Model Mathematics

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Component: Protocol

Component: interface

Component: environment

Component: parameters

epi = 1 R = 8314 Frdy = 96485 Temp = 310 FoRT = \frac{Frdy}{R Temp} Cmem = 1.381 e -10 Qpow = \frac{Temp - 310}{10} cellLength = 100 cellRadius = 10.25 junctionLength = 160 e -3 junctionRadius = 15 e -3 distSLcyto = 0.45 distJuncSL = 0.5 DcaJuncSL = 1.64 e -6 DcaSLcyto = 1.22 e -6 DnaJuncSL = 1.09 e -5 DnaSLcyto = 1.79 e -5 Vcell = π {cellRadius}^{2} cellLength 1 e -15 Vmyo = 0.65 Vcell Vsr = 0.035 Vcell Vsl = 0.02 Vcell Vjunc = 0.0539 0.01 Vcell SAjunc = 20150 π 2 junctionLength junctionRadius SAsl = π 2 cellRadius cellLength J_ca_juncsl = 8.2413 e -13 J_ca_slmyo = 3.2743 e -12 J_na_juncsl = 1.8313 e -14 J_na_slmyo = 1.6386 e -12 Fjunc = 0.11 Fsl = 1 - Fjunc Fjunc_CaL = 0.9 Fsl_CaL = 1 - Fjunc_CaL Cli = 15 Clo = 150 Ko = 5.4 Nao = 140 Cao = 1.8 Mgi = 1 ena_junc = \frac{1}{FoRT} \ln (\frac{Nao}{Na_j}) ena_sl = \frac{1}{FoRT} \ln (\frac{Nao}{Na_sl}) ek = \frac{1}{FoRT} \ln (\frac{Ko}{K_i}) eca_junc = \frac{\frac{1}{FoRT}}{2} \ln (\frac{Cao}{Ca_j}) eca_sl = \frac{\frac{1}{FoRT}}{2} \ln (\frac{Cao}{Ca_sl}) ecl = \frac{1}{FoRT} \ln (\frac{Cli}{Clo}) GNa = 23 GNaB = 0.597 e -3 IbarNaK = 1 1.8 KmNaip = 11 KmKo = 1.5 Q10NaK = 1.63 Q10KmNai = 1.39 pNaK = 0.01833 gkp = 2 0.001 GClCa = 0.5 0.109625 GClB = 1 9 e -3 KdClCa = 100 e -3 pNa = 0.5 1.5 e -8 pCa = 0.5 5.4 e -4 pK = 0.5 2.7 e -7 Q10CaL = 1.8 IbarNCX = 1 4.5 KmCai = 3.59 e -3 KmCao = 1.3 KmNai = 12.29 KmNao = 87.5 ksat = 0.32 nu = 0.27 Kdact = 0.15 e -3 Q10NCX = 1.57 IbarSLCaP = 0.0673 KmPCa = 0.5 e -3 GCaB = 5.513 e -4 Q10SLCaP = 2.35 Q10SRCaP = 2.6 Vmax_SRCaP = 5.3114 e -3 Kmf = 0.246 e -3 Kmr = 1.7 hillSRCaP = 1.787 ks = 25 koCa = 10 kom = 0.06 kiCa = 0.5 kim = 0.005 ec50SR = 0.45 Bmax_Naj = 7.561 Bmax_Nasl = 1.65 koff_na = 1 e -3 kon_na = 0.1 e -3 Bmax_TnClow = 70 e -3 koff_tncl = 19.6 e -3 kon_tncl = 32.7 Bmax_TnChigh = 140 e -3 koff_tnchca = 0.032 e -3 kon_tnchca = 2.37 koff_tnchmg = 3.33 e -3 kon_tnchmg = 3 e -3 Bmax_CaM = 24 e -3 koff_cam = 238 e -3 kon_cam = 34 Bmax_myosin = 140 e -3 koff_myoca = 0.46 e -3 kon_myoca = 13.8 koff_myomg = 0.057 e -3 kon_myomg = 0.0157 Bmax_SR = 19 0.9 e -3 koff_sr = 60 e -3 kon_sr = 100 Bmax_SLlowsl = \frac{37.4 e -3 Vmyo}{Vsl} Bmax_SLlowj = \frac{4.6 e -3 Vmyo}{Vjunc} 0.1 koff_sll = 1300 e -3 kon_sll = 100 Bmax_SLhighsl = \frac{13.4 e -3 Vmyo}{Vsl} Bmax_SLhighj = \frac{1.65 e -3 Vmyo}{Vjunc} 0.1 koff_slh = 30 e -3 kon_slh = 100 Bmax_Csqn = \frac{140 e -3 Vmyo}{Vsr} koff_csqn = 65 kon_csqn = 100

