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IsoMito_dXdT.m
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IsoMito_dXdT.m
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function [f] = IsoMito_dXdT(t,x,param,ExpType,StateType,J_AtC)
% Computing the time derivatives of state variables, according to types of
% experiments or energy states
% Implementing computer model presented in Wu et al.'s "Computer modeling of
% mitochondrial TCA cycle, oxidative phosphorylation, metabolite transport, and
% electrophysiology" and its Appendices
% Update from Version: 1.4 (previous update on 10/27/08)
%% Defining global variables
global iH_x idPsi iATP_x iADP_x iAMP_x iGTP_x iGDP_x iPi_x iNADH_x ...
iQH2_x iOAA_x iACCOA_x iCIT_x iICIT_x iAKG_x iSCOA_x iCOASH_x ...
iSUC_x iFUM_x iMAL_x iGLU_x iASP_x iK_x iMg_x iO2_x iCO2tot_x ...
iCred_i iATP_i iADP_i iAMP_i iPi_i iH_i iMg_i iK_i ...
iATP_c iADP_c iPi_c iH_c iMg_c iK_c ...
iPYR_x iPYR_i iPYR_c iCIT_i iCIT_c iAKG_i iAKG_c iSUC_i iSUC_c ...
iMAL_i iMAL_c iASP_i iASP_c iGLU_i iGLU_c iFUM_i iFUM_c ...
iICIT_i iICIT_c iGLC_c iG6P_c iPCr_c iAMP_c;
%% Defining indices for all reactions in the TCA cycle
ipdh = 1;
icits = 2;
iacon = 3;
iisod = 4;
iakgd = 5;
iscoas = 6;
isdh = 7;
ifum = 8;
imdh = 9;
indk = 10;
igot = 11;
%% Setting adjustable parameter values
% Vmax values of TCA cycle fluxes
Vmax(1) = param(1);
Vmax(2) = param(2);
Vmax(3) = param(3);
Vmax(4) = param(4);
Vmax(5) = param(5);
Vmax(6) = param(6);
Vmax(7) = param(7);
Vmax(8) = param(8);
Vmax(9) = param(9);
Vmax(10)= param(10);
Vmax(11)= param(11);
% Activities of transporters
x_PYR_H = param(12);
x_GLU_H = param(13);
x_CIT_MAL = param(14);
x_AKG_MAL = param(15);
% param(16) not used
x_MAL_PI = param(17);
x_ASP_GLU = param(18);
% param(19) not used
% param(20) not used
x_SUC_MAL = param(21);
% param(22) not used
% param(23) was used by Kir1 in J_akgd
% param(24) was not used
% Hexokinase activity (for LaNoue state-3 experiments)
if (ExpType == 1) && (StateType == 3)
x_HK = param(25);
else
x_HK = 0;
end
% Parameters for oxidative phosphorylation
x_C1 = param(31);
x_C3 = param(32);
x_C4 = param(33);
x_F1 = param(34);
x_ANT = param(35);
x_Pi1 = param(36);
k_PiH = param(37);
x_KH = param(38);
x_Hle = param(39);
k_Pi1 = param(40);
k_Pi2 = param(41);
% Permeability coefficients for TCA intermediates
p_TI = 85; % assumed to be equal to x_A for nucleotides (micro sec^-1)
x_PYRt = p_TI;
x_GLUt = p_TI;
x_ASPt = p_TI;
x_CITt = p_TI;
x_ICITt = p_TI;
x_AKGt = p_TI;
x_FUMt = 0*p_TI;
x_SUCt = p_TI;
x_MALt = p_TI;
%% Defining indices of reactants
iH = 1;
iATP = 2;
iADP = 3;
iAMP = 4;
iGTP = 5;
iGDP = 6;
iPi = 7;
iNADH = 8;
iNAD = 9;
iQH2 = 10;
iCOQ = 11;
iOAA = 12;
iACCOA = 13;
iCIT = 14;
iICIT = 15;
iAKG = 16;
iSCOA = 17;
iCOASH = 18;
iSUC = 19;
iFUM = 20;
iMAL = 21;
iGLU = 22;
iASP = 23;
iK = 24;
iMg = 25;
iCox = 26;
iCred = 27;
iO2 = 28;
iH2O = 29;
iFADH2 = 30;
iFAD = 31;
iCO2tot = 32;
iPCr = 33;
iCr = 34;
iPYR = 35;
iGLC = 36;
iG6P = 37;
N_reactant = 37;
%% Listing fixed model parameters
% (i) Thermochemical constants
if ExpType == 1
RT = 8.314*(28+273.15)/1e3; % kJ mol^{-1}
else
RT = 8.314*(37+273.15)/1e3; % kJ mol^{-1}
end;
F = 0.096484; % kJ mol^{-1} mV^{-1}
% (ii) Subcelular volumes and water spaces
if (ExpType == 1) % LaNoue et al.'s experiments (JBC, 1970)
W_c = 80; % buffer water space for LaNoue experiments
elseif (ExpType == 2) % Bose et al.'s experiments (JBC, 2003)
W_c = 80*10; % buffer water space for Bose experiments
elseif (ExpType == 3)|| (ExpType == 8) % Caridac Tissue
Vmito = 0.2882; % (ml mito / ml cell)
