Model Mathematics

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Component: BG_parameters

Component: environment

\frac{d}{d time} (q_Ca_SR) = (- v_leak - v_RyR) + v_Ca_SR_SERCA \frac{d}{d time} (q_Ca_i) = ((- v_R_TRPNCa) n_CaTRPN + v_Ca_i_SERCA + v_leak + v_diadDf + v_Ca_i_NCX - v_pCa_R1) + v_Ca_stim \frac{d}{d time} (q_TRPN) = - v_R_TRPNCa \frac{d}{d time} (q_Ca_TRPN) = v_R_TRPNCa \frac{d}{d time} (q_B_XB) = - v_R_BU \frac{d}{d time} (q_U_XB) = (v_R_BU - v_R_UW) + v_R_SU \frac{d}{d time} (q_W_XB) = v_R_UW - v_R_WS \frac{d}{d time} (q_S_XB) = v_R_WS - v_R_SU \frac{d}{d time} (q_Ca_D) = (- v_diadDf) + v_Ca_D_LCC + v_RyR + v_RyRgate_Ca_D \frac{d}{d time} (q_Ca_o) = v_Ca_o_LCC + v_Ca_o_NCX + v_pCa_R2 \frac{d}{d time} (q_Na_i) = v_Na_i_NCX \frac{d}{d time} (q_Na_o) = v_Na_o_NCX \frac{d}{d time} (q_pCa) = (- v_pCa_R1) + v_pCa_R2 \frac{d}{d time} (q_pCa_Ca) = v_pCa_R1 - v_pCa_R2 \frac{d}{d time} (q_PLB) = v_PLBd2 - v_PLBph1 \frac{d}{d time} (q_PKACI) = v_PLBph2 - v_PLBph1 \frac{d}{d time} (q_PLB_PKACI) = v_PLBph1 - v_PLBph2 \frac{d}{d time} (q_PP1) = v_PLBph1 - v_PLBph2 \frac{d}{d time} (q_PLBp_PP1) = v_PLBd1 - v_PLBd2 \frac{d}{d time} (q_PLBp) = v_PLBph2 - v_PLBd1 \frac{d}{d time} (q_Ip) = - v_Inh \frac{d}{d time} (q_Ip_PP1) = v_Inh \frac{d}{d time} (q_H) = v_H_SERCA \frac{d}{d time} (q_MgADP) = v_MgADP_SERCA \frac{d}{d time} (q_MgATP) = v_MgATP_SERCA \frac{d}{d time} (q_Pi) = v_Pi_SERCA

V_m = \frac{q_membrane}{C_m}

tPeriod = time - (⌊ \frac{time}{stimPeriod} ⌋ stimPeriod) I_stim = \{\begin{matrix} \frac{0 0.03 C_m}{stimDuration} if tPeriod \geq 0.3 \land tPeriod ≦ 0.3 + stimDuration \\ 0.0 otherwise \end{matrix}

v_Ca_stim = \{\begin{matrix} 0 8 e 3 if tPeriod \geq 0.3 \land tPeriod ≦ 0.3 + stimDuration \\ 0.0 otherwise \end{matrix}

sum_I = I_mem_LCC + I_mem_NCX + I_mem_pCa + I_stim \frac{d}{d time} (q_membrane) = sum_I

dSL = \{\begin{matrix} 1 V_max if time < 0.06 \\ (- 0.1) V_max if time > 0.5 \land time < 1.1 \\ 0 V_max otherwise \end{matrix}

vol_SR = vol_cell 0.035 cCai = \frac{q_Ca_i}{vol_myo} cCao = \frac{q_Ca_o}{vol_o} cCaD = \frac{q_Ca_D}{vol_D} cCaSR = \frac{q_Ca_SR}{vol_SR} cNai = \frac{q_Na_i}{vol_myo} pHi = - (\log_{10} (\frac{q_H}{vol_myo}))

Ca_tot = q_Ca_i + q_Ca_o + q_Ca_TRPN + q_Ca_SR + q_Ca_D + q_pCa_Ca + 2 (q_P4_SERCA + q_P5_SERCA + q_P6_SERCA) + q_P3_NCX + q_P4_NCX