Component: I_Na

mss = \frac{1}{{(1 + ⅇ^{\frac{- (56.86 + V_m)}{9.03}})}^{2}} taum = 0.1292 ⅇ^{- ({(\frac{V_m + 45.79}{15.54})}^{2})} + 0.06487 ⅇ^{- ({(\frac{V_m - 4.823}{51.12})}^{2})} ah = \{\begin{matrix} 0 if V_m \geq - 40 \\ 0.057 ⅇ^{\frac{- (V_m + 80)}{6.8}} otherwise \end{matrix} bh = \{\begin{matrix} \frac{0.77}{0.13 (1 + ⅇ^{\frac{- (V_m + 10.66)}{11.1}})} if V_m \geq - 40 \\ 2.7 ⅇ^{0.079 V_m} + 3.1 e 5 ⅇ^{0.3485 V_m} otherwise \end{matrix} tauh = \frac{1}{ah + bh} hss = \frac{1}{{(1 + ⅇ^{\frac{V_m + 71.55}{7.43}})}^{2}} aj = \{\begin{matrix} 0 if V_m \geq - 40 \\ \frac{((- 2.5428 e 4) ⅇ^{0.2444 V_m} - (6.948 e -6 ⅇ^{(- 0.04391) V_m})) (V_m + 37.78)}{1 + ⅇ^{0.311 (V_m + 79.23)}} otherwise \end{matrix} bj = \{\begin{matrix} \frac{0.6 ⅇ^{0.057 V_m}}{1 + ⅇ^{(- 0.1) (V_m + 32)}} if V_m \geq - 40 \\ \frac{0.02424 ⅇ^{(- 0.01052) V_m}}{1 + ⅇ^{(- 0.1378) (V_m + 40.14)}} otherwise \end{matrix} tauj = \frac{1}{aj + bj} jss = \frac{1}{{(1 + ⅇ^{\frac{V_m + 71.55}{7.43}})}^{2}} \frac{d}{d time} (m) = \frac{mss - m}{taum} \frac{d}{d time} (h) = \frac{hss - h}{tauh} \frac{d}{d time} (j) = \frac{jss - j}{tauj} I_Na_junc = Fjunc GNa m^{3} h j (V_m - ena_junc) I_Na_sl = Fsl GNa m^{3} h j (V_m - ena_sl) I_Na = I_Na_junc + I_Na_sl

Component: I_NaBK

I_nabk_junc = Fjunc GNaB (V_m - ena_junc) I_nabk_sl = Fsl GNaB (V_m - ena_sl) I_nabk = I_nabk_junc + I_nabk_sl

Component: I_NaK

sigma = \frac{ⅇ^{\frac{Nao}{67.3}} - 1}{7} fnak = \frac{1}{1 + 0.1245 ⅇ^{(- 0.1) V_m FoRT} + 0.0365 sigma ⅇ^{(- V_m) FoRT}} I_nak_junc = \frac{\frac{Fjunc IbarNaK fnak Ko}{1 + {(\frac{KmNaip}{Na_j})}^{4}}}{Ko + KmKo} I_nak_sl = \frac{\frac{Fsl IbarNaK fnak Ko}{1 + {(\frac{KmNaip}{Na_sl})}^{4}}}{Ko + KmKo} I_nak = I_nak_junc + I_nak_sl