Vcyto = 0.6801; % (ml cyto / ml cell)
Rm_cyto = Vmito / Vcyto; % Volume ratio mito volume / cytoplasm volume
Rm_cell = Vmito; % Volume ratio mito volume / cell volume
Rc_cell = Vcyto; % Volume ratio of cytosol / cell volume
W_c = 0.807*1.044; % cytosol water space (ml water per ml cytosol) [VB2002]
elseif (ExpType == 4) % Skeletal Muscle
Vmito = 0.056; % (ml mito / ml cell)
Vcyto = 0.894; % (ml cyto / ml cell)
Rm_cyto = Vmito / Vcyto; % Volume ratio mito volume / cytoplasm volume
Rm_cell = Vmito; % Volume ratio mito volume / cell volume
Rc_cell = Vcyto; % Volume ratio of cytosol / cell volume
W_c = 0.807*1.044; % cytosol water space (ml water per ml cytosol) [VB2002]
elseif (ExpType == 7)
rho_m = 3.6697e-6; % (l mito) (mg protein)^{-1} %%assume 0.025 mg/mL * 2mL rxn volume
W_c = 1090; % 2 mL *0.025 mg protein ref.supp. Muoio
else
W_c = 80;
end
W_m = 0.664*1.09; % mitochondrial water space (ml water per ml mito) [VB2002]
W_x = 0.9*W_m; % Matrix water space (90% is matrix)
W_i = 0.1*W_m; % IM water space (10% is intermembranee-space)
% (iii) Pooled concentrations
Ctot = 2.70e-3; % M; total cytoC
Qtot = 1.35e-3; % M; total Q + QH2
NADtot = 2.97e-3; % M; total NAD+NADH
FADtot = 0.1e-3; % M; total FADred+FADox (from Feng Yang)
% (iv) Ox Phos Model Parameters
n_A = 3.0; % unitless 3 protons
k_O2 = 1.2e-4; % kinetic constant for complex 4
k_mADP = 3.5e-6; % ANT MM constant
% (v) Outer membrane transport parameters
x_A = 85; % micron sec^{-1}
x_Pi2 = 327; % micron sec^{-1}
gamma = 5.99; % mito membrane area per cell volume micron^{-1}
%% Loading values of state variables
MinCon = 1e-32;
% (i) Matrix species and dPsi
dPsi = x(idPsi);
ATP_x = x(iATP_x);
ADP_x = x(iADP_x);
AMP_x = x(iAMP_x);
GTP_x = x(iGTP_x);
GDP_x = x(iGDP_x);
Pi_x = x(iPi_x);
NADH_x = x(iNADH_x);
QH2_x = x(iQH2_x);
PYR_x = x(iPYR_x);
OAA_x = x(iOAA_x);
ACCOA_x = x(iACCOA_x);
CIT_x = x(iCIT_x);
ICIT_x = x(iICIT_x);
AKG_x = x(iAKG_x);
SCOA_x = x(iSCOA_x);
COASH_x = x(iCOASH_x);
SUC_x = x(iSUC_x);
FUM_x = x(iFUM_x);
MAL_x = x(iMAL_x);
GLU_x = x(iGLU_x);
ASP_x = x(iASP_x);
H_x = x(iH_x);
K_x = x(iK_x);
Mg_x = x(iMg_x);
O2 = x(iO2_x);
CO2tot = x(iCO2tot_x);
% (ii) IM space species
Cred_i = max(0,x(iCred_i));
ATP_i = x(iATP_i);
ADP_i = x(iADP_i);
AMP_i = x(iAMP_i);
Pi_i = x(iPi_i);
PYR_i = x(iPYR_i);
CIT_i = x(iCIT_i);
AKG_i = x(iAKG_i);
SUC_i = x(iSUC_i);
MAL_i = x(iMAL_i);
GLU_i = x(iGLU_i);
ASP_i = x(iASP_i);
H_i = x(iH_i);
Mg_i = x(iMg_i);
K_i = x(iK_i);
FUM_i = x(iFUM_i);
ICIT_i = x(iICIT_i);
% (iii) Cytoplasmic species
ATP_c = x(iATP_c);
ADP_c = x(iADP_c);
Pi_c = x(iPi_c);
PYR_c = x(iPYR_c);
CIT_c = x(iCIT_c);
AKG_c = x(iAKG_c);
SUC_c = x(iSUC_c);
MAL_c = x(iMAL_c);
GLU_c = x(iGLU_c);
ASP_c = x(iASP_c);
H_c = x(iH_c);
Mg_c = x(iMg_c);
K_c = x(iK_c);
FUM_c = x(iFUM_c);
ICIT_c = x(iICIT_c);
GLC_c = x(iGLC_c);
G6P_c = x(iG6P_c);
AMP_c = x(iAMP_c);
% (iv) Other concentrations computed from the state variables:
NAD_x = NADtot - NADH_x;
COQ_x = Qtot - QH2_x;
Cox_i = Ctot - Cred_i;
% (v) set the H+, Mg2+, and K+ are permeable for outer mito membrane
H_i = H_c;
Mg_i = Mg_c;
K_i = K_c;
%% Loading thermodynamic data (deltG, pK, etc.)
% T = 298.15K (25 C) I = 0.17 M
% standard Gibbs free energy of formation of reference species, (kJ/mol)
% without temperature correction on dGf
dGf1(1:N_reactant) = 0;
dGf1(iH2O) = -235.74; % H2O
dGf1(iO2) = 16.40; % O2(aq)
dGf1(iNADH) = 39.31; % NADH
dGf1(iNAD) = 18.10; % NAD+
dGf1(iQH2) = -23.30; % QH2
dGf1(iCOQ) = 65.17; % Q
dGf1(iATP) = -2771.00; % ATP4-
dGf1(iADP) = -1903.96; % ADP3-
dGf1(iAMP) = -1034.66; % AMP2-