Component: units

Component: constants

Component: ion_valences

Component: environment

w_SR = w_i 0.088235 \frac{d}{d t} (q_Ca_SR) = - v_leak \frac{d}{d t} (q_Ca_i) = v_leak

Component: Ca_leak_parameters

Component: Ca_leak

mu_Ca_SR = R T \ln (K_Ca_SR q_Ca_SR) mu_Ca_i = R T \ln (K_Ca_i q_Ca_i) v_leak = kappa_leak (ⅇ^{\frac{mu_Ca_SR}{R T}} - (ⅇ^{\frac{mu_Ca_i}{R T}}))

Component: units

Component: environment

\frac{d}{d time} (q_Ca_i) = (- v_R_TRPNCa) n_CaTRPN + v_Ca_stim \frac{d}{d time} (q_TRPN) = - v_R_TRPNCa \frac{d}{d time} (q_Ca_TRPN) = v_R_TRPNCa \frac{d}{d time} (q_B_XB) = - v_R_BU \frac{d}{d time} (q_U_XB) = (v_R_BU - v_R_UW) + v_R_SU \frac{d}{d time} (q_W_XB) = v_R_UW - v_R_WS \frac{d}{d time} (q_S_XB) = v_R_WS - v_R_SU

tPeriod = time - (⌊ \frac{time}{stimPeriod} ⌋ stimPeriod) v_Ca_stim = \{\begin{matrix} 1 80 if tPeriod \geq 0.3 \land tPeriod ≦ 0.3 + stimDuration \\ 0.0 otherwise \end{matrix}

dSL = \{\begin{matrix} 1 V_max if time < 0.06 \\ (- 1) V_max if time > 0.5 \land time < 0.56 \\ 0 V_max otherwise \end{matrix}

Component: crossbridge_TRPN_parameters

Component: crossbridge_TRPN

mu_TRPN = R T \ln (K_TRPN q_TRPN) mu_Ca_i = R T \ln (K_Ca_i q_Ca_i) mu_Ca_TRPN = R T \ln (K_Ca_TRPN q_Ca_TRPN) mu_B_XB = R T \ln (K_B_XB q_B_XB) mu_U_XB = R T \ln (K_U_XB q_U_XB) mu_W_XB = R T \ln (K_W_XB q_W_XB) mu_S_XB = R T \ln (K_S_XB q_S_XB) v_R_TRPNCa = kappa_R_TRPNCa (ⅇ^{\frac{n_CaTRPN mu_Ca_i + mu_TRPN}{R T}} - (ⅇ^{\frac{mu_Ca_TRPN}{R T}})) v_R_BU = kappa_R_BU (ⅇ^{\frac{mu_B_XB + n_Tm mu_Ca_TRPN}{R T}} - (ⅇ^{\frac{mu_U_XB + n_Tm mu_Ca_TRPN}{R T}})) v_R_UW = kappa_R_UW (ⅇ^{\frac{mu_U_XB}{R T}} - (ⅇ^{\frac{mu_W_XB}{R T}})) v_R_WS = kappa_R_WS (ⅇ^{\frac{mu_W_XB}{R T}} - (ⅇ^{\frac{mu_S_XB}{R T}})) v_R_SU = kappa_R_SU (ⅇ^{\frac{mu_S_XB}{R T}} - (ⅇ^{\frac{mu_U_XB}{R T}}))

A_w = \frac{A_eff r_s}{(1 - r_s) r_w + r_s} A_s = A_w c_w = \frac{phi k_uw (1 - r_w)}{r_w} c_s = \frac{phi k_ws (1 - r_s) r_w}{r_s}

v_2 = dSL v_1 = nu_1 nu_2 = (- A_w) v_2 nu_3 = c_w G_w v_4 = nu_4 nu_5 = (- A_s) v_2 nu_6 = c_s G_s \frac{d}{d time} (G_w) = v_1 \frac{d}{d time} (SL) = v_2 \frac{d}{d time} (G_s) = v_4 nu_1 = - nu_2 - nu_3 nu_4 = - nu_5 - nu_6