Component: I_Kr

gkr = 0.035 \sqrt{\frac{Ko}{5.4}} xrss = \frac{1}{1 + ⅇ^{\frac{- (V_m + 10)}{5}}} tauxr = \frac{\frac{550}{1 + ⅇ^{\frac{- 22 - V_m}{9}}} 6}{1 + ⅇ^{\frac{V_m - (- 11)}{9}}} + \frac{230}{1 + ⅇ^{\frac{V_m - (- 40)}{20}}} \frac{d}{d time} (x_kr) = \frac{xrss - x_kr}{tauxr} rkr = \frac{1}{1 + ⅇ^{\frac{V_m + 74}{24}}} I_kr = gkr x_kr rkr (V_m - ek)

Component: I_Kp

kp_kp = \frac{1}{1 + ⅇ^{7.488 - (\frac{V_m}{5.98})}} I_kp_junc = Fjunc gkp kp_kp (V_m - ek) I_kp_sl = Fsl gkp kp_kp (V_m - ek) I_kp = I_kp_junc + I_kp_sl

Component: I_Ks

eks = \frac{1}{FoRT} \ln (\frac{Ko + pNaK Nao}{K_i + pNaK Na_i}) gks_junc = 0.0035 gks_sl = 0.0035 xsss = \frac{1}{1 + ⅇ^{\frac{- (V_m + 3.8)}{14.25}}} tauxs = \frac{990.1}{1 + ⅇ^{\frac{- (V_m + 2.436)}{14.12}}} \frac{d}{d time} (x_ks) = \frac{xsss - x_ks}{tauxs} I_ks_junc = Fjunc gks_junc {x_ks}^{2} (V_m - eks) I_ks_sl = Fsl gks_sl {x_ks}^{2} (V_m - eks) I_ks = I_ks_junc + I_ks_sl

Component: I_to

GtoSlow = \{\begin{matrix} 1 0.13 0.12 if epi = 1 \\ 0.13 0.3 0.964 otherwise \end{matrix} GtoFast = \{\begin{matrix} 1 0.13 0.88 if epi = 1 \\ 0.13 0.3 0.036 otherwise \end{matrix} xtoss = \frac{1}{1 + ⅇ^{\frac{- (V_m - 19)}{13}}} ytoss = \frac{1}{1 + ⅇ^{\frac{V_m + 19.5}{5}}} tauxtos = \frac{9}{1 + ⅇ^{\frac{V_m + 3}{15}}} + 0.5 tauytos = \frac{800}{1 + ⅇ^{\frac{V_m + 60}{10}}} + 30 \frac{d}{d time} (x_to_s) = \frac{xtoss - x_to_s}{tauxtos} \frac{d}{d time} (y_to_s) = \frac{ytoss - y_to_s}{tauytos} I_tos = GtoSlow x_to_s y_to_s (V_m - ek) tauxtof = 8.5 ⅇ^{- ({(\frac{V_m + 45}{50})}^{2})} + 0.5 tauytof = 85 ⅇ^{\frac{- ({(V_m + 40)}^{2})}{220}} + 7 \frac{d}{d time} (x_to_f) = \frac{xtoss - x_to_f}{tauxtof} \frac{d}{d time} (y_to_f) = \frac{ytoss - y_to_f}{tauytof} I_tof = GtoFast x_to_f y_to_f (V_m - ek) I_to = I_tos + I_tof

