F = Fmax \frac{{Cai}^{nh}}{{Cai}^{nh} + {Ca50}^{nh}}

Model Mathematics

Component: environment

Component: membrane

Component: fast_sodium_current

Component: fast_sodium_current_m_gate

Component: fast_sodium_current_h_gate

Component: fast_sodium_current_j_gate

Component: slow_calcium_current

Component: slow_calcium_current_d_gate

Component: slow_calcium_current_f_gate

Component: slow_calcium_current_f_Ca_gate

Component: transient_outward_current

Component: transient_outward_current_r_gate

Component: transient_outward_current_t_gate

Component: slowly_activating_delayed_rectifier_potassium_current

Component: slowly_activating_delayed_rectifier_potassium_current_Xs_gate

Component: rapidly_activating_delayed_rectifier_potassium_current

Component: rapidly_activating_delayed_rectifier_potassium_current_Xr_gate

Component: inward_rectifier_potassium_current

Component: inward_rectifier_potassium_current_K1_gate

Component: calcium_background_current

Component: sodium_background_current

Component: sodium_potassium_pump

Component: Na_Ca_exchanger

Component: CICR_of_JSR

Component: Ca_uptake_of_NSR

Component: Ca_leakage_of_NSR

Component: translocation_of_Ca_from_NSR_to_JSR

Component: calcium_buffers_in_the_myoplasm

Component: calcium_buffers_in_the_JSR

Component: ionic_concentrations

Component: ATP

Component: T

Component: TCa

Component: TMoff

Component: TMon

Component: M_ATP

Component: M_ADP_Pi

Component: A_M__ADP_Pi

Component: A_M_ADP_Pi

Component: A_M__ADP

Component: A_M_ADP

Component: A_M

Component: A__M_ATP

Component: M

Component: M_ADP

Component: S_A_M

Component: t1

Component: t2

Component: t3

Component: t4

Component: t5

Component: t6

Component: t7

Component: t8

Component: t9

Component: t10

Component: t11

Component: t12

Component: t13

Component: t14

Component: v_factor

Component: F

Component: parameters