F_T_S = \frac{T_ref}{SL_0 q_MS r_s} q_S_XB (G_s + SL_0) F_T_W = \frac{T_ref}{SL_0 q_MS r_s} q_W_XB G_w T_active = F_T_S + F_T_W

eta = \{\begin{matrix} eta_l if v_Cdd > 0 \\ eta_s otherwise \end{matrix} \frac{d}{d time} (Cdd) = v_Cdd v_Cdd = nu_d nu_k = \frac{k}{eta} Cdd nu_f = \frac{k}{eta} (SL - SL_0) nu_d = (- nu_k) + nu_f

F_1 = alpha (ⅇ^{\frac{b SL}{SL_0}} - 1) F_d = \frac{alpha eta}{SL_0} v_Cdd T_passive = F_1 + F_d

T_total = T_active + T_passive

Component: units

Component: constants

Component: environment

\frac{d}{d time} (q_Ca_D) = - v_diadDf \frac{d}{d time} (q_Ca_i) = v_diadDf

Component: diadCaDiffusion_parameters

Component: diadCaDiffusion

mu_Ca_D = R T \ln (K_Ca_D q_Ca_D) mu_Ca_i = R T \ln (K_Ca_i q_Ca_i) v_diadDf = kappa_diadDf (ⅇ^{\frac{mu_Ca_D}{R T}} - (ⅇ^{\frac{mu_Ca_i}{R T}}))

Component: units

Component: constants

Component: environment

\frac{d}{d t} (q_Ca_o) = v_Ca_o_LCC \frac{d}{d t} (q_Ca_D) = v_Ca_D_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_D = R T \ln (K_Ca_D q_Ca_D) 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_D + zCa F V_mem + mu_S111_LCC Af_LCC_Ca2 = mu_Ca_D + zCa 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 Ar_LCC_Ca1 = mu_Ca_o + mu_S111_LCC Ar_LCC_Ca2 = mu_Ca_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_D Ar_fCa01 = R T \ln (K_011_LCC q_S011_LCC) + z_rCa mu_Ca_D Ar_fCa02 = R T \ln (K_021_LCC q_S021_LCC) + z_rCa mu_Ca_D Ar_fCa10 = R T \ln (K_101_LCC q_S101_LCC) + z_rCa mu_Ca_D Ar_fCa11 = R T \ln (K_111_LCC q_S111_LCC) + z_rCa mu_Ca_D Ar_fCa12 = R T \ln (K_121_LCC q_S121_LCC) + z_rCa mu_Ca_D I_mem_LCC = F (((((((((((((((() + z_rf2 v_f2_101 - (z_ff2 v_f2_101)) + 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)) v_Ca_o_LCC = v_LCC_Ca2 + v_LCC_Ca1 v_Ca_D_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_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_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_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}

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

Component: units

Component: constants

Component: environment

\frac{d}{d t} (q_Ca_o) = v_Ca_o_NCX \frac{d}{d t} (q_Ca_i) = v_Ca_i_NCX \frac{d}{d t} (q_Na_o) = v_Na_o_NCX \frac{d}{d t} (q_Na_i) = v_Na_i_NCX

