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Component: calcium

\frac{d}{d time} (CaSR1) = calcium_CaSR1_beta DCaSR (\frac{(CaSR2 - (2.0 CaSR1)) + CaSR1}{{dx}^{2.0}} + \frac{CaSR2 - CaSR1}{2.0 1.0 {dx}^{2.0}}) + \frac{JSRCa1}{VSR1} calcium_CaSR1_beta \frac{d}{d time} (CaSR2) = calcium_CaSR2_beta DCaSR (\frac{(CaSR3 - (2.0 CaSR2)) + CaSR1}{{dx}^{2.0}} + \frac{CaSR3 - CaSR1}{2.0 2.0 {dx}^{2.0}}) + \frac{JSRCa2}{VSR2} calcium_CaSR2_beta \frac{d}{d time} (CaSR3) = calcium_CaSR3_beta DCaSR (\frac{(CaSR4 - (2.0 CaSR3)) + CaSR2}{{dx}^{2.0}} + \frac{CaSR4 - CaSR2}{2.0 3.0 {dx}^{2.0}}) + \frac{JSRCa3}{VSR3} calcium_CaSR3_beta \frac{d}{d time} (CaSR4) = calcium_CaSR4_beta DCaSR (\frac{(CaSR4 - (2.0 CaSR4)) + CaSR3}{{dx}^{2.0}} + \frac{CaSR4 - CaSR3}{2.0 4.0 {dx}^{2.0}}) + \frac{JSRCa4}{VSR4} calcium_CaSR4_beta \frac{d}{d time} (Cai1) = (calcium_Cai1_beta (DCa + calcium_Cai1_gamma DCaBm) (\frac{(Cai2 - (2.0 Cai1)) + Cai1}{{dx}^{2.0}} + \frac{Cai2 - Cai1}{2.0 1.0 {dx}^{2.0}}) - (\frac{2.0 calcium_Cai1_beta calcium_Cai1_gamma DCaBm}{KdBCa + Cai1} {(\frac{Cai2 - Cai1}{2.0 dx})}^{2.0})) + \frac{JCa1}{Vnonjunct1} calcium_Cai1_beta \frac{d}{d time} (Cai2) = (calcium_Cai2_beta (DCa + calcium_Cai2_gamma DCaBm) (\frac{(Cai3 - (2.0 Cai2)) + Cai1}{{dx}^{2.0}} + \frac{Cai3 - Cai1}{2.0 2.0 {dx}^{2.0}}) - (\frac{2.0 calcium_Cai2_beta calcium_Cai2_gamma DCaBm}{KdBCa + Cai2} {(\frac{Cai3 - Cai1}{2.0 dx})}^{2.0})) + \frac{JCa2}{Vnonjunct2} calcium_Cai2_beta \frac{d}{d time} (Cai3) = (calcium_Cai3_beta (DCa + calcium_Cai3_gamma DCaBm) (\frac{(Cai4 - (2.0 Cai3)) + Cai2}{{dx}^{2.0}} + \frac{Cai4 - Cai2}{2.0 3.0 {dx}^{2.0}}) - (\frac{2.0 calcium_Cai3_beta calcium_Cai3_gamma DCaBm}{KdBCa + Cai3} {(\frac{Cai4 - Cai2}{2.0 dx})}^{2.0})) + \frac{JCa3}{Vnonjunct3} calcium_Cai3_beta \frac{d}{d time} (Cai4) = (calcium_Cai4_beta (DCa + calcium_Cai4_gamma DCaBm) (\frac{(Cai4 - (2.0 Cai4)) + Cai3}{{dx}^{2.0}} + \frac{Cai4 - Cai3}{2.0 