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Model Mathematics

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Component: environment

Component: extracellular

Component: physical_constants

Component: cell_geometry

vcell = 1000 3.1416 rad rad L Ageo = 2 3.1416 rad rad + 2 3.1416 rad L Acap = 2 Ageo vmyo = 0.68 vcell vnsr = 0.0552 vcell vjsr = 0.0048 vcell vss = 0.02 vcell vsr = 0.95 (vnsr + vjsr)

Component: membrane

Istim = \{\begin{matrix} i_Stim_Amplitude if time \geq i_Stim_Start \land time ≦ i_Stim_End \land time - i_Stim_Start - (⌊ \frac{time - i_Stim_Start}{i_Stim_Period} ⌋ i_Stim_Period) ≦ i_Stim_PulseDuration \\ 0.0 otherwise \end{matrix} vffrt = \frac{v F F}{R T} vfrt = \frac{v F}{R T} \frac{d}{d time} (v) = - (INa + INaL + Ito + ICaL + ICaNa + ICaK + IKr + IKs + IK1 + INaCa_i + INaCa_ss + INaK + INab + IKb + IpCa + ICab + Istim)

Component: CaMK

CaMKb = \frac{CaMKo (1.0 - CaMKt)}{1.0 + \frac{KmCaM}{cass}} CaMKa = CaMKb + CaMKt \frac{d}{d time} (CaMKt) = aCaMK CaMKb (CaMKb + CaMKt) - (bCaMK CaMKt)

Component: intracellular_ions

cmdnmax = \{\begin{matrix} cmdnmax_b 1.2 if celltype = 1 \\ cmdnmax_b otherwise \end{matrix} \frac{d}{d time} (nai) = \frac{(- (INa + INaL + 3 INaCa_i + 3 INaK + INab)) Acap cm}{F vmyo} + \frac{JdiffNa vss}{vmyo} \frac{d}{d time} (nass) = \frac{(- (ICaNa + 3 INaCa_ss)) cm Acap}{F vss} - JdiffNa \frac{d}{d time} (ki) = \frac{(- (Ito + IKr + IKs + IK1 + IKb + Istim - (2 INaK))) cm Acap}{F vmyo} + \frac{JdiffK vss}{vmyo} \frac{d}{d time} (kss) = \frac{(- ICaK) cm Acap}{F vss} - JdiffK Bcai = \frac{1}{1 + \frac{cmdnmax kmcmdn}{{(kmcmdn + cai)}^{2}} + \frac{trpnmax kmtrpn}{{(kmtrpn + cai)}^{2}}} \frac{d}{d time} (cai) = Bcai ((\frac{(- (IpCa + ICab - (2 INaCa_i))) Acap}{2 F vmyo} - (\frac{Jup vsr}{vmyo})) + \frac{Jleak vsr}{vmyo} + \frac{Jdiff vss}{vmyo}) Bcass = \frac{1}{1 + \frac{BSRmax KmBSR}{{(KmBSR + cass)}^{2}} + \frac{BSLmax KmBSL}{{(KmBSL + cass)}^{2}}} \frac{d}{d time} (cass) = Bcass (\frac{(- (ICaL - (2 INaCa_ss))) Acap}{2 F vss} + \frac{Jrel vsr}{vss} - Jdiff) Bcasr = \frac{1}{1 + \frac{csqnmax kmcsqn}{{(kmcsqn + casr)}^{2}}} \frac{d}{d time} (casr) = Bcasr (Jup - Jleak - Jrel)

Component: reversal_potentials

ENa = \frac{R T}{F} \ln (\frac{nao}{nai}) EK = \frac{R T}{F} \ln (\frac{ko}{ki}) EKs = \frac{R T}{F} \ln (\frac{ko + PKNa nao}{ki + PKNa nai})

Component: INa

mss = \frac{1.0}{1.0 + ⅇ^{\frac{- (v + mssV1)}{mssV2}}} tm = \frac{1}{mtD1 ⅇ^{\frac{v + mtV1}{mtV2}} + mtD2 ⅇ^{\frac{- (v + mtV3)}{mtV4}}} \frac{d}{d time} (m) = \frac{mss - m}{tm} hss = \frac{1.0}{1.0 + ⅇ^{\frac{v + hssV1}{hssV2}}} thf = \frac{1.0}{3.6860 e -6 ⅇ^{\frac{- (v + 3.8875)}{7.8579}} + 16 ⅇ^{\frac{v - 0.4963}{9.1843}}} + 0.075 ths = \frac{1.0}{0.009794 ⅇ^{\frac{- (v + 17.95)}{28.05}} + 0.3343 ⅇ^{\frac{v + 5.73}{56.66}}} Ahs = 1.0 - Ahf \frac{d}{d time} (hf) = \frac{hss - hf}{thf} \frac{d}{d time} (hs) = \frac{hss - hs}{ths} h = Ahf hf + Ahs hs jss = hss tj = (4.8590 + \frac{1.0}{0.8628 ⅇ^{\frac{- (v + 116.7258)}{7.6005}} + 1.1096 ⅇ^{\frac{v + 6.2719}{9.0358}}}) btj \frac{d}{d time} (j) = \frac{jss - j}{tj} hssp = \frac{1}{1 + ⅇ^{\frac{v + 84.7}{6.220}}} thsp = 3 ths \frac{d}{d time} (hsp) = \frac{hssp - hsp}{thsp} hp = Ahf hf + Ahs hsp tjp = 1.46 tj \frac{d}{d time} (jp) = \frac{jss - jp}{tjp} fINap = \frac{1.0}{1.0 + \frac{KmCaMK}{CaMKa}} INa = GNa bGNa (v - ENa) m^{3} ((1 - fINap) h j + fINap hp jp)