dGf1(iGTP) = dGf1(iATP);
dGf1(iGDP) = dGf1(iADP);
dGf1(iCred) = -27.41; % CytoC(red)2+
dGf1(iCox) = -6.52; % CytoC(ox)3+
dGf1(iPi) = -1098.27; % HPO42-
dGf1(iPCr) = 0; % PCr2-
dGf1(iCr) = -252.68; % HCr
dGf1(iFADH2) = -67.60; % FADH2-enz
dGf1(iFAD) = 19.55; % FAD-enz
dGf1(iCOASH) = -0.72; % CoAS-
dGf1(iACCOA) = -178.19; % AcCoA
dGf1(iOAA) = -794.74; % OAA2-
dGf1(iCIT) = -1165.59; % CIT3-
dGf1(iICIT) = -1158.94; % ICIT3-
dGf1(iAKG) = -793.41; % AKG2-
dGf1(iSCOA) = -507.55; % SCoA-
dGf1(iSUC) = -690.44; % SUC2-
dGf1(iFUM) = -603.32; % FUM2-
dGf1(iMAL) = -842.66; % MAL2-
dGf1(iASP) = -692.26; % ASP-
dGf1(iGLU) = -692.40; % GLU- (L-glutamate)
dGf1(iCO2tot) = -530.71; % CO2tot
dGf1(iPYR) = -470.82; % PYR2-
dGf1(iGLC) = -907.21; % Glucose
dGf1(iG6P) = -1758.87; % Glucose-6-phosphate
% K values for reference species
% pK_KATP is corrected to be 1.013, 08/26/08
% pK_KADP is corrected to be 0.882, 08/26/08
% pK_KAMP is corrected to be 0.6215, 08/26/08
% pK_MgOAA is corrected to be 0.8629, 08/26/08
% pK_KSUC is corrected to be 0.3525, 08/26/08
Kh(1:N_reactant) = inf; Km(1:N_reactant) = inf; Kk(1:N_reactant) = inf;
Kh(iATP) = 10^(-6.59); Km(iATP) = 10^(-3.82); Kk(iATP) = 10^(-1.013);
Kh(iADP) = 10^(-6.42); Km(iADP) = 10^(-2.79); Kk(iADP) = 10^(-0.882);
Kh(iAMP) = 10^(-6.22); Km(iAMP) = 10^(-1.86); Kk(iAMP) = 10^(-0.6215);
Kh(iGTP) = Kh(iATP); Km(iGTP) = Km(iATP); Kk(iGTP) = Kk(iATP);
Kh(iGDP) = Kh(iADP); Km(iGDP) = Km(iADP); Kk(iGDP) = Kk(iADP);
Kh(iPi) = 10^(-6.71); Km(iPi) = 10^(-1.69); Kk(iPi) = 10^(+0.0074);
Kh(iCOASH) = 10^(-8.13);
Km(iOAA) = 10^(-0.8629);
Kh(iCIT) = 10^(-5.63); Km(iCIT) = 10^(-3.37); Kk(iCIT) = 10^(-0.339);
Kh(iICIT) = 10^(-5.64); Km(iICIT) = 10^(-2.46);
Kh(iSCOA) = 10^(-3.96);
Kh(iSUC) = 10^(-5.13); Km(iSUC) = 10^(-1.17); Kk(iSUC) = 10^(-0.3525);
Kh(iFUM) = 10^(-4.10);
Kh(iMAL) = 10^(-4.75); Km(iMAL) = 10^(-1.55); Kk(iMAL) = 10^(+0.107);
Kh(iCO2tot) = 10^(-9.82);
Km(iPYR) = 10^(-1.02);
Kh(iG6P) = 10^(-5.91);
% Kh(iGLU) = 10^(-4.25); % from Nelson & Cox, "Lehninger's Princinples of Biochemistry", p78
Kh(iGLU) = 10^(-4.06); % 37 C, I = 0.15
Km(iGLU) = 10^(-1.82);
% Kh(iASP) = 10^(-3.65); % from Nelson & Cox, "Lehninger's Princinples of Biochemistry", p78
Kh(iASP) = 10^(-3.65); % 37 C, I = 0.15
Km(iASP) = 10^(-2.32);
% compute binding polynomials for reactants
P_x(1:N_reactant) = 1; P_c(1:N_reactant) = 1; P_i(1:N_reactant) =1;
P_x(iATP) = 1 + H_x/Kh(iATP) + Mg_x/Km(iATP) + K_x/Kk(iATP);
P_c(iATP) = 1 + H_c/Kh(iATP) + Mg_c/Km(iATP) + K_c/Kk(iATP);
P_i(iATP) = 1 + H_i/Kh(iATP) + Mg_i/Km(iATP) + K_i/Kk(iATP);
P_x(iADP) = 1 + H_x/Kh(iADP) + Mg_x/Km(iADP) + K_x/Kk(iADP);
P_c(iADP) = 1 + H_c/Kh(iADP) + Mg_c/Km(iADP) + K_c/Kk(iADP);
P_i(iADP) = 1 + H_i/Kh(iADP) + Mg_i/Km(iADP) + K_i/Kk(iADP);
P_x(iAMP) = 1 + H_x/Kh(iAMP) + Mg_x/Km(iAMP) + K_x/Kk(iAMP);
P_c(iAMP) = 1 + H_c/Kh(iAMP) + Mg_c/Km(iAMP) + K_c/Kk(iAMP);
P_i(iAMP) = 1 + H_i/Kh(iAMP) + Mg_i/Km(iAMP) + K_i/Kk(iAMP);
P_x(iGTP) = P_x(iATP);
P_c(iGTP) = P_c(iATP);
P_i(iGTP) = P_i(iATP);
P_x(iGDP) = P_x(iADP);
P_c(iGDP) = P_c(iADP);
P_i(iGDP) = P_i(iADP);
P_x(iPi) = 1 + H_x/Kh(iPi) + Mg_x/Km(iPi) + K_x/Kk(iPi); % add K-bound item, 06/10/08
P_c(iPi) = 1 + H_c/Kh(iPi) + Mg_c/Km(iPi) + K_c/Kk(iPi); % add K-bound item, 06/10/08
P_i(iPi) = 1 + H_i/Kh(iPi) + Mg_i/Km(iPi) + K_i/Kk(iPi); % add K-bound item, 06/10/08
P_x(iCOASH) = 1 + H_x/Kh(iCOASH);
P_i(iCOASH) = 1 + H_i/Kh(iCOASH);
P_c(iCOASH) = 1 + H_c/Kh(iCOASH);
P_x(iOAA) = 1 + Mg_x/Km(iOAA);
P_i(iOAA) = 1 + Mg_i/Km(iOAA);
P_c(iOAA) = 1 + Mg_c/Km(iOAA);
P_x(iCIT) = 1 + H_x/Kh(iCIT) + Mg_x/Km(iCIT) + K_x/Kk(iCIT);
