//Created by libAntimony v2.4 // Warnings from automatic translation: // Unable to use the formula "-(g * I_Ca * Q * (I_r / taur))" to set the assignment rule for I_r: Loop detected: I_r's definition (-(g * I_Ca * Q * (I_r / taur))) either includes itself directly (i.e. 's5 := 6 + s5') or by proxy (i.e. 's5 := 8*d3' and 'd3 := 9*s5'). model shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__environment(time_) // Variable initializations: time_ = ; end model shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__Ca_concentration_in_the_dyadic_space(cp, I_rel, I_d, i_Ca, time_) // Rate Rules: cp' = alpha * ((I_rel - I_d) + i_Ca); // Variable initializations: cp = ; alpha = 50.0; I_rel = ; I_d = ; i_Ca = ; time_ = ; end model shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__Ca_concentration_in_the_local_JSR(cf_jsr, I_rel, I_tr, time_) // Rate Rules: cf_jsr' = I_tr - I_rel; // Variable initializations: cf_jsr = ; I_rel = ; I_tr = ; time_ = ; end model shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__release_current(I_rel, cp, cf_jsr, time_) // Assignment Rules: I_rel := gs * a * (cf_jsr - cp); a_infinity := power(cp, 2.0) / (power(cp, 2.0) + power(cp_, 2.0)); tau_a := 1.0 / (kd * (power(cp, 2.0) + power(cp_, 2.0))); // Rate Rules: a' = (a_infinity - a) / tau_a; // Variable initializations: gs = 120.0; a = ; cp_ = 65.0; kd = 0.5; cp = ; cf_jsr = ; time_ = ; end model shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__diffusion_current(I_d, cs, cp, time_) // Assignment Rules: I_d := (cp - cs) / tau_p; // Variable initializations: tau_p = 0.0025; cs = ; cp = ; time_ = ; end model shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__transfer_current(I_tr, cf_jsr, time_) // Assignment Rules: I_tr := (cf_nsr - cf_jsr) / tau_tr; // Variable initializations: tau_tr = 0.05; cf_nsr = ; cf_jsr = ; time_ = ; end model shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__L_type_Ca_channel_d_gate(d_infinity, V, time_) // Assignment Rules: d_infinity := 1.0 / (1.0 + exp(-(V - 5.0) / 6.24)); alpha_d := d_infinity / tau_d; beta_d := (1.0 - d_infinity) / tau_d; // Rate Rules: d' = alpha_d * (1.0 - d) - beta_d * d; // Variable initializations: d = ; tau_d = 4.0; V = ; time_ = ; end model shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__L_type_Ca_channel_f_gate(f, V, time_) // Assignment Rules: alpha_f := f_infinity / tau_f; beta_f := (1.0 - f_infinity) / tau_f; f_infinity := 1.0 / (1.0 + exp((V + 35.0) / 8.6)); // Rate Rules: f' = alpha_f * (1.0 - f) - beta_f * f; // Variable initializations: f = ; tau_f = 30.0; V = ; time_ = ; end model shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__L_type_Ca_channel(i_Ca, I_Ca, time_, V, cs, R, T, F, Cao, d_infinity, f) // Sub-modules, and any changes to those submodules: L_type_Ca_channel_d_gate: shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__L_type_Ca_channel_d_gate(d_infinity, V, time_); L_type_Ca_channel_f_gate: shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__L_type_Ca_channel_f_gate(f, V, time_); // Assignment Rules: i_Ca := (i_Ca_ * P_Ca * ((4.0 * V * power(F, 2.0)) / (R * T)) * ((cs * exp((2.0 * V * power(F, 2.0)) / (R * T)) - 0.341 * Cao) / (exp((2.0 * V * power(F, 2.0)) / (R * T)) - 1.0))) / M; I_Ca := M * Po * i_Ca; Po := d_infinity * f * q; alpha_q := q_infinity / tau_q; beta_q := (1.0 - q_infinity) / tau_q; q_infinity := 1.0 / (1.0 + power(cs / cs_, gamma)); tau_q := q_infinity / ko; // Rate Rules: q' = alpha_q * (1.0 - q) - beta_q * q; // Variable initializations: M = ; ko = 8.0; q = ; gamma = ; i_Ca_ = 25.0; P_Ca = 5.4E-4; cs_ = 0.5; cs = ; R = ; T = ; F = ; Cao = ; end model shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__Na_Ca_exchanger(I_NaCa, V, R, T, F, Nai, Nao, cs, Cao) // Assignment Rules: I_NaCa := K_NaCa * (1.0 / (power(K_mNa, 3.0) + power(Nao, 3.0))) * (1.0 / (K_mCa + Cao)) * (1.0 / (1.0 + K_sat * exp((eta - 1.0) * V * (F / (R * T))))) * (exp(eta * V * (F / (R * T))) * power(Nai, 3.0) * Cao - exp((eta - 1.0) * V * (F / (R * T))) * power(Nao, 3.0) * cs); // Variable initializations: K_NaCa = 2E4; K_mNa = 87.5; K_mCa = 1.38; K_sat = 0.1; eta = 0.35; V = ; R = ; T = ; F = ; Nai = ; Nao = ; cs = ; Cao = ; end model shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__uptake_current(I_up, ci) // Assignment Rules: I_up := (vup * power(ci, 2.0)) / (power(ci, 2.0) + power(cup, 2.0)); // Variable initializations: vup = 250.0; cup = 0.5; ci = ; end model shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__calcium_buffering(beta_ci, beta_cs, I_trpn_i, I_trpn_s, ci, cs, time_) // Assignment Rules: beta_ci := power(1.0 + (BSR * KSR) / power(ci + KSR, 2.0) + (BCd * KCd) / power(ci + KCd, 2.0), -1.0); beta_cs := power(1.0 + (BSR * KSR) / power(cs + KSR, 2.0) + (BCd * KCd) / power(cs + KCd, 2.0), -1.0); I_trpn_i := kT_on * ci * (BT - CaTi) - kT_off * CaTi; I_trpn_s := kT_on * cs * (BT - CaTs) - kT_off * CaTs; // Rate Rules: CaTi' = I_trpn_i; CaTs' = I_trpn_s; // Variable initializations: CaTi = ; CaTs = ; kT_on = 32.7; kT_off = 19.6; BT = 70.0; BSR = 47.0; BCd = 24.0; KSR = 0.6; KCd = 7.0; ci = ; cs = ; time_ = ; end model shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__Ca_concentration_in_the_submembrane_space(cs, taus, beta_cs, ci, I_Ca, I_NaCa, I_r, I_trpn_s, time_) // Rate Rules: cs' = beta_cs * ((vi / vs) * ((I_r - ((cs - ci) / taus + I_Ca)) + I_NaCa) - I_trpn_s); // Variable initializations: cs = ; vi = 0.0001; vs = 0.00001; taus = ; beta_cs = ; ci = ; I_Ca = ; I_NaCa = ; I_r = ; I_trpn_s = ; time_ = ; end model shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__Ca_concentration_in_the_cytosol(ci, taus, beta_ci, cs, I_up, I_trpn_i, time_) // Rate Rules: ci' = beta_ci * ((cs - ci) / taus - (I_up + I_trpn_i)); // Variable initializations: ci = ; taus = ; beta_ci = ; cs = ; I_up = ; I_trpn_i = ; time_ = ; end model shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__total_Ca_concentration_in_the_SR(cj, I_up, I_r, time_) // Rate Rules: cj' = I_up - I_r; // Variable initializations: cj = ; I_up = ; I_r = ; time_ = ; end model shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__average_Ca_concentration_in_unrecruited_JSR_compartments(cj_, cj, time_) // Rate Rules: cj_' = (cj - cj_) / taua; // Variable initializations: cj_ = ; taua = 50.0; cj = ; time_ = ; end model shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__Ca_flux_out_of_the_SR(I_r, I_Ca, cj_) // Assignment Rules: N := -(g * I_Ca * A); Q := piecewise( 0.0 , ( cj_ < 50.0) && (cj_ > 0.0 ), cj_ - 50.0 , ( cj_ < 115.0) && (geq(cj_, 50.0) ), u * cj_ + s , geq(cj_, 115.0) ); // Variable initializations: I_r = ; taur = 20.0; g = 1.5E4; s = ; A = ; u = 11.3; I_Ca = ; cj_ = ; end model shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__membrane(V, time_) // Assignment