Model Mathematics

Component: environment

Component: membrane

dd time V =- 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_B_Cl + i_stim Cm

Component: fast_sodium_current

i_Na = g_Na m 3.0 h j V - E_Na E_Na = R T F ln Na_o Na_i

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 V + 80.0 -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 1.0 + 0.311 V + 79.23 V + 37.78 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: time_independent_potassium_current

i_K1 = g_K1 V - E_K 1.0 + 0.07 V + 80.0 E_K = R T F ln 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

dd time oa = oa_infinity - oa tau_oa alpha_oa = 0.65 V + 18.0 -8.5 + V - 16.0 -59.0 -1.0 beta_oa = 1.2 2.2 + V + 75.0 18.0 -1.0 tau_oa = alpha_oa + beta_oa -1.0 oa_infinity = 1.0 + V + 0.5 -10.5 - 1.0 3.0

Component: transient_outward_K_current_oi_gate

dd time oi = oi_infinity - oi tau_oi alpha_oi = 6.2 + V + 105.2 9.85 -1.0 beta_oi = 7.54 + V - 8.89 -12.87 -1.0 tau_oi = alpha_oi + beta_oi -1.0 oi_infinity = 1.0 + 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 + 0.0779 1.0 + V + 11.0 -16.0

Component: ultrarapid_delayed_rectifier_K_current_ua_gate

dd time ua = ua_infinity - ua tau_ua alpha_ua = 1.47 V + 33.2 -30.63 + V - 27.6 -30.65 -1.0 beta_ua = 0.42 V + 26.64 2.49 + V + 44.41 20.36 -1.0 tau_ua = alpha_ua + beta_ua -1.0 ua_infinity = 1.0 + V + 2.81 -9.49 - 1.0 3.0

Component: ultrarapid_delayed_rectifier_K_current_ui_gate

dd time ui = ui_infinity - ui tau_ui alpha_ui = 21.0 + V - 185.0 -28.0 -1.0 beta_ui = V - 158.0 16.0 tau_ui = alpha_ui + beta_ui -1.0 ui_infinity = 1.0 + V - 99.45 27.48 -1.0

Component: rapid_delayed_rectifier_K_current

i_Kr = g_Kr xr 0.07 + 0.58 1.0 + V + 15.0 22.4 V - E_K

Component: rapid_delayed_rectifier_K_current_xr_gate

dd time xr = xr_infinity - xr tau_xr alpha_xr = 0.04 V - 248.0 1.0 - V - 248.0 -28.0 beta_xr = 0.028 V + 163.0 V + 163.0 21.0 - 1.0 tau_xr = alpha_xr + beta_xr -1.0 xr_infinity = 1.0 + 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

dd time xs = xs_infinity - xs tau_xs alpha_xs = 0.00001 V + 28.5 1.0 - V + 28.5 -115.0 beta_xs = 0.00023 V + 28.5 V + 28.5 3.3 - 1.0 tau_xs = alpha_xs + beta_xs -1.0 xs_infinity = 1.0 + 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

dd time d = d_infinity - d tau_d d_infinity = 1.0 + V + 10.0 -6.0 -1.0 tau_d = 1.0 - V + 10.0 -6.24 0.035 V + 10.0 1.0 + V + 10.0 6.24

Component: sarcolemmal_Ca_current_f_gate

dd time f = f_infinity - f tau_f f_infinity = 1.0 + V + 24.6 6.2 -1.0 tau_f = 400.0 1.0 + 4.5 -0.0007 V - 9.0 2.0 -1.0

Component: sarcolemmal_Ca_current_f_Ca_gate

dd time f_Ca = f_Ca_infinity - f_Ca tau_f_Ca f_Ca_infinity = 0.29 + 0.8 1.0 + 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 = R T F ln Cl_o Cl_i

Component: Ca_activated_Cl_current_q_Ca_gate

q_Ca_infinity = 1.0 - 1.0 + Fn 0.00000000011 3.0 -1.0

Component: Na_Cl_cotransporter

CT_NaCl = g_CT delta_CT_n E_Na - E_Cl + delta_CT_n

Component: sodium_potassium_pump

i_NaK = i_NaK_max f_NaK 1.0 1.0 + Km_Na_i Na_i 1.5 K_o K_o + Km_K_o f_NaK = 1.0 + 0.1245 -0.1 F V R T + 0.0365 sigma - F V R T -1.0 sigma = 1.0 7.0 Na_o 67.3 - 1.0

Component: Na_Ca_exchanger_current

i_NaCa = I_NaCa_max 0.35 F V R T Na_i 3.0 Ca_o - -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 -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 i_B_K = g_B_K V - E_K i_B_Cl = g_B_Cl V - E_Cl E_Ca = R T 2.0 F ln Ca_o Ca_i

Component: Ca_pump_current

i_p_Ca = i_p_Ca_max 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 = 1E-12 V_rel i_rel - 5E-13 1.0 2.0 F i_Ca - 1.0 5.0 F i_NaCa

Component: Ca_release_current_from_JSR_u_gate

dd time u = u_infinity - u tau_u tau_u = 8.0 u_infinity = 1.0 + Fn - 3.4175E-13 -13.67E-16 -1.0

Component: Ca_release_current_from_JSR_v_gate

dd time v = v_infinity - v tau_v tau_v = 1.91 + 2.09 1.0 + Fn - 3.4175E-13 -13.67E-16 -1.0 v_infinity = 1.0 - 1.0 + Fn - 6.835E-14 -13.67E-16 -1.0

Component: Ca_release_current_from_JSR_w_gate

dd time w = w_infinity - w tau_w tau_w = 6.0 - 6.0 V - 7.9 -5.0 1.0 + 0.3 V - 7.9 -5.0 V - 7.9 w_infinity = 1.0 - 1.0 + V - 40.0 -17.0 -1.0

Component: transfer_current_from_NSR_to_JSR

i_tr = Ca_up - Ca_rel tau_tr

Component: Ca_uptake_current_by_the_NSR

i_up = I_up_max 1.0 + K_up Ca_i

Component: Ca_leak_current_by_the_NSR

i_up_leak = I_up_max Ca_up Ca_up_max

Component: Ca_buffers

Ca_CMDN = 200.0 Ca_i 1.0 - Ca_CMDN CMDN_max - 0.476 Ca_CMDN CMDN_max J_Ca_CMDN =dd time Ca_CMDN Ca_TRPN = 78.4 Ca_i 1.0 - Ca_TRPN TRPN_max - 0.392 Ca_TRPN TRPN_max J_Ca_TRPN =dd time Ca_TRPN Ca_CSQN = 0.48 Ca_rel 1.0 - Ca_CSQN CSQN_max - 0.4 Ca_CSQN CSQN_max J_Ca_CSQN =dd time Ca_CSQN

Component: intracellular_ion_concentrations

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

Component: standard_ionic_concentrations