Model Mathematics

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Component: Time

Component: Environment

FoRT = \frac{F}{R T} RToF = \frac{R T}{F} T_correction_Ca = {Q10Ca}^{\frac{T - T_exp}{10}} T_correction_K = {Q10K}^{\frac{T - T_exp}{10}} T_correction_Na = {Q10Na}^{\frac{T - T_exp}{10}} T_correction_BK = 1.1 (T - T_exp)

Component: ICC_Membrane

V_cyto = Vol P_cyto \frac{d}{d time} (Vm) = \frac{(- 1) 1}{Cm} (I_Na + I_Ltype + I_VDDR + I_kv11 + I_ERG + I_BK + I_CaCl + I_NSCC + I_bk + J_PMCA 2 1000000 1000000 F V_cyto) \frac{d}{d time} (Ca_i) = fc (\frac{(- 1) I_Ltype + (- 1) I_VDDR}{2 1000000 1000000 F V_cyto} + J_leak + (- 1) J_PMCA)

Component: d_Ltype

d_inf_Ltype = \frac{1}{1 + ⅇ^{\frac{Vm + 17}{- 4.3}}} tau_d_Ltype = T_correction_Ca 0.001 \frac{d}{d time} (d_Ltype) = \frac{d_inf_Ltype - d_Ltype}{tau_d_Ltype}

Component: f_Ltype

f_inf_Ltype = \frac{1}{1 + ⅇ^{\frac{Vm + 43}{8.9}}} tau_f_Ltype = T_correction_Ca 0.086 \frac{d}{d time} (f_Ltype) = \frac{f_inf_Ltype - f_Ltype}{tau_f_Ltype}

Component: f_ca_Ltype

f_ca_inf_Ltype = 1 - (\frac{1}{1 + ⅇ^{\frac{Ca_i - 0.0001 - 0.000214}{- 0.0000131}}}) tau_f_ca_Ltype = T_correction_Ca 0.002 \frac{d}{d time} (f_ca_Ltype) = \frac{f_ca_inf_Ltype - f_ca_Ltype}{tau_f_ca_Ltype}

Component: I_Ltype

E_Ca = 0.5 RToF \ln (\frac{Ca_o}{Ca_i}) I_Ltype = G_max_Ltype f_Ltype d_Ltype f_ca_Ltype (Vm - E_Ca)

Component: J_PMCA

J_PMCA = \frac{J_max_PMCA 1}{1 + \frac{0.000298}{Ca_i}}

Component: d_VDDR

d_inf_VDDR = \frac{1}{1 + ⅇ^{\frac{Vm + 26}{- 6}}} tau_d_VDDR = T_correction_Ca 0.006 \frac{d}{d time} (d_VDDR) = \frac{d_inf_VDDR - d_VDDR}{tau_d_VDDR}

Component: f_VDDR

f_inf_VDDR = \frac{1}{1 + ⅇ^{\frac{Vm + 66}{6}}} tau_f_VDDR = T_correction_Ca 0.04 \frac{d}{d time} (f_VDDR) = \frac{f_inf_VDDR - f_VDDR}{tau_f_VDDR}

Component: I_VDDR

E_Ca = 0.5 RToF \ln (\frac{Ca_o}{Ca_i}) I_VDDR = G_max_VDDR f_VDDR d_VDDR (Vm - E_Ca)

Component: d_CaCl

d_inf_CaCl = \frac{1}{1 + {(\frac{0.00014}{Ca_i})}^{3}} \frac{d}{d time} (d_CaCl) = \frac{d_inf_CaCl - d_CaCl}{tau_d_CaCl}

Component: I_CaCl

E_Cl = RToF \ln (\frac{Cl_i}{Cl_o}) I_CaCl = G_max_CaCl d_CaCl (Vm - E_Cl)

Component: d_BK

d_BK = \frac{1}{1 + ⅇ^{\frac{Vm}{- 17} - (2 \ln (\frac{Ca_i}{0.001}))}}

Component: I_BK

E_K = RToF \ln (\frac{K_o}{K_i}) I_BK = (G_max_BK + T_correction_BK) d_BK (Vm - E_K)

Component: I_bk

E_K = RToF \ln (\frac{K_o}{K_i}) I_bk = G_max_bk (Vm - E_K)

Component: d_ERG

d_inf_ERG = 0.2 + \frac{0.8}{1 + ⅇ^{\frac{Vm + 20}{- 1.8}}} tau_d_ERG = T_correction_K 0.003 \frac{d}{d time} (d_ERG) = \frac{d_inf_ERG - d_ERG}{tau_d_ERG}

