//Created by libAntimony v2.4 model lindblad_1996__environment(time_) // Variable initializations: time_ = ; end model lindblad_1996__membrane(V, R, T, F, time_, i_Na, i_Ca_L, i_Ca_T, i_to, i_K1, i_Kr, i_Ks, i_B_Na, i_B_Ca, i_B_Cl, i_p, i_CaP, i_NaCa) // Assignment Rules: i_Stim := piecewise( stim_amplitude , (( geq(time_, stim_start)) && (time_ <= stim_end) && ((time_ - stim_start) - floor((time_ - stim_start) / stim_period) * stim_period <= stim_duration )), 0 ); // Rate Rules: V' = (-(1) / Cm) * (i_Kr + i_Ks + i_Na + i_Ca_L + i_Ca_T + i_to + i_K1 + i_B_Na + i_B_Ca + i_B_Cl + i_p + i_CaP + i_NaCa + i_Stim); // Variable initializations: V = -69.83663; R = 8314.472; T = 308; F = 96485.3415; Cm = 0.00005; time_ = ; i_Na = ; i_Ca_L = ; i_Ca_T = ; i_to = ; i_K1 = ; i_Kr = ; i_Ks = ; i_B_Na = ; i_B_Ca = ; i_B_Cl = ; i_p = ; i_CaP = ; i_NaCa = ; stim_start = 0.1; stim_end = 100000; stim_period = 1; stim_duration = 0.0008; stim_amplitude = -2; end model lindblad_1996__sodium_current_m_gate(m, V, time_) // Assignment Rules: E0_m := V + 44.4; alpha_m := (-(460) * E0_m) / (exp(E0_m / -(12.673)) - 1); beta_m := 18400 * exp(E0_m / -(12.673)); // Rate Rules: m' = alpha_m * (1 - m) - beta_m * m; // Variable initializations: m = 0.01309; V = ; time_ = ; end model lindblad_1996__sodium_current_h1_gate(h1, h_infinity, V, time_) // Assignment Rules: alpha_h := 44.9 * exp((V + 66.9) / -(5.57)); beta_h := 1491 / (1 + 323.3 * exp((V + 94.6) / -(12.9))); h_infinity := alpha_h / (alpha_h + beta_h); tau_h1 := 0.03 / (1 + exp((V + 40) / 6)) + 3.5E-4; // Rate Rules: h1' = (h_infinity - h1) / tau_h1; // Variable initializations: h1 = 0.706; V = ; time_ = ; end model lindblad_1996__sodium_current_h2_gate(h2, h_infinity, V, time_) // Assignment Rules: tau_h2 := 0.12 / (1 + exp((V + 60) / 2)) + 0.00295; // Rate Rules: h2' = (h_infinity - h2) / tau_h2; // Variable initializations: h2 = 0.61493; h_infinity = ; V = ; time_ = ; end model lindblad_1996__sodium_current(i_Na, E_Na, time_, V, Na_c, Na_i, R, F, T, m, h1, h2) // Sub-modules, and any changes to those submodules: sodium_current_m_gate: lindblad_1996__sodium_current_m_gate(m, V, time_); sodium_current_h1_gate: lindblad_1996__sodium_current_h1_gate(h1, h_infinity, V, time_); sodium_current_h2_gate: lindblad_1996__sodium_current_h2_gate(h2, h_infinity, V, time_); // Assignment Rules: i_Na := (((P_Na * power(m, 3) * (0.635 * h1 + 0.365 * h2) * Na_c * V * power(F, 2)) / (R * T)) * (exp(((V - E_Na) * F) / (R * T)) - 1)) / (exp((V * F) / (R * T)) - 1); E_Na := ((R * T) / F) * ln(Na_c / Na_i); // Variable initializations: P_Na = 0.0000014; Na_c = ; Na_i = ; R = ; F = ; T = ; end model