Model Mathematics

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Component: environment

\frac{d}{d t} (q_Na_o) = v_Na \frac{d}{d t} (q_Na_i) = - v_Na

\frac{d}{d t} (q_mem) = I_mem_Na

Component: Na_parameters

Component: fast_Na

V_mem = \frac{q_mem}{C_m} I_mem_Na = F ((((((((((((((((- ()) + z_rj v_j000 - (z_fj v_j000)) + z_rm v_m001 - (z_fm v_m001)) + z_rm v_m101 - (z_fm v_m101)) + z_rm v_m011 - (z_fm v_m011)) + z_rm v_m111 - (z_fm v_m111)) + z_rm v_m211 - (z_fm v_m211)) + z_rh v_h001 - (z_fh v_h001)) + z_rh v_h201 - (z_fh v_h201)) + z_rj v_j010 - (z_fj v_j010)) + z_rj v_j110 - (z_fj v_j110)) + z_rj v_j210 - (z_fj v_j210)) + z_rj v_j310 - (z_fj v_j310)) + z_rm v_m201 - (z_fm v_m201)) + z_rh v_h101 - (z_fh v_h101)) + z_rh v_h301 - (z_fh v_h301)) mu_Na_o = R T \ln (K_Na_o q_Na_o) mu_Na_i = R T \ln (K_Na_i q_Na_i) mu_S000_Na = R T \ln (K_000_Na q_S000_Na) mu_S001_Na = R T \ln (K_001_Na q_S001_Na) mu_S010_Na = R T \ln (K_010_Na q_S010_Na) mu_S011_Na = R T \ln (K_011_Na q_S011_Na) mu_S100_Na = R T \ln (K_100_Na q_S100_Na) mu_S101_Na = R T \ln (K_101_Na q_S101_Na) mu_S110_Na = R T \ln (K_110_Na q_S110_Na) mu_S111_Na = R T \ln (K_111_Na q_S111_Na) mu_S200_Na = R T \ln (K_200_Na q_S200_Na) mu_S201_Na = R T \ln (K_201_Na q_S201_Na) mu_S210_Na = R T \ln (K_210_Na q_S210_Na) mu_S211_Na = R T \ln (K_211_Na q_S211_Na) mu_S300_Na = R T \ln (K_300_Na q_S300_Na) mu_S301_Na = R T \ln (K_301_Na q_S301_Na) mu_S310_Na = R T \ln (K_310_Na q_S310_Na) mu_S311_Na = R T \ln (K_311_Na q_S311_Na) v_h000 = kappa_h000 (ⅇ^{\frac{Af_h000}{R T}} - (ⅇ^{\frac{Ar_h000}{R T}})) v_h001 = kappa_h001 (ⅇ^{\frac{Af_h001}{R T}} - (ⅇ^{\frac{Ar_h001}{R T}})) v_h100 = kappa_h100 (ⅇ^{\frac{Af_h100}{R T}} - (ⅇ^{\frac{Ar_h100}{R T}})) v_h101 = kappa_h101 (ⅇ^{\frac{Af_h101}{R T}} - (ⅇ^{\frac{Ar_h101}{R T}})) v_h200 = kappa_h200 (ⅇ^{\frac{Af_h200}{R T}} - (ⅇ^{\frac{Ar_h200}{R T}})) v_h201 = kappa_h201 (ⅇ^{\frac{Af_h201}{R T}} - (ⅇ^{\frac{Ar_h201}{R T}})) v_h300 = kappa_h300 (ⅇ^{\frac{Af_h300}{R T}} - (ⅇ^{\frac{Ar_h300}{R T}})) v_h301 = kappa_h301 (ⅇ^{\frac{Af_h301}{R T}} - (ⅇ^{\frac{Ar_h301}{R T}})) v_j000 = kappa_j000 (ⅇ^{\frac{Af_j000}{R T}} - (ⅇ^{\frac{Ar_j000}{R T}})) v_j010 = kappa_j010 (ⅇ^{\frac{Af_j010}{R T}} - (ⅇ^{\frac{Ar_j010}{R T}})) v_j100 = kappa_j100 (ⅇ^{\frac{Af_j100}{R T}} - (ⅇ^{\frac{Ar_j100}{R T}})) v_j110 = kappa_j110 (ⅇ^{\frac{Af_j110}{R T}} - (ⅇ^{\frac{Ar_j110}{R T}})) v_j200 = kappa_j200 (ⅇ^{\frac{Af_j200}{R T}} - (ⅇ^{\frac{Ar_j200}{R T}})) v_j210 = kappa_j210 (ⅇ^{\frac{Af_j210}{R T}} - (ⅇ^{\frac{Ar_j210}{R T}})) v_j300 = kappa_j300 (ⅇ^{\frac{Af_j300}{R T}} - (ⅇ^{\frac{Ar_j300}{R T}})) v_j310 = kappa_j310 (ⅇ^{\frac{Af_j310}{R T}} - (ⅇ^{\frac{Ar_j310}{R T}})) v_m000 = kappa_m000 (ⅇ^{\frac{Af_m000}{R T}} - (ⅇ^{\frac{Ar_m000}{R