Component: INaL

mLss = \frac{1}{1 + ⅇ^{\frac{- (v + 42.85)}{5.264}}} tmL = tm \frac{d}{d time} (mL) = \frac{mLss - mL}{tmL} hLss = \frac{1.0}{1.0 + ⅇ^{\frac{v + 87.61}{7.488}}} thL = 200.0 bthL \frac{d}{d time} (hL) = \frac{hLss - hL}{thL} hLssp = \frac{1}{1 + ⅇ^{\frac{v + 93.81}{7.488}}} thLp = 3.0 thL \frac{d}{d time} (hLp) = \frac{hLssp - hLp}{thLp} GNaL = \{\begin{matrix} GNaL_b bGnal 0.7 if celltype = 1 \\ GNaL_b bGnal otherwise \end{matrix} fINaLp = \frac{1.0}{1.0 + \frac{KmCaMK}{CaMKa}} INaL = GNaL (v - ENa) mL ((1.0 - fINaLp) hL + fINaLp hLp)

Component: Ito

ass = \frac{1}{1 + ⅇ^{\frac{- (v + EKshift - 14.34)}{14.82}}} ta = \frac{1.0515}{\frac{1.0}{1.2089 (1.0 + ⅇ^{\frac{- (v + EKshift - 18.4099)}{29.3814}})} + \frac{3.5}{1.0 + ⅇ^{\frac{v + EKshift + 100.0}{29.3814}}}} \frac{d}{d time} (a) = \frac{ass - a}{ta} iss = \frac{1.0}{1.0 + ⅇ^{\frac{v + EKshift + 43.94}{5.711}}} delta_epi = \{\begin{matrix} 1.0 - (\frac{0.95}{1 + ⅇ^{\frac{v + EKshift + 70}{5}}}) if celltype = 1 \\ 1.0 otherwise \end{matrix} tiF_b = 4.562 + \frac{1.0}{0.3933 ⅇ^{\frac{- (v + EKshift + 100.0)}{100.0}} + 0.08004 ⅇ^{\frac{v + EKshift + 50.0}{16.59}}} tiS_b = 23.62 + \frac{1}{0.001416 ⅇ^{\frac{- (v + EKshift + 96.52)}{59.05}} + 1.78 e -8 ⅇ^{\frac{v + EKshift + 114.1}{8.079}}} tiF = tiF_b delta_epi tiS = tiS_b delta_epi AiF = \frac{1.0}{1.0 + ⅇ^{\frac{v + EKshift - 213.6}{151.2}}} AiS = 1.0 - AiF \frac{d}{d time} (iF) = \frac{iss - iF}{tiF} \frac{d}{d time} (iS) = \frac{iss - iS}{tiS} i = AiF iF + AiS iS assp = \frac{1.0}{1.0 + ⅇ^{\frac{- (v + EKshift - 24.34)}{14.82}}} \frac{d}{d time} (ap) = \frac{assp - ap}{ta} dti_develop = 1.354 + \frac{1 e -4}{ⅇ^{\frac{v + EKshift - 167.4}{15.89}} + ⅇ^{\frac{- (v + EKshift - 12.23)}{0.2154}}} dti_recover = 1.0 - (\frac{0.5}{1 + ⅇ^{\frac{v + EKshift + 70.0}{20.0}}}) tiFp = dti_develop dti_recover tiF tiSp = dti_develop dti_recover tiS \frac{d}{d time} (iFp) = \frac{iss - iFp}{tiFp} \frac{d}{d time} (iSp) = \frac{iss - iSp}{tiSp} ip = AiF iFp + AiS iSp Gto = \{\begin{matrix} bGto Gto_b 4 if celltype = 1 \\ bGto Gto_b 4 if celltype = 2 \\ Gto_b bGto otherwise \end{matrix} fItop = \frac{1.0}{1.0 + \frac{KmCaMK}{CaMKa}} Ito = Gto (v - EK) ((1.0 - fItop) a i + fItop ap ip)