4.0 {dx}^{2.0}}) - (\frac{2.0 calcium_Cai4_beta calcium_Cai4_gamma DCaBm}{KdBCa + Cai4} {(\frac{Cai4 - Cai3}{2.0 dx})}^{2.0})) + \frac{JCa4}{Vnonjunct4} calcium_Cai4_beta \frac{d}{d time} (Cass) = calcium_Cass_beta (\frac{JCass}{Vss} + \frac{calcium_Cass_i_tot}{2.0 Vss F}) JCa1 = (- J_bulkSERCA1) + JSRCaleak1 + Jrel1 JCa2 = (- J_bulkSERCA2) + JSRCaleak2 + Jrel2 JCa3 = (- J_bulkSERCA3) + JSRCaleak3 + Jrel3 JCa4 = Jj_nj JCass = ((- Jj_nj) + JSRCaleakss - J_bulkSERCAss) + Jrelss JSRCa1 = J_SERCASR1 - JSRCaleak1 - Jrel1 JSRCa2 = J_SERCASR2 - JSRCaleak2 - Jrel2 JSRCa3 = J_SERCASR3 - JSRCaleak3 - Jrel3 JSRCa4 = J_SERCASRss - JSRCaleakss - Jrelss JSRCaleak1 = kSRleak (CaSR1 - Cai1) Vnonjunct1 JSRCaleak2 = kSRleak (CaSR2 - Cai2) Vnonjunct2 JSRCaleak3 = kSRleak (CaSR3 - Cai3) Vnonjunct3 JSRCaleakss = kSRleak (CaSR4 - Cass) Vss Jj_nj = \frac{DCa Aj_nj}{xj_nj} (Cass - Cai4) (1e-06) calcium_CaSR1_beta = \frac{1.0}{1.0 + \frac{CSQN KdCSQN}{{(CaSR1 + KdCSQN)}^{2.0}}} calcium_CaSR2_beta = \frac{1.0}{1.0 + \frac{CSQN KdCSQN}{{(CaSR2 + KdCSQN)}^{2.0}}} calcium_CaSR3_beta = \frac{1.0}{1.0 + \frac{CSQN KdCSQN}{{(CaSR3 + KdCSQN)}^{2.0}}} calcium_CaSR4_beta = \frac{1.0}{1.0 + \frac{CSQN KdCSQN}{{(CaSR4 + KdCSQN)}^{2.0}}} calcium_Cai1_beta = \frac{1.0}{1.0 + calcium_Cai1_gamma} calcium_Cai1_gamma = \frac{BCa KdBCa}{{(Cai1 + KdBCa)}^{2.0}} calcium_Cai2_beta = \frac{1.0}{1.0 + calcium_Cai2_gamma} calcium_Cai2_gamma = \frac{BCa KdBCa}{{(Cai2 + KdBCa)}^{2.0}} calcium_Cai3_beta = \frac{1.0}{1.0 + calcium_Cai3_gamma} calcium_Cai3_gamma = \frac{BCa KdBCa}{{(Cai3 + KdBCa)}^{2.0}} calcium_Cai4_beta = \frac{1.0}{1.0 + calcium_Cai4_gamma} calcium_Cai4_gamma = \frac{BCa KdBCa}{{(Cai4 + KdBCa)}^{2.0}} calcium_Cass_beta = \frac{1.0}{1.0 + \frac{SLlow KdSLlow}{{(Cass + KdSLlow)}^{2.0}} + \frac{SLhigh KdSLhigh}{{(Cass + KdSLhigh)}^{2.0}} + \frac{BCa KdBCa}{{(Cass + KdBCa)}^{2.0}}} calcium_Cass_i_tot = (- ICaL - ICab - ICaP) + 2.0 INaCa