P_i(iCIT) = 1 + H_i/Kh(iCIT) + Mg_i/Km(iCIT) + K_i/Kk(iCIT);
P_c(iCIT) = 1 + H_c/Kh(iCIT) + Mg_c/Km(iCIT) + K_c/Kk(iCIT);
P_x(iICIT) = 1 + H_x/Kh(iICIT) + Mg_x/Km(iICIT);
P_i(iICIT) = 1 + H_i/Kh(iICIT) + Mg_i/Km(iICIT);
P_c(iICIT) = 1 + H_c/Kh(iICIT) + Mg_c/Km(iICIT);
P_x(iSCOA) = 1 + H_x/Kh(iSCOA);
P_i(iSCOA) = 1 + H_i/Kh(iSCOA);
P_c(iSCOA) = 1 + H_c/Kh(iSCOA);
P_x(iSUC) = 1 + H_x/Kh(iSUC) + Mg_x/Km(iSUC) + K_x/Kk(iSUC);
P_i(iSUC) = 1 + H_i/Kh(iSUC) + Mg_i/Km(iSUC) + K_i/Kk(iSUC);
P_c(iSUC) = 1 + H_c/Kh(iSUC) + Mg_c/Km(iSUC) + K_c/Kk(iSUC);
P_x(iFUM) = 1 + H_x/Kh(iFUM);
P_i(iFUM) = 1 + H_i/Kh(iFUM);
P_c(iFUM) = 1 + H_c/Kh(iFUM);
P_x(iMAL) = 1 + H_x/Kh(iMAL) + Mg_x/Km(iMAL) + K_x/Kk(iMAL);
P_i(iMAL) = 1 + H_i/Kh(iMAL) + Mg_i/Km(iMAL) + K_i/Kk(iMAL);
P_c(iMAL) = 1 + H_c/Kh(iMAL) + Mg_c/Km(iMAL) + K_c/Kk(iMAL);
P_x(iCO2tot) = 1 + H_x/Kh(iCO2tot);
P_i(iCO2tot) = 1 + H_i/Kh(iCO2tot);
P_c(iCO2tot) = 1 + H_c/Kh(iCO2tot);
P_x(iPYR) = 1 + Mg_x/Km(iPYR);
P_i(iPYR) = 1 + Mg_i/Km(iPYR);
P_c(iPYR) = 1 + Mg_c/Km(iPYR);
P_x(iG6P) = 1 + H_x/Kh(iG6P);
P_i(iG6P) = 1 + H_i/Kh(iG6P);
P_c(iG6P) = 1 + H_c/Kh(iG6P);
P_x(iGLU) = 1 + H_x/Kh(iGLU) + Mg_x/Km(iGLU); % correct Mg-bound item, 06/10/08
P_i(iGLU) = 1 + H_i/Kh(iGLU) + Mg_i/Km(iGLU); % correct Mg-bound item, 06/10/08
P_c(iGLU) = 1 + H_c/Kh(iGLU) + Mg_c/Km(iGLU); % correct Mg-bound item, 06/10/08
P_x(iASP) = 1 + H_x/Kh(iASP) + Mg_x/Km(iASP); % correct Mg-bound item, 06/10/08
P_i(iASP) = 1 + H_i/Kh(iASP) + Mg_i/Km(iASP); % correct Mg-bound item, 06/10/08
P_c(iASP) = 1 + H_c/Kh(iASP) + Mg_c/Km(iASP); % correct Mg-bound item, 06/10/08
%% I. Flux expresssions in the TCA cycle
%% -------------------------------
% 1. Pyruvate dehydrogenase
% PYR + COASH + NAD (+H2O) = CO2tot + SCOA + NADH
% A - PYR; B - COASH; C - NAD; P - CO2tot; Q - SCOA; R - NADH;
% load concentrations of reactants and products
A = PYR_x;
B = COASH_x;
C = NAD_x;
P = CO2tot;
Q = ACCOA_x;
R = NADH_x;
% dG and Keq vlaues
dGr_pdho = dGf1(iCO2tot) + dGf1(iACCOA) + dGf1(iNADH) ...
- dGf1(iPYR) - dGf1(iCOASH) - dGf1(iNAD) - dGf1(iH2O);
Keq_pdho = exp(-dGr_pdho/RT);
Keq_pdh = Keq_pdho*(1/H_x)*(P_x(iCO2tot)*P_x(iACCOA)*P_x(iNADH)) ...
/(P_x(iPYR)*P_x(iCOASH)*P_x(iNAD));
% Km and Ki values (Molar)
KmA = 38.3e-6;
KmB = 9.9e-6;
KmC = 60.7e-6;
KiACCOA = 40.2e-6;
KiNADH = 40.0e-6;
% Inhibition Constants
ai1 = 1 + ACCOA_x/KiACCOA;
ai2 = 1 + NADH_x/KiNADH;
% Vm values
Vmf = Vmax(ipdh);
% total reaction flux
if (A > MinCon) && (B > MinCon) && (C > MinCon)
J_pdh = Vmf*(A*B*C-P*Q*R/Keq_pdh)/ (KmC*ai2*A*B + KmB*ai1*A*C + KmA*B*C + A*B*C);
else
J_pdh = 0;
end
%% -------------------------------
% 2. Citrate synthetase
% OAA + ACCOA (+H2O) = COASH + CIT
% A - OAA; B - ACCOA; P - COASH; Q - CIT;
% load concentrations of reactants and products
A = OAA_x;
B = ACCOA_x;
P = COASH_x;
Q = CIT_x;
% dG and Keq values
dGr_citso = dGf1(iCOASH) + dGf1(iCIT) - dGf1(iACCOA) - dGf1(iOAA) - dGf1(iH2O);
Keq_citso = exp(-dGr_citso/RT);
Keq_cits = Keq_citso*(1/H_x^2)*(P_x(iCOASH)*P_x(iCIT)) ...
/(P_x(iACCOA)*P_x(iOAA));
% Km and Ki values (Molar)
KmA = 4e-6;
KmB = 14e-6;
Kia = 3.33e-6;
KiCIT = 1600e-6;
KiATP = 900e-6;
KiADP = 1800e-6;
KiAMP = 6000e-6;
KiCOASH = 67e-6;
KiSCOA = 140e-6;
% inhibition coefficients
uCIT_x = CIT_x * (1+H_x/Kh(iCIT))/P_x(iCIT); % unchelated
uATP_x = ATP_x * (1+H_x/Kh(iATP))/P_x(iATP); % unchelated
uADP_x = ADP_x * (1+H_x/Kh(iADP))/P_x(iADP); % unchelated
uAMP_x = AMP_x * (1+H_x/Kh(iAMP))/P_x(iAMP); % unchelated
ai1 = 1 + uCIT_x/KiCIT;
ai2 = 1 + uATP_x/KiATP + uADP_x/KiADP + uAMP_x/KiAMP ...