Component: ICaL

fICaLp = \frac{1}{1 + \frac{KmCaMK}{CaMKa}} r_down = 1 e -1 (1 - undo_CDI) r_up = \frac{r_down nca}{1 - nca} (1 - undo_CDI) jncass = \frac{1.0}{1.0 + ⅇ^{\frac{v + 19.58 + 25}{3.696}}} \frac{d}{d time} (jnca) = \frac{jncass - jnca}{tjnca} km2n = jnca 150 anca = \frac{1 - nca}{{(1 + \frac{Kmn}{cass})}^{4}} \frac{d}{d time} (nca) = anca k2n - (nca km2n) dss = \frac{1.0}{1.0 + ⅇ^{\frac{- (v + 3.940)}{4.230}}} td = 0.6 + \frac{1}{ⅇ^{(- 0.05) (v + 6)} + ⅇ^{0.09 (v + 14)}} alpha = \frac{dss}{td} beta = \frac{1 - dss}{td} jcass_new = \frac{1.0}{1.0 + ⅇ^{\frac{v + 19.58}{3.696}}} jcass_VD = jcass_new jcass_CD = jcass_new jcass_VDp = jcass_new jcass_CDp = jcass_new tjca_new = 35 + 350 ⅇ^{\frac{- ({(v + 20)}^{2})}{2 100}} tjca_VD = tjca_new tjca_CD = tjca_new tjca_VDp = tjca_new tjca_CDp = tjca_new psi_VD = \frac{jcass_VD}{tjca_VD} psi_VDp = \frac{jcass_VDp}{tjca_VDp} psi_CD = \frac{jcass_CD}{tjca_CD} psi_CDp = \frac{jcass_CDp}{tjca_CDp} omega_VD = \frac{1 - jcass_VD}{tjca_VD} omega_VDp = \frac{1 - jcass_VDp}{tjca_VDp} omega_CD = \frac{1 - jcass_CD}{tjca_CD} omega_CDp = \frac{1 - jcass_CDp}{tjca_CDp} f1ss_0 = \frac{0.8}{1.0 + ⅇ^{\frac{v + 19.58}{3.696}}} + 0.2 tf1_0 = 1 (70 + \frac{1.2}{0.0045 ⅇ^{\frac{v + 20}{- 50}} + 0.0045 ⅇ^{\frac{v + 30}{10}}}) ktaup = 2.5 gamma_VD = \frac{1 - f1ss_0}{tf1_0} delta_VD = \frac{f1ss_0}{tf1_0} gamma_VDp = \frac{gamma_VD}{ktaup} delta_VDp = \frac{delta_VD}{ktaup} gamma_CD = gamma_VD kCDI delta_CD = delta_VD kCDI gamma_CDp = gamma_VDp kCDI delta_CDp = delta_VDp kCDI tf1_VD = \frac{1}{gamma_VD + delta_VD} tf1_CD = \frac{1}{gamma_CD + delta_CD} f1ss_VD = \frac{gamma_VD}{gamma_VD + delta_VD} f1ss_CD = \frac{gamma_CD}{gamma_CD + delta_CD} tf2_new = 1 (100 + \frac{0}{0.0035 ⅇ^{\frac{v + 5}{- 84}} + 0.0035 ⅇ^{\frac{v + 5}{4}}}) tf2_VD = tf2_new tf2_CD = \frac{tf2_VD}{kCDI} tf2_VDp = tf2_new ktaup tf2_CDp = \frac{tf2_VD}{kCDI} ktaup theta_VD = \frac{\frac{alpha gamma_VD psi_VD}{tf2_VD}}{alpha gamma_VD psi_VD + beta delta_VD omega_VD} theta_CD = \frac{\frac{alpha gamma_CD psi_CD}{tf2_CD}}{alpha gamma_CD psi_CD + beta delta_CD omega_CD} theta_VDp = \frac{\frac{alpha gamma_VDp psi_VDp}{tf2_VDp}}{alpha gamma_VDp psi_VDp + beta delta_VDp omega_VDp} theta_CDp = \frac{\frac{alpha gamma_CDp psi_CDp}{tf2_CDp}}{alpha gamma_CDp psi_CDp + beta delta_CDp omega_CDp} eta_VD = \frac{1}{tf2_VD} - theta_VD eta_VDp = \frac{1}{tf2_VDp} - theta_VDp eta_CD = \frac{1}{tf2_CD} - theta_CD eta_CDp = \frac{1}{tf2_CDp} - theta_CDp tf2post_VD = \frac{1}{eta_VD + theta_VD} tf2post_CD = \frac{1}{eta_CD + theta_CD} f2ss_VD = \frac{eta_VD}{eta_VD + theta_VD} f2ss_CD = \frac{eta_CD}{eta_CD + theta_CD} PhiCaL = \frac{4.0 vffrt (1.2 cass ⅇ^{2 vfrt} - (0.341 cao))}{ⅇ^{2.0 vfrt} - 1.0} PhiCaNa = \frac{1.0 vffrt (0.75 nass ⅇ^{1.0 vfrt} - (0.75 nao))}{ⅇ^{1.0 