Component: I_Ki

aki = \frac{1.02}{1 + ⅇ^{0.2385 (V_m - ek - 59.215)}} bki = \frac{0.49124 ⅇ^{0.08032 (V_m + 5.476 - ek)} + ⅇ^{0.06175 (V_m - ek - 594.31)}}{1 + ⅇ^{(- 0.5143) ((V_m - ek) + 4.753)}} kiss = \frac{aki}{aki + bki} I_ki = 1 0.35 \sqrt{\frac{Ko}{5.4}} kiss (V_m - ek)

Component: I_ClCa

I_ClCa_junc = \frac{Fjunc GClCa}{1 + \frac{KdClCa}{Ca_j}} (V_m - ecl) I_ClCa_sl = \frac{Fsl GClCa}{1 + \frac{KdClCa}{Ca_sl}} (V_m - ecl) I_ClCa = I_ClCa_junc + I_ClCa_sl I_Clbk = GClB (V_m - ecl)

Component: I_Ca

fss = \frac{1}{1 + ⅇ^{\frac{V_m + 35}{9}}} + \frac{0.6}{1 + ⅇ^{\frac{50 - V_m}{20}}} dss = \frac{1}{1 + ⅇ^{\frac{- (V_m + 5)}{6}}} taud = \frac{1 dss (1 - (ⅇ^{\frac{- (V_m + 5)}{6}}))}{0.035 (V_m + 5)} tauf = \frac{1}{0.0197 ⅇ^{- ({(0.0337 (V_m + 14.5))}^{2})} + 0.02} \frac{d}{d time} (d) = \frac{dss - d}{taud} \frac{d}{d time} (f) = \frac{fss - f}{tauf} \frac{d}{d time} (f_Ca_Bj) = \frac{1.7 Ca_j}{1} (1 - f_Ca_Bj) - (11.9 e -3 f_Ca_Bj) \frac{d}{d time} (f_Ca_Bsl) = \frac{1.7 Ca_sl}{1} (1 - f_Ca_Bsl) - (11.9 e -3 f_Ca_Bsl) fcaCaMSL = 0 fcaCaj = 0 ibarca_j = \frac{pCa 4 V_m Frdy FoRT (0.341 Ca_j ⅇ^{2 V_m FoRT} - (0.341 Cao))}{ⅇ^{2 V_m FoRT} - 1} ibarca_sl = \frac{pCa 4 V_m Frdy FoRT (0.341 Ca_sl ⅇ^{2 V_m FoRT} - (0.341 Cao))}{ⅇ^{2 V_m FoRT} - 1} ibark = \frac{pK V_m Frdy FoRT (0.75 K_i ⅇ^{V_m FoRT} - (0.75 Ko))}{ⅇ^{V_m FoRT} - 1} ibarna_j = \frac{pNa V_m Frdy FoRT (0.75 Na_j ⅇ^{V_m FoRT} - (0.75 Nao))}{ⅇ^{V_m FoRT} - 1} ibarna_sl = \frac{pNa V_m Frdy FoRT (0.75 Na_sl ⅇ^{V_m FoRT} - (0.75 Nao))}{ⅇ^{V_m FoRT} - 1} I_Ca_junc = Fjunc_CaL ibarca_j d f ((1 - f_Ca_Bj) + fcaCaj) {Q10CaL}^{Qpow} 0.45 1 I_Ca_sl = Fsl_CaL ibarca_sl d f ((1 - f_Ca_Bsl) + fcaCaMSL) {Q10CaL}^{Qpow} 0.45 1 I_Ca = I_Ca_junc + I_Ca_sl I_CaK = ibark d f (Fjunc_CaL (fcaCaj + (1 - f_Ca_Bj)) + Fsl_CaL (fcaCaMSL + (1 - f_Ca_Bsl))) {Q10CaL}^{Qpow} 0.45 1 I_CaNa_junc = Fjunc_CaL ibarna_j d f ((1 - f_Ca_Bj) + fcaCaj) {Q10CaL}^{Qpow} 0.45 1 I_CaNa_sl = Fsl_CaL ibarna_sl d f ((1 - f_Ca_Bsl) + fcaCaMSL) {Q10CaL}^{Qpow} 0.45 1 I_CaNa = I_CaNa_junc + I_CaNa_sl I_Catot = I_Ca + I_CaK + I_CaNa