lindblad_1996__L_type_Ca_channel_d_L_gate(d_L, V, time_) // Assignment Rules: E0_alpha_d_L := V + 35; E0_beta_d_L := V - 5; alpha_d_L := (-(16.72) * E0_alpha_d_L) / (exp(E0_alpha_d_L / -(2.5)) - 1) + (-(50) * V) / (exp(V / -(4.808)) - 1); beta_d_L := (4.48 * E0_beta_d_L) / (exp(E0_beta_d_L / 2.5) - 1); d_L_infinity := 1 / (1 + exp((V + 0.95) / -(6.6))); tau_d_L := 1 / (alpha_d_L + beta_d_L); // Rate Rules: d_L' = (d_L_infinity - d_L) / tau_d_L; // Variable initializations: d_L = 3e-5; V = ; time_ = ; end model lindblad_1996__L_type_Ca_channel_f_L_gate(f_L, f_L_infinity, V, time_) // Assignment Rules: E0_f_L := V + 28; alpha_f_L := (8.49 * E0_f_L) / (exp(E0_f_L / 4) - 1); beta_f_L := 67.922 / (1 + exp(E0_f_L / -(4))); f_L_infinity := alpha_f_L / (alpha_f_L + beta_f_L); x_f := (V + 37.427) / 20.213; tau_f_L := 0.211 * exp(- x_f * x_f) + 0.015; // Rate Rules: f_L' = (f_L_infinity - f_L) / tau_f_L; // Variable initializations: f_L = 0.99981; V = ; time_ = ; end model lindblad_1996__L_type_Ca_channel(i_Ca_L, time_, V, d_L, f_L) // Sub-modules, and any changes to those submodules: L_type_Ca_channel_d_L_gate: lindblad_1996__L_type_Ca_channel_d_L_gate(d_L, V, time_); L_type_Ca_channel_f_L_gate: lindblad_1996__L_type_Ca_channel_f_L_gate(f_L, f_L_infinity, V, time_); // Assignment Rules: i_Ca_L := g_Ca_L * d_L * f_L * d_prime * (V - E_Ca_app); d_prime := 1 / (1 + exp((V - 33) / -(12))); // Variable initializations: g_Ca_L = 0.004; E_Ca_app = 60; end model lindblad_1996__T_type_Ca_channel_d_T_gate(d_T, V, time_) // Assignment Rules: E0_d_T := V + 23; alpha_d_T := 674.173 * exp(E0_d_T / 30); beta_d_T := 674.173 * exp(E0_d_T / -(30)); d_T_infinity := 1 / (1 + exp(E0_d_T / -(6.1))); tau_d_T := 1 / (alpha_d_T + beta_d_T); // Rate Rules: d_T' = (d_T_infinity - d_T) / tau_d_T; // Variable initializations: d_T = 4.6e-4; V = ; time_ = ; end model lindblad_1996__T_type_Ca_channel_f_T_gate(f_T, f_T_infinity, V, time_) // Assignment Rules: E0_f_T := V + 75; alpha_f_T := 9.637 * exp(E0_f_T / -(83.333)); beta_f_T := 9.637 * exp(E0_f_T / 15.385); f_T_infinity := alpha_f_T / (alpha_f_T + beta_f_T); tau_f_T := 1 / (alpha_f_T + beta_f_T); // Rate Rules: f_T' = (f_T_infinity - f_T) / tau_f_T; // Variable initializations: f_T = 0.30752; V = ; time_ = ; end model lindblad_1996__T_type_Ca_channel(i_Ca_T, time_, V, d_T, f_T) // Sub-modules, and any changes to those submodules: T_type_Ca_channel_d_T_gate: lindblad_1996__T_type_Ca_channel_d_T_gate(d_T, V, time_); T_type_Ca_channel_f_T_gate: lindblad_1996__T_type_Ca_channel_f_T_gate(f_T, f_T_infinity, V, time_); // Assignment Rules: i_Ca_T := g_Ca_T * d_T * f_T * (V - E_Ca_T); // Variable initializations: g_Ca_T = 