Future Work - CONCLUSIONS AND FUTURE WORK

CHAPTER V CONCLUSIONS AND FUTURE WORK

5.2 Future Work

Besides enzyme kinetics, theories such as biochemical thermodynamics have been developed for biochemical systems in the literature. For the completeness of the model and the accuracy of simulation, we suggest the following issues as future work:

(1) Add respiration chain:

After the preliminary reactions, the catabolic pathways undergo the TCA cycle,

electron transport, and oxidative phosphorylation. The components of the biochemical apparatus for respiration include uptake of O2, electron transport and ATP synthesis. It means that adding a component which can describe the respiratory chain is helpful to complete the model and to account for the total ATP production.

(2) Consider thermodynamics of biochemical reactions:

Considering thermodynamics in the model makes it possible to calculate the effects of changing pH, free concentrations of the metal ions that are bound by the reactants, and the steady state concentrations of coenzymes. Although considering thermodynamics complicates the structure of the model and increase the number of governing equations, it increases the accuracy of the model and makes the predictions of the model more reliable.

(3) Enrich experimental measurement:

The number of measurements and the kinds of metabolites to be measured must be enough in order to construct a complete model. Instead of the relative change of concentrations in percentage, the absolute change of concentrations represented by mM helps to identify the kinetic parameters involved in the model.

(4) Modify the cell growth

The adopted rate of cell growth of E. coli in the model differs from the one actually observed in the experiment. We should take the cell growth data from the

experiment to increase the accuracy of the proposed model.

References

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Appendix A

Phosphotransferase system (PTS) The reaction can be

6 . PEPGLCPYRG P

It is Bi-Uni system, G6P as noncompetitive is cooperative n and irreversible, so the equation

Uni-Uni system, 6PG as competitive is reversible, so we get equation

   

The reaction can be written

6 .

F P ATP FDP ADP

It is Bi-Bi reaction, PEP as uncompetitive is cooperative n and irreversible, then

  

Owing to the assumption in figure 3.8, the modified reaction .

FDP GAP

It is Uni-Uni and irreversible, so the equation

    

Glyceraldehyde 3-phosphate dehydrogenase (GAPDH)

The reaction is

. GAP NAD PEP NADH

It is Bi-Bi system, there are two competitive inhibitions, PEP and NADH, which are reversible. The equation can be rewritten

It is Bi-Bi system, there are two activities, ADP and AMP. And ATP is competitive inhibition, cooperative n and irreversible, so we get

     

It exhibits hyperbolic function with respect to PEP concentration. AcCoA is a very potent activator, and FDP alone exhibits no activation, but it produces a strong synergistic activation with AcCoA.

Phosphoenolpyruvate carboxykinase (PCK) Consider the reaction

. OAAATPPEPADP

It is in the reverse direction to follow rapid equilibrium mechanism. The rate is inhibited by PEP and ADP as competitive inhibition

   

PCK ATP OAA ATP OAA ATP OAA

OAA i m i m i m

The reaction can be

. PYR CoA NAD AcCoA NADH

The hyperbolic function is considered with respect to PYR, and assumed to be inhibited by NADH

PYR NAD NADH COA AcCoA

m m m m m

PYR COA

NAD NADH K K K

K NAD

v PYR NADH COA AcCoA

K NAD K K NAD K K

It is Bi-Bi system, CoA and ACP are competitive inhibition and reversible, so

     

AcCoA P ACP COA AcCoA P ACP COA

i i i i i m m i

It is also Bi-Bi system, ACE and ATP are noncompetitive inhibition and reversible, and the equation The reaction can be

. ACENADPAcCoA

It assumed to be expressed by simple Michaelis-Menten equation.

  

. AcCoA OAA CIT CoA

It is Bi-Bi system, and is inhibited by NADH.

