Model Mathematics

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Component: environment

Component: membrane

\frac{d}{d time} (V) = \frac{- (i_Na + i_K1 + i_to + i_Kur_d + i_Kr + i_Ks + i_Ca + i_Cl_Ca + i_p_Ca + i_NaCa + i_NaK + i_B_Na + i_B_Ca + i_stim)}{Cm}

Component: fast_sodium_current

i_Na = g_Na m^{3.0} h j (V - E_Na) E_Na = \frac{R T}{F} \ln (\frac{Na_o}{Na_i})

Component: fast_sodium_current_m_gate

alpha_m = 0.32 \frac{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{V + 80.0}{-6.8}} if V < -40.0 \\ 0.0 otherwise \end{matrix} beta_h = \{\begin{matrix} 3.56 ⅇ^{0.079 V} + 310000.0 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} \frac{(-127140.0) ⅇ^{0.2444 V} - (0.00003474 ⅇ^{(-0.04391) V})}{1.0 + ⅇ^{0.311 (V + 79.23)}} (V + 37.78) 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: time_independent_potassium_current

i_K1 = \frac{g_K1 (V - E_K)}{1.0 + ⅇ^{0.07 (V + 80.0)}} E_K = \frac{R T}{F} \ln (\frac{K_o}{K_i})

Component: transient_outward_K_current

i_to = g_to {oa}^{3.0} oi (V - E_K)

Component: transient_outward_K_current_oa_gate

\frac{d}{d time} (oa) = \frac{oa_infinity - oa}{tau_oa} alpha_oa = 0.65 {(ⅇ^{\frac{V + 18.0}{-8.5}} + ⅇ^{\frac{V - 16.0}{-59.0}})}^{-1.0} beta_oa = 1.2 {(2.2 + ⅇ^{\frac{V + 75.0}{18.0}})}^{-1.0} tau_oa = {(alpha_oa + beta_oa)}^{-1.0} oa_infinity = {(1.0 + ⅇ^{\frac{V + 0.5}{-10.5}})}^{- (\frac{1.0}{3.0})}

Component: transient_outward_K_current_oi_gate

\frac{d}{d time} (oi) = \frac{oi_infinity - oi}{tau_oi} alpha_oi = {(6.2 + ⅇ^{\frac{V + 105.2}{9.85}})}^{-1.0} beta_oi = {(7.54 + ⅇ^{\frac{V - 8.89}{-12.87}})}^{-1.0} tau_oi = {(alpha_oi + beta_oi)}^{-1.0} oi_infinity = {(1.0 + ⅇ^{\frac{V + 43.377}{6.45}})}^{-1.0}

Component: ultrarapid_delayed_rectifier_K_current

i_Kur_d = g_Kur_d {ua}^{3.0} ui (V - E_K) g_Kur_d = 0.00855 + \frac{0.0779}{1.0 + ⅇ^{\frac{V + 11.0}{-16.0}}}

Component: ultrarapid_delayed_rectifier_K_current_ua_gate

\frac{d}{d time} (ua) = \frac{ua_infinity - ua}{tau_ua} alpha_ua = 1.47 {(ⅇ^{\frac{V + 33.2}{-30.63}} + ⅇ^{\frac{V - 27.6}{-30.65}})}^{-1.0} beta_ua = 0.42 {(ⅇ^{\frac{V + 26.64}{2.49}} + ⅇ^{\frac{V + 44.41}{20.36}})}^{-1.0} tau_ua = {(alpha_ua + beta_ua)}^{-1.0} ua_infinity = {(1.0 + ⅇ^{\frac{V + 2.81}{-9.49}})}^{- (\frac{1.0}{3.0})}

Component: ultrarapid_delayed_rectifier_K_current_ui_gate

\frac{d}{d time} (ui) = \frac{ui_infinity - ui}{tau_ui} alpha_ui = {(21.0 + ⅇ^{\frac{V - 185.0}{-28.0}})}^{-1.0} beta_ui = ⅇ^{\frac{V - 158.0}{16.0}} tau_ui = {(alpha_ui + beta_ui)}^{-1.0} ui_infinity = {(1.0 + ⅇ^{\frac{V - 99.45}{27.48}})}^{-1.0}

Component: rapid_delayed_rectifier_K_current

i_Kr = g_Kr xr (0.07 + \frac{0.58}{1.0 + ⅇ^{\frac{V + 15.0}{22.4}}}) (V - E_K)

Component: rapid_delayed_rectifier_K_current_xr_gate

\frac{d}{d time} (xr) = \frac{xr_infinity - xr}{tau_xr} alpha_xr = 0.04 \frac{V - 248.0}{1.0 - (ⅇ^{\frac{V - 248.0}{-28.0}})} beta_xr = 0.028 \frac{V + 163.0}{ⅇ^{\frac{V + 163.0}{21.0}} - 1.0} tau_xr = {(alpha_xr + beta_xr)}^{-1.0} xr_infinity = {(1.0 + ⅇ^{\frac{V + 7.654}{-5.377}})}^{-1.0}