vfrt} - 1.0} PhiCaK = \frac{1.0 vffrt (0.75 kss ⅇ^{1.0 vfrt} - (0.75 ko))}{ⅇ^{1.0 vfrt} - 1.0} PCa = \{\begin{matrix} PCa_b 0.9 1.4 if celltype = 1 \\ PCa_b 0.9 2.0 if celltype = 2 \\ PCa_b 0.9 otherwise \end{matrix} PCap = 1.1 PCa PCaNa = 0.00125 PCa PCaK = 3.574 e -4 PCa PCaNap = 0.00125 PCap PCaKp = 3.574 e -4 PCap OCak = 1 - CCak - I1Cak - I2Cak - Ck - I1k - I2k - Ok OCakp = 1 - CCakp - I1Cakp - I2Cakp - Ckp - I1kp - I2kp - Okp \frac{d}{d time} (Ok) = (alpha Ck + delta_VD I1k - ((beta + gamma_VD) Ok) - (r_up Ok)) + r_down OCak \frac{d}{d time} (I2k) = (eta_VD I1k + omega_VD Ck - ((theta_VD + psi_VD) I2k) - (r_up I2k)) + r_down I2Cak \frac{d}{d time} (I1k) = (theta_VD I2k + gamma_VD Ok - ((eta_VD + delta_VD) I1k) - (r_up I1k)) + r_down I1Cak \frac{d}{d time} (Ck) = (beta Ok + psi_VD I2k - ((omega_VD + alpha) Ck) - (r_up Ck)) + r_down CCak \frac{d}{d time} (Okp) = (alpha Ckp + delta_VDp I1kp - ((beta + gamma_VDp) Okp) - (r_up Okp)) + r_down OCakp \frac{d}{d time} (I2kp) = (eta_VDp I1kp + omega_VDp Ckp - ((theta_VDp + psi_VDp) I2kp) - (r_up I2kp)) + r_down I2Cakp \frac{d}{d time} (I1kp) = (theta_VDp I2kp + gamma_VDp Okp - ((eta_VDp + delta_VDp) I1kp) - (r_up I1kp)) + r_down I1Cakp \frac{d}{d time} (Ckp) = (beta Okp + psi_VDp I2kp - ((omega_VDp + alpha) Ckp) - (r_up Ckp)) + r_down CCakp \frac{d}{d time} (I2Cak) = (eta_CD I1Cak + omega_CD CCak - ((theta_CD + psi_CD) I2Cak)) + r_up I2k - (r_down I2Cak) \frac{d}{d time} (I1Cak) = (theta_CD I2Cak + gamma_CD OCak - ((eta_CD + delta_CD) I1Cak)) + r_up I1k - (r_down I1Cak) \frac{d}{d time} (CCak) = (beta OCak + psi_CD I2Cak - ((omega_CD + alpha) CCak)) + r_up Ck - (r_down CCak) \frac{d}{d time} (I2Cakp) = (eta_CDp I1Cakp + omega_CDp CCakp - ((theta_CDp + psi_CDp) I2Cakp)) + r_up I2kp - (r_down I2Cakp) \frac{d}{d time} (I1Cakp) = (theta_CDp I2Cakp + gamma_CDp OCakp - ((eta_CDp + delta_CDp) I1Cakp)) + r_up I1kp - (r_down I1Cakp) \frac{d}{d time} (CCakp) = (beta OCakp + psi_CDp I2Cakp - ((omega_CDp + alpha) CCakp)) + r_up Ckp - (r_down CCakp) ICaL_VD = PCa PhiCaL Ok ICaL_VDp = PCap PhiCaL Okp ICaL_CD = PCa PhiCaL OCak ICaL_CDp = PCap PhiCaL OCakp ICaNa_VD = PCaNa PhiCaNa Ok ICaNa_VDp = PCaNap PhiCaNa Okp ICaNa_CD = PCaNa PhiCaNa OCak ICaNa_CDp = PCaNap PhiCaNa OCakp ICaK_VD = PCaK PhiCaK Ok ICaK_VDp = PCaKp PhiCaK Okp ICaK_CD = PCaK PhiCaK OCak ICaK_CDp = PCaKp PhiCaK OCakp ICaLnp = ICaL_VD + ICaL_CD ICaLp = ICaL_VDp + ICaL_CDp ICaLVD = ICaL_VD (1 - fICaLp) + ICaL_VDp fICaLp ICaLCD = ICaL_CD (1 - fICaLp) + ICaL_CDp fICaLp ICaNanp = ICaNa_VD + ICaNa_CD ICaNap = ICaNa_VDp + ICaNa_CDp ICaKnp = ICaK_VD + ICaK_CD ICaKp = ICaK_VDp + ICaK_CDp ICaL = (ICaLp fICaLp + ICaLnp (1 - fICaLp)) bGCaL ICaNa = (ICaNap fICaLp + ICaNanp (1 - fICaLp)) bGCaL ICaK = (ICaKp fICaLp + ICaKnp (1 - fICaLp)) bGCaL gICaL = \frac{ICaL}{PhiCaL}