  

Bi-Bi system is inhibited by NADPH which is competitive and reversible. The equation rewritten

ICIT NADP NADP ICIT NADP

m d d m d

NADP KG

m eknh

ICIT ICIT NADP NADPH KG NADPH

d m d einh m enhe

ICIT NADPH K NADPH K

K NADP K K K K K NADP

KG NADPH KG NADPH KG NADPH NADPH

m enhe m enhe m enhe enhe

KG NADPH KG K NADPH

K^ K NADP K^ K NADP K^ K K NADP

It’s Uni-Bi and reversible.

ICIT SUC GOX ICIT SUC SUC GOX

m m m m m m m I

It’s Bi-Uni and reversible. The equation will be

     

Combining αKGDH and SCoA in this reaction is inhibited by competitive NADH, so we can get

Succinate dehydrogenase (SDH) The reaction can be

. SUC FUM

It is Uni-Uni system and reversible reaction, so we get the equation

   

It is Uni-Uni system, and reversible reaction. The equation rewritten

   

The system inhibited by NADH as competitive inhibitor is Uni-Uni and reversible. So the equation can be

The reaction considered

. MALNADPPYRNAPDH

The system derived by simple Michaelis-Menten equation is Bi-Bi and irreversible, so we can get

Glucose 6-phosphate dehydrogenase (G6PDH) Consider the reaction

6 6 .

G PNADP PGNAPDH

It is Bi-Bi reaction inhibited by uncompetitive and irreversible. The equation as follow

The reaction inhibited by uncompetitive is Bi-Bi system and irreversible. The equation will be

Other equations for PP pathway such as RPE, RPI, TkTA, TkTB, and TAL were considered in the form of mass-action kinetic, and they are different each other owing to the number of substrate, given in the following:

Phosphopentose epimerase (RPE)

The cell growth effects the change of intercellular metabolites during culture as the μ:

Cell growth

Appendix B

function dx = modelinEcoliwithSDH(t ,x , K)

ADP = 0.595; AMP = 0.955; ATP = 4.27;

COA = 0.001; NAD = 1.47; NADH = 0.1;

NADP = 0.195; NADPH = 0.062; P = 10;

k6_PPC = K(1); K_OAA_m_PCK = K(2);

K_PEP_i_PCK = K(3); K_PEP_PYK = K(4);

K_eq_PGI = K(5); K_G6P_G6PDH = K(6);

K_SUC_m_SDH = K(7); K_eq_SDH = K(8);

K_b_ADP_AMP_PFK = K(9); K_ICIT_m_ICL = K(10);

K_eq_TAL = K(11); K_eq_FUM = K(12);

K_MAL_m_MDH = K(13); K_PGP_GAPDH = K(14);

I_ICL = 1.431; % mM for I/K_I_ICL = 477

The followings are rate equation from [11] and [12]:

% PTS 酵素速率方程式

v_PTSmax = 469786.8; % mM/min

K_a1_PTS = 3082.3; % mM K_a2_PTS = 0.01; % mM K_a3_PTS = 245.3; n_G6P = 3.66; K_G6P = 2.15; % mM

vPTS = v_PTSmax*x(2)*(x(7)/x(8))/((K_a1_PTS + K_a2_PTS*(x(7)/x(8)) + K_a3_PTS*x(2) + x(2)*(x(7)/x(8)))*(1 + (x(3)^n_G6P)/K_G6P));

% PGI 酵素速率方程式

v_PGImax = 39059.27; % mM/min

K_G6P_m_PGI = 2.9; % mM K_F6P_m_PGI = 0.266; % mM

K_G6P_6pginh_PGI = 0.2; % mM K_F6P_6pginh_PGI = 0.2; % mM vPGI = v_PGImax*(x(3) - x(4)/K_eq_PGI)/(K_G6P_m_PGI*

(1 + x(4)/(K_F6P_m_PGI*(1 + x(19)/K_F6P_6pginh_PGI)) + x(19)/K_G6P_6pginh_PGI) + x(3));

Energy-transfered metabolites

Adjustable parameters

% PFK 酵素速率方程式

v_PFKmax = 110435.0848; %mM/min

K_ATP_PFK = 4.27; % mM K_ATP_ADP_PFK = 4.41; % mM

K_a_ADP_AMP_PFK = 1.0546; % mM n_PFK = 11.1; L_PFK = 5629067;