Component: cell

Aj_nj = pi rjunct 2.0 lcell 0.5 VSR1 = \frac{0.05 Vnonjunct1}{2.0} 0.9 VSR2 = \frac{0.05 Vnonjunct2}{2.0} 0.9 VSR3 = \frac{0.05 Vnonjunct3}{2.0} 0.9 VSR4 = \frac{0.05 Vnonjunct4}{2.0} 0.9 Vcytosol = Vnonjunct_Nai + Vss Vnonjunct1 = ({(1.0 dx)}^{2.0} - ({(0.0 dx)}^{2.0})) pi lcell 0.5 (1e-06) Vnonjunct2 = ({(2.0 dx)}^{2.0} - ({(1.0 dx)}^{2.0})) pi lcell 0.5 (1e-06) Vnonjunct3 = ({(3.0 dx)}^{2.0} - ({(2.0 dx)}^{2.0})) pi lcell 0.5 (1e-06) Vnonjunct4 = ({(4.0 dx)}^{2.0} - ({(3.0 dx)}^{2.0})) pi lcell 0.5 (1e-06) Vnonjunct_Nai = Vnonjunct1 + Vnonjunct2 + Vnonjunct3 + Vnonjunct4 xj_nj = \frac{0.02}{2.0} + \frac{dx}{2.0} xj_nj_Nai = \frac{0.02}{2.0} + 2.0 dx

Component: engine

Component: extra

Component: icab

ICab = gCab (V - ECa)

Component: ical

ICaL = gCaL d fca f1 f2 (V - ECa_app) \frac{d}{d time} (d) = \frac{ical_d_inf - d}{ical_d_tau} \frac{d}{d time} (f1) = \frac{f_inf - f1}{ical_f1_tau} \frac{d}{d time} (f2) = \frac{f_inf - f2}{ical_f2_tau} f_inf = \frac{1.0}{1.0 + ⅇ^{\frac{V + 27.4}{7.1}}} \frac{d}{d time} (fca) = \frac{ical_fca_inf - fca}{ical_fca_tau} ical_d_inf = \frac{1.0}{1.0 + ⅇ^{\frac{V + 9.0}{- 5.8}}} ical_d_tau = 0.0027 ⅇ^{- ({(\frac{V + 35.0}{30.0})}^{2.0})} + 0.002 ical_f1_tau = 0.98698 ⅇ^{- ({(\frac{V + 30.16047}{7.09396})}^{2.0})} + \frac{0.04275}{1.0 + ⅇ^{\frac{V - 51.61555}{- 80.61331}}} + \frac{0.03576}{1.0 + ⅇ^{\frac{V + 29.57272}{13.21758}}} - 0.00821 ical_f2_tau = 1.3323 ⅇ^{- ({(\frac{V + 40.0}{14.2})}^{2.0})} + 0.0626 ical_fca_inf = 1.0 - (\frac{1.0}{1.0 + {(\frac{kCa}{Cass})}^{kCan}})

Component: icap

ICaP = \frac{ICaPmax Cass}{kCaP + Cass}

Component: if

If = IfK + IfNa IfK = gIf y (1.0 - 0.2677) (V - EK) IfNa = gIf y 0.2677 (V - ENa) if_y_inf = \frac{1.0}{1.0 + ⅇ^{\frac{V + 97.82874}{12.48025}}} if_y_tau = \frac{1.0}{0.00332 ⅇ^{\frac{- V}{16.54103}} + 23.71839 ⅇ^{\frac{V}{16.54103}}} \frac{d}{d time} (y) = \frac{if_y_inf - y}{if_y_tau}

Component: ik1

IK1 = \frac{gK1 {(Ko 1.0)}^{0.4457} (V - EK)}{1.0 + ⅇ^{1.5 ((V - EK) + 3.6) FRT}} gK1 = 3.825 0.9

Component: ikr

IKr = gKr pa pi (V - EK) ikr_pa_inf = \frac{1.0}{1.0 + ⅇ^{\frac{V + 15.0}{- 6.0}}} ikr_pa_tau = 0.21718 ⅇ^{- ({(\frac{V + 20.1376}{22.1996})}^{2.0})} + 0.03118 \frac{d}{d time} (pa) = \frac{ikr_pa_inf - pa}{ikr_pa_tau} pi = \frac{1.0}{1.0 + ⅇ^{\frac{V + 55.0}{24.0}}}