Component: IKr

\frac{d}{d time} (IC1) = (- (A11 ⅇ^{B11 v} IC1 ⅇ^{\frac{(Temp - 293) \ln q11}{10}} - (A21 ⅇ^{B21 v} IC2 ⅇ^{\frac{(Temp - 293) \ln q21}{10}}))) + A51 ⅇ^{B51 v} C1 ⅇ^{\frac{(Temp - 293) \ln q51}{10}} - (A61 ⅇ^{B61 v} IC1 ⅇ^{\frac{(Temp - 293) \ln q61}{10}}) \frac{d}{d time} (IC2) = (A11 ⅇ^{B11 v} IC1 ⅇ^{\frac{(Temp - 293) \ln q11}{10}} - (A21 ⅇ^{B21 v} IC2 ⅇ^{\frac{(Temp - 293) \ln q21}{10}}) - (A3 ⅇ^{B3 v} IC2 ⅇ^{\frac{(Temp - 293) \ln q3}{10}} - (A4 ⅇ^{B4 v} IO ⅇ^{\frac{(Temp - 293) \ln q4}{10}}))) + A52 ⅇ^{B52 v} C2 ⅇ^{\frac{(Temp - 293) \ln q52}{10}} - (A62 ⅇ^{B62 v} IC2 ⅇ^{\frac{(Temp - 293) \ln q62}{10}}) \frac{d}{d time} (C1) = - (A1 ⅇ^{B1 v} C1 ⅇ^{\frac{(Temp - 293) \ln q1}{10}} - (A2 ⅇ^{B2 v} C2 ⅇ^{\frac{(Temp - 293) \ln q2}{10}})) - (A51 ⅇ^{B51 v} C1 ⅇ^{\frac{(Temp - 293) \ln q51}{10}} - (A61 ⅇ^{B61 v} IC1 ⅇ^{\frac{(Temp - 293) \ln q61}{10}})) \frac{d}{d time} (C2) = A1 ⅇ^{B1 v} C1 ⅇ^{\frac{(Temp - 293) \ln q1}{10}} - (A2 ⅇ^{B2 v} C2 ⅇ^{\frac{(Temp - 293) \ln q2}{10}}) - (A31 ⅇ^{B31 v} C2 ⅇ^{\frac{(Temp - 293) \ln q31}{10}} - (A41 ⅇ^{B41 v} O ⅇ^{\frac{(Temp - 293) \ln q41}{10}})) - (A52 ⅇ^{B52 v} C2 ⅇ^{\frac{(Temp - 293) \ln q52}{10}} - (A62 ⅇ^{B62 v} IC2 ⅇ^{\frac{(Temp - 293) \ln q62}{10}})) \frac{d}{d time} (O) = A31 ⅇ^{B31 v} C2 ⅇ^{\frac{(Temp - 293) \ln q31}{10}} - (A41 ⅇ^{B41 v} O ⅇ^{\frac{(Temp - 293) \ln q41}{10}}) - (A53 ⅇ^{B53 v} O ⅇ^{\frac{(Temp - 293) \ln q53}{10}} - (A63 ⅇ^{B63 v} IO ⅇ^{\frac{(Temp - 293) \ln q63}{10}})) - (\frac{Kmax Ku ⅇ^{n \ln D}}{ⅇ^{n \ln D} + halfmax} O - (Ku Obound)) \frac{d}{d time} (IO) = (A3 ⅇ^{B3 v} IC2 ⅇ^{\frac{(Temp - 293) \ln q3}{10}} - (A4 ⅇ^{B4 v} IO ⅇ^{\frac{(Temp - 293) \ln q4}{10}})) + A53 ⅇ^{B53 v} O ⅇ^{\frac{(Temp - 293) \ln q53}{10}} - (A63 ⅇ^{B63 v} IO ⅇ^{\frac{(Temp - 293) \ln q63}{10}}) - (\frac{Kmax Ku ⅇ^{n \ln D}}{ⅇ^{n \ln D} + halfmax} IO - (\frac{Ku A53 ⅇ^{B53 v} ⅇ^{\frac{(Temp - 293) \ln q53}{10}}}{A63 ⅇ^{B63 v} ⅇ^{\frac{(Temp - 293) \ln q63}{10}}} IObound)) \frac{d}{d time} (IObound) = (\frac{Kmax Ku ⅇ^{n \ln D}}{ⅇ^{n \ln D} + halfmax} IO - (\frac{Ku A53 ⅇ^{B53 v} ⅇ^{\frac{(Temp - 293) \ln q53}{10}}}{A63 ⅇ^{B63 v} ⅇ^{\frac{(Temp - 293) \ln q63}{10}}} IObound)) + \frac{Kt}{1 + ⅇ^{\frac{- (v - Vhalf)}{6.789}}} Cbound - (Kt IObound) \frac{d}{d time} (Obound) = (\frac{Kmax Ku ⅇ^{n \ln D}}{ⅇ^{n \ln D} + halfmax} O - (Ku Obound)) + \frac{Kt}{1 + ⅇ^{\frac{- (v - Vhalf)}{6.789}}} Cbound - (Kt Obound) \frac{d}{d time} (Cbound) = - (\frac{Kt}{1 + ⅇ^{\frac{- (v - Vhalf)}{6.789}}} Cbound - (Kt Obound)) - (\frac{Kt}{1 + ⅇ^{\frac{- (v - Vhalf)}{6.789}}} Cbound - (Kt IObound)) \frac{d}{d time} (D) = 0 GKr = \{\begin{matrix} GKr_b bGKr 1.1 if celltype = 1 \\ GKr_b bGKr 0.8 if celltype = 2 \\ GKr_b bGKr otherwise \end{matrix} GKr_total = GKr \sqrt{\frac{ko}{5.4}} IKr = GKr_total O (v - EK)

