//Created by libAntimony v2.4 model hund_rudy_2004_tissue__Environment(time_, F, K_o, Ca_o, Na_o, Cl_o, FonRT, tissue) // Variable initializations: time_ = ; F = 96485; K_o = 5.4; Ca_o = 1.8; Na_o = 140; Cl_o = 100; FonRT = 0.0374358835078; tissue = 0; end model hund_rudy_2004_tissue__cell(time_, V, F, INa, ICaL, IK1, IKp, IKs, IKr, IpCa, ICab, INaCa, INaK, Ito, Ito2, IClb, INal, naiont, kiont, clont, vmyo, vsr, vnsr, vjsr, vss, AF, i_Stim) // Assignment Rules: caiont := (ICaL + ICab + IpCa) - 2 * INaCa; naiont := INa + 3 * INaCa + 3 * INaK + INal; kiont := ((IKr + IKs + IK1 + IKp) - 2 * INaK) + Ito + 0.5 * i_Stim; clont := IClb + Ito2 + 0.5 * i_Stim; vcell := 1000 * pi * a * a * l; ageo := 2 * pi * a * a + 2 * pi * a * l; Acap := ageo * 2; vmyo := vcell * 0.68; vmito := vcell * 0.26; vsr := vcell * 0.06; vnsr := vcell * 0.0552; vjsr := vcell * 0.0048; vss := vcell * 0.02; AF := Acap / F; i_Stim := piecewise( stim_amplitude , ( geq(time_ - past, stim_offset)) && (time_ - past <= stim_offset + stim_duration ), 0 ); past := floor(time_ / stim_period) * stim_period; // Rate Rules: V' = -(naiont + kiont + caiont + clont); // Variable initializations: time_ = ; V = -85.781844107117; F = ; INa = ; ICaL = ; IK1 = ; IKp = ; IKs = ; IKr = ; IpCa = ; ICab = ; INaCa = ; INaK = ; Ito = ; Ito2 = ; IClb = ; INal = ; l = 0.01; a = 0.0011; stim_offset = 0; stim_period = 1e3; stim_duration = 3; stim_amplitude = -15; end model hund_rudy_2004_tissue__INa(V, time_, ENa, tissue, INa) // Assignment Rules: GNa := piecewise( 8.25 , tissue == 0 , 4 * 8.25 ); gNa := GNa * m * m * m * H * J; am := (0.32 * 1 * (V + 47.13)) / (1 - exp(-(0.1) * (V + 47.13))); bm := 0.08 * exp(- V / 11); ah := piecewise( 0 , geq(V, -(40)) , 0.135 * exp((80 + V) / -(6.8)) ); bh := piecewise( 1 / (0.13 * (1 + exp((V + 10.66) / -(11.1)))) , geq(V, -(40)) , 3.56 * exp(0.079 * V) + 3.1E5 * exp(0.35 * V) ); aj := piecewise( 0 , geq(V, -(40)) , ((-(1.2714E5) * exp(0.2444 * V) - 3.474E-5 * exp(-(0.04391) * V)) * 1 * (V + 37.78)) / (1 + exp(0.311 * (V + 79.23))) ); bj := piecewise( (0.3 * exp(-(2.535E-7) * V)) / (1 + exp(-(0.1) * (V + 32))) , geq(V, -(40)) , (0.1212 * exp(-(0.01052) * V)) / (1 + exp(-(0.1378) * (V + 40.14))) ); INa := gNa * (V - ENa); // Rate Rules: H' = ah * (1 - H) - bh * H; m' = am * (1 - m) - bm * m; J' = aj * (1 - J) - bj * J; // Variable initializations: V = ; time_ = ; ENa = ; tissue = ; H = 0.987317750543; m = 0.001356538159; J = 0.991924983076; end model hund_rudy_2004_tissue__ICaL(V, F, FonRT, time_, tissue, Ca_o, Ca_ss, CaMKactive, ibarca, ICaL) // Assignment Rules: ibarca := (pca * 4 * (V - 15) * F * FonRT * (gacai * Ca_ss * exp(2 * (V - 15) * FonRT) - gacao * Ca_o)) / (exp(2 * (V - 15) * FonRT) - 1); dss := 1 / (1 + exp(-(V - 4) / 6.74)); taud := 0.59 + (0.8 * exp(0.052 * (V + 13))) / (1 + exp(0.132 * (V + 13))); fss := 0.7 / (1 + exp((V + 17.12) / 7)) + 0.3; f2ss := 0.77 / (1 + exp((V + 17.12) / 7)) + 0.23; tauf := 1 / (0.2411 * exp(-power(0.045 * (V - 9.6914), 2)) + 0.0529); tauf2 := 1 / (0.0423 * exp(-power(0.059 * (V - 18.5726), 2)) + 0.0054); dpss := 9 - 8 / (1 + exp(-(V + 65) / 3.4)); fcass := 0.3 / (1 - ICaL / 0.05) + 0.55 / (1 + Ca_ss / 0.003) + 0.15; fca2ss := 1 / (1 - ICaL / 0.01); taufca := (10 * CaMKactive) / (0.15 + CaMKactive) + 1 / (1 + Ca_ss / 0.003) + 0.5; taufca2 := 300 / (1 + exp((- ICaL - 0.175) / 0.04)) + 125; ICaL := piecewise( power(d, dp) * f * f2 * fca * fca2 * ibarca , tissue == 0 , d * f * f2 * fca * fca2 * ibarca ); // Rate Rules: d' = (dss - d) / taud; dp' = (dpss - dp) / 10; f' = (fss - f) / tauf; fca' = (fcass - fca) / taufca; fca2' = (fca2ss - fca2) / taufca2; f2' = (f2ss - f2) / tauf2; // Variable initializations: V = ; F = ; FonRT = ; time_ = ; tissue = ; Ca_o = ; Ca_ss = ; d = 0.00000164013; dp = 8.98230672628; f = 0.999961508634; fca = 0.97836624923; fca2 = 0.893052931249; f2 = 0.992234519148; pca = 2.43e-4; gacai = 1; gacao = 0.341; CaMKactive = ; end model hund_rudy_2004_tissue__IK1(V, EK, K_o, IK1) // Assignment Rules: ak1 := 1.02 / (1 + exp(0.2385 * ((V - EK) - 59.215))); bk1 := (0.49124 * exp(0.08032 * ((V - EK) + 5.476)) + 1 * exp(0.06175 * ((V - EK) - 594.31))) / (1 + exp(-(0.5143) * ((V - EK) + 4.753))); IK1 := ((0.5 * root(K_o / 5.4) * ak1) / (ak1 + bk1)) * (V - EK); // Variable initializations: V = ; EK = ; K_o = ; end model hund_rudy_2004_tissue__IKr(V, EK, K_o, time_, IKr) // Assignment Rules: gkr := 0.0138542 * root(K_o / 5.4); r := 1 / (1 + exp((V + 10) / 15.4)); xrss := 1 / (1 + exp(-(V + 10.085) / 4.25)); tauxr := 1 / ((6E-4 * (V - 1.7384)) / (1 - exp(-(0.136) * (V - 1.7384))) + (3E-4 * (V + 38.3608)) / (exp(0.1522 * (V + 38.3608)) - 1)); IKr := gkr * xr * r * (V - EK); // Rate Rules: xr' = (xrss - xr) / tauxr; // Variable initializations: V = ; EK = ; K_o = ; xr = 0.00000724074; time_ = ; end model hund_rudy_2004_tissue__IKs(V, Ca_i, time_, EKs, IKs) // Assignment Rules: gks := 0.0248975 * (1 + 0.6 / (1 + power(3.8E-5 / Ca_i, 1.4))); xss := 1 / (1 + exp(-(V - 10.5) / 24.7)); tauxs := 1 / ((7.61E-5 * (V + 44.6)) / (1 - exp(-(9.97) * (V + 44.6))) + (3.6E-4 * (V - 0.55)) / (exp(0.128 * (V - 0.55)) - 1)); IKs := gks * xs1 * xs2 * (V - EKs); // Rate Rules: xs1' = (xss - xs1) / tauxs; xs2' = ((xss - xs2) / tauxs) / 2; // Variable initializations: V = ; Ca_i = ; time_ = ; EKs = ; xs1 = 0.019883138161; xs2 = 0.019890650554; end model hund_rudy_2004_tissue__Ito(V, EK, time_, Ito) // Assignment Rules: rv := exp(V / 300); ay := (25 * exp((V - 40) / 25)) / (1 + exp((V - 40) / 25)); by := (25 * exp(-(V + 90) / 25)) / (1 + exp(-(V + 90) / 25)); ay2 := 0.03 / (1 + exp((V + 60) / 5)); by2 := (0.2 * exp((V + 25) / 5)) / (1 + exp((V + 25) / 5)); ay3 := 0.00225 / (1 + exp((V + 60) / 5)); by3 := (0.1 * exp((V + 25) / 5)) / (1 + exp((V + 25) / 5)); Ito := gitodv * power(ydv, 3) * ydv2 * zdv * rv * (V - EK); // Rate Rules: ydv' = ay * (1 - ydv) - by * ydv; ydv2' = ay2 * (1 - ydv2) - by2 * ydv2; zdv' = ay3 * (1 - zdv) - by3 * zdv; // Variable initializations: V = ; gitodv = 0.19; EK = ; time_ = ; ydv = 0.013970786703; ydv2 = 0.99996472752; zdv = 0.829206149767; end model hund_rudy_2004_tissue__INaK(V, Na_i, Na_o, K_o, FonRT, INaK) // Assignment Rules: sigma := (exp(Na_o / 67.3) - 1) / 7; fnak := 1 / (1 + 0.1245 * exp(-(0.1) * V * FonRT) + 0.0365 * sigma * exp(- V * FonRT)); INaK := (((ibarnak * fnak * 1) / (1 + power(kmnai / Na_i, 2))) * K_o) / (K_o + kmko); // Variable initializations: V = ; Na_i = ; Na_o = ; K_o = ; FonRT = ; kmnai = 10; kmko = 1.5; ibarnak = 0.61875; end model hund_rudy_2004_tissue__INaCa(V, FonRT, Ca_i, Ca_o, Na_i, Na_o, INaCa) // Assignment Rules: ca_i_NaCa := 1.5 * Ca_i; allo := 1 / (1 + power(KmCa / ca_i_NaCa, 2)); num := power(Na_i, 3) * Ca_o * exp(eta * V * FonRT) - power(Na_o, 3) * ca_i_NaCa * exp((eta - 1) * V * FonRT); denom1 := 1 + ksat * exp((eta - 1) * V * FonRT); denom2 := KmCao * power(Na_i, 3) + power(KmNao, 3) * ca_i_NaCa + power(KmNai, 3) * Ca_o * (1 + ca_i_NaCa / KmCai); denom3 := KmCai * power(Na_o, 3) * (1 + power(Na_i / KmNai, 3)) + power(Na_i, 3) * Ca_o + power(Na_o, 3) * ca_i_NaCa; INaCa := (NCXmax * allo * num) / (denom1 * (denom2 + denom3)); // Variable initializations: V = ; FonRT = ; Ca_i = ; Ca_o = ; Na_i = ; Na_o = ; KmCa = 1.25e-4; NCXmax = 4.5; ksat = 0.27; eta = 0.35; KmNai = 12.3; KmNao = 87.5; KmCai = 0.0036; KmCao = 1.3; end model hund_rudy_2004_tissue__IKp(V, EK, IKp) // Assignment Rules: IKp := (0.00276 * (V - EK)) / (1 + exp((7.488 - V) / 5.98)); // Variable initializations: V = ; EK = ; end model hund_rudy_2004_tissue__IpCa(Ca_i, IpCa) // Assignment Rules: IpCa := (ibarpca * Ca_i) / (kmpca + Ca_i); // Variable initializations: Ca_i = ; ibarpca = 0.0575; kmpca = 0.5e-3; end model hund_rudy_2004_tissue__ICab(V, F, FonRT, Ca_i, Ca_o, ICab) // Assignment Rules: ICab := (1.995084E-7 * 4 * V * F * FonRT * (Ca_i * exp(2 * V * FonRT) - 0.341 * Ca_o)) / (exp(2 * V * FonRT) - 1); // Variable initializations: V = ; F = ; FonRT = ; Ca_i = ; Ca_o = ; end model hund_rudy_2004_tissue__Ito2(time_, V, F, FonRT, Cl_i, Cl_o, Ca_ss, Ito2) // Assignment Rules: Ito2_max := (PCl * V * F * FonRT * (Cl_i - Cl_o * exp(V * FonRT))) / (1 - exp(V * FonRT)); AAss := 1 / (1 + Kmto2 / Ca_ss); Ito2 := Ito2_max * AA; // Rate Rules: AA' = (AAss - AA) / 1; // Variable initializations: time_ = ; V = ; F = ; FonRT = ; Cl_i = ; Cl_o = ; Ca_ss = ; PCl = 4e-7; AA = 0.000816605172; Kmto2 = 0.1502; end model hund_rudy_2004_tissue__IClb(V, ECl, IClb) // Assignment Rules: IClb := GClb * (V - ECl); // Variable initializations: V = ; ECl = ; GClb = 2.25e-4; end model hund_rudy_2004_tissue__INal(time_, V, ENa, INal) // Assignment Rules: amL := (0.32 * 1 * (V + 47.13)) / (1 - exp(-(0.1) * (V + 47.13))); bmL := 0.08 * exp(- V / 11); hLss := 1 / (1 + exp((V + 91) / 6.1)); INal := GNaL * power(mL, 3) * hL * (V - ENa); // Rate Rules: mL' = amL * (1 - mL) - bmL * mL; hL' = (hLss - hL) / 600; // Variable initializations: time_ = ; V = ; ENa = ; GNaL = 65e-4; mL = 0.001356538159; hL = 0.26130711759; end model hund_rudy_2004_tissue__reversal_potentials(Na_i, Na_o, K_o, K_i, Cl_o, Cl_i, FonRT, ENa, EK, EKs, ECl) // Assignment Rules: ENa := ln(Na_o / Na_i) / FonRT; EK := ln(K_o / K_i) / FonRT; EKs := ln((K_o + prnak * Na_o) / (K_i + prnak * Na_i)) / FonRT; ECl := -ln(Cl_o / Cl_i) / FonRT; // Variable initializations: Na_i = ; Na_o = ; K_o = ; K_i = ; Cl_o = ; Cl_i = ; FonRT = ; prnak = 0.01833; end model hund_rudy_2004_tissue__Irel(time_, tissue, Ca_ss, Ca_jsr, ibarca, ICaL, irelcicr, KmCaMK, CaMKactive) // Assignment Rules: Grel := 3000 * vg; dro_inf := power(Ca_jsr, 1.9) / (power(Ca_jsr, 1.9) + power((49.28 * Ca_ss) / (Ca_ss + 0.0028), 1.9)); dtau_rel := (dtau_rel_max * CaMKactive) / (KmCaMK + CaMKactive); ross := dro_inf / (power(1 / ICaL, 2) + 1); riss := 1 / (1 + exp(((Ca_ss - 4E-4) + 0.002 * cafac) / 2.5E-5)); tauri := 3 + dtau_rel + (350 - dtau_rel) / (1 + exp(((Ca_ss - 0.003) + 0.003 * cafac) / 2E-4)); irelcicr := Grel * ro * ri * (Ca_jsr - Ca_ss); CaMKbound := (CaMK0 * (1 - CaMKtrap)) / (1 + Km / Ca_ss); CaMKactive := CaMKbound + CaMKtrap; vg := piecewise( 1 / (1 + exp((ibarca + 13) / 5)) , tissue == 0 , 1 ); cafac := 1 / (1 + exp((ICaL + 0.05) / 0.015)); // Rate Rules: CaMKtrap' = 0.05 * CaMKactive * (CaMKactive - CaMKtrap) - 6.8E-4 * CaMKtrap; ro' = (ross - ro) / 3; ri' = (riss - ri) / tauri; // Variable initializations: time_ = ; tissue = ; Ca_ss = ; Ca_jsr = ; ibarca = ; ICaL = ; dtau_rel_max = 10; CaMK0 = 0.05; Km = 0.0015; KmCaMK = 0.15; CaMKtrap = 0.021123704774; ro = 0; ri = 0.862666650318; end model hund_rudy_2004_tissue__Iup_Ileak(iup, ileak, KmCaMK, CaMKactive, Ca_i, Ca_nsr) // Assignment