Component: slow_delayed_rectifier_K_current

i_Ks = g_Ks {xs}^{2.0} (V - E_K)

Component: slow_delayed_rectifier_K_current_xs_gate

\frac{d}{d time} (xs) = \frac{xs_infinity - xs}{tau_xs} alpha_xs = 0.00001 \frac{V + 28.5}{1.0 - (ⅇ^{\frac{V + 28.5}{-115.0}})} beta_xs = 0.00023 \frac{V + 28.5}{ⅇ^{\frac{V + 28.5}{3.3}} - 1.0} tau_xs = {(alpha_xs + beta_xs)}^{-1.0} xs_infinity = {(1.0 + ⅇ^{\frac{V - 13.0}{-12.0}})}^{-0.5}

Component: sarcolemmal_Ca_current

i_Ca = g_Ca d f f_Ca (V - 65.0)

Component: sarcolemmal_Ca_current_d_gate

\frac{d}{d time} (d) = \frac{d_infinity - d}{tau_d} d_infinity = {(1.0 + ⅇ^{\frac{V + 10.0}{-6.0}})}^{-1.0} tau_d = \frac{1.0 - (ⅇ^{\frac{V + 10.0}{-6.24}})}{0.035 (V + 10.0) (1.0 + ⅇ^{\frac{V + 10.0}{-6.24}})}

Component: sarcolemmal_Ca_current_f_gate

\frac{d}{d time} (f) = \frac{f_infinity - f}{tau_f} f_infinity = {(1.0 + ⅇ^{\frac{V + 24.6}{6.2}})}^{-1.0} tau_f = 400.0 {(1.0 + 4.5 ⅇ^{(-0.0007) {(V - 9.0)}^{2.0}})}^{-1.0}

Component: sarcolemmal_Ca_current_f_Ca_gate

\frac{d}{d time} (f_Ca) = \frac{f_Ca_infinity - f_Ca}{tau_f_Ca} f_Ca_infinity = 0.29 + 0.8 {(1.0 + ⅇ^{\frac{Ca_i - 0.00012}{0.00006}})}^{-1.0}

Component: Ca_activated_Cl_current

i_Cl_Ca = g_Cl_Ca q_Ca (V - E_Cl) E_Cl = \frac{R T}{(-1.0) F} \ln (\frac{Cl_o}{Cl_i})

Component: Ca_activated_Cl_current_q_Ca_gate

q_Ca_infinity = 1.0 - ({(1.0 + {(\frac{Fn}{0.00000000011})}^{3.0})}^{-1.0})

Component: sodium_potassium_pump

i_NaK = i_NaK_max f_NaK \frac{1.0}{1.0 + {(\frac{Km_Na_i}{Na_i})}^{1.5}} \frac{K_o}{K_o + Km_K_o} f_NaK = {(1.0 + 0.1245 ⅇ^{(-0.1) \frac{F V}{R T}} + 0.0365 sigma ⅇ^{- (\frac{F V}{R T})})}^{-1.0} sigma = \frac{1.0}{7.0} (ⅇ^{\frac{Na_o}{67.3}} - 1.0)

Component: Na_Ca_exchanger_current

i_NaCa = \frac{I_NaCa_max (ⅇ^{\frac{0.35 F V}{R T}} {Na_i}^{3.0} Ca_o - (ⅇ^{\frac{(-0.65) F V}{R T}} {Na_o}^{3.0} Ca_i))}{({K_mNa}^{3.0} + {Na_o}^{3.0}) (K_mCa + Ca_o) (1.0 + K_sat ⅇ^{\frac{(-0.65) V F}{R T}})}

Component: background_currents

i_B_Na = g_B_Na (V - E_Na) i_B_Ca = g_B_Ca (V - E_Ca) E_Ca = \frac{R T}{2.0 F} \ln (\frac{Ca_o}{Ca_i})

Component: Ca_pump_current

i_p_Ca = i_p_Ca_max \frac{Ca_i}{0.0005 + Ca_i}

Component: Ca_release_current_from_JSR

i_rel = K_rel u^{2.0} v w (Ca_rel - Ca_i) Fn = 0.000000000001 V_rel i_rel - (0.0000000000005 (\frac{1.0}{2.0 F} i_Ca - (\frac{1.0}{5.0 F} i_NaCa)))

Component: Ca_release_current_from_JSR_u_gate

\frac{d}{d time} (u) = \frac{u_infinity - u}{tau_u} tau_u = 8.0 u_infinity = {(1.0 + ⅇ^{\frac{Fn - 0.00000000000034175}{-0.000000000000001367}})}^{-1.0}