+ COASH_x/KiCOASH + SCOA_x/KiSCOA;
% Vm values
Vmf = Vmax(icits);
% forward reaction flux
J_cits_f = Vmf*A*B / (Kia*KmB*ai1 + KmA*ai1*B + KmB*ai2*A + A*B);
% overall reaction flux
J_cits = J_cits_f - Vmf*(P*Q/Keq_cits) / (Kia*KmB*ai1 + KmA*ai1*B + KmB*ai2*A + A*B);
%% -------------------------------
% 3. Aconitase
% CIT = ICIT
% A - CIT; P - ICIT;
% load concentrations of reactants and products
A = CIT_x;
P = ICIT_x;
% dG and Keq values
dGr_acono = dGf1(iICIT) - dGf1(iCIT);
Keq_acono = exp(-dGr_acono/RT);
% Keq_acon = Keq_acono;
Keq_acon = Keq_acono*P_x(iICIT)/P_x(iCIT);
% Km and Ki values (Molar)
KmA = 1161e-6;
KmP = 434e-6;
% Vm values
Vmf = Vmax(iacon);
Vmr = Vmf*(KmP/KmA/Keq_acon);
% forward reaction flux
J_acon_f = Vmf*Vmr*A /(KmA*Vmr+Vmr*A+Vmf/Keq_acon*P);
% total reaction flux
J_acon = J_acon_f - Vmf*Vmr*(P/Keq_acon)/(KmA*Vmr+Vmr*A+Vmf/Keq_acon*P);
%% -------------------------------
% 4. Isocitrate dehydrogenase
% NAD + ICIT (+ H2O) = AKG + NADH + CO2tot
% A - NAD; B - ICIT; P - AKG; Q - NADH; R - CO2tot;
% load concentrations of reactants and products
A = NAD_x;
B = ICIT_x;
P = AKG_x;
Q = NADH_x;
R = CO2tot;
% dG and Keq values
dGr_isodo = dGf1(iAKG) + dGf1(iNADH) + dGf1(iCO2tot) ...
- dGf1(iICIT) - dGf1(iNAD) - dGf1(iH2O);
Keq_isodo = exp(-dGr_isodo/RT);
% Keq_isod = Keq_isodo*(1/H_x^2);
Keq_isod = Keq_isodo*(1/H_x^2)*(P_x(iAKG)*P_x(iNADH)*P_x(iCO2tot)) ...
/(P_x(iICIT)*P_x(iNAD));
% Km and Ki values (Molar)
KmA = 74e-6;
KmB = 183e-6;
nH = 3.0;
Kib = 23.8e-6;
Kiq = 29e-6;
KiATP = 91e-6;
KaADP = 50e-6;
% inhibition coefficients
fATP_x = ATP_x * (1+H_x/Kh(iATP))/P_x(iATP);
fADP_x = ADP_x * (1+H_x/Kh(iADP))/P_x(iADP);
ai = 1 + KaADP/fADP_x*(1+fATP_x/KiATP);
% Vm values
Vmf = Vmax(iisod);
% total reaction flux
if (A > MinCon) && (B > MinCon)
J_isod = Vmf/(1+(KmB/B)^nH*ai+KmA/A*(1+(Kib/B)^nH*ai+Q*ai/Kiq))*(1-1/Keq_isod*P*Q*R/A/B);
else
J_isod = 0;
end
%% -------------------------------
% 5. alpha-Ketoglutarate dehydrogenase
% AKG + COASH + NAD (+ H2O) = CO2tot + SCOA + NADH
% A - AKG; B - COASH; C - NAD; P - CO2tot; Q - SCOA; R - NADH;
% load concentrations of reactants and products
A = AKG_x;
B = COASH_x;
C = NAD_x;
P = CO2tot;
Q = SCOA_x;
R = NADH_x;
% dG and Keq values
dGr_akgdo = dGf1(iCO2tot) + dGf1(iSCOA) + dGf1(iNADH) ...
- dGf1(iAKG) - dGf1(iCOASH) - dGf1(iNAD) - dGf1(iH2O);
Keq_akgdo = exp(-dGr_akgdo/RT);
% Keq_akgd = Keq_akgdo*(1/H_x);
Keq_akgd = Keq_akgdo*(1/H_x)*(P_x(iCO2tot)*P_x(iSCOA)*P_x(iNADH)) ...
/(P_x(iAKG)*P_x(iCOASH)*P_x(iNAD));
% Km and Ki values (Molar)
KmA = 80e-6;
KmB = 55e-6;
KmC = 21e-6;
Kiq = 6.9e-6;
Kir1 = 4.5e-6;
Kir2 = 12.7e-6;
KiATP = 50e-6;
KaADP = 100e-6;
% inhibition coefficients
fATP_x = ATP_x * (1+H_x/Kh(iATP))/P_x(iATP);
fADP_x = ADP_x * (1+H_x/Kh(iADP))/P_x(iADP);
ai = 1 + KaADP/fADP_x*(1+fATP_x/KiATP);
% Vm values
Vmf = Vmax(iakgd);
% % for testing
Kir1 = param(23);
Kir2 = 1e3;
% total reaction flux
if (A > MinCon) && (B > MinCon) && (C > MinCon)
J_akgd = Vmf/(1+KmA/A*ai+KmB/B*(1+Q/Kiq)+KmC/C*(1+R/Kir1))/(1+R/Kir2)*(1-1/Keq_akgd*P*Q*R/A/B/C);
else
J_akgd = 0;
end
%% -------------------------------
% 6. Succinyl-CoA synthetase
% GDP + SCOA + PI = COASH + SUC + GTP
% load concentrations of reactants and products
A = GDP_x;
B = SCOA_x;
C = Pi_x;
P = COASH_x;
Q = SUC_x;
R = GTP_x;
% dG and Keq values
dGr_scoaso = dGf1(iCOASH) + dGf1(iSUC) + dGf1(iGTP) ...