0.006; E_Ca_T = 38; end model lindblad_1996__Ca_independent_transient_outward_K_current_r_gate(r, V, time_) // Assignment Rules: alpha_r := 386.6 * exp(V / 12); beta_r := 8.011 * exp(V / -(7.2)); tau_r := 1 / (alpha_r + beta_r) + 4E-4; r_infinity := 1 / (1 + exp((V + 15) / -(5.633))); // Rate Rules: r' = (r_infinity - r) / tau_r; // Variable initializations: r = 6e-5; V = ; time_ = ; end model lindblad_1996__Ca_independent_transient_outward_K_current_s1_gate(s1, V, time_) // Assignment Rules: tau_s1 := 0.5466 / (1 + exp((V + 32.8) / 0.1)) + 0.0204; s1_infinity := 1 / (1 + exp((V + 28.29) / 7.06)); // Rate Rules: s1' = (s1_infinity - s1) / tau_s1; // Variable initializations: s1 = 0.5753; V = ; time_ = ; end model lindblad_1996__Ca_independent_transient_outward_K_current_s2_gate(s2, V, time_) // Assignment Rules: tau_s2 := 5.75 / (1 + exp((V + 32.8) / 0.1)) + 0.45 / (1 + exp((V - 13.54) / -(13.97))); s2_infinity := 1 / (1 + exp((V + 28.29) / 7.06)); // Rate Rules: s2' = (s2_infinity - s2) / tau_s2; // Variable initializations: s2 = 0.39871; V = ; time_ = ; end model lindblad_1996__Ca_independent_transient_outward_K_current_s3_gate(s3, V, time_) // Assignment Rules: tau_s3 := 7.5 / (1 + exp((V + 23) / 0.5)) + 0.5; s3_infinity := (1 / (1 + exp((V + 50.67) / 27.38)) + 0.666) / 1.666; // Rate Rules: s3' = (s3_infinity - s3) / tau_s3; // Variable initializations: s3 = 0.57363; V = ; time_ = ; end model lindblad_1996__Ca_independent_transient_outward_K_current(i_to, E_K, time_, V, R, F, T, K_c, K_i, r, s1, s2, s3) // Sub-modules, and any changes to those submodules: Ca_independent_transient_outward_K_current_r_gate: lindblad_1996__Ca_independent_transient_outward_K_current_r_gate(r, V, time_); Ca_independent_transient_outward_K_current_s1_gate: lindblad_1996__Ca_independent_transient_outward_K_current_s1_gate(s1, V, time_); Ca_independent_transient_outward_K_current_s2_gate: lindblad_1996__Ca_independent_transient_outward_K_current_s2_gate(s2, V, time_); Ca_independent_transient_outward_K_current_s3_gate: lindblad_1996__Ca_independent_transient_outward_K_current_s3_gate(s3, V, time_); // Assignment Rules: i_to := g_to * r * (0.59 * power(s1, 3) + 0.41 * power(s2, 3)) * (0.6 * power(s3, 6) + 0.4) * (V - E_K); E_K := ((R * T) / F) * ln(K_c / K_i); // Variable initializations: g_to = 0.050002; R = ; F = ; T = ; K_c = ; K_i = ; end model lindblad_1996__delayed_rectifier_K_current_z_gate(z, V, time_) // Assignment Rules: alpha_z := 1.66 * exp(V / 69.452); beta_z := 0.3 * exp(V / -(21.826)); tau_z := 1 / (alpha_z + beta_z) + 0.06; z_infinity := 1 / (1 + exp((V - 0.9) / -(13.8))); // Rate Rules: z' = (z_infinity - z) / tau_z; // Variable