Model Mathematics

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Component: environment

\frac{d}{d t} (q_Ca_o) = v_Ca_o_LCC \frac{d}{d t} (q_Ca_i) = v_Ca_i_LCC \frac{d}{d t} (q_K_o) = v_K_o_LCC \frac{d}{d t} (q_K_i) = v_K_i_LCC \frac{d}{d t} (q_mem) = I_mem_LCC

Component: LCC_parameters

Component: LCC

V_mem = \frac{q_mem}{C_m} mu_Ca_o = R T \ln (K_Ca_o q_Ca_o) mu_Ca_i = R T \ln (K_Ca_i q_Ca_i) mu_K_o = R T \ln (K_K_o q_K_o) mu_K_i = R T \ln (K_K_i q_K_i) mu_S000_LCC = R T \ln (K_000_LCC q_S000_LCC) mu_S001_LCC = R T \ln (K_001_LCC q_S001_LCC) mu_S010_LCC = R T \ln (K_010_LCC q_S010_LCC) mu_S011_LCC = R T \ln (K_011_LCC q_S011_LCC) mu_S020_LCC = R T \ln (K_020_LCC q_S020_LCC) mu_S021_LCC = R T \ln (K_021_LCC q_S021_LCC) mu_S100_LCC = R T \ln (K_100_LCC q_S100_LCC) mu_S101_LCC = R T \ln (K_101_LCC q_S101_LCC) mu_S110_LCC = R T \ln (K_110_LCC q_S110_LCC) mu_S111_LCC = R T \ln (K_111_LCC q_S111_LCC) mu_S120_LCC = R T \ln (K_120_LCC q_S120_LCC) mu_S121_LCC = R T \ln (K_121_LCC q_S121_LCC) v_d000 = kappa_d000 (ⅇ^{\frac{Af_d000}{R T}} - (ⅇ^{\frac{Ar_d000}{R T}})) v_d001 = kappa_d001 (ⅇ^{\frac{Af_d001}{R T}} - (ⅇ^{\frac{Ar_d001}{R T}})) v_d010 = kappa_d010 (ⅇ^{\frac{Af_d010}{R T}} - (ⅇ^{\frac{Ar_d010}{R T}})) v_d011 = kappa_d011 (ⅇ^{\frac{Af_d011}{R T}} - (ⅇ^{\frac{Ar_d011}{R T}})) v_d020 = kappa_d020 (ⅇ^{\frac{Af_d020}{R T}} - (ⅇ^{\frac{Ar_d020}{R T}})) v_d021 = kappa_d021 (ⅇ^{\frac{Af_d021}{R T}} - (ⅇ^{\frac{Ar_d021}{R T}})) v_f1_000 = kappa_f1_000 (ⅇ^{\frac{Af_f1_000}{R T}} - (ⅇ^{\frac{Ar_f1_000}{R T}})) v_f1_001 = kappa_f1_001 (ⅇ^{\frac{Af_f1_001}{R T}} - (ⅇ^{\frac{Ar_f1_001}{R T}})) v_f1_100 = kappa_f1_100 (ⅇ^{\frac{Af_f1_100}{R T}} - (ⅇ^{\frac{Ar_f1_100}{R T}})) v_f1_101 = kappa_f1_101 (ⅇ^{\frac{Af_f1_101}{R T}} - (ⅇ^{\frac{Ar_f1_101}{R T}})) v_f2_000 = kappa_f2_000 (ⅇ^{\frac{Af_f2_000}{R T}} - (ⅇ^{\frac{Ar_f2_000}{R T}})) v_f2_001 = kappa_f2_001 (ⅇ^{\frac{Af_f2_001}{R T}} - (ⅇ^{\frac{Ar_f2_001}{R T}})) v_f2_100 = kappa_f2_100 (ⅇ^{\frac{Af_f2_100}{R T}} - (ⅇ^{\frac{Ar_f2_100}{R T}})) v_f2_101 = kappa_f2_101 (ⅇ^{\frac{Af_f2_101}{R T}} - (ⅇ^{\frac{Ar_f2_101}{R T}})) v_f3_010 = kappa_f3_010 (ⅇ^{\frac{Af_f3_010}{R T}} - (ⅇ^{\frac{Ar_f3_010}{R T}})) v_f3_011 = kappa_f3_011 (ⅇ^{\frac{Af_f3_011}{R T}} - (ⅇ^{\frac{Ar_f3_011}{R T}})) v_f3_110 = kappa_f3_110 (ⅇ^{\frac{Af_f3_110}{R