K_F6P_s_PFK = 0.325; % mM K_PEP_PFK = 3.26; % mM vPFK = v_PFKmax*ATP*x(4)/(K_ATP_ADP_PFK*(x(4) +

K_F6P_s_PFK*(K_b_ADP_AMP_PFK + x(7)/K_PEP_PFK)/K_a_ADP_AMP_PFK)*

(1 + L_PFK/(1 + x(4)*(K_a_ADP_AMP_PFK/(K_F6P_s_PFK*(K_b_ADP_AMP_PFK + x(7)/K_PEP_PFK))))^n_PFK));

% PYK 酵素速率方程式

v_PYKmax = 3.66789; % mM/min

K_FDP_PYK = 0.19; % mM K_AMP_PYK = 0.2; % mM K_ATP_PYK = 22.5; % mM K_ADP_PYK = 0.26; % mM n_PYK = 4; L_PYK = 1000;

vPYK = (v_PYKmax*x(7)*ADP*(x(7)/K_PEP_PYK + 1)^(n_PYK -

1))/(K_PEP_PYK*(L_PYK*((1 + ATP/K_ATP_PYK)/(x(5)/K_FDP_PYK + AMP/K_AMP_PYK + 1))^n_PYK + (x(7)/K_PEP_PYK + 1)^n_PYK)*(ADP + K_ADP_PYK));

% PPC 和 PCK 酵素速率方程式 K_PEP_m_PPC = 0.3231; % mM

k1_PPC = 0.03176; k2_PPC = 1.2878; % mM k3_PPC = 0.05425; % mM k4_PPC = 0.8139; % mM k5_PPC = 0.0939; % mM

vPPC = (k1_PPC + k2_PPC*x(9) + k3_PPC*x(5) + k4_PPC*x(9)*x(5))*x(7)/((1 + k5_PPC*x(9) + k6_PPC*x(5))*(K_PEP_m_PPC + x(7)));

v_PCKmax = 55.5; % mM/min

K_ATP_m_PCK = 0.06; % mM K_ATP_I_PCK = 0.04; % mM K_ATP_i_PCK = 0.04; % mM K_OAA_I_PCK = 0.67; % mM K_PEP_m_PCK = 0.07; % mM K_ADP_i_PCK = 0.04; % mM

vPCK = v_PCKmax*x(15)*ATP/ADP/(K_OAA_m_PCK*ATP/ADP + x(15)*ATP/ADP + K_ATP_i_PCK*K_OAA_m_PCK/K_ADP_i_PCK +

K_ATP_i_PCK*K_OAA_m_PCK*x(7)/(K_PEP_m_PCK*K_ADP_i_PCK) +

K_ATP_i_PCK*K_OAA_m_PCK*ATP*x(7)/(K_PEP_i_PCK*K_ATP_I_PCK*ADP) + K_ATP_i_PCK*K_OAA_m_PCK*x(15)/(K_ADP_i_PCK*K_OAA_I_PCK));

% PDH 酵素速率方程式

v_PDHmax = 259; % mM/min

K_PYR_m_PDH = 1; % mM K_NAD_m_PDH = 0.4; % mM

K_AcCoA_m_PDH = 0.008; % mM K_NADH_m_PDH = 0.1; % mM K_COA_m_PDH = 0.014; % mM K_PDH_i_PDH = 46.416; % mM vPDH = v_PDHmax*x(8)*COA/(NAD*

(1 + K_PDH_i_PDH*NADH/NAD)*K_PYR_m_PDH*K_NAD_m_PDH*K_COA_m_PDH)/

((1 + x(8)/K_PYR_m_PDH)*(1/NAD + 1/K_NAD_m_PDH +

NADH/(NAD*K_NADH_m_PDH))*(1 + COA/K_COA_m_PDH + x(9)/K_AcCoA_m_PDH));