Component: iks

IKs = gKs n (V - EK) iks_n_inf = \frac{1.0}{1.0 + ⅇ^{\frac{V - 19.9}{- 12.7}}} iks_n_tau = 0.4 ⅇ^{- ({(\frac{V - 20.0}{20.0})}^{2.0})} + 0.7 \frac{d}{d time} (n) = \frac{iks_n_inf - n}{iks_n_tau}

Component: ikur

IKur = gKur r s (V - EK) gKur = 0.89 2.75 ikur_r_inf = \frac{1.0}{1.0 + ⅇ^{\frac{V + 6.0}{- 8.6}}} ikur_r_tau = \frac{0.009}{1.0 + ⅇ^{\frac{V + 5.0}{12.0}}} + 0.0005 ikur_s_inf = \frac{1.0}{1.0 + ⅇ^{\frac{V + 7.5}{10.0}}} ikur_s_tau = \frac{0.59}{1.0 + ⅇ^{\frac{V + 60.0}{10.0}}} + 3.05 \frac{d}{d time} (r) = \frac{ikur_r_inf - r}{ikur_r_tau} \frac{d}{d time} (s) = \frac{ikur_s_inf - s}{ikur_s_tau}

Component: ina

INa = \frac{PNa m^{3.0} (0.9 h1 + 0.1 h2) Nao V F FRT (ⅇ^{(V - ENa) FRT} - 1.0)}{ⅇ^{V FRT} - 1.0} \frac{d}{d time} (h1) = \frac{h_inf - h1}{ina_h1_tau} \frac{d}{d time} (h2) = \frac{h_inf - h2}{ina_h2_tau} h_inf = \frac{1.0}{1.0 + ⅇ^{\frac{V + 63.6}{5.3}}} ina_h1_tau = \frac{0.03}{1.0 + ⅇ^{\frac{V + 35.1}{3.2}}} + 0.0003 ina_h2_tau = \frac{0.12}{1.0 + ⅇ^{\frac{V + 35.1}{3.2}}} + 0.003 ina_m_inf = \frac{1.0}{1.0 + ⅇ^{\frac{V + 27.12}{- 8.21}}} ina_m_tau = (4.2e-05) ⅇ^{- ({(\frac{V + 25.57}{28.8})}^{2.0})} + (2.4e-05) \frac{d}{d time} (m) = \frac{ina_m_inf - m}{ina_m_tau}

Component: inab

INab = gNab (V - ENa)

Component: inaca

INaCa = \frac{kNaCa (ⅇ^{gam V FRT} {Nass}^{3.0} Cao - (ⅇ^{(gam - 1.0) V FRT} {Nao}^{3.0} Cass fCaNCX))}{1.0 + dNaCa ({Nao}^{3.0} Cass fCaNCX + {Nass}^{3.0} Cao)}

Component: inak

INaK = \frac{\frac{\frac{INaKmax Ko}{Ko + kNaKK} Nass15}{Nass15 + {kNaKNa}^{1.5}} (V + 150.0)}{V + 200.0} Nass15 = {(Nass 1.0)}^{1.5}

Component: it

It = gt r s (V - EK) gt = 1.09 7.5 it_r_inf = \frac{1.0}{1.0 + ⅇ^{\frac{V - 1.0}{- 11.0}}} it_r_tau = 0.0035 ⅇ^{- ({(\frac{V + 0.0}{30.0})}^{2.0})} + 0.0015 it_s_inf = \frac{1.0}{1.0 + ⅇ^{\frac{V + 40.5}{11.5}}} it_s_tau = 0.025635 ⅇ^{- ({(\frac{V + 52.45}{15.8827})}^{2.0})} + 0.01414 \frac{d}{d time} (r) = \frac{it_r_inf - r}{it_r_tau} \frac{d}{d time} (s) = \frac{it_s_inf - s}{it_s_tau}