Component: I_ERG

E_K = RToF \ln (\frac{K_o}{K_i}) I_ERG = G_max_ERG d_ERG (Vm - E_K)

Component: d_kv11

d_inf_kv11 = \frac{1}{1 + ⅇ^{\frac{Vm + 25}{- 7.7}}} tau_d_kv11 = T_correction_K 0.005 \frac{d}{d time} (d_kv11) = \frac{d_inf_kv11 - d_kv11}{tau_d_kv11}

Component: f_kv11

f_inf_kv11 = 0.5 + \frac{0.5}{1 + ⅇ^{\frac{Vm + 44.8}{4.4}}} tau_f_kv11 = T_correction_K 0.005 \frac{d}{d time} (f_kv11) = \frac{f_inf_kv11 - f_kv11}{tau_f_kv11}

Component: I_kv11

E_K = RToF \ln (\frac{K_o}{K_i}) I_kv11 = G_max_kv11 f_kv11 d_kv11 (Vm - E_K)

Component: d_Na

d_inf_Na = \frac{1}{1 + ⅇ^{\frac{Vm + 47}{- 4.8}}} tau_d_Na = T_correction_Na 0.003 \frac{d}{d time} (d_Na) = \frac{d_inf_Na - d_Na}{tau_d_Na}

Component: f_Na

f_inf_Na = \frac{1}{1 + ⅇ^{\frac{Vm + 78}{7}}} tau_f_Na = T_correction_Na 0.0016 \frac{d}{d time} (f_Na) = \frac{f_inf_Na - f_Na}{tau_f_Na}

Component: I_Na

E_Na = RToF \ln (\frac{Na_o}{Na_i}) I_Na = G_max_Na f_Na d_Na (Vm - E_Na)

Component: d_NSCC

d_inf_NSCC = \frac{1}{1 + {(\frac{0.0000745}{Ca_PU})}^{- 85}} \frac{d}{d time} (d_NSCC) = \frac{d_inf_NSCC - d_NSCC}{tau_d_NSCC}

Component: I_NSCC

E_NSCC = RToF \ln (\frac{K_o + Na_o NaPerm_o_Kperm}{K_i + Na_i NaPerm_o_Kperm}) I_NSCC = G_max_NSCC d_NSCC (Vm - E_NSCC)