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

Component: NCX_parameters

Component: NCX

V_mem = \frac{q_mem}{C_m} I_mem_NCX = F ((- zf_NCX) v_r6 + zr_NCX v_r6) 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_Na_o = R T \ln (K_Na_o q_Na_o) mu_Na_i = R T \ln (K_Na_i q_Na_i) mu_P1_NCX = R T \ln (K_1_NCX q_P1_NCX) mu_P2_NCX = R T \ln (K_2_NCX q_P2_NCX) mu_P3_NCX = R T \ln (K_3_NCX q_P3_NCX) mu_P4_NCX = R T \ln (K_4_NCX q_P4_NCX) mu_P5_NCX = R T \ln (K_5_NCX q_P5_NCX) mu_P6_NCX = R T \ln (K_6_NCX q_P6_NCX) v_r1 = kappa_1_NCX (ⅇ^{\frac{Af_r1}{R T}} - (ⅇ^{\frac{Ar_r1}{R T}})) v_r2 = kappa_2_NCX (ⅇ^{\frac{Af_r2}{R T}} - (ⅇ^{\frac{Ar_r2}{R T}})) v_r3 = kappa_3_NCX (ⅇ^{\frac{Af_r3}{R T}} - (ⅇ^{\frac{Ar_r3}{R T}})) v_r4 = kappa_4_NCX (ⅇ^{\frac{Af_r4}{R T}} - (ⅇ^{\frac{Ar_r4}{R T}})) v_r5 = kappa_5_NCX (ⅇ^{\frac{Af_r5}{R T}} - (ⅇ^{\frac{Ar_r5}{R T}})) v_r6 = kappa_6_NCX (ⅇ^{\frac{Af_r6}{R T}} - (ⅇ^{\frac{Ar_r6}{R T}})) Af_r1 = mu_P1_NCX Af_r2 = mu_P2_NCX + mu_Ca_i Af_r3 = mu_P3_NCX Af_r4 = mu_P4_NCX Af_r5 = mu_P5_NCX + nNa_o_NCX mu_Na_o Af_r6 = R T \ln (K_6_NCX q_P6_NCX) + zf_NCX F V_mem Ar_r1 = nNa_i_NCX mu_Na_i + mu_P2_NCX Ar_r2 = mu_P3_NCX Ar_r3 = mu_P4_NCX Ar_r4 = mu_P5_NCX + mu_Ca_o Ar_r5 = mu_P6_NCX Ar_r6 = R T \ln (K_1_NCX q_P1_NCX) + zr_NCX F V_mem v_Ca_o_NCX = v_r4 v_Ca_i_NCX = - v_r2 v_Na_o_NCX = (- nNa_o_NCX) v_r5 v_Na_i_NCX = nNa_i_NCX v_r1 v_P1_NCX = v_r6 - v_r1 v_P2_NCX = v_r1 - v_r2 v_P3_NCX = v_r2 - v_r3 v_P4_NCX = (- v_r4) + v_r3 v_P5_NCX = (- v_r5) + v_r4 v_P6_NCX = (- v_r6) + v_r5 \frac{d}{d t} (q_P1_NCX) = v_P1_NCX \frac{d}{d t} (q_P2_NCX) = v_P2_NCX \frac{d}{d t} (q_P3_NCX) = v_P3_NCX \frac{d}{d t} (q_P4_NCX) = v_P4_NCX \frac{d}{d t} (q_P5_NCX) = v_P5_NCX \frac{d}{d t} (q_P6_NCX) = v_P6_NCX

Component: units

Component: environment

\frac{d}{d t} (q_Ca_i) = - v_pCa_R1 \frac{d}{d t} (q_Ca_o) = v_pCa_R2 \frac{d}{d t} (q_pCa) = (- v_pCa_R1) + v_pCa_R2 \frac{d}{d t} (q_pCa_Ca) = v_pCa_R1 - v_pCa_R2 \frac{d}{d t} (q_mem) = I_mem_pCa V_mem = \frac{q_mem}{C_m}

Ca_T = q_Ca_i + q_Ca_o + q_pCa_Ca channel_T = q_pCa + q_pCa_Ca

Component: pCa_parameters

Component: pCa

mu_Ca_i = R T \ln (K_Ca_i q_Ca_i) mu_Ca_o = R T \ln (K_Ca_o q_Ca_o) mu_pCa = R T \ln (K_pCa q_pCa) mu_pCa_Ca = R T \ln (K_pCa_Ca q_pCa_Ca) v_pCa_R1 = kappa_pCa_R1 (ⅇ^{\frac{mu_Ca_i + mu_pCa}{R T}} - (ⅇ^{\frac{mu_pCa_Ca}{R T}})) v_pCa_R2 = kappa_pCa_R2 (ⅇ^{\frac{mu_pCa_Ca}{R T}} - (ⅇ^{\frac{mu_Ca_o + mu_pCa}{R T}})) I_mem_pCa = (- zCa) F v_pCa_R2