Component: membrane

\frac{d}{d time} (V) = \frac{- (i_ion + i_stim)}{Cm} i_ion = + INa + ICaL + It + IKur + IK1 + IKr + IKs + INab + ICab + INaK + ICaP + INaCa + If

Component: nernst

ECa = \frac{RTF \ln (\frac{Cao}{Cass})}{2.0} EK = RTF \ln (\frac{Ko}{Ki}) ENa = RTF \ln (\frac{Nao}{Nass})

Component: phys

FRT = \frac{1.0}{RTF} RTF = \frac{R T}{F}

Component: potassium

\frac{d}{d time} (Ki) = \frac{- i_tot}{Vcytosol F} i_tot = (+ It + IKur + IK1 + IKr + IKs - (2.0 INaK)) + IfK + i_stim

Component: ryr

Jrel1 = nu1 o1 c1 SRCa1 (CaSR1 - Cai1) Jrel2 = nu2 o2 c2 SRCa2 (CaSR2 - Cai2) Jrel3 = nu3 o3 c3 SRCa3 (CaSR3 - Cai3) Jrelss = nuss oss css SRCass (CaSR4 - Cass) SRCa1 = 1.0 - (\frac{1.0}{1.0 + ⅇ^{\frac{CaSR1 - 0.3}{0.1}}}) SRCa2 = 1.0 - (\frac{1.0}{1.0 + ⅇ^{\frac{CaSR2 - 0.3}{0.1}}}) SRCa3 = 1.0 - (\frac{1.0}{1.0 + ⅇ^{\frac{CaSR3 - 0.3}{0.1}}}) SRCass = 1.0 - (\frac{1.0}{1.0 + ⅇ^{\frac{CaSR4 - 0.3}{0.1}}}) \frac{d}{d time} (a1) = \frac{ainf1 - a1}{tau_adapt} \frac{d}{d time} (a2) = \frac{ainf2 - a2}{tau_adapt} \frac{d}{d time} (a3) = \frac{ainf3 - a3}{tau_adapt} ainf1 = 0.505 - (\frac{0.427}{1.0 + ⅇ^{\frac{Cai1 1000.0 - 0.29}{0.082}}}) ainf2 = 0.505 - (\frac{0.427}{1.0 + ⅇ^{\frac{Cai2 1000.0 - 0.29}{0.082}}}) ainf3 = 0.505 - (\frac{0.427}{1.0 + ⅇ^{\frac{Cai3 1000.0 - 0.29}{0.082}}}) ainfss = 0.505 - (\frac{0.427}{1.0 + ⅇ^{\frac{Cass 1000.0 - 0.29}{0.082}}}) \frac{d}{d time} (ass) = \frac{ainfss - ass}{tau_adapt} \frac{d}{d time} (c1) = \frac{cinf1 - c1}{tau_inact} \frac{d}{d time} (c2) = \frac{cinf2 - c2}{tau_inact} \frac{d}{d time} (c3) = \frac{cinf3 - c3}{tau_inact} cinf1 = \frac{1.0}{1.0 + ⅇ^{\frac{Cai1 1000.0 - (a1 + 0.02)}{0.01}}} cinf2 = \frac{1.0}{1.0 + ⅇ^{\frac{Cai2 1000.0 - (a2 + 0.02)}{0.01}}} cinf3 = \frac{1.0}{1.0 + ⅇ^{\frac{Cai3 1000.0 - (a3 + 0.02)}{0.01}}} cinfss = \frac{1.0}{1.0 + ⅇ^{\frac{Cass 1000.0 - (ass + 0.02)}{0.01}}} \frac{d}{d time} (css) = \frac{cinfss - css}{tau_inactss} nu1 = 1.0 Vnonjunct1 nu2 = 1.0 Vnonjunct2 nu3 = 1.0 Vnonjunct3 nuss = 625.0 Vss \frac{d}{d time} (o1) = \frac{oinf1 - o1}{tau_act} \frac{d}{d time} (o2) = \frac{oinf2 - o2}{tau_act} \frac{d}{d time} (o3) = \frac{oinf3 - o3}{tau_act} oinf1 = 1.0 - (\frac{1.0}{1.0 + ⅇ^{\frac{Cai1 1000.0 - (a1 + 0.22)}{0.03}}}) oinf2 = 1.0 - (\frac{1.0}{1.0 + ⅇ^{\frac{Cai2 1000.0 - (a2 + 0.22)}{0.03}}}) oinf3 = 1.0 - (\frac{1.0}{1.0 + ⅇ^{\frac{Cai3 1000.0 - (a3 + 0.22)}{0.03}}}) oinfss = 1.0 - (\frac{1.0}{1.0 + ⅇ^{\frac{Cass 1000.0 - (ass + 0.22)}{0.03}}}) \frac{d}{d time} (oss) = \frac{oinfss - oss}{tau_actss}