Component: PU_unit

V_MITO = Vol P_mito V_PU = Vol P_PU V_ER = Vol P_ER J_ERout = (Jmax_IP3 {(\frac{IP3}{IP3 + d_IP3})}^{3} {(\frac{Ca_PU}{Ca_PU + d_ACT})}^{3} h^{3} + J_ERleak) (Ca_ER - Ca_PU) J_SERCA = \frac{Jmax_serca {Ca_PU}^{2}}{{k_serca}^{2} + {Ca_PU}^{2}} MWC = \frac{\frac{conc Ca_PU}{K_trans} {(1 + \frac{Ca_PU}{K_trans})}^{3}}{{(1 + \frac{Ca_PU}{K_trans})}^{4} + \frac{L}{{(1 + \frac{Ca_PU}{K_act})}^{na}}} J_uni = \frac{Jmax_uni (MWC - (Ca_m ⅇ^{(- 2) FoRT (deltaPsi - deltaPsi_star)})) 2 FoRT (deltaPsi - deltaPsi_star)}{1 - (ⅇ^{(- 2) FoRT (deltaPsi - deltaPsi_star)})} J_NaCa = \frac{Jmax_NaCa ⅇ^{b FoRT (deltaPsi - deltaPsi_star)}}{(1 + {(\frac{K_Na}{Na_i})}^{n}) (1 + \frac{K_Ca}{Ca_m})} J_leak = J_max_leak (Ca_PU - Ca_i) A_res = RToF \ln (\frac{K_res \sqrt{NADH_m}}{\sqrt{NAD_m}}) J_o = \frac{rho_res 0.5 ((ra 10^{6 deltapH} + rc1 ⅇ^{6 deltaPsi_B FoRT}) ⅇ^{A_res FoRT} + (- 1) ra ⅇ^{g 6 FoRT deltaPsi} + rc2 ⅇ^{FoRT A_res} ⅇ^{FoRT deltaPsi 6 g})}{(1 + r1 ⅇ^{FoRT A_res}) ⅇ^{FoRT deltaPsi_B 6} + (r2 + r3 ⅇ^{FoRT A_res}) ⅇ^{FoRT deltaPsi g 6}} J_Hres = \frac{rho_res 3.966 (ra 10^{6 deltapH} ⅇ^{FoRT A_res} + rb 10^{6 deltapH} + (- 1) (ra + rb) ⅇ^{g FoRT deltaPsi 6})}{(1 + r1 ⅇ^{FoRT A_res}) ⅇ^{6 FoRT deltaPsi_B} + (r2 + r3 ⅇ^{FoRT A_res}) ⅇ^{g 6 FoRT deltaPsi}} J_glyTotal = \frac{beta_max (1 + beta1 Glc) beta2 Glc ATP_i}{1 + beta3 ATP_i + (1 + beta4 ATP_i) beta5 Glc + (1 + beta6 ATP_i) beta7 Glc} f_PDHa = \frac{1}{1 + u2 (1 + \frac{u1}{{(1 + \frac{Ca_m}{KCa_PDH})}^{2}})} J_red = J_red_basal + 6.3944 f_PDHa J_glyTotal J_pTCA = \frac{J_red_basal}{3} + 0.84 f_PDHa J_glyTotal A_F1 = RToF \ln (\frac{K_F1 ATP_m}{ADP_mfree Pi_m}) J_pF1 = \frac{rho_F1 (- 1) ((pa 10^{3 deltapH} + pc1 ⅇ^{3 FoRT deltaPsi_B}) ⅇ^{FoRT A_F1} + (- 1) pa ⅇ^{3 FoRT deltaPsi} + pc2 ⅇ^{FoRT A_F1} ⅇ^{3 FoRT deltaPsi})}{(1 + p1 ⅇ^{FoRT A_F1}) ⅇ^{3 FoRT deltaPsi_B} + (p2 + p3 ⅇ^{FoRT A_F1}) ⅇ^{3 FoRT deltaPsi}} J_HF1 = \frac{(- 1) rho_F1 3 (pa 10^{3 deltapH} ⅇ^{FoRT A_F1} + pb 10^{3 deltapH} + (- 1) (pa + pb) ⅇ^{3 FoRT deltaPsi})}{(1 + p1 ⅇ^{FoRT A_F1}) ⅇ^{3 FoRT deltaPsi_B} + (p2 + p3 ⅇ^{FoRT A_F1}) ⅇ^{3 FoRT deltaPsi}} J_ANT = \frac{Jmax_ANT (1 - (\frac{ATP4_i ADP3_m}{ADP3_i ATP4_m} ⅇ^{(- 1) FoRT deltaPsi}))}{(1 + \frac{ATP4_i}{ADP3_i} ⅇ^{(- 1) frac FoRT deltaPsi}) (1 + \frac{ADP3_m}{ATP4_m})} PMF = deltaPsi - (2.303 RToF deltapH) J_Hleak = g_H PMF J_pGly = 0.15 J_glyTotal J_hydSS = \frac{J_hyd_max}{1 + {(\frac{K_Glc}{Glc})}^{nhyd}} J_hyd = K_hyd ATP_i + J_hydSS \frac{d}{d time} (NADH_m) = J_red - J_o NAD_m = total_NAD_m - NADH_m \frac{d}{d time} (ADP_m) = J_ANT + (- 1) J_pTCA + (- 1) J_pF1 ATP_m = total_ANP_m - ADP_m ADP_mfree = 0.8 ADP_m ADP3_m = 0.45 ADP_mfree ATP4_m = 0.05 ATP_m \frac{d}{d time} (ADP_i) = \frac{(- 1) J_ANT V_MITO}{V_cyto} + J_hyd + (- 1) J_pGly ATP_i = total_ANP_i - ADP_i ADP_ifree = 0.3 ADP_i ADP3_i = 0.45 ADP_ifree MgADP_i = 0.55 ADP_ifree ATP4_i = 0.05 ATP_i \frac{d}{d time} (Ca_PU) = fc (\frac{(J_NaCa - J_uni) V_MITO}{V_PU} + \frac{(J_ERout - J_SERCA) V_ER}{V_PU} + \frac{(- 1) J_leak V_cyto}{V_PU}) \frac{d}{d time} (Ca_m) = fm (J_uni - J_NaCa) \frac{d}{d time} (Ca_ER) = fe (J_SERCA - J_ERout) \frac{d}{d time} (deltaPsi) = \frac{(- 1) F V_MITO 1000000 1}{Cmito} (J_Hleak + (- 1) J_Hres + J_ANT + J_HF1 + 2 J_uni) \frac{d}{d time} (h) = \frac{1 (d_INH - (h (Ca_PU + d_INH)))}{tauh}