Component: I_NCX

Ka_junc = \frac{1}{1 + {(\frac{Kdact}{Ca_j})}^{2}} Ka_sl = \frac{1}{1 + {(\frac{Kdact}{Ca_sl})}^{2}} s1_junc = ⅇ^{nu V_m FoRT} {Na_j}^{3} Cao s1_sl = ⅇ^{nu V_m FoRT} {Na_sl}^{3} Cao s2_junc = ⅇ^{(nu - 1) V_m FoRT} {Nao}^{3} Ca_j s3_junc = KmCai {Nao}^{3} (1 + {(\frac{Na_j}{KmNai})}^{3}) + {KmNao}^{3} Ca_j (1 + \frac{Ca_j}{KmCai}) + KmCao {Na_j}^{3} + {Na_j}^{3} Cao + {Nao}^{3} Ca_j s2_sl = ⅇ^{(nu - 1) V_m FoRT} {Nao}^{3} Ca_sl s3_sl = KmCai {Nao}^{3} (1 + {(\frac{Na_sl}{KmNai})}^{3}) + {KmNao}^{3} Ca_sl (1 + \frac{Ca_sl}{KmCai}) + KmCao {Na_sl}^{3} + {Na_sl}^{3} Cao + {Nao}^{3} Ca_sl I_ncx_junc = \frac{\frac{Fjunc IbarNCX {Q10NCX}^{Qpow} Ka_junc (s1_junc - s2_junc)}{s3_junc}}{1 + ksat ⅇ^{(nu - 1) V_m FoRT}} I_ncx_sl = \frac{\frac{Fsl IbarNCX {Q10NCX}^{Qpow} Ka_sl (s1_sl - s2_sl)}{s3_sl}}{1 + ksat ⅇ^{(nu - 1) V_m FoRT}} I_ncx = I_ncx_junc + I_ncx_sl

Component: I_PCa

I_pca_junc = \frac{Fjunc {Q10SLCaP}^{Qpow} IbarSLCaP {Ca_j}^{1.6}}{{KmPCa}^{1.6} + {Ca_j}^{1.6}} I_pca_sl = \frac{Fsl {Q10SLCaP}^{Qpow} IbarSLCaP {Ca_sl}^{1.6}}{{KmPCa}^{1.6} + {Ca_sl}^{1.6}} I_pca = I_pca_junc + I_pca_sl

Component: I_CaBK

I_cabk_junc = Fjunc GCaB (V_m - eca_junc) I_cabk_sl = Fsl GCaB (V_m - eca_sl) I_cabk = I_cabk_junc + I_cabk_sl

Component: SR_Fluxes

MaxSR = 15 MinSR = 1 kCaSR = MaxSR - (\frac{MaxSR - MinSR}{1 + {(\frac{ec50SR}{Ca_sr})}^{2.5}}) koSRCa = \frac{koCa}{kCaSR} kiSRCa = kiCa kCaSR RI = 1 - Ry_Rr - Ry_Ro - Ry_Ri \frac{d}{d time} (Ry_Rr) = kim RI - (kiSRCa Ca_j Ry_Rr) - (koSRCa {Ca_j}^{2} Ry_Rr - (kom Ry_Ro)) \frac{d}{d time} (Ry_Ro) = koSRCa {Ca_j}^{2} Ry_Rr - (kom Ry_Ro) - (kiSRCa Ca_j Ry_Ro - (kim Ry_Ri)) \frac{d}{d time} (Ry_Ri) = kiSRCa Ca_j Ry_Ro - (kim Ry_Ri) - (kom Ry_Ri - (koSRCa {Ca_j}^{2} RI)) J_SRCarel = \frac{ks Ry_Ro}{1} (Ca_sr - Ca_j) J_serca = \frac{{Q10SRCaP}^{Qpow} Vmax_SRCaP ({(\frac{Ca_i}{Kmf})}^{hillSRCaP} - ({(\frac{Ca_sr}{Kmr})}^{hillSRCaP}))}{1 + {(\frac{Ca_i}{Kmf})}^{hillSRCaP} + {(\frac{Ca_sr}{Kmr})}^{hillSRCaP}} J_SRleak = 5.348 e -6 (Ca_sr - Ca_j)