% PTA, ACK 和 ACS 酵素速率方程式 v_PTAmax = 42; % mM/min

K_AcCoA_i_PTA = 0.2; % mM K_P_m_PTA = 2.6; % mM K_P_i_PTA = 2.6; % mM K_ACP_m_PTA = 0.7; % mM K_ACP_i_PTA = 0.2; % mM K_COA_i_PTA = 0.029; % mM K_eq_PTA = 0.0281; % mM

vPTA = (v_PTAmax*(1/(K_AcCoA_i_PTA*K_P_m_PTA))*(x(9)*P - x(17)*COA/K_eq_PTA))/(1 + x(9)/K_AcCoA_i_PTA + P/K_P_i_PTA +

x(17)/K_ACP_i_PTA + COA/K_COA_i_PTA +x(9)*P/(K_AcCoA_i_PTA*K_P_m_PTA) + x(17)*COA/(K_ACP_m_PTA*K_COA_i_PTA));

v_ACKmax = 2700; % mM/min

K_ACP_m_ACK = 0.16; % mM K_ADP_m_ACK = 0.5; % mM K_ACE_m_ACK = 7; % mM K_ATP_m_ACK = 0.07; % mM K_eq_ACK = 174.217; % mM

vACK = v_ACKmax*(x(17)*ADP –

x(18)*ATP/K_eq_ACK)/(K_ADP_m_ACK*K_ACP_m_ACK)/((1 + x(17)/K_ACP_m_ACK + x(18)/K_ACE_m_ACK)*(1 + ADP/K_ADP_m_ACK + ATP/K_ATP_m_ACK));

v_ACSmax = 55;

K_ACS = 0.089971; % mM K_m_ACS = 0.07; % mM

vACS = v_ACSmax*x(18)*NADP/((K_m_ACS + x(18))*(K_ACS + NADP));

% ICDH 和 ICL 酵素速率方程式 v_ICDHmax = 270; % mM/min

K_eq_ICDH = 1000; % mM k_f_ICDH = 48301; % l/min

K_2KG_m_ICDH = 0.038; % mM K_ICIT_m_ICDH = 0.0059; % mM

K_NADP_d_ICDH = 0.0013; % mM K_NADP_m_ICDH = 0.0227; % mM K_NADH_d_ICDH = 0.12; % mM K_ICIT_d_ICDH = 0.03; % mM

K_NADPH_einh_ICDH = 0.007; % mM K_2KG_eknh_ICDH = 5.5; % mM K_CO2_d_ICDH = 1.6; % mM K_CO2_eke_ICDH = 1.6; % mM

K_NADP_ekn_ICDH = 0.00016; % mM K_NADPH_m_ICDH = 0.0036; % mM K_NADPH_enhe_ICDH = 0.028; % mM

IDH = 1; % mM

vICDH = (IDH*k_f_ICDH/K_ICIT_m_ICDH*K_NADP_d_ICDH*(x(10)*NADP - NADPH*x(11)/K_eq_ICDH))/(1 +

x(10)*K_NADP_m_ICDH/(K_ICIT_m_ICDH*K_NADP_d_ICDH) + NADP/K_NADP_d_ICDH + x(10)*NADP/(K_ICIT_m_ICDH*K_NADP_d_ICDH) +

x(10)*NADPH*K_NADP_m_ICDH/(K_ICIT_d_ICDH*K_ICIT_m_ICDH*K_NADP_d_ICDH*K_NA DPH_einh_ICDH) + NADPH*K_2KG_eknh_ICDH/(K_2KG_m_ICDH*K_NADPH_enhe_ICDH) + x(11)*K_NADPH_m_ICDH/(K_2KG_m_ICDH*K_NADPH_enhe_ICDH) +

x(11)*NADPH/(K_2KG_m_ICDH*K_NADPH_enhe_ICDH) +

x(11)*K_NADPH_m_ICDH*NADPH/(K_2KG_m_ICDH*K_NADPH_enhe_ICDH*

K_NADP_ekn_ICDH));