initializations: z = 0.02032; V = ; time_ = ; end model lindblad_1996__delayed_rectifier_K_current_pa_gate(p_a, V, time_) // Assignment Rules: alpha_p_a := 9 * exp(V / 25.371); beta_p_a := 1.3 * exp(V / -(13.026)); tau_p_a := 1 / (alpha_p_a + beta_p_a); p_a_infinity := 1 / (1 + exp((V + 5.1) / -(7.4))); // Rate Rules: p_a' = (p_a_infinity - p_a) / tau_p_a; // Variable initializations: p_a = 1.6e-4; V = ; time_ = ; end model lindblad_1996__delayed_rectifier_K_current_pi_gate(p_i, V, time_) // Assignment Rules: alpha_p_i := 100 * exp(V / -(54.645)); beta_p_i := 656 * exp(V / 106.157); tau_p_i := 1 / (alpha_p_i + beta_p_i); p_i_infinity := 1 / (1 + exp((V + 47.3921) / 18.6603)); // Rate Rules: p_i' = (p_i_infinity - p_i) / tau_p_i; // Variable initializations: p_i = 0.76898; V = ; time_ = ; end model lindblad_1996__delayed_rectifier_K_current(i_Ks, i_Kr, time_, V, E_K, z, p_a, p_i) // Sub-modules, and any changes to those submodules: delayed_rectifier_K_current_z_gate: lindblad_1996__delayed_rectifier_K_current_z_gate(z, V, time_); delayed_rectifier_K_current_pa_gate: lindblad_1996__delayed_rectifier_K_current_pa_gate(p_a, V, time_); delayed_rectifier_K_current_pi_gate: lindblad_1996__delayed_rectifier_K_current_pi_gate(p_i, V, time_); // Assignment Rules: i_Ks := g_Ks * z * (V - E_K); i_Kr := g_Kr * p_a * p_i * (V - E_K); // Variable initializations: g_Ks = 0.0025; g_Kr = 0.0035; E_K = ; end model lindblad_1996__inward_rectifier(i_K1, time_, V, R, F, T, K_c, E_K) // Assignment Rules: i_K1 := (g_K1 * (V - E_K) * power(K_c / (K_c + KmK1), 3) * 1) / (1 + exp((steepK1 * F * ((V - E_K) - shiftK1)) / (R * T))); // Variable initializations: g_K1 = 0.005088; KmK1 = 0.59; steepK1 = 1.393; shiftK1 = -3.6; time_ = ; V = ; R = ; F = ; T = ; K_c = ; E_K = ; end model lindblad_1996__background_currents(i_B_Na, i_B_Ca, i_B_Cl, E_Na, R, F, T, Ca_c, Ca_i, Cl_c, Cl_i, time_, V) // Assignment Rules: i_B_Na := g_B_Na * (V - E_Na); i_B_Ca := g_B_Ca * (V - E_Ca); i_B_Cl := g_B_Cl * (V - E_B_Cl) * (1 + exp((V - (E_Cl + 36.95)) / 74.514)); E_Ca := ((R * T) / (2 * F)) * ln(Ca_c / Ca_i); E_Cl := ((R * T) / F) * ln(Cl_i / Cl_c); E_B_Cl := E_Cl - 0.49 * (E_Cl + 30.59); // Variable initializations: g_B_Na = 6.4e-5; g_B_Ca = 3.1e-5; g_B_Cl = 1.2e-4; E_Na = ; R = ; F = ; T = ; Ca_c = ; Ca_i = ; Cl_c = ; Cl_i = ; time_ = ; V = ; end model lindblad_1996__sodium_potassium_pump(i_p, K_c, Na_i, V, time_) // Assignment Rules: i_p := (((((i_NaK_max * K_c) / (K_c + k_NaK_K)) * power(Na_i, 1.5)) / (power(Na_i, 1.5) + power(k_NaK_Na, 1.5))) * 1.6) / (1.5 + exp((V + 60) / -(40))); // Variable initializations: k_NaK_K = 1; k_NaK_Na = 11; i_NaK_max = 