Component: serca

J_SERCASR1 = ((- k3) {CaSR1}^{2.0} (cpumps - a1) + k4 a1) Vnonjunct1 2.0 J_SERCASR2 = ((- k3) {CaSR2}^{2.0} (cpumps - a2) + k4 a2) Vnonjunct2 2.0 J_SERCASR3 = ((- k3) {CaSR3}^{2.0} (cpumps - a3) + k4 a3) Vnonjunct3 2.0 J_SERCASRss = ((- k3) {CaSR4}^{2.0} (cpumps - ass) + k4 ass) Vss 2.0 J_bulkSERCA1 = (k1 {Cai1}^{2.0} (cpumps - a1) - (k2 a1)) Vnonjunct1 2.0 J_bulkSERCA2 = (k1 {Cai2}^{2.0} (cpumps - a2) - (k2 a2)) Vnonjunct2 2.0 J_bulkSERCA3 = (k1 {Cai3}^{2.0} (cpumps - a3) - (k2 a3)) Vnonjunct3 2.0 J_bulkSERCAss = (k1 {Cass}^{2.0} (cpumps - ass) - (k2 ass)) Vss 2.0 \frac{d}{d time} (a1) = \frac{0.5 ((- J_SERCASR1) + J_bulkSERCA1)}{Vnonjunct1} \frac{d}{d time} (a2) = \frac{0.5 ((- J_SERCASR2) + J_bulkSERCA2)}{Vnonjunct2} \frac{d}{d time} (a3) = \frac{0.5 ((- J_SERCASR3) + J_bulkSERCA3)}{Vnonjunct3} \frac{d}{d time} (ass) = \frac{0.5 ((- J_SERCASRss) + J_bulkSERCAss)}{Vss} k1 = {1000.0}^{2.0} k4 k2 = k1 {SERCAKmf}^{2.0} k3 = \frac{k4}{{SERCAKmr}^{2.0}}

Component: sodium

BNa = 0.49 2.31 JNa = \frac{DNa Aj_nj}{xj_nj_Nai} (Nass - Nai) (1e-06) \frac{d}{d time} (Nai) = \frac{JNa}{Vnonjunct_Nai} \frac{d}{d time} (Nass) = betaNass (\frac{- JNa}{Vss} - (\frac{i_ss}{Vss F})) betaNass = \frac{1.0}{1.0 + \frac{BNa KdBNa}{{(Nass + KdBNa)}^{2.0}}} i_ss = + INa + INab + 3.0 INaK + 3.0 INaCa + IfNa

Component: stimulus

amplitude = - 2500.0 i_stim = \{\begin{matrix} 1.0 if time - offset - (period ⌊ \frac{time - offset}{period} ⌋) < duration \\ 0.0 otherwise \end{matrix} amplitude

Source: Derived from workspace Koivumäki, Korhonen, Tavi 2011 Atrial AP model at changeset dbf305e925d3.

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Koivumäki, Korhonen, Tavi 2011 Atrial AP model