v_ICLmax_f = 28.5; % mM/min v_ICLmax_r = 0.285; % mM/min

K_SUC_m_ICL = 0.59; % mM K_GOX_m_ICL = 0.13; % mM K_ICL_I_ICL = 0.003; % mM

vICL = (v_ICLmax_f*x(10)/K_ICIT_m_ICL -

v_ICLmax_r*x(12)*x(16)/(K_SUC_m_ICL*K_GOX_m_ICL))/

(1 + x(10)/K_ICIT_m_ICL + x(12)/K_SUC_m_ICL + x(16)/K_GOX_m_ICL + x(10)*x(12)/(K_SUC_m_ICL*K_ICIT_m_ICL) +

x(12)*x(16)/(K_GOX_m_ICL*K_SUC_m_ICL) + I_ICL/K_ICL_I_ICL);

% ALDO 酵素速率方程式

v_ALDOmax = 1044.879; % mM/min

K_FDP_ALDO = 0.175; % mM K_GAP_ALDO = 0.088; % mM K_DHAP_ALDO = 0.088; % mM K_GAP_inh_ALDO = 0.6; % mM K_eq_ALDO = 0.144; % mM Vblf = 2;

vALDO = v_ALDOmax*(x(5) - x(6)*x(6)/K_eq_ALDO)/(K_FDP_ALDO + x(5) + K_GAP_ALDO*x(6)/(K_eq_ALDO*Vblf) + K_DHAP_ALDO*x(6)/(K_eq_ALDO*Vblf) + x(5)*x(6)/K_GAP_inh_ALDO + x(6)*x(6)/(K_eq_ALDO*Vblf));

% GAP 酵素速率方程式

v_GAPDHmax = 55295.65717; % mM/min

K_GAP_GAPDH = 0.683; % mM K_NAD_GAPDH = 0.252; % mM K_NADH_GAPDH = 1.09; % mM K_eq_GAPDH = 0.63;

vGAPDH = v_GAPDHmax*(x(6)*NAD - x(7)*NADH/K_eq_GAPDH)/((K_GAP_GAPDH*(1 + x(7)/K_PGP_GAPDH) + x(6))*(K_NAD_GAPDH*(1 + NADH/K_NADH_GAPDH)) + NAD);

% CS 酵素速率方程式

v_CSmax = 8.23; % mM/min

K_H_d1_CS = 0.00001; % mM K_H_d2_CS = 0.0002; % mM K_AcCoA_m_CS = 0.18; % mM K_OAA_m_CS = 0.04; % mM K_AcCoA_d_CS = 0.1; % mM K_ATP_i_CS = 0.58; % mM K_2KG_i1_CS = 0.015; % mM K_2KG_i2_CS = 0.256; % mM K_NADH_i1_CS = 0.00033; % mM K_NADH_i2_CS = 0.0084; % mM K_cat0_CS = 1; % 1 /min

vCS = v_CSmax*K_cat0_CS*x(9)*x(15)/(K_AcCoA_d_CS*K_OAA_m_CS +

K_AcCoA_m_CS*x(15) + x(9)*K_OAA_m_CS*(1 + NADH/K_NADH_i1_CS) + x(9)*x(15)*(1 + NADH/K_NADH_i2_CS));

% MS 酵素速率方程式

v_MSmax_f = 28.5; % mM/min v_MSmax_r = 0.285; % mM/min K_GOX_m_MS = 2; % mM K_AcCoA_m_MS = 0.01; % mM

K_MAL_m_MS = 1; % mM K_COA_m_MS = 0.1; % mM

vMS = (v_MSmax_f*x(16)*x(9)/(K_GOX_m_MS*K_AcCoA_m_MS) -

v_MSmax_r*x(14)/K_MAL_m_MS)/(1 + x(16)/K_GOX_m_MS + x(14)/K_MAL_m_MS + (1 + x(9)/K_AcCoA_m_MS));

% 2KGDH 酵素速率方程式

v_2KGDHmax = 7608; % mM/min

K_2KG_m_2KGDH = 1; % mM K_2KG_I_2KGDH = 0.75; % mM K_COA_m_2KGDH = 0.002; % mM K_NAD_m_2KGDH = 0.07; % mM K_SUC_m_2KGDH = 1; % mM K_SUC_I_2KGDH = 1; % mM