Component: Na_Buffers

\frac{d}{d time} (Na_Bj) = dNa_Bj_dt dNa_Bj_dt = kon_na Na_j (Bmax_Naj - Na_Bj) - (koff_na Na_Bj) \frac{d}{d time} (Na_Bsl) = dNa_Bsl_dt dNa_Bsl_dt = kon_na Na_sl (Bmax_Nasl - Na_Bsl) - (koff_na Na_Bsl)

Component: Cytosolic_Ca_Buffers

\frac{d}{d time} (Tn_CL) = kon_tncl Ca_i (Bmax_TnClow - Tn_CL) - (koff_tncl Tn_CL) \frac{d}{d time} (Tn_CHc) = kon_tnchca Ca_i (Bmax_TnChigh - Tn_CHc - Tn_CHm) - (koff_tnchca Tn_CHc) \frac{d}{d time} (Tn_CHm) = kon_tnchmg Mgi (Bmax_TnChigh - Tn_CHc - Tn_CHm) - (koff_tnchmg Tn_CHm) \frac{d}{d time} (CaM) = kon_cam Ca_i (Bmax_CaM - CaM) - (koff_cam CaM) \frac{d}{d time} (Myo_c) = kon_myoca Ca_i (Bmax_myosin - Myo_c - Myo_m) - (koff_myoca Myo_c) \frac{d}{d time} (Myo_m) = kon_myomg Mgi (Bmax_myosin - Myo_c - Myo_m) - (koff_myomg Myo_m) \frac{d}{d time} (SRB) = kon_sr Ca_i (Bmax_SR - SRB) - (koff_sr SRB) J_CaB_cytosol = ((((((kon_tncl Ca_i (Bmax_TnClow - Tn_CL) - (koff_tncl Tn_CL)) + kon_tnchca Ca_i (Bmax_TnChigh - Tn_CHc - Tn_CHm) - (koff_tnchca Tn_CHc)) + kon_tnchmg Mgi (Bmax_TnChigh - Tn_CHc - Tn_CHm) - (koff_tnchmg Tn_CHm)) + kon_cam Ca_i (Bmax_CaM - CaM) - (koff_cam CaM)) + kon_myoca Ca_i (Bmax_myosin - Myo_c - Myo_m) - (koff_myoca Myo_c)) + kon_myomg Mgi (Bmax_myosin - Myo_c - Myo_m) - (koff_myomg Myo_m)) + (kon_sr Ca_i (Bmax_SR - SRB) - (koff_sr SRB))

Component: Junctional_and_SL_Ca_Buffers

\frac{d}{d time} (SLL_j) = kon_sll Ca_j (Bmax_SLlowj - SLL_j) - (koff_sll SLL_j) \frac{d}{d time} (SLL_sl) = kon_sll Ca_sl (Bmax_SLlowsl - SLL_sl) - (koff_sll SLL_sl) \frac{d}{d time} (SLH_j) = kon_slh Ca_j (Bmax_SLhighj - SLH_j) - (koff_slh SLH_j) \frac{d}{d time} (SLH_sl) = kon_slh Ca_sl (Bmax_SLhighsl - SLH_sl) - (koff_slh SLH_sl) J_CaB_junction = (kon_sll Ca_j (Bmax_SLlowj - SLL_j) - (koff_sll SLL_j)) + (kon_slh Ca_j (Bmax_SLhighj - SLH_j) - (koff_slh SLH_j)) J_CaB_sl = (kon_sll Ca_sl (Bmax_SLlowsl - SLL_sl) - (koff_sll SLL_sl)) + (kon_slh Ca_sl (Bmax_SLhighsl - SLH_sl) - (koff_slh SLH_sl))