Component: IKs

xs1ss = \frac{1}{1 + ⅇ^{\frac{- (v + 11.6 + EKshift)}{8.932}}} txs1 = 817.3 + \frac{1}{2.326 e -4 ⅇ^{\frac{v + 48.28 + EKshift}{17.8}} + 0.001292 ⅇ^{\frac{- (v + 210 + EKshift)}{230.0}}} \frac{d}{d time} (xs1) = \frac{xs1ss - xs1}{txs1} xs2ss = xs1ss txs2 = \frac{1}{0.01 ⅇ^{\frac{(v - 50) + EKshift}{20}} + 0.0193 ⅇ^{\frac{- (v + 66.54 + EKshift)}{31.0}}} \frac{d}{d time} (xs2) = \frac{xs2ss - xs2}{txs2} KsCa = 1.0 + \frac{0.6}{1 + {(\frac{3.8 e -5}{cai})}^{1.4}} GKs = \{\begin{matrix} bGKs GKs_b 1.4 if celltype = 1 \\ bGKs GKs_b otherwise \end{matrix} IKs = GKs KsCa xs1 xs2 (v - EKs)

Component: IK1

xk1ss = \frac{1}{1 + ⅇ^{\frac{- (v + 2.5538 ko + 144.59 + EKshift)}{1.5692 ko + 3.8115}}} txk1 = \frac{122.2}{ⅇ^{\frac{- (v + EKshift + 127.2)}{20.36}} + ⅇ^{\frac{v + EKshift + 236.8}{69.33}}} \frac{d}{d time} (xk1) = \frac{xk1ss - xk1}{txk1} rk1 = \frac{1}{1 + ⅇ^{\frac{(v + 105.8 - (2.6 ko)) + EKshift}{kslope_rk1 9.493}}} GK1 = \{\begin{matrix} bGK1 GK1_b 1.2 if celltype = 1 \\ bGK1 GK1_b 1.3 if celltype = 2 \\ bGK1 GK1_b otherwise \end{matrix} IK1 = GK1 \sqrt{ko} rk1 xk1 (v - EK)