0.06441; K_c = ; Na_i = ; V = ; time_ = ; end model lindblad_1996__sarcolemmal_calcium_pump_current(i_CaP, Ca_i, time_) // Assignment Rules: i_CaP := (i_CaP_max * Ca_i) / (Ca_i + k_CaP); // Variable initializations: i_CaP_max = 0.009509; k_CaP = 2e-4; Ca_i = ; time_ = ; end model lindblad_1996__Na_Ca_ion_exchanger_current(i_NaCa, Na_i, Na_c, Ca_i, Ca_c, R, F, T, V, time_) // Assignment Rules: i_NaCa := (k_NaCa * (power(Na_i, 3) * Ca_c * exp((gamma * F * V) / (R * T)) - power(Na_c, 3) * Ca_i * exp(((gamma - 1) * V * F) / (R * T)))) / (1 + d_NaCa * (power(Na_c, 3) * Ca_i + power(Na_i, 3) * Ca_c) * (1 + Ca_i / 0.0069)); // Variable initializations: k_NaCa = 2e-5; d_NaCa = 3e-4; gamma = 0.45; Na_i = ; Na_c = ; Ca_i = ; Ca_c = ; R = ; F = ; T = ; V = ; time_ = ; end model lindblad_1996__intracellular_ion_concentrations(Na_i, Ca_i, K_i, Cl_i, Vol_i, time_, F, i_Na, i_Ca_L, i_Ca_T, i_B_Na, i_NaCa, i_p, i_Kr, i_Ks, i_K1, i_to, i_CaP, i_B_Ca, i_up, i_rel, dOCdt, dOTCdt, dOTMgCdt) // Rate Rules: Na_i' = -(i_Na + i_B_Na + 3 * i_p + 3 * i_NaCa) / (Vol_i * F); Ca_i' = -((((i_Ca_L + i_Ca_T + i_B_Ca + i_CaP) - 2 * i_NaCa) + i_up) - i_rel) / (2 * Vol_Ca * F) - (0.08 * dOTCdt + 0.16 * dOTMgCdt + 0.045 * dOCdt); K_i' = -((i_to + i_K1 + i_Kr + i_Ks) - 2 * i_p) / (Vol_i * F); // Variable initializations: Na_i = 8.4; Ca_i = 7.305e-5; K_i = 100; Cl_i = 30; Vol_i = 1.26e-5; Vol_Ca = 5.884e-6; time_ = ; F = ; i_Na = ; i_Ca_L = ; i_Ca_T = ; i_B_Na = ; i_NaCa = ; i_p = ; i_Kr = ; i_Ks = ; i_K1 = ; i_to = ; i_CaP = ; i_B_Ca = ; i_up = ; i_rel = ; dOCdt = ; dOTCdt = ; dOTMgCdt = ; end model lindblad_1996__intracellular_Ca_buffering(dOCdt, dOTCdt, dOTMgCdt, O_TMgMg, Ca_i, time_) // Assignment Rules: dOCdt := 200000 * Ca_i * (1 - O_C) - 476 * O_C; dOTCdt := 78400 * Ca_i * (1 - O_TC) - 392 * O_TC; dOTMgCdt := 200000 * Ca_i * ((1 - O_TMgC) - O_TMgMg) - 6.6 * O_TMgC; // Rate Rules: O_C' = dOCdt; O_TC' = dOTCdt; O_TMgC' = dOTMgCdt; O_TMgMg' = 2000 * Mg_i * ((1 - O_TMgC) - O_TMgMg) - 666 * O_TMgMg; // Variable initializations: O_C = 0.02981; O_TC = 0.01442; O_TMgC = 0.23532; O_TMgMg = 0.67476; Mg_i = 2.5; Ca_i = ; time_ = ; end model lindblad_1996__cleft_space_ion_concentrations(Na_c, Ca_c, K_c, Cl_c) // Variable initializations: Na_c = 140; Ca_c = 2.5; K_c = 5; Cl_c = 132; end model lindblad_1996__Ca_handling_by_the_SR(i_rel, i_up, time_, Ca_i, V, F) // Assignment Rules: i_rel := alpha_rel * power(F2 / (F2 + 0.25), 2) * (Ca_rel - Ca_i); i_up := (I_up_max * (Ca_i / k_cyca - (power(k_xcs, 2) * Ca_up) / k_srca)) / ((Ca_i + k_cyca) / k_cyca + (k_xcs * (Ca_up + k_srca)) / k_srca); i_tr := ((Ca_up - Ca_rel) * 2 * F * Vol_rel) / tau_tr; r_act := 203.8 * exp(0.08 * (V - 40)) + 203.8 * power(Ca_i / (Ca_i + k_rel), 4); r_inact := 33.96 + 339.6 * power(Ca_i / (Ca_i + k_rel), 4); // Rate Rules: Ca_rel' = (i_tr - i_rel) / (2 * Vol_rel * F) - 31 * d(O_Calse)/ d(unknown- element); Ca_up' = (i_up - i_tr) / (2 * Vol_up * F); O_Calse' = 480 * Ca_rel * (1 - O_Calse) - 400 * O_Calse; F1' = k_F3 * F3 - r_act * F1; F2' = r_act * F1 - r_inact * F2; F3' = F2 * r_inact - k_F3 * F3; // Variable initializations: I_up_max = 2.8; k_cyca = 0.0003; k_srca = 0.5; k_xcs = 0.4; alpha_rel = 200; Ca_rel = 0.59984; Ca_up = 0.64913; Vol_up = 3.969e-7; Vol_rel = 4.41e-8; O_Calse = 0.41837; F1 = 0.21603; F2 = 0.00205; F3 = 0.68492; tau_tr = 0.01; k_rel = 0.0003; k_F3 = 0.815; time_ = ; Ca_i = ; V = ; F = ; d = ; unknown = ; element = ; end model *lindblad_1996____main() // Sub-modules, and any changes to those submodules: environment: lindblad_1996__environment(time_); membrane: lindblad_1996__membrane(V, R, T, F, time_, i_Na, i_Ca_L, i_Ca_T, i_to, i_K1, i_Kr, i_Ks, i_B_Na, i_B_Ca, i_B_Cl, i_p, i_CaP, i_NaCa); sodium_current: lindblad_1996__sodium_current(i_Na, E_Na, time_, V, Na_c, Na_i, R, F, T, m, h1, h2); L_type_Ca_channel: lindblad_1996__L_type_Ca_channel(i_Ca_L, time_, V, d_L, f_L); T_type_Ca_channel: lindblad_1996__T_type_Ca_channel(i_Ca_T, time_, V, d_T, f_T); Ca_independent_transient_outward_K_current: lindblad_1996__Ca_independent_transient_outward_K_current(i_to, E_K, time_, V, R, F, T, K_c, K_i, r, s1, s2, s3); delayed_rectifier_K_current: lindblad_1996__delayed_rectifier_K_current(i_Ks, i_Kr, time_, V, E_K, z, p_a, p_i); inward_rectifier: lindblad_1996__inward_rectifier(i_K1, time_, V, R, F, T, K_c, E_K); background_currents: lindblad_1996__background_currents(i_B_Na, i_B_Ca, i_B_Cl, E_Na, R, F, T, Ca_c, Ca_i, Cl_c, Cl_i, time_, V); sodium_potassium_pump: lindblad_1996__sodium_potassium_pump(i_p, K_c, Na_i, V, time_); sarcolemmal_calcium_pump_current: lindblad_1996__sarcolemmal_calcium_pump_current(i_CaP, Ca_i, time_); Na_Ca_ion_exchanger_current: lindblad_1996__Na_Ca_ion_exchanger_current(i_NaCa, Na_i, Na_c, Ca_i, Ca_c, R, F, T, V, time_); intracellular_ion_concentrations: lindblad_1996__intracellular_ion_concentrations(Na_i, Ca_i, K_i, Cl_i, Vol_i, time_, F, i_Na, i_Ca_L, i_Ca_T, i_B_Na, i_NaCa, i_p, i_Kr, i_Ks, i_K1, i_to, i_CaP, i_B_Ca, i_up, i_rel, dOCdt, dOTCdt, dOTMgCdt); intracellular_Ca_buffering: lindblad_1996__intracellular_Ca_buffering(dOCdt, dOTCdt, dOTMgCdt, O_TMgMg, Ca_i, time_); cleft_space_ion_concentrations: lindblad_1996__cleft_space_ion_concentrations(Na_c, Ca_c, K_c, Cl_c); Ca_handling_by_the_SR: lindblad_1996__Ca_handling_by_the_SR(i_rel, i_up, time_, Ca_i, V, F); end