Rules: dKmPLB := (dKmPLBmax * CaMKactive) / (KmCaMK + CaMKactive); dJup := (dJupmax * CaMKactive) / (KmCaMK + CaMKactive); iup := ((dJup + 1) * iupmax * Ca_i) / ((Ca_i + Kmup) - dKmPLB); ileak := (iupmax * Ca_nsr) / nsrmax; // Variable initializations: dKmPLBmax = 0.00017; dJupmax = 0.75; iupmax = 0.004375; Kmup = 0.00092; nsrmax = 15; KmCaMK = ; CaMKactive = ; Ca_i = ; Ca_nsr = ; end model hund_rudy_2004_tissue__Idiff_Itr(idiff, itr, Ca_ss, Ca_i, Ca_nsr, Ca_jsr) // Assignment Rules: idiff := (Ca_ss - Ca_i) / 0.2; itr := (Ca_nsr - Ca_jsr) / 120; // Variable initializations: Ca_ss = ; Ca_i = ; Ca_nsr = ; Ca_jsr = ; end model hund_rudy_2004_tissue__Na(time_, Na_i, naiont, AF, vmyo, CTNaCl, ENa, ECl) // Assignment Rules: CTNaCl := (CTNaClmax * power(ENa - ECl, 4)) / (power(ENa - ECl, 4) + power(87.8251, 4)); // Rate Rules: Na_i' = (- naiont * AF) / vmyo + CTNaCl; // Variable initializations: time_ = ; Na_i = 12.972433387269; naiont = ; AF = ; vmyo = ; CTNaClmax = 9.8443e-6; ENa = ; ECl = ; end model hund_rudy_2004_tissue__K(time_, K_i, kiont, AF, vmyo, CTKCl, EK, ECl) // Assignment Rules: CTKCl := (CTKClmax * (EK - ECl)) / ((EK - ECl) + 87.8251); // Rate Rules: K_i' = (- kiont * AF) / vmyo + CTKCl; // Variable initializations: time_ = ; K_i = 135.469546216758; kiont = ; AF = ; vmyo = ; CTKClmax = 7.0756e-6; EK = ; ECl = ; end model hund_rudy_2004_tissue__Cl(time_, Cl_i, clont, AF, vmyo, CTNaCl, CTKCl) // Rate Rules: Cl_i' = (clont * AF) / vmyo + CTNaCl + CTKCl; // Variable initializations: time_ = ; Cl_i = 15.59207157178; clont = ; AF = ; vmyo = ; CTNaCl = ; CTKCl = ; end model hund_rudy_2004_tissue__Ca(time_, Ca_i, Ca_jsr, Ca_nsr, Ca_ss, ICab, ICaL, IpCa, INaCa, vmyo, vsr, vnsr, vjsr, vss, AF, iup, ileak, irelcicr, idiff, itr) // Assignment Rules: bcsqn := 1 / (1 + (kmcsqn * csqnbar) / power(Ca_jsr + kmcsqn, 2)); bmyo := 1 / (1 + (cbar * kmc) / power(Ca_i + kmc, 2) + (kmt * tbar) / power(Ca_i + kmt, 2)); bss := 1 / (1 + (BSRmax * KmBSR) / power(KmBSR + Ca_ss, 2) + (BSLmax * KmBSL) / power(KmBSL + Ca_ss, 2)); // Rate Rules: Ca_i' = bmyo * ((-((ICab + IpCa) - 2 * INaCa) * AF) / (vmyo * 2) + ((ileak - iup) * vnsr) / vmyo + (idiff * vss) / vmyo); Ca_jsr' = bcsqn * (itr - irelcicr); Ca_nsr' = (iup - (itr * vjsr) / vnsr) - ileak; Ca_ss' = bss * (((- ICaL * AF) / (vss * 2) + (irelcicr * vjsr) / vss) - idiff); // Variable initializations: time_ = ; Ca_i = 0.00012131666; Ca_jsr = 1.737580994071; Ca_nsr = 1.832822335168; Ca_ss = 0.00012271265; kmt = 0.5e-3; kmc = 2.38e-3; tbar = 70e-3; cbar = 50e-3; kmcsqn = 0.8; csqnbar = 10; BSRmax = 0.047; KmBSR = 0.00087; BSLmax = 