Component: INaCa_i

hca = ⅇ^{\frac{qca v F}{R T}} hna = ⅇ^{\frac{qna v F}{R T}} h1_i = 1.0 + \frac{nai}{kna3} (1.0 + hna) h2_i = \frac{nai hna}{kna3 h1_i} h3_i = \frac{1.0}{h1_i} h4_i = 1.0 + \frac{nai}{kna1} (1.0 + \frac{nai}{kna2}) h5_i = \frac{nai nai}{h4_i kna1 kna2} h6_i = \frac{1.0}{h4_i} h7_i = 1.0 + \frac{nao}{kna3} (1.0 + \frac{1}{hna}) h8_i = \frac{nao}{kna3 hna h7_i} h9_i = \frac{1}{h7_i} h10_i = kasymm + 1.0 + \frac{nao}{kna1} (1 + \frac{nao}{kna2}) h11_i = \frac{nao nao}{h10_i kna1 kna2} h12_i = \frac{1.0}{h10_i} k1_i = h12_i cao kcaon k2_i = kcaoff k3p_i = h9_i wca k3pp_i = h8_i wnaca k3_i = k3p_i + k3pp_i k4p_i = \frac{h3_i wca}{hca} k4pp_i = h2_i wnaca k4_i = k4p_i + k4pp_i k5_i = kcaoff k6_i = h6_i cai kcaon k7_i = h5_i h2_i wna k8_i = h8_i h11_i wna x1_i = k2_i k4_i (k7_i + k6_i) + k5_i k7_i (k2_i + k3_i) x2_i = k1_i k7_i (k4_i + k5_i) + k4_i k6_i (k1_i + k8_i) x3_i = k1_i k3_i (k7_i + k6_i) + k8_i k6_i (k2_i + k3_i) x4_i = k2_i k8_i (k4_i + k5_i) + k3_i k5_i (k1_i + k8_i) E1_i = \frac{x1_i}{x1_i + x2_i + x3_i + x4_i} E2_i = \frac{x2_i}{x1_i + x2_i + x3_i + x4_i} E3_i = \frac{x3_i}{x1_i + x2_i + x3_i + x4_i} E4_i = \frac{x4_i}{x1_i + x2_i + x3_i + x4_i} allo_i = \frac{1}{1 + {(\frac{KmCaAct}{cai})}^{2}} JncxNa_i = 3.0 (E4_i k7_i - (E1_i k8_i)) + E3_i k4pp_i - (E2_i k3pp_i) JncxCa_i = E2_i k2_i - (E1_i k1_i) Gncx = \{\begin{matrix} bGncx Gncx_b 1.2 if celltype = 1 \\ bGncx Gncx_b 1.4 if celltype = 2 \\ bGncx Gncx_b otherwise \end{matrix} INaCa_i = 0.8 Gncx allo_i (zna JncxNa_i + zca JncxCa_i) h1_ss = 1 + \frac{nass}{kna3} (1 + hna) h2_ss = \frac{nass hna}{kna3 h1_ss} h3_ss = \frac{1}{h1_ss} h4_ss = 1 + \frac{nass}{kna1} (1 + \frac{nass}{kna2}) h5_ss = \frac{nass nass}{h4_ss kna1 kna2} h6_ss = \frac{1}{h4_ss} h7_ss = 1 + \frac{nao}{kna3} (1 + \frac{1}{hna}) h8_ss = \frac{nao}{kna3 hna h7_ss} h9_ss = \frac{1}{h7_ss} h10_ss = kasymm + 1 + \frac{nao}{kna1} (1 + \frac{nao}{kna2}) h11_ss = \frac{nao nao}{h10_ss kna1 kna2} h12_ss = \frac{1}{h10_ss} k1_ss = h12_ss cao kcaon k2_ss = kcaoff k3p_ss = h9_ss wca k3pp_ss = h8_ss wnaca k3_ss = k3p_ss + k3pp_ss k4p_ss = \frac{h3_ss wca}{hca} k4pp_ss = h2_ss wnaca k4_ss = k4p_ss + k4pp_ss k5_ss = kcaoff k6_ss = h6_ss cass kcaon k7_ss = h5_ss h2_ss wna k8_ss = h8_ss h11_ss wna x1_ss = k2_ss k4_ss (k7_ss + k6_ss) + k5_ss k7_ss (k2_ss + k3_ss) x2_ss = k1_ss k7_ss (k4_ss + k5_ss) + k4_ss k6_ss (k1_ss + k8_ss) x3_ss = k1_ss k3_ss (k7_ss + k6_ss) + k8_ss k6_ss (k2_ss + k3_ss) x4_ss = k2_ss k8_ss (k4_ss + k5_ss) + k3_ss k5_ss (k1_ss + k8_ss) E1_ss = \frac{x1_ss}{x1_ss + x2_ss + x3_ss + x4_ss} E2_ss = \frac{x2_ss}{x1_ss + x2_ss + x3_ss + x4_ss} E3_ss = \frac{x3_ss}{x1_ss + x2_ss + x3_ss + x4_ss} E4_ss = \frac{x4_ss}{x1_ss + x2_ss + x3_ss + x4_ss} allo_ss = \frac{1}{1 + {(\frac{KmCaAct}{cass})}^{2}} JncxNa_ss = 3 (E4_ss k7_ss - (E1_ss k8_ss)) + E3_ss k4pp_ss - (E2_ss k3pp_ss) JncxCa_ss = E2_ss k2_ss - (E1_ss k1_ss) INaCa_ss = 0.2 Gncx allo_ss (zna JncxNa_ss + zca JncxCa_ss)

Component: INaK

Knai = Knai0 ⅇ^{\frac{delta v F}{3.0 R T}} Knao = Knao0 ⅇ^{\frac{(1.0 - delta) v F}{3.0 R T}} P = \frac{eP}{1 + \frac{H}{Khp} + \frac{nai}{Knap} + \frac{ki}{Kxkur}} a1 = \frac{k1p {(\frac{nai}{Knai})}^{3}}{{(1 + \frac{nai}{Knai})}^{3} + {(1 + \frac{ki}{Kki})}^{2} - 1.0} b1 = k1m MgADP a2 = k2p b2 = \frac{k2m {(\frac{nao}{Knao})}^{3}}{{(1 + \frac{nao}{Knao})}^{3} + {(1 + \frac{ko}{Kko})}^{2} - 1} a3 = \frac{k3p {(\frac{ko}{Kko})}^{2}}{{(1 + \frac{nao}{Knao})}^{3} + {(1 + \frac{ko}{Kko})}^{2} - 1.0} b3 = \frac{k3m P H}{1 + \frac{MgATP}{Kmgatp}} a4 = \frac{\frac{k4p MgATP}{Kmgatp}}{1 + \frac{MgATP}{Kmgatp}} b4 = \frac{k4m {(\frac{ki}{Kki})}^{2}}{{(1 + \frac{nai}{Knai})}^{3} + {(1 + \frac{ki}{Kki})}^{2} - 1.0} x1 = a4 a1 a2 + b2 b4 b3 + a2 b4 b3 + b3 a1 a2 x2 = b2 b1 b4 + a1 a2 a3 + a3 b1 b4 + a2 a3 b4 x3 = a2 a3 a4 + b3 b2 b1 + b2 b1 a4 + a3 a4 b1 x4 = b4 b3 b2 + a3 a4 a1 + b2 a4 a1 + b3 b2 a1 E1 = \frac{x1}{x1 + x2 + x3 + x4} E2 = \frac{x2}{x1 + x2 + x3 + x4} E3 = \frac{x3}{x1 + x2 + x3 + x4} E4 = \frac{x4}{x1 + x2 + x3 + x4} JnakNa = 3 (E1 a3 - (E2 b3)) JnakK = 2 (E4 b1 - (E3 a1)) Pnak = \{\begin{matrix} bGnak Pnak_b 0.9 if celltype = 1 \\ bGnak Pnak_b 0.7 if celltype = 2 \\ bGnak Pnak_b otherwise \end{matrix} INaK = Pnak (zna JnakNa + zk JnakK)