T}} - (ⅇ^{\frac{Ar_f3_110}{R T}})) v_f3_111 = kappa_f3_111 (ⅇ^{\frac{Af_f3_111}{R T}} - (ⅇ^{\frac{Ar_f3_111}{R T}})) v_fCa00 = kappa_fCa000 (ⅇ^{\frac{Af_fCa00}{R T}} - (ⅇ^{\frac{Ar_fCa00}{R T}})) v_fCa01 = kappa_fCa010 (ⅇ^{\frac{Af_fCa01}{R T}} - (ⅇ^{\frac{Ar_fCa01}{R T}})) v_fCa02 = kappa_fCa020 (ⅇ^{\frac{Af_fCa02}{R T}} - (ⅇ^{\frac{Ar_fCa02}{R T}})) v_fCa10 = kappa_fCa100 (ⅇ^{\frac{Af_fCa10}{R T}} - (ⅇ^{\frac{Ar_fCa10}{R T}})) v_fCa11 = kappa_fCa110 (ⅇ^{\frac{Af_fCa11}{R T}} - (ⅇ^{\frac{Ar_fCa11}{R T}})) v_fCa12 = kappa_fCa120 (ⅇ^{\frac{Af_fCa12}{R T}} - (ⅇ^{\frac{Ar_fCa12}{R T}})) Af_LCC_Ca1 = mu_Ca_i + zCa F V_mem + mu_S111_LCC Af_LCC_Ca2 = mu_Ca_i + zCa F V_mem + mu_S121_LCC Af_LCC_K1 = mu_K_i + zK F V_mem + mu_S111_LCC Af_LCC_K2 = mu_K_i + zK F V_mem + mu_S121_LCC Af_d000 = R T \ln (K_000_LCC q_S000_LCC) + z_fd F V_mem Af_d001 = R T \ln (K_001_LCC q_S001_LCC) + z_fd F V_mem Af_d010 = R T \ln (K_010_LCC q_S010_LCC) + z_fd F V_mem Af_d011 = R T \ln (K_011_LCC q_S011_LCC) + z_fd F V_mem Af_d020 = R T \ln (K_020_LCC q_S020_LCC) + z_fd F V_mem Af_d021 = R T \ln (K_021_LCC q_S021_LCC) + z_fd F V_mem Af_f1_000 = R T \ln (K_000_LCC q_S000_LCC) + z_ff1 F V_mem Af_f1_001 = R T \ln (K_001_LCC q_S001_LCC) + z_ff1 F V_mem Af_f1_100 = R T \ln (K_100_LCC q_S100_LCC) + z_ff1 F V_mem Af_f1_101 = R T \ln (K_101_LCC q_S101_LCC) + z_ff1 F V_mem Af_f2_000 = R T \ln (K_000_LCC q_S000_LCC) + z_ff2 F V_mem Af_f2_001 = R T \ln (K_001_LCC q_S001_LCC) + z_ff2 F V_mem Af_f2_100 = R T \ln (K_100_LCC q_S100_LCC) + z_ff2 F V_mem Af_f2_101 = R T \ln (K_101_LCC q_S101_LCC) + z_ff2 F V_mem Af_f3_010 = R T \ln (K_010_LCC q_S010_LCC) + z_ff3 F V_mem Af_f3_011 = R T \ln (K_011_LCC q_S011_LCC) + z_ff3 F V_mem Af_f3_110 = R T \ln (K_110_LCC q_S110_LCC) + z_ff3 F V_mem Af_f3_111 = R T \ln (K_111_LCC q_S111_LCC) + z_ff3 F V_mem Af_fCa00 = mu_S000_LCC Af_fCa01 = mu_S010_LCC Af_fCa02 = mu_S020_LCC Af_fCa10 = mu_S100_LCC Af_fCa11 = mu_S110_LCC Af_fCa12 = mu_S120_LCC Am_LCC_Ca1 = zCa F V_mem Am_LCC_Ca2 = zCa F V_mem Am_LCC_K1 = zK F V_mem Am_LCC_K2 = zK F V_mem Ar_LCC_Ca1 = mu_Ca_o + mu_S111_LCC Ar_LCC_Ca2 = mu_Ca_o + mu_S121_LCC Ar_LCC_K1 = mu_K_o + mu_S111_LCC Ar_LCC_K2 = mu_K_o + mu_S121_LCC Ar_d000 = R T \ln (K_100_LCC q_S100_LCC) + z_rd F V_mem Ar_d001 = R T \ln (K_101_LCC q_S101_LCC) + z_rd F V_mem Ar_d010 = R T \ln (K_110_LCC q_S110_LCC) + z_rd