- dGf1(iGDP) - dGf1(iSCOA) - dGf1(iPi);
Keq_scoaso = exp(-dGr_scoaso/RT);
% Keq_scoas = Keq_scoaso*(1/H_x);
Keq_scoas = Keq_scoaso*(1/H_x)*(P_x(iCOASH)*P_x(iSUC)*P_x(iGTP)) ...
/(P_x(iSCOA)*P_x(iPi)*P_x(iGDP));
% Km and Ki values (Molar)
KmA = 16e-6;
KmB = 55e-6;
KmC = 660e-6;
KmP = 20e-6;
KmQ = 880e-6;
KmR = 11.1e-6;
Kia = 5.5e-6;
Kib = 100e-6;
Kic = 2000e-6;
Kip = 20e-6;
Kiq = 3000e-6;
Kir = 11.1e-6;
% Vm values
Vmf = Vmax(iscoas);
Vmr = Vmf/Keq_scoas*KmP*Kiq*Kir/(Kia*Kib*KmC);
% total reaction flux
% Correct typos in J_scoas expression (10/27/08):
% Vmf*KmQ*Kir*A*B*Q ->Vmf*KmQ*Kir*A*B*P;
% Vmf*KmA*B*C*Q*R -> Vmr*KmA*B*C*Q*R;
% Vmf*KmA*B*C*P*Q*R -> Vmr*KmA*B*C*P*Q*R
J_scoas = (Vmf*Vmr*A*B*C - Vmf*Vmr*(P*Q*R/Keq_scoas)) ...
/(Vmr*Kia*Kib*KmC+Vmr*Kib*KmC*A+Vmr*Kia*KmB*C ...
+ Vmr*KmC*A*B+Vmr*KmB*A*C+Vmr*KmA*B*C+Vmr*A*B*C ...
+ Vmf*Kir*KmQ*P/Keq_scoas+Vmf*Kiq*KmP*R/Keq_scoas+Vmf*KmR*P*Q/Keq_scoas+Vmf*KmQ*P*R/Keq_scoas...
+ Vmf*KmP*Q*R/Keq_scoas+Vmf*P*Q*R/Keq_scoas+Vmf*KmQ*Kir*A*P/Kia/Keq_scoas+Vmr*Kia*KmB*C*R/Kir...
+ Vmf*KmQ*Kir*A*B*P/Kia/Kib/Keq_scoas+Vmr*KmA*B*C*R/Kir+Vmf*KmR*A*P*Q/Kia/Keq_scoas...
+ Vmr*Kia*KmB*C*Q*R/Kiq/Kir+Vmf*Kir*KmQ*A*B*C*P/Kia/Kib/Kic/Keq_scoas+Vmf*Kip*KmR*A*B*C*Q/Kia/Kib/Kic/Keq_scoas...
+ Vmf*KmR*A*B*P*Q/Kia/Kib/Keq_scoas+Vmr*KmA*B*C*Q*R/Kiq/Kir+Vmr*KmA*Kic*B*P*Q*R/Kip/Kiq/Kir...
+ Vmr*Kia*KmB*C*P*Q*R/Kip/Kiq/Kir+Vmf*KmR*A*B*C*P*Q/Kia/Kib/Kic/Keq_scoas+Vmr*KmA*B*C*P*Q*R/Kip/Kiq/Kir);
%% -------------------------------
% 7. Succinate dehydrogenase
% SUC + COQ = QH2 + FUM
% load concentrations of reactants and products
A = SUC_x;
B = COQ_x;
P = QH2_x;
Q = FUM_x;
% dG and Keq values
dGr_sdho = dGf1(iQH2) + dGf1(iFUM) - dGf1(iSUC) - dGf1(iCOQ);
Keq_sdho = exp(-dGr_sdho/RT);
% Keq_sdh = Keq_sdho;
Keq_sdh = Keq_sdho*(P_x(iFUM)*P_x(iQH2))/(P_x(iSUC)*P_x(iCOQ));
% Km and Ki values (Molar)
KmA = 467e-6;
KmB = 480e-6;
KmP = 2.45e-6;
KmQ = 1200e-6;
Kia = 120e-6;
Kiq = 1275e-6;
KiOAA = 1.5e-6;
% % from Gopher and Gutman
% KaSUC = 800e-6;
% KaFUM = 6400e-6;
% from Kohn et al.
KaSUC = 450e-6;
KaFUM = 375e-6;
% inhibition coefficients
ai = (1+OAA_x/KiOAA+SUC_x/KaSUC+FUM_x/KaFUM)/(1+SUC_x/KaSUC+FUM_x/KaFUM);
% Vm values
Vmf = Vmax(isdh);
Vmr = Vmf/Keq_sdh*(KmP*Kiq/Kia/KmB);
% total reaction flux
J_sdh = (Vmf*Vmr*A*B - Vmf*Vmr*(P*Q/Keq_sdh)) / (Vmr*Kia*KmB*ai+Vmr*KmB*A ...
+Vmr*KmA*ai*B+Vmf*KmQ*ai/Keq_sdh*P+Vmf*KmP/Keq_sdh*Q ...
+Vmr*A*B+Vmf*KmQ/Kia/Keq_sdh*A*P+Vmr*KmA/Kiq*B*Q ...