T}})) v_m001 = kappa_m001 (ⅇ^{\frac{Af_m001}{R T}} - (ⅇ^{\frac{Ar_m001}{R T}})) v_m010 = kappa_m010 (ⅇ^{\frac{Af_m010}{R T}} - (ⅇ^{\frac{Ar_m010}{R T}})) v_m011 = kappa_m011 (ⅇ^{\frac{Af_m011}{R T}} - (ⅇ^{\frac{Ar_m011}{R T}})) v_m100 = kappa_m100 (ⅇ^{\frac{Af_m100}{R T}} - (ⅇ^{\frac{Ar_m100}{R T}})) v_m101 = kappa_m101 (ⅇ^{\frac{Af_m101}{R T}} - (ⅇ^{\frac{Ar_m101}{R T}})) v_m110 = kappa_m110 (ⅇ^{\frac{Af_m110}{R T}} - (ⅇ^{\frac{Ar_m110}{R T}})) v_m111 = kappa_m111 (ⅇ^{\frac{Af_m111}{R T}} - (ⅇ^{\frac{Ar_m111}{R T}})) v_m200 = kappa_m200 (ⅇ^{\frac{Af_m200}{R T}} - (ⅇ^{\frac{Ar_m200}{R T}})) v_m201 = kappa_m201 (ⅇ^{\frac{Af_m201}{R T}} - (ⅇ^{\frac{Ar_m201}{R T}})) v_m210 = kappa_m210 (ⅇ^{\frac{Af_m210}{R T}} - (ⅇ^{\frac{Ar_m210}{R T}})) v_m211 = kappa_m211 (ⅇ^{\frac{Af_m211}{R T}} - (ⅇ^{\frac{Ar_m211}{R T}})) Af_Na = mu_Na_i + zNa F V_mem + mu_S311_Na Af_h000 = R T \ln (K_000_Na q_S000_Na) + z_fh F V_mem Af_h001 = R T \ln (K_001_Na q_S001_Na) + z_fh F V_mem Af_h100 = R T \ln (K_100_Na q_S100_Na) + z_fh F V_mem Af_h101 = R T \ln (K_101_Na q_S101_Na) + z_fh F V_mem Af_h200 = R T \ln (K_200_Na q_S200_Na) + z_fh F V_mem Af_h201 = R T \ln (K_201_Na q_S201_Na) + z_fh F V_mem Af_h300 = R T \ln (K_300_Na q_S300_Na) + z_fh F V_mem Af_h301 = R T \ln (K_301_Na q_S301_Na) + z_fh F V_mem Af_j000 = R T \ln (K_000_Na q_S000_Na) + z_fj F V_mem Af_j010 = R T \ln (K_010_Na q_S010_Na) + z_fj F V_mem Af_j100 = R T \ln (K_100_Na q_S100_Na) + z_fj F V_mem Af_j110 = R T \ln (K_110_Na q_S110_Na) + z_fj F V_mem Af_j200 = R T \ln (K_200_Na q_S200_Na) + z_fj F V_mem Af_j210 = R T \ln (K_210_Na q_S210_Na) + z_fj F V_mem Af_j300 = R T \ln (K_300_Na q_S300_Na) + z_fj F V_mem Af_j310 = R T \ln (K_310_Na q_S310_Na) + z_fj F V_mem Af_m000 = R T \ln (K_000_Na q_S000_Na) + z_fm F V_mem Af_m001 = R T \ln (K_001_Na q_S001_Na) + z_fm F V_mem Af_m010 = R T \ln (K_010_Na q_S010_Na) + z_fm F V_mem Af_m011 = R T \ln (K_011_Na q_S011_Na) + z_fm F V_mem Af_m100 = R T \ln (K_100_Na q_S100_Na) + z_fm F V_mem Af_m101 = R T \ln (K_101_Na q_S101_Na) + z_fm F V_mem Af_m110 = R T \ln (K_110_Na q_S110_Na) + z_fm F V_mem Af_m111 = R T \ln (K_111_Na q_S111_Na) + z_fm F V_mem Af_m200 = R T \ln (K_200_Na q_S200_Na) + z_fm F V_mem Af_m201 = R T \ln (K_201_Na q_S201_Na) + z_fm F V_mem Af_m210 = R T \ln (K_210_Na q_S210_Na) + z_fm F V_mem Af_m211 = R T \ln (K_211_Na q_S211_Na) + z_fm F V_mem Am_Na = zNa F V_mem Ar_Na = mu_Na_o + mu_S311_Na Ar_h000 = R T \ln (K_010_Na q_S010_Na) + z_rh F V_mem Ar_h001 = R T \ln (K_011_Na q_S011_Na) + z_rh F V_mem Ar_h100 = R T \ln (K_110_Na q_S110_Na) + z_rh F V_mem Ar_h101 = R T \ln (K_111_Na q_S111_Na) + z_rh F V_mem Ar_h200 = R T \ln (K_210_Na q_S210_Na) + z_rh F V_mem Ar_h201 = R T \ln (K_211_Na q_S211_Na) + z_rh F V_mem Ar_h300 = R T \ln (K_310_Na q_S310_Na) + z_rh F V_mem Ar_h301 = R T \ln (K_311_Na q_S311_Na) + z_rh F V_mem Ar_j000 = R T \ln (K_001_Na q_S001_Na) + z_rj F V_mem Ar_j010 = R T \ln (K_011_Na q_S011_Na) + z_rj F V_mem Ar_j100 = R T \ln (K_101_Na q_S101_Na) + z_rj F V_mem Ar_j110 = R T \ln (K_111_Na q_S111_Na) + z_rj F V_mem Ar_j200 = R T \ln (K_201_Na q_S201_Na) + z_rj F V_mem Ar_j210 = R T \ln (K_211_Na q_S211_Na) + z_rj F V_mem Ar_j300 = R T \ln (K_301_Na q_S301_Na) + z_rj F V_mem Ar_j310 = R T \ln (K_311_Na q_S311_Na) + z_rj F V_mem Ar_m000 = R T \ln (K_100_Na q_S100_Na) + z_rm F V_mem Ar_m001 = R T \ln (K_101_Na q_S101_Na) + z_rm F V_mem Ar_m010 = R T \ln (K_110_Na q_S110_Na) + z_rm F V_mem Ar_m011 = R T \ln (K_111_Na q_S111_Na) + z_rm F V_mem Ar_m100 = R T \ln (K_200_Na q_S200_Na) + z_rm F V_mem Ar_m101 = R T \ln (K_201_Na q_S201_Na) + z_rm F V_mem Ar_m110 = R T \ln (K_210_Na q_S210_Na) + z_rm F V_mem Ar_m111 = R T \ln (K_211_Na q_S211_Na) + z_rm F V_mem Ar_m200 = R T \ln (K_300_Na q_S300_Na) + z_rm F V_mem Ar_m201 = R T \ln (K_301_Na q_S301_Na) + z_rm F V_mem Ar_m210 = R T \ln (K_310_Na q_S310_Na) + z_rm F V_mem Ar_m211 = R T \ln (K_311_Na q_S311_Na) + z_rm F V_mem v_S000_Na = - v_m000 - v_h000 - v_j000 v_S001_Na = - v_m001 - v_h001 - (- v_j000) v_S010_Na = (- v_m010) + v_h000 - v_j010 v_S011_Na = (- v_m011) + v_h001 - (- v_j010) v_S100_Na = v_m000 - v_m100 - v_h100 - v_j100 v_S101_Na = v_m001 - v_m101 - v_h101 - (- v_j100) v_S110_Na = (v_m010 - v_m110) + v_h100 - v_j110 v_S111_Na = (v_m011 - v_m111) + v_h101 - (- v_j110) v_S200_Na = v_m100 - v_m200 - v_h200 - v_j200 v_S201_Na = v_m101 - v_m201 - v_h201 - (- v_j200) v_S210_Na = (v_m110 - v_m210) + v_h200 - v_j210 v_S211_Na = (v_m111 - v_m211) + v_h201 - (- v_j210) v_S300_Na = v_m200 - v_h300 - v_j300 v_S301_Na = v_m201 - v_h301 - (- v_j300) v_S310_Na = v_m210 + v_h300 - v_j310 v_S311_Na = v_m211 + v_h301 - ((- v_j310) + v_Na - v_Na) \frac{d}{d t} (q_S000_Na) = v_S000_Na \frac{d}{d t} (q_S010_Na) = v_S010_Na \frac{d}{d t} (q_S100_Na) = v_S100_Na \frac{d}{d t} (q_S110_Na) = v_S110_Na \frac{d}{d t} (q_S200_Na) = v_S200_Na \frac{d}{d t} (q_S210_Na) = v_S210_Na \frac{d}{d t} (q_S300_Na) = v_S300_Na \frac{d}{d t} (q_S310_Na) = v_S310_Na \frac{d}{d t} (q_S001_Na) = v_S001_Na \frac{d}{d t} (q_S011_Na) = v_S011_Na \frac{d}{d t} (q_S101_Na) = v_S101_Na \frac{d}{d t} (q_S111_Na) = v_S111_Na \frac{d}{d t} (q_S201_Na) = v_S201_Na \frac{d}{d t} (q_S211_Na) = v_S211_Na \frac{d}{d t} (q_S301_Na) = v_S301_Na \frac{d}{d t} (q_S311_Na) = v_S311_Na v_Na = \{\begin{matrix} kappa_Na (ⅇ^{\frac{Af_Na}{R T}} - (ⅇ^{\frac{Ar_Na}{R T}})) if Am_Na = 0 \\ \frac{\frac{kappa_Na Am_Na}{R T}}{ⅇ^{\frac{Am_Na}{R T}} - 1} (ⅇ^{\frac{Af_Na}{R T}} - (ⅇ^{\frac{Ar_Na}{R T}})) otherwise \end{matrix}