F V_mem Ar_d011 = R T \ln (K_111_LCC q_S111_LCC) + z_rd F V_mem Ar_d020 = R T \ln (K_120_LCC q_S120_LCC) + z_rd F V_mem Ar_d021 = R T \ln (K_121_LCC q_S121_LCC) + z_rd F V_mem Ar_f1_000 = R T \ln (K_010_LCC q_S010_LCC) + z_rf1 F V_mem Ar_f1_001 = R T \ln (K_011_LCC q_S011_LCC) + z_rf1 F V_mem Ar_f1_100 = R T \ln (K_110_LCC q_S110_LCC) + z_rf1 F V_mem Ar_f1_101 = R T \ln (K_111_LCC q_S111_LCC) + z_rf1 F V_mem Ar_f2_000 = R T \ln (K_020_LCC q_S020_LCC) + z_rf2 F V_mem Ar_f2_001 = R T \ln (K_021_LCC q_S021_LCC) + z_rf2 F V_mem Ar_f2_100 = R T \ln (K_120_LCC q_S120_LCC) + z_rf2 F V_mem Ar_f2_101 = R T \ln (K_121_LCC q_S121_LCC) + z_rf2 F V_mem Ar_f3_010 = R T \ln (K_020_LCC q_S020_LCC) + z_rf3 F V_mem Ar_f3_011 = R T \ln (K_021_LCC q_S021_LCC) + z_rf3 F V_mem Ar_f3_110 = R T \ln (K_120_LCC q_S120_LCC) + z_rf3 F V_mem Ar_f3_111 = R T \ln (K_121_LCC q_S121_LCC) + z_rf3 F V_mem Ar_fCa00 = R T \ln (K_001_LCC q_S001_LCC) + z_rCa mu_Ca_i Ar_fCa01 = R T \ln (K_011_LCC q_S011_LCC) + z_rCa mu_Ca_i Ar_fCa02 = R T \ln (K_021_LCC q_S021_LCC) + z_rCa mu_Ca_i Ar_fCa10 = R T \ln (K_101_LCC q_S101_LCC) + z_rCa mu_Ca_i Ar_fCa11 = R T \ln (K_111_LCC q_S111_LCC) + z_rCa mu_Ca_i Ar_fCa12 = R T \ln (K_121_LCC q_S121_LCC) + z_rCa mu_Ca_i I_mem_LCC = F (((((((((((((((() + - ()) + z_rf3 v_f3_111 - (z_ff3 v_f3_111)) + z_rf1 v_f1_001 - (z_ff1 v_f1_001)) + z_rd v_d021 - (z_fd v_d021)) + z_rd v_d011 - (z_fd v_d011)) + z_rd v_d001 - (z_fd v_d001)) + z_rf3 v_f3_110 - (z_ff3 v_f3_110)) + z_rf2 v_f2_100 - (z_ff2 v_f2_100)) + z_rf1 v_f1_100 - (z_ff1 v_f1_100)) + z_rf3 v_f3_010 - (z_ff3 v_f3_010)) + z_rf2 v_f2_000 - (z_ff2 v_f2_000)) + z_rf1 v_f1_000 - (z_ff1 v_f1_000)) + z_rd v_d020 - (z_fd v_d020)) + z_rd v_d010 - (z_fd v_d010)) + z_rd v_d000 - (z_fd v_d000) - (zCa v_LCC_Ca1 + zCa v_LCC_Ca2) - (zK v_LCC_K1 + zK v_LCC_K2)) v_Ca_o_LCC = v_LCC_Ca2 + v_LCC_Ca1 v_Ca_i_LCC = (+ z_rCa) v_fCa10 + z_rCa v_fCa11 + z_rCa v_fCa02 + z_rCa v_fCa01 + z_rCa v_fCa00 + z_rCa v_fCa12 - v_LCC_Ca1 - v_LCC_Ca2 v_K_o_LCC = v_LCC_K2 + v_LCC_K1 v_K_i_LCC = - v_LCC_K1 - v_LCC_K2 v_S000_LCC = - v_d000 - v_f1_000 - v_f2_000 - v_fCa00 v_S001_LCC = - v_d001 - v_f1_001 - v_f2_001 - (- v_fCa00) v_S010_LCC = (- v_d010) + v_f1_000 - v_fCa01 - v_f3_010 v_S011_LCC = (- v_d011) + v_f1_001 - (- v_fCa01) - v_f3_011 v_S020_LCC = ((- v_d020) + v_f2_000 - v_fCa02) + v_f3_010 v_S021_LCC = ((- v_d021) + v_f2_001 - (- v_fCa02)) + v_f3_011 v_S100_LCC = (- v_f2_100) + v_d000 - v_f1_100 - v_fCa10 v_S101_LCC = (- v_f2_101) + v_d001 - v_f1_101 - (- v_fCa10) v_S110_LCC = v_f1_100 + v_d010 - v_fCa11 - v_f3_110 v_S111_LCC = v_f1_101 + v_d011 - (((- v_fCa11) + v_LCC_Ca1 - v_LCC_Ca1) + v_LCC_K1 - v_LCC_K1) - v_f3_111 v_S120_LCC = (v_f2_100 + v_d020 - v_fCa12) + v_f3_110 v_S121_LCC = (v_f2_101 + v_d021 - (((- v_fCa12) + v_LCC_Ca2 - v_LCC_Ca2) + v_LCC_K2 - v_LCC_K2)) + v_f3_111 \frac{d}{d t} (q_S000_LCC) = v_S000_LCC \frac{d}{d t} (q_S010_LCC) = v_S010_LCC \frac{d}{d t} (q_S020_LCC) = v_S020_LCC \frac{d}{d t} (q_S100_LCC) = v_S100_LCC \frac{d}{d t} (q_S110_LCC) = v_S110_LCC \frac{d}{d t} (q_S120_LCC) = v_S120_LCC \frac{d}{d t} (q_S001_LCC) = v_S001_LCC \frac{d}{d t} (q_S011_LCC) = v_S011_LCC \frac{d}{d t} (q_S021_LCC) = v_S021_LCC \frac{d}{d t} (q_S101_LCC) = v_S101_LCC \frac{d}{d t} (q_S111_LCC) = v_S111_LCC \frac{d}{d t} (q_S121_LCC) = v_S121_LCC v_LCC_Ca1 = \{\begin{matrix} kappa_LCC_Ca1 (ⅇ^{\frac{Af_LCC_Ca1}{R T}} - (ⅇ^{\frac{Ar_LCC_Ca1}{R T}})) if Am_LCC_Ca1 = 0 \\ \frac{\frac{kappa_LCC_Ca1 Am_LCC_Ca1}{R T}}{ⅇ^{\frac{Am_LCC_Ca1}{R T}} - 1} (ⅇ^{\frac{Af_LCC_Ca1}{R T}} - (ⅇ^{\frac{Ar_LCC_Ca1}{R T}})) otherwise \end{matrix} v_LCC_Ca2 = \{\begin{matrix} kappa_LCC_Ca2 (ⅇ^{\frac{Af_LCC_Ca2}{R T}} - (ⅇ^{\frac{Ar_LCC_Ca2}{R T}})) if Am_LCC_Ca2 = 0 \\ \frac{\frac{kappa_LCC_Ca2 Am_LCC_Ca2}{R T}}{ⅇ^{\frac{Am_LCC_Ca2}{R T}} - 1} (ⅇ^{\frac{Af_LCC_Ca2}{R T}} - (ⅇ^{\frac{Ar_LCC_Ca2}{R T}})) otherwise \end{matrix} v_LCC_K1 = \{\begin{matrix} kappa_LCC_K1 (ⅇ^{\frac{Af_LCC_K1}{R T}} - (ⅇ^{\frac{Ar_LCC_K1}{R T}})) if Am_LCC_K1 = 0 \\ \frac{\frac{kappa_LCC_K1 Am_LCC_K1}{R T}}{ⅇ^{\frac{Am_LCC_K1}{R T}} - 1} (ⅇ^{\frac{Af_LCC_K1}{R T}} - (ⅇ^{\frac{Ar_LCC_K1}{R T}})) otherwise \end{matrix} v_LCC_K2 = \{\begin{matrix} kappa_LCC_K2 (ⅇ^{\frac{Af_LCC_K2}{R T}} - (ⅇ^{\frac{Ar_LCC_K2}{R T}})) if Am_LCC_K2 = 0 \\ \frac{\frac{kappa_LCC_K2 Am_LCC_K2}{R T}}{ⅇ^{\frac{Am_LCC_K2}{R T}} - 1} (ⅇ^{\frac{Af_LCC_K2}{R T}} - (ⅇ^{\frac{Ar_LCC_K2}{R T}})) otherwise \end{matrix}

Ca_tot = q_Ca_o + q_Ca_i + q_S001_LCC + q_S011_LCC + q_S021_LCC + q_S101_LCC + q_S111_LCC + q_S121_LCC

Model Mathematics

Component: environment

Component: LCC_parameters

Component: LCC

Component: units

Component: constants