K_NADH_m_2KGDH = 0.018; % mM K_NADH_I_2KGDH = 0.018; % mM K_z_2KGDH = 1.5;

v2KGDH = v_2KGDHmax*x(11)*COA/(K_NAD_m_2KGDH*x(11)*COA/NAD + K_COA_m_2KGDH*x(11) + K_2KG_m_2KGDH*COA + x(11)*COA +

vSDH = v_SDH1*v_SDH2*(x(12) - x(13)/K_eq_SDH)/(K_SUC_m_SDH*v_SDH2 + v_SDH2*x(12) + v_SDH1*x(13)/K_eq_SDH );

Here we adjust the SDH mutant, set the rate equal to 0.

% FUMe 酵素速率方程式

v_FUM1 = 25.7; % mM/min v_FUM2 = 25.7; % mM/min K_FUM_m_FUM = 0.01; % mM

vFUM = v_FUM1*v_FUM2*(x(13) - x(14)/K_eq_FUM)/(K_FUM_m_FUM*v_FUM1 + v_FUM2*x(13) + v_FUM1*x(14)/K_eq_FUM );

% MDH 酵素速率方程式

v_MDH1 = 77.8; % mM/min v_MDH2 = 77.8; % mM/min K_eq_MDH = 1; K_NAD_I_MDH = 0.31; % mM

K_NADH_I_MDH = 0.04; % mM K_MAL_I_MDH = 3.3; % mM K_OAA_I_MDH = 0.27; % mM K_NAD_m_MDH = 0.1; % mM K_NADH_m_MDH = 0.04; % mM K_OAA_m_MDH = 0.27; % mM K_NAD_II_MDH = 0.31; % mM K_OAA_II_MDH = 0.17; % mM vMDH = v_MDH1*v_MDH2*(x(14) -

x(15)*NADH/(K_eq_MDH*NAD))/(K_NAD_I_MDH*K_MAL_m_MDH*v_MDH2/NAD + K_MAL_m_MDH*v_MDH2 + K_NAD_m_MDH*v_MDH2*x(14)/NAD + v_MDH2*x(14)+

K_OAA_m_MDH*v_MDH1*NADH/(K_eq_MDH*NAD) +

% MEZ 酵素速率方程式

v_MEZmax = 3.08; % mM/min K_MAL_m_MEZ = 0.37; % mM K_eq_MEZ = 0.1;

vMEZ = v_MEZmax*x(14)*NADP/((K_MAL_m_MEZ + x(14))*(K_eq_MEZ + NADP));

% G6PDH 酵素速率方程式

v_G6PDHmax = 82.8; % mM/min K_NADP_G6PDH = 0.0246; % mM

K_NADPinh_NADPH_G6PDH = 0.01; % mM K_G6Pinh_NADPH_G6PDH = 6.43; % mM vG6PDH = v_G6PDHmax*x(3)/((x(3) + K_G6P_G6PDH)*

(1 + NADPH/K_G6Pinh_NADPH_G6PDH)*(K_NADP_G6PDH*

((1 + NADPH)/K_NADPinh_NADPH_G6PDH)/NADP + 1));

% PGDH 酵素速率方程式

v_PGDHmax = 973.9416; %mM/min

K_G6P_PGDH = 37.5; % mM K_NADP_PGDH = 0.0506; % mM

K_NADPHinh_PGDH = 0.0138; % mM K_ATPinh_PGDH = 208; % mM

vPGDH = v_PGDHmax*x(19)/((x(19) + K_G6P_PGDH)*(1 + K_NADP_PGDH/NADP*

(1 + NADPH/K_NADPHinh_PGDH)*(1 + ATP/K_ATPinh_PGDH)));

% RPE 酵素速率方程式

v_RPEmax = 404.34; % 1/min K_eq_RPE = 1.4; % mM vRPE = v_RPEmax*(x(20) - x(22)/K_eq_RPE);