Rules: V := piecewise( Vmin + (Vmax - Vmin) * power(1.0 - power((time_ - m * T) / (m * T), 2.0), 0.5) , ( time_ <= m * T + x * T) && (geq(time_, m * T) ), Vmin , ( time_ < (m + 1.0) * T) && (time_ > m * T + x * T ) ); x := a / (a + T); // Variable initializations: Vmin = -80.0; Vmax = 30.0; m = ; a = 0.666667; T = ; time_ = ; end model shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__intracellular_Na_concentration(Nai) // Assignment Rules: Nai := a / (1.0 + b * power(T, 0.5)); // Variable initializations: a = ; b = ; T = ; end model shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__physical_constants_and_ionic_concentrations(Nao, Cao, R, T, F, taus) // Variable initializations: Nao = 140.0; Cao = 1.8; R = 8.314; T = 310.0; F = 9.65E4; taus = 10.0; end model *shiferaw_watanabe_garfinkel_weiss_karma_2003_version01____main() // Sub-modules, and any changes to those submodules: environment: shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__environment(time_); Ca_concentration_in_the_dyadic_space: shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__Ca_concentration_in_the_dyadic_space(cp, I_rel, I_d, i_Ca, time_); Ca_concentration_in_the_local_JSR: shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__Ca_concentration_in_the_local_JSR(cf_jsr, I_rel, I_tr, time_); release_current: shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__release_current(I_rel, cp, cf_jsr, time_); diffusion_current: shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__diffusion_current(I_d, cs, cp, time_); transfer_current: shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__transfer_current(I_tr, cf_jsr, time_); L_type_Ca_channel: shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__L_type_Ca_channel(i_Ca, I_Ca, time_, V, cs, R, T, F, Cao, d_infinity, f); Na_Ca_exchanger: shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__Na_Ca_exchanger(I_NaCa, V, R, T, F, Nai, Nao, cs, Cao); uptake_current: shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__uptake_current(I_up, ci); calcium_buffering: shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__calcium_buffering(beta_ci, beta_cs, I_trpn_i, I_trpn_s, ci, cs, time_); Ca_concentration_in_the_submembrane_space: shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__Ca_concentration_in_the_submembrane_space(cs, taus, beta_cs, ci, I_Ca, I_NaCa, I_r, I_trpn_s, time_); Ca_concentration_in_the_cytosol: shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__Ca_concentration_in_the_cytosol(ci, taus, beta_ci, cs, I_up, I_trpn_i, time_); total_Ca_concentration_in_the_SR: shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__total_Ca_concentration_in_the_SR(cj, I_up, I_r, time_); average_Ca_concentration_in_unrecruited_JSR_compartments: shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__average_Ca_concentration_in_unrecruited_JSR_compartments(cj_, cj, time_); Ca_flux_out_of_the_SR: shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__Ca_flux_out_of_the_SR(I_r, I_Ca, cj_); membrane: shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__membrane(V, time_); intracellular_Na_concentration: shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__intracellular_Na_concentration(Nai); physical_constants_and_ionic_concentrations: shiferaw_watanabe_garfinkel_weiss_karma_2003_version01__physical_constants_and_ionic_concentrations(Nao, Cao, R, T, F, taus); end