+Vmf/Keq_sdh*P*Q);
%% -------------------------------
% 8. Fumarase
% FUM (+ H2O) = MAL
% load concentrations of reactants and products
A = FUM_x;
P = MAL_x;
% dG and Keq values
dGr_fumo = dGf1(iMAL) - dGf1(iFUM) - dGf1(iH2O);
Keq_fumo = exp(-dGr_fumo/RT);
% Keq_fum = Keq_fumo;
Keq_fum = Keq_fumo*P_x(iMAL)/P_x(iFUM);
% Km and Ki values (Molar)
KmA = 44.7e-6;
KmP = 197.7e-6;
% KmA = 2.34e-6;
% KmP = 8e-6;
KiCIT = 3500e-6;
KiATP = 40e-6;
KiADP = 400e-6;
KiGTP = 80e-6;
KiGDP = 330e-6;
% inhibition coefficients
fATP_x = ATP_x * (1+H_x/Kh(iATP))/P_x(iATP);
fADP_x = ADP_x * (1+H_x/Kh(iADP))/P_x(iADP);
fGTP_x = GTP_x * (1+H_x/Kh(iGTP))/P_x(iGTP);
fGDP_x = GDP_x * (1+H_x/Kh(iGDP))/P_x(iGDP);
ai = 1+CIT_x/KiCIT+fATP_x/KiATP+fADP_x/KiADP+fGTP_x/KiGTP+fGDP_x/KiGDP;
% Vm values
Vmf = Vmax(ifum);
Vmr = Vmf/Keq_fum*(KmP/KmA);
% total reaction flux
J_fum = (Vmf*Vmr*A - Vmf*Vmr*(P/Keq_fum))/(KmA*Vmr*ai+Vmr*A+Vmf/Keq_fum*P);
%% -------------------------------
% 9. Malate dehydrogenase
% NAD + MAL = OAA + NADH (+ H^+)
% load concentrations of reactants and products
A = NAD_x;
B = MAL_x;
P = OAA_x;
Q = NADH_x;
% dG and Keq values
dGr_mdho = dGf1(iOAA) + dGf1(iNADH) - dGf1(iNAD) - dGf1(iMAL);
Keq_mdho = exp(-dGr_mdho/RT);
% Keq_mdh = Keq_mdho*1/H_x;
Keq_mdh = Keq_mdho*1/H_x*(P_x(iOAA)*P_x(iNADH))/(P_x(iMAL)*P_x(iNAD));
% Km and Ki values (Molar)
KmA = 90.55e-6;
KmB = 250e-6;
KmP = 6.128e-6;
KmQ = 2.58e-6;
Kia = 279e-6;
Kib = 360e-6;
Kip = 5.5e-6;
Kiq = 3.18e-6;
% % from Kohn et al.
% KiATP = 709.3e-6;
% KiADP = 383.2e-6;
% KiAMP = 793.0e-6;
% from Oza and Shore
KiATP = 183.2e-6;
KiADP = 394.4e-6;
KiAMP = 420.0e-6;
% inhibition coefficients
fATP_x = ATP_x * (1+H_x/Kh(iATP))/P_x(iATP);
fADP_x = ADP_x * (1+H_x/Kh(iADP))/P_x(iADP);
fAMP_x = AMP_x * (1+H_x/Kh(iAMP))/P_x(iAMP);
ai = 1+fATP_x/KiATP+fADP_x/KiADP+fAMP_x/KiAMP;
% Vm values
Vmf = Vmax(imdh);
Vmr = Vmf/Keq_mdh*(Kiq*KmP/Kia/KmB);
% total reaction flux
J_mdh = (Vmf*Vmr*A*B - Vmf*Vmr*(P*Q/Keq_mdh)) / (Vmr*Kia*KmB*ai+Vmr*KmB*A ...
+Vmr*KmA*ai*B+Vmf*KmQ*ai/Keq_mdh*P+Vmf*KmP/Keq_mdh*Q ...
+Vmr*A*B+Vmf*KmQ/Kia/Keq_mdh*A*P+Vmf/Keq_mdh*P*Q ...
+Vmr*KmA/Kiq*B*Q+Vmr/Kip*A*B*P+Vmf/Kib/Keq_mdh*B*P*Q);
%% -------------------------------
% 10. Nucleoside diphosphokinase
% GTP + ADP = GDP + ATP
% load concentrations of reactants and products
A = GTP_x;
B = ADP_x;
P = GDP_x;
Q = ATP_x;
% dG and Keq values
dGr_ndko = dGf1(iGDP) + dGf1(iATP) - dGf1(iGTP) - dGf1(iADP);
Keq_ndko = exp(-dGr_ndko/RT);
% Keq_ndk = Keq_ndko;
Keq_ndk = Keq_ndko*(P_x(iGDP)*P_x(iATP))/(P_x(iGTP)*P_x(iADP));
% Km and Ki values (Molar)
KmA = 111e-6;
KmB = 100e-6;
KmP = 260e-6;
KmQ = 278e-6;
Kia = 170e-6;
Kib = 143.6e-6;
Kip = 146.6e-6;
Kiq = 156.5e-6;
KiAMP = 650e-6;
% inhibition coefficients
fAMP_x = AMP_x * (1+H_x/Kh(iAMP))/P_x(iAMP);
ai = 1 + fAMP_x/KiAMP;
% Vm values
Vmf = Vmax(indk);
Vmr = Vmf/Keq_ndk*(KmQ*Kip/Kia/KmB);
% forward reaction flux
if (A > MinCon) && (B > MinCon)
J_ndk_f = Vmf*Vmr*A*B /ai / (Vmr*KmB*A+Vmr*KmA*B ...
+Vmf*KmQ/Keq_ndk*P+Vmf*KmP/Keq_ndk*Q+Vmr*A*B ...
+Vmf*KmQ/Kia/Keq_ndk*A*P+Vmf/Keq_ndk*P*Q ...
+Vmr*KmA/Kiq*B*Q);
else
J_ndk_f = 0;
end
% total reaction flux
if (P > MinCon) && (Q > MinCon)
J_ndk = J_ndk_f - Vmf*Vmr*(P*Q/Keq_ndk)/ai / (Vmr*KmB*A+Vmr*KmA*B ...
+Vmf*KmQ/Keq_ndk*P+Vmf*KmP/Keq_ndk*Q+Vmr*A*B ...
+Vmf*KmQ/Kia/Keq_ndk*A*P+Vmf/Keq_ndk*P*Q ...