Component: units

Component: environment

\frac{d}{d time} (q_PLB) = v_PLBd2 - v_PLBph1 \frac{d}{d time} (q_PKACI) = v_PLBph2 - v_PLBph1 \frac{d}{d time} (q_PLB_PKACI) = v_PLBph1 - v_PLBph2 \frac{d}{d time} (q_PP1) = v_PLBd2 - v_PLBd1 - v_Inh \frac{d}{d time} (q_PLBp_PP1) = v_PLBd1 - v_PLBd2 \frac{d}{d time} (q_PLBp) = v_PLBph2 - v_PLBd1 \frac{d}{d time} (q_Ip) = - v_Inh \frac{d}{d time} (q_Ip_PP1) = v_Inh

Component: PLB_parameters

Component: PLB

mu_PLB = R T \ln (K_PLB q_PLB) mu_PKACI = R T \ln (K_PKACI q_PKACI) mu_PLB_PKACI = R T \ln (K_PLB_PKACI q_PLB_PKACI) mu_PP1 = R T \ln (K_PP1 q_PP1) mu_PLBp_PP1 = R T \ln (K_PLBp_PP1 q_PLBp_PP1) mu_PLBp = R T \ln (K_PLBp q_PLBp) mu_Ip = R T \ln (K_Ip q_Ip) mu_Ip_PP1 = R T \ln (K_Ip_PP1 q_Ip_PP1) v_PLBph1 = kappa_PLBph1 (ⅇ^{\frac{mu_PLB + mu_PKACI}{R T}} - (ⅇ^{\frac{mu_PLB_PKACI}{R T}})) v_PLBph2 = kappa_PLBph2 (ⅇ^{\frac{mu_PLB_PKACI}{R T}} - (ⅇ^{\frac{mu_PLBp + mu_PKACI}{R T}})) v_PLBd1 = kappa_PLBd1 (ⅇ^{\frac{mu_PLBp + mu_PP1}{R T}} - (ⅇ^{\frac{mu_PLBp_PP1}{R T}})) v_PLBd2 = kappa_PLBd2 (ⅇ^{\frac{mu_PLBp_PP1}{R T}} - (ⅇ^{\frac{mu_PLB + mu_PP1}{R T}})) v_Inh = kappa_Inh (ⅇ^{\frac{mu_PP1 + mu_Ip}{R T}} - (ⅇ^{\frac{mu_Ip_PP1}{R T}}))

Component: units

Component: constants

Component: environment

\frac{d}{d t} (q_Ca_SR) = - v_RyR \frac{d}{d t} (q_Ca_D) = v_RyR + v_RyRgate_Ca_D

Component: RyR_parameters

Component: RyR

mu_Ca_SR = R T \ln (K_Ca_SR q_Ca_SR) mu_Ca_D = R T \ln (K_Ca_D q_Ca_D) v_RyR = kappa_RyR ⅇ^{\frac{mu_O_RyR}{R T}} (ⅇ^{\frac{mu_Ca_SR}{R T}} - (ⅇ^{\frac{mu_Ca_D}{R T}})) v_RyRgate_Ca_D = (nCa_2 v_OC - (nCa_1 v_CCI) - (nCa_2 v_CII)) + nCa_1 v_IO

q_Ca_gate_complexes = nCa_2 q_O_RyR + nCa_1 q_CI_RyR + (nCa_1 + nCa_2) q_I_RyR

mu_C_RyR = R T \ln (K_C_RyR q_C_RyR) mu_CI_RyR = R T \ln (K_CI_RyR q_CI_RyR) mu_I_RyR = R T \ln (K_I_RyR q_I_RyR) mu_O_RyR = R T \ln (K_O_RyR q_O_RyR) v_OC = kappa_OC (ⅇ^{\frac{mu_O_RyR}{R T}} - (ⅇ^{\frac{mu_C_RyR + nCa_2 mu_Ca_D}{R T}})) v_CCI = kappa_CCI (ⅇ^{\frac{mu_C_RyR + nCa_1 mu_Ca_D}{R T}} - (ⅇ^{\frac{mu_CI_RyR}{R T}})) v_CII = kappa_CII (ⅇ^{\frac{mu_CI_RyR + nCa_2 mu_Ca_D}{R T}} - (ⅇ^{\frac{mu_I_RyR}{R T}})) v_IO = kappa_IO (ⅇ^{\frac{mu_I_RyR}{R T}} - (ⅇ^{\frac{mu_O_RyR + nCa_1 mu_Ca_D}{R T}})) \frac{d}{d t} (q_O_RyR) = v_IO - v_OC \frac{d}{d t} (q_C_RyR) = v_OC - v_CCI \frac{d}{d t} (q_CI_RyR) = v_CCI - v_CII \frac{d}{d t} (q_I_RyR) = v_CII - v_IO