Component: IKb

xkb = \frac{1}{1 + ⅇ^{\frac{- (v - 14.48)}{18.34}}} GKb = \{\begin{matrix} GKb_b 0.6 if celltype = 1 \\ GKb_b otherwise \end{matrix} IKb = GKb xkb (v - EK)

Component: INab

INab = \frac{PNab vffrt (nai ⅇ^{vfrt} - nao)}{ⅇ^{vfrt} - 1.0}

Component: ICab

ICab = \frac{(1 - undo_ICab) PCab 16 vffrt (1.2 cai ⅇ^{2 vfrt} - (0.341 cao))}{ⅇ^{2 vfrt} - 1.0}

Component: IpCa

IpCa = \frac{GpCa cai}{KmCap + cai}

Component: diff

JdiffNa = \frac{nass - nai}{2.0} JdiffK = \frac{kss - ki}{2.0} Jdiff = \frac{(cass - cai) 1.7}{0.2}

Component: ryr

RyRohalf = 0.12 - (RyRa1 - (\frac{RyRa2}{2})) RyRchalf = 0.10 - (RyRa1 - (\frac{RyRa2}{2})) RyRSRCass = 1 - (\frac{1}{1 + ⅇ^{\frac{casr - 0.3}{0.1}}}) RyRainfss = RyRa1 - (\frac{RyRa2}{1 + ⅇ^{\frac{1000 cass - 0.043}{0.0082}}}) RyRtauadapt = 1000 \frac{d}{d time} (RyRa) = \frac{RyRainfss - RyRa}{RyRtauadapt} RyRoinfss = 1 - (\frac{1}{1 + ⅇ^{\frac{1000 cass - (RyRa + RyRohalf)}{0.003}}}) RyRtauact = \frac{18.75 e -1}{1.875} \frac{d}{d time} (RyRo) = \frac{RyRoinfss - RyRo}{RyRtauact} RyRcinfss = \frac{1}{1 + ⅇ^{\frac{1000 cass - (RyRa + RyRchalf)}{0.001}}} RyRtauinact = \frac{2 87.5}{10} \frac{d}{d time} (RyRc) = \frac{RyRcinfss - RyRc}{RyRtauinact} RyRtauinactp = RyRtauinact 1.25 \frac{d}{d time} (RyRcp) = \frac{RyRcinfss - RyRcp}{RyRtauinactp} fJrelp = \frac{1}{1 + \frac{KmCaMK}{CaMKa}} g_irel_max_M = g_irel_max 1.7 Jrelnp = \{\begin{matrix} g_irel_max_M RyRSRCass RyRo RyRc (casr - cass) if celltype = 2 \\ g_irel_max RyRSRCass RyRo RyRc (casr - cass) otherwise \end{matrix} g_irel_max_p = g_irel_max 1.25 Jrelp = \{\begin{matrix} g_irel_max_p 1.7 RyRSRCass RyRo RyRcp (casr - cass) if celltype = 2 \\ g_irel_max_p RyRSRCass RyRo RyRcp (casr - cass) otherwise \end{matrix} Jrel = (1 - fJrelp) Jrelnp + fJrelp Jrelp

Component: SERCA

upScale = \{\begin{matrix} 1.3 if celltype = 1 \\ 1 otherwise \end{matrix} Jupnp = \frac{upScale 0.004375 cai}{cai + 0.00092} Jupp = \frac{upScale 2.75 0.004375 cai}{cai + 0.00092 - 0.00017} fJupp = \frac{1}{1 + \frac{KmCaMK}{CaMKa}} Jleak = \frac{0.0123 casr}{15.0} Jup = cJup ((1 - fJupp) Jupnp + fJupp Jupp) Vmax_SRCaP = 1.0 5.3114 e -3 Kmf = 0.246 e -3 Kmr = 1.7 hillSRCaP = 1.787 Jup2 = \frac{Vmax_SRCaP ({(\frac{cai}{Kmf})}^{hillSRCaP} - ({(\frac{casr}{Kmr})}^{hillSRCaP}))}{1 + {(\frac{cai}{Kmf})}^{hillSRCaP} + {(\frac{casr}{Kmr})}^{hillSRCaP}}

Component: trans_flux

Jtr = 0

Source: Derived from workspace BPS2020 model at changeset 3384b6e8f86b.

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Simulation of the Effects of Extracellular Calcium Changes Leads to a Novel Computational Model of Human Ventricular Action Potential With a Revised Calcium Handling