+Vmr*KmA/Kiq*B*Q);
else
J_ndk = J_ndk_f;
end
%% -------------------------------
% 11. Glutamate oxaloacetate transaminase (aspartate transaminase)
% ASP + AKG = OAA + GLU
% load concentrations of reactants and products
A = ASP_x;
B = AKG_x;
P = OAA_x;
Q = GLU_x;
% dG and Keq values
dGr_goto = dGf1(iOAA) + dGf1(iGLU) - dGf1(iASP) - dGf1(iAKG);
Keq_goto = exp(-dGr_goto/RT);
% Keq_got = Keq_goto;
Keq_got = Keq_goto*(P_x(iOAA)*P_x(iGLU))/(P_x(iASP)*P_x(iAKG));
% Km and Ki values (Molar)
KmA = 3900e-6;
KmB = 430e-6;
KmP = 88e-6;
KmQ = 8900e-6;
% Kia = 8400e-6;
% Kib = 50e-6;
% Kip = 710e-6;
% Kiq = 3480e-6;
Kia = 3480e-6;
Kib = 710e-6;
Kip = 50e-6;
Kiq = 8400e-6;
KiAKG = 16.6e-3;
ai = 1 + AKG_x/KiAKG;
% Vm values
Vmf = Vmax(igot);
Vmr = Vmf/Keq_got*(KmQ*Kip/Kia/KmB);
% Vmr1 = Vmf/Keq_got*(KmP*Kiq/Kib/KmA);
% forward reaction flux
if (A > MinCon) && (B > MinCon)
J_got_f = Vmf*Vmr*A*B / (Vmr*KmB*A+Vmr*KmA*ai*B ...
+Vmf*KmQ/Keq_got*ai*P+Vmf*KmP/Keq_got*Q+Vmr*A*B ...
+Vmf*KmQ/Kia/Keq_got*A*P+Vmf/Keq_got*P*Q ...
+Vmr*KmA/Kiq*B*Q);
else
J_got_f = 0;
end
% total reaction flux
if (P > MinCon) && (Q > MinCon)
J_got = J_got_f - Vmf*Vmr*(P*Q/Keq_got) / (Vmr*KmB*A+Vmr*KmA*ai*B ...
+Vmf*KmQ/Keq_got*ai*P+Vmf*KmP/Keq_got*Q+Vmr*A*B ...
+Vmf*KmQ/Kia/Keq_got*A*P+Vmf/Keq_got*P*Q ...
+Vmr*KmA/Kiq*B*Q);
else
J_got = J_got_f;
end
%% -------------------------------
% 12. Anti- and co-transporter fluxes of substrates involved in the TCA cycle
% Fluxes are defined to be positive when the first reactant(s) move from IM
% into mito. matrix
% --------------------------------
% (1) PYR^{-}-H^{+} co-transporter
PYR_i1 = PYR_i*1/P_i(iPYR);
PYR_x1 = PYR_x*1/P_x(iPYR);
J_PYR_H = x_PYR_H * (PYR_i1*H_i - PYR_x1*H_x);
% --------------------------------
% (2) GLU^{-}-H^{+} co-transporter
GLU_i1 = GLU_i*1/P_i(iGLU);
GLU_x1 = GLU_x*1/P_x(iGLU);
J_GLU_H = x_GLU_H * (GLU_i1*H_i - GLU_x1*H_x);
% --------------------------------
% (3) CIT^{2-}/MAL^{2-} anti-transporter
CIT_i1 = CIT_i*(H_i/Kh(iCIT))/P_i(iCIT);
CIT_x1 = CIT_x*(H_x/Kh(iCIT))/P_x(iCIT);
MAL_i1 = MAL_i*1/P_i(iMAL);
MAL_x1 = MAL_x*1/P_x(iMAL);
J_CIT_MAL = x_CIT_MAL * (CIT_i1*MAL_x1 - CIT_x1*MAL_i1);
% --------------------------------
% (4) AKG^{2-}/MAL^{2-} anti-transporter
KmMALi = 1.4e-3;
KmMALx = 0.7e-3;
KmAKGi = 0.3e-3;
KmAKGx = 0.17e-3;
J_AKG_MAL = x_AKG_MAL/(KmMALx*KmAKGi)*(MAL_x*AKG_i-MAL_i*AKG_x)/ ...
(2 + MAL_i/KmMALi + MAL_x/KmMALx + AKG_i/KmAKGi + AKG_x/KmAKGx + ...
MAL_i*AKG_x/(KmMALi*KmAKGx) + MAL_x*AKG_i/(KmMALx*KmAKGi));
% --------------------------------
% (5) MAL^{2-}/PI^{2-} anti-transporter
MAL_i1 = MAL_i*1/P_i(iMAL);
MAL_x1 = MAL_x*1/P_x(iMAL);
Pi_i1 = Pi_i*1/P_i(iPi);
Pi_x1 = Pi_x*1/P_x(iPi);
J_MAL_PI = x_MAL_PI * (MAL_i1*Pi_x1 - MAL_x1*Pi_i1);
% --------------------------------
% (6) ASP^{-}/H.GLU{0} antitransporter (with one negative charge
% translocated from IM into mito matrix)
Kiaspi = 28e-6;
Kiaspx = 2.8e-3;
Kiglui = 180e-6;
Kiglux = 1.6e-3;
pKa_gaa = 6.5;
Kh_gaa = 10^(-pKa_gaa);
Keq_gaa = exp(-F*dPsi/RT)*P_x(iASP)*P_i(iGLU)/P_i(iASP)/P_x(iGLU); % Modified, 06/11/08
m = 1.8;
J_ASP_GLU = x_ASP_GLU/(Keq_gaa*Kiaspi*Kiglux*Kh_gaa)*(Keq_gaa*ASP_i*GLU_x*H_x - ASP_x*GLU_i*H_i)/ ...
(2*m + m*ASP_i/Kiaspi + ASP_i*GLU_x*H_x/(Kiaspi*Kiglux*Kh_gaa) + m*ASP_x*H_i/(Kiaspx*Kh_gaa) + ...
ASP_x*GLU_i*H_i/(Kiaspx*Kiglui*Kh_gaa) + m*ASP_x/Kiaspx + m*ASP_i*H_x/(Kiaspi*Kh_gaa) + ...
m*H_x/Kh_gaa + m*GLU_i*H_i/(Kiglui*Kh_gaa) + m*H_i/Kh_gaa + m*GLU_x*H_x/(Kiglux*Kh_gaa));
% --------------------------------
% (7) SUC^{2-}/MAL^{2-} anti-transporter
MAL_i1 = MAL_i*1/P_i(iMAL);
MAL_x1 = MAL_x*1/P_x(iMAL);
SUC_i1 = SUC_i*1/P_i(iSUC);
SUC_x1 = SUC_x*1/P_x(iSUC);
J_SUC_MAL = x_SUC_MAL * (SUC_i1*MAL_x1 - SUC_x1*MAL_i1);