Component: units

Component: constants

Component: ion_valences

Component: environment

\frac{d}{d t} (q_Ca_i) = v_Ca_i_SERCA \frac{d}{d t} (q_Ca_SR) = v_Ca_SR_SERCA \frac{d}{d t} (q_H) = v_H_SERCA \frac{d}{d t} (q_MgADP) = v_MgADP_SERCA \frac{d}{d t} (q_MgATP) = v_MgATP_SERCA \frac{d}{d t} (q_Pi) = v_Pi_SERCA

Component: SERCA_parameters

Component: SERCA

q_SERCA_Ca_complexes = n_Ca_i q_P4_SERCA + n_Ca_i q_P5_SERCA + n_Ca_SR q_P6_SERCA

vol_sr = vol_i 0.035 vol_isr = vol_i + vol_sr c_Ca_i = \frac{q_Ca_i}{vol_i} c_Ca_SR = \frac{q_Ca_SR}{vol_sr} c_H = \frac{q_H}{vol_isr} c_MgADP = \frac{q_MgADP}{vol_i} c_MgATP = \frac{q_MgATP}{vol_i} c_Pi = \frac{q_Pi}{vol_i}

mu_Ca_i = R T \ln (K_Ca_i q_Ca_i) mu_Ca_SR = R T \ln (K_Ca_SR q_Ca_SR) mu_H = R T \ln (K_H q_H) mu_MgADP = R T \ln (K_MgADP q_MgADP) mu_MgATP = R T \ln (K_MgATP q_MgATP) mu_Pi = R T \ln (K_Pi q_Pi) mu_P1 = R T \ln (K_P1_SERCA q_P1_SERCA) mu_P2 = R T \ln (K_P2_SERCA q_P2_SERCA) mu_P2a = R T \ln (K_P2a_SERCA q_P2a_SERCA) mu_P4 = R T \ln (K_P4_SERCA q_P4_SERCA) mu_P5 = R T \ln (K_P5_SERCA q_P5_SERCA) mu_P10 = R T \ln (K_P10_SERCA q_P10_SERCA) mu_P6 = R T \ln (K_P6_SERCA q_P6_SERCA) mu_P8 = R T \ln (K_P8_SERCA q_P8_SERCA) mu_P9 = R T \ln (K_P9_SERCA q_P9_SERCA) mu_PLBp_baseline = R T \ln (K_PLBp q_PLBp) mu_PLBp = R T \ln (K_PLBp q_PLBp_baseline) mu_PLBp_eff = mu_PLBp_baseline - mu_PLBp Af_R10_1 = mu_P10 + mu_PLBp_eff Ar_R10_1 = mu_P1 + mu_Pi + mu_PLBp_eff Af_R1_2 = mu_P1 + mu_MgATP + mu_PLBp_eff Ar_R1_2 = mu_P2 + mu_PLBp_eff Af_R5_6 = mu_P5 + mu_PLBp_eff Ar_R5_6 = mu_MgADP + mu_P6 + mu_PLBp_eff Af_R2_2a = mu_P2 + mu_H + mu_PLBp_eff Ar_R2_2a = mu_P2a + mu_PLBp_eff Af_R2_4 = mu_P2 + n_Ca_i mu_Ca_i + mu_PLBp_eff Ar_R2_4 = mu_P4 + mu_PLBp_eff Af_R4_5 = mu_P4 + mu_PLBp_eff Ar_R4_5 = mu_P5 + n_H mu_H + mu_PLBp_eff Af_R6_8 = mu_P6 + mu_PLBp_eff Ar_R6_8 = mu_P8 + n_Ca_SR mu_Ca_SR + mu_PLBp_eff Af_R8_9 = mu_P8 + n_H mu_H + mu_PLBp_eff Ar_R8_9 = mu_P9 + mu_PLBp_eff Af_R9_10 = mu_P9 + mu_PLBp_eff Ar_R9_10 = mu_H + mu_P10 + mu_PLBp_eff v_SERCA_R10_1 = kappa_SERCA_R10_1 (ⅇ^{\frac{Af_R10_1}{R T}} - (ⅇ^{\frac{Ar_R10_1}{R T}})) v_SERCA_R10_1_noPLBp = kappa_SERCA_R10_1 (ⅇ^{\frac{mu_P10}{R T}} - (ⅇ^{\frac{mu_P1 + mu_Pi}{R T}})) v_SERCA_R1_2 = kappa_SERCA_R1_2 (ⅇ^{\frac{Af_R1_2}{R T}} - (ⅇ^{\frac{Ar_R1_2}{R T}})) v_SERCA_R5_6 = kappa_SERCA_R5_6 (ⅇ^{\frac{Af_R5_6}{R T}} - (ⅇ^{\frac{Ar_R5_6}{R T}})) v_SERCA_R2_2a = kappa_SERCA_R2_2a (ⅇ^{\frac{Af_R2_2a}{R T}} - (ⅇ^{\frac{Ar_R2_2a}{R T}})) v_SERCA_R2_4 = kappa_SERCA_R2_4 (ⅇ^{\frac{Af_R2_4}{R T}} - (ⅇ^{\frac{Ar_R2_4}{R T}})) v_SERCA_R4_5 = kappa_SERCA_R4_5 (ⅇ^{\frac{Af_R4_5}{R T}} - (ⅇ^{\frac{Ar_R4_5}{R T}})) v_SERCA_R6_8 = kappa_SERCA_R6_8 (ⅇ^{\frac{Af_R6_8}{R T}} - (ⅇ^{\frac{Ar_R6_8}{R T}})) v_SERCA_R8_9 = kappa_SERCA_R8_9 (ⅇ^{\frac{Af_R8_9}{R T}} - (ⅇ^{\frac{Ar_R8_9}{R T}})) v_SERCA_R9_10 = kappa_SERCA_R9_10 (ⅇ^{\frac{Af_R9_10}{R T}} - (ⅇ^{\frac{Ar_R9_10}{R T}})) v_Ca_i_SERCA = (- n_Ca_i) v_SERCA_R2_4 v_Ca_SR_SERCA = n_Ca_SR v_SERCA_R6_8 v_H_SERCA = (n_H v_SERCA_R4_5 - v_SERCA_R2_2a - (n_H v_SERCA_R8_9)) + v_SERCA_R9_10 v_MgADP_SERCA = v_SERCA_R5_6 v_MgATP_SERCA = - v_SERCA_R1_2 v_Pi_SERCA = v_SERCA_R10_1 v_P1 = v_SERCA_R10_1 - v_SERCA_R1_2 v_P2 = v_SERCA_R1_2 - v_SERCA_R2_4 v_P2a = v_SERCA_R2_2a v_P4 = v_SERCA_R2_4 - v_SERCA_R4_5 v_P5 = v_SERCA_R4_5 - v_SERCA_R5_6 v_P10 = v_SERCA_R9_10 - v_SERCA_R10_1 v_P6 = v_SERCA_R5_6 - v_SERCA_R6_8 v_P8 = v_SERCA_R6_8 - v_SERCA_R8_9 v_P9 = v_SERCA_R8_9 - v_SERCA_R9_10 \frac{d}{d t} (q_P1_SERCA) = v_P1 \frac{d}{d t} (q_P2_SERCA) = v_P2 \frac{d}{d t} (q_P2a_SERCA) = v_P2a \frac{d}{d t} (q_P4_SERCA) = v_P4 \frac{d}{d t} (q_P5_SERCA) = v_P5 \frac{d}{d t} (q_P10_SERCA) = v_P10 \frac{d}{d t} (q_P6_SERCA) = v_P6 \frac{d}{d t} (q_P8_SERCA) = v_P8 \frac{d}{d t} (q_P9_SERCA) = v_P9