Component: SR_Ca_Concentrations

\frac{d}{d time} (Csqn_b) = kon_csqn Ca_sr (Bmax_Csqn - Csqn_b) - (koff_csqn Csqn_b) \frac{d}{d time} (Ca_sr) = J_serca - (\frac{J_SRleak Vmyo}{Vsr} + J_SRCarel) - (kon_csqn Ca_sr (Bmax_Csqn - Csqn_b) - (koff_csqn Csqn_b))

Component: Na_Concentrations

I_Na_tot_junc = I_Na_junc + I_nabk_junc + 3 I_ncx_junc + 3 I_nak_junc + I_CaNa_junc I_Na_tot_sl = I_Na_sl + I_nabk_sl + 3 I_ncx_sl + 3 I_nak_sl + I_CaNa_sl I_Na_tot_sl2 = 3 I_ncx_sl + 3 I_nak_sl + I_CaNa_sl I_Na_tot_junc2 = 3 I_ncx_junc + 3 I_nak_junc + I_CaNa_junc \frac{d}{d time} (Na_j) = \frac{(- I_Na_tot_junc) Cmem}{Vjunc Frdy} + \frac{J_na_juncsl}{Vjunc} (Na_sl - Na_j) - dNa_Bj_dt \frac{d}{d time} (Na_sl) = \frac{(- I_Na_tot_sl) Cmem}{Vsl Frdy} + \frac{J_na_juncsl}{Vsl} (Na_j - Na_sl) + \frac{J_na_slmyo}{Vsl} (Na_i - Na_sl) - dNa_Bsl_dt \frac{d}{d time} (Na_i) = \frac{J_na_slmyo}{Vmyo} (Na_sl - Na_i)

Component: K_Concentration

I_K_tot = (I_to + I_kr + I_ks + I_ki - (2 I_nak)) + I_CaK + I_kp \frac{d}{d time} (K_i) = 0

Component: Ca_Concentrations

I_Ca_tot_junc = I_Ca_junc + I_cabk_junc + I_pca_junc - (2 I_ncx_junc) I_Ca_tot_sl = I_Ca_sl + I_cabk_sl + I_pca_sl - (2 I_ncx_sl) \frac{d}{d time} (Ca_j) = (\frac{(- I_Ca_tot_junc) Cmem}{Vjunc 2 Frdy} + \frac{J_ca_juncsl}{Vjunc} (Ca_sl - Ca_j) - J_CaB_junction) + \frac{J_SRCarel Vsr}{Vjunc} + \frac{J_SRleak Vmyo}{Vjunc} \frac{d}{d time} (Ca_sl) = \frac{(- I_Ca_tot_sl) Cmem}{Vsl 2 Frdy} + \frac{J_ca_juncsl}{Vsl} (Ca_j - Ca_sl) + \frac{J_ca_slmyo}{Vsl} (Ca_i - Ca_sl) - J_CaB_sl \frac{d}{d time} (Ca_i) = (\frac{(- J_serca) Vsr}{Vmyo} - J_CaB_cytosol) + \frac{J_ca_slmyo}{Vmyo} (Ca_sl - Ca_i)

Component: membrane_potential

I_Na_tot = I_Na_tot_junc + I_Na_tot_sl I_Cl_tot = I_ClCa + I_Clbk I_Ca_tot = I_Ca_tot_junc + I_Ca_tot_sl I_tot = I_Na_tot + I_Cl_tot + I_Ca_tot + I_K_tot \frac{d}{d time} (V_m) = - (I_tot - I_app)