1.124; KmBSL = 0.0087; ICab = ; ICaL = ; IpCa = ; INaCa = ; vmyo = ; vsr = ; vnsr = ; vjsr = ; vss = ; AF = ; iup = ; ileak = ; irelcicr = ; idiff = ; itr = ; end model hund_rudy_2004_tissue__intracellular_currents() end model hund_rudy_2004_tissue__transmembrane_currents() end model hund_rudy_2004_tissue__Ions_n_reversal_potentials() end model *hund_rudy_2004_tissue____main() // Sub-modules, and any changes to those submodules: Environment: hund_rudy_2004_tissue__Environment(time_, F, K_o, Ca_o, Na_o, Cl_o, FonRT, tissue); cell: hund_rudy_2004_tissue__cell(time_, V, F, INa0, ICaL0, IK10, IKp0, IKs0, IKr0, IpCa0, ICab0, INaCa0, INaK0, Ito0, Ito20, IClb0, INal0, naiont, kiont, clont, vmyo, vsr, vnsr, vjsr, vss, AF, i_Stim); INa: hund_rudy_2004_tissue__INa(V, time_, ENa, tissue, INa0); ICaL: hund_rudy_2004_tissue__ICaL(V, F, FonRT, time_, tissue, Ca_o, Ca_ss, CaMKactive, ibarca, ICaL0); IK1: hund_rudy_2004_tissue__IK1(V, EK, K_o, IK10); IKr: hund_rudy_2004_tissue__IKr(V, EK, K_o, time_, IKr0); IKs: hund_rudy_2004_tissue__IKs(V, Ca_i, time_, EKs, IKs0); Ito: hund_rudy_2004_tissue__Ito(V, EK, time_, Ito0); INaK: hund_rudy_2004_tissue__INaK(V, Na_i, Na_o, K_o, FonRT, INaK0); INaCa: hund_rudy_2004_tissue__INaCa(V, FonRT, Ca_i, Ca_o, Na_i, Na_o, INaCa0); IKp: hund_rudy_2004_tissue__IKp(V, EK, IKp0); IpCa: hund_rudy_2004_tissue__IpCa(Ca_i, IpCa0); ICab: hund_rudy_2004_tissue__ICab(V, F, FonRT, Ca_i, Ca_o, ICab0); Ito2: hund_rudy_2004_tissue__Ito2(time_, V, F, FonRT, Cl_i, Cl_o, Ca_ss, Ito20); IClb: hund_rudy_2004_tissue__IClb(V, ECl, IClb0); INal: hund_rudy_2004_tissue__INal(time_, V, ENa, INal0); reversal_potentials: hund_rudy_2004_tissue__reversal_potentials(Na_i, Na_o, K_o, K_i, Cl_o, Cl_i, FonRT, ENa, EK, EKs, ECl); Irel: hund_rudy_2004_tissue__Irel(time_, tissue, Ca_ss, Ca_jsr, ibarca, ICaL0, irelcicr, KmCaMK, CaMKactive); Iup_Ileak: hund_rudy_2004_tissue__Iup_Ileak(iup, ileak, KmCaMK, CaMKactive, Ca_i, Ca_nsr); Idiff_Itr: hund_rudy_2004_tissue__Idiff_Itr(idiff, itr, Ca_ss, Ca_i, Ca_nsr, Ca_jsr); Na: hund_rudy_2004_tissue__Na(time_, Na_i, naiont, AF, vmyo, CTNaCl, ENa, ECl); K: hund_rudy_2004_tissue__K(time_, K_i, kiont, AF, vmyo, CTKCl, EK, ECl); Cl: hund_rudy_2004_tissue__Cl(time_, Cl_i, clont, AF, vmyo, CTNaCl, CTKCl); Ca: hund_rudy_2004_tissue__Ca(time_, Ca_i, Ca_jsr, Ca_nsr, Ca_ss, ICab0, ICaL0, IpCa0, INaCa0, vmyo, vsr, vnsr, vjsr, vss, AF, iup, ileak, irelcicr, idiff, itr); intracellular_currents: hund_rudy_2004_tissue__intracellular_currents(); transmembrane_currents: hund_rudy_2004_tissue__transmembrane_currents(); Ions_n_reversal_potentials: hund_rudy_2004_tissue__Ions_n_reversal_potentials(); end