Component: Ca_release_current_from_JSR_v_gate

\frac{d}{d time} (v) = \frac{v_infinity - v}{tau_v} tau_v = 1.91 + 2.09 {(1.0 + ⅇ^{\frac{Fn - 0.00000000000034175}{-0.000000000000001367}})}^{-1.0} v_infinity = 1.0 - ({(1.0 + ⅇ^{\frac{Fn - 6.835 e -14}{-0.000000000000001367}})}^{-1.0})

Component: Ca_release_current_from_JSR_w_gate

\frac{d}{d time} (w) = \frac{w_infinity - w}{tau_w} tau_w = \frac{6.0 - (6.0 ⅇ^{\frac{V - 7.9}{-5.0}})}{(1.0 + 0.3 ⅇ^{\frac{V - 7.9}{-5.0}}) (V - 7.9)} w_infinity = 1.0 - ({(1.0 + ⅇ^{\frac{V - 40.0}{-17.0}})}^{-1.0})

Component: transfer_current_from_NSR_to_JSR

i_tr = \frac{Ca_up - Ca_rel}{tau_tr}

Component: Ca_uptake_current_by_the_NSR

i_up = \frac{I_up_max}{1.0 + \frac{K_up}{Ca_i}}

Component: Ca_leak_current_by_the_NSR

i_up_leak = I_up_max \frac{Ca_up}{Ca_up_max}

Component: Ca_buffers

\frac{d}{d time} (Ca_CMDN) = 200.0 Ca_i (1.0 - (\frac{Ca_CMDN}{CMDN_max})) - (0.476 \frac{Ca_CMDN}{CMDN_max}) J_Ca_CMDN = \frac{d}{d time} (Ca_CMDN) \frac{d}{d time} (Ca_TRPN) = 78.4 Ca_i (1.0 - (\frac{Ca_TRPN}{TRPN_max})) - (0.392 \frac{Ca_TRPN}{TRPN_max}) J_Ca_TRPN = \frac{d}{d time} (Ca_TRPN) \frac{d}{d time} (Ca_CSQN) = 0.48 Ca_rel (1.0 - (\frac{Ca_CSQN}{CSQN_max})) - (0.4 \frac{Ca_CSQN}{CSQN_max}) J_Ca_CSQN = \frac{d}{d time} (Ca_CSQN)

Component: intracellular_ion_concentrations

\frac{d}{d time} (Na_i) = \frac{(-3.0) i_NaK - (3.0 i_NaCa + i_B_Na + i_Na)}{V_i F} \frac{d}{d time} (K_i) = \frac{2.0 i_NaK - (i_K1 + i_to + i_Kur_d + i_Kr + i_Ks)}{V_i F} \frac{d}{d time} (Cl_i) = \frac{i_Cl_Ca}{V_i F} \frac{d}{d time} (Ca_i) = \frac{2.0 i_NaCa - (i_p_Ca + i_Ca + i_B_Ca)}{2.0 V_i F} + \frac{V_up (i_up_leak - i_up) + i_rel V_rel}{V_i} - (TRPN_max J_Ca_TRPN + CMDN_max J_Ca_CMDN) \frac{d}{d time} (Ca_up) = i_up - (i_up_leak + i_tr \frac{V_rel}{V_up}) \frac{d}{d time} (Ca_rel) = i_tr - (i_rel + 31.0 J_Ca_CSQN)

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: time_independent_potassium_current

Component: transient_outward_K_current

Component: transient_outward_K_current_oa_gate

Component: transient_outward_K_current_oi_gate

Component: ultrarapid_delayed_rectifier_K_current

Component: ultrarapid_delayed_rectifier_K_current_ua_gate

Component: ultrarapid_delayed_rectifier_K_current_ui_gate

Component: rapid_delayed_rectifier_K_current

Component: rapid_delayed_rectifier_K_current_xr_gate

Component: slow_delayed_rectifier_K_current

Component: slow_delayed_rectifier_K_current_xs_gate

Component: sarcolemmal_Ca_current

Component: sarcolemmal_Ca_current_d_gate

Component: sarcolemmal_Ca_current_f_gate

Component: sarcolemmal_Ca_current_f_Ca_gate

Component: Ca_activated_Cl_current

Component: Ca_activated_Cl_current_q_Ca_gate

Component: sodium_potassium_pump

Component: Na_Ca_exchanger_current

Component: background_currents

Component: Ca_pump_current

Component: Ca_release_current_from_JSR

Component: Ca_release_current_from_JSR_u_gate

Component: Ca_release_current_from_JSR_v_gate

Component: Ca_release_current_from_JSR_w_gate

Component: transfer_current_from_NSR_to_JSR

Component: Ca_uptake_current_by_the_NSR

Component: Ca_leak_current_by_the_NSR

Component: Ca_buffers

Component: intracellular_ion_concentrations

Component: standard_ionic_concentrations