% RPI 酵素速率方程式

v_RPImax = 290.304; % 1/min K_eq_RPI = 4; % mM original:4 vRPI = v_RPImax*(x(20) - x(21)/K_eq_RPI);

% TKTA 酵素速率方程式

v_TKTAmax = 568.4028; % 1/mM/min K_eq_TKTA = 1.2; % mM vTKTA = v_TKTAmax*(x(21)*x(22) - x(23)*x(6)/K_eq_TKTA);

% TKTB 酵素速率方程式

v_TKTBmax =5193.5135 ; % 1/mM/min K_eq_TKTB = 10; % mM vTKTB = v_TKTBmax*(x(22)*x(24) - x(4)*x(6)/K_eq_TKTB);

% TAL 酵素速率方程式

89 v_TALmax = 652.2984; % 1/mM/min

vTAL = v_TALmax*(x(6)*x(23) - x(24)*x(4)/K_eq_TAL);

% 細胞成長率

amum_cell = 0.6; Ks_cell = 0.1; Xm_cell = 2.3; P_O = 2.5;

amumA_cell = 0.9; KsA_cell = 0.01; k_ATP_cell = 0.09;

OP_NADH = (vGAPDH + vPDH + vICDH + v2KGDH + vMDH)*P_O;

OP_FADH2 = vSDH*P_O;

vATP = OP_NADH + OP_FADH2 + vGAPDH + vPYK + vACK + vSDH - vPFK - vPCK;

if x(2)>0

amu = amum_cell*(1 - x(1)/Xm_cell)*x(2)/(Ks_cell + x(2))*k_ATP_cell*vATP;

elseif x(2)<=1 && x(18)>0

amu = amumA_cell*x(18)/(KsA_cell + x(18))*k_ATP_cell*vATP;

end

Comparing the value we get with experiment after solving the ODES.

function [y W]= modelinEcolilsqcurvefit( K, xdata) tol = 1e-6;

% Solver for the whole reaction and SDH knockout

[ta1 xa1] = ode45(@modelinEcoliwithSDH, tspans, x0, options, K);

[ta2 xa2] = ode45(@modelinEcolinoSDH, tspans, x0, options, K);

% Computing the relation between original and SDH mutant.

y = [(xa2(N(2),3) - xa1(N(2),3))/xa1(N(2),3);

(xa2(N(2),4) - xa1(N(2),4))/xa1(N(2),4);

% lsqcurvit is applied to ODE mfiles.

Clear;clc;

tic;

tspans = 0:0.01:10;

% Initial value, modifying the parameters.

K0 = [3 0.15 1.5 1 1 18 10 0.01 0.01 0.5 0.1 1 1 1.2e-5];

x0 = [1; 1; 3.48; 0.6; 0.59; 0.29; 2.67; 2.67; 0.5; 0.018; 0.2;

0.6; 0.3; 1.8; 0.004; 0.2; 0.05; 1; 0.808; 0.13; 0.398;

0.18; 0.276; 0.098];

% Observation from experiment

ydata = [-0.08819; -0.08819; -0.1894; -0.0354; -0.2908; -0.5906;

-0.34338; 1.1896; -0.701; 0.3191; -0.0794; -0.0954; -0.1008];

xdata = 0; % not need

% Set the rules, function, error, iterations, and plots the process.

options = optimset( 'Algorithm', 'Levenberg-Marquardt','TolX', 0.01, 'Display','iter', 'PlotFcns',@optimplotresnorm,'TolFun',

0.01,'MaxFunEvals', 80, 'MaxIter', 20);

% Starts the lsqcurvefit, transfering K0 into the ODES.

[Ecoliparamfit, resnorm,FVAL,EXITFLAG,OUTPUT,LAMBDA,JACOB] =

lsqcurvefit(@(K, xdata) modelinEcolilsqcurvefit( K, xdata), K0, xdata, ydata, [],[], options);

toc;

VITA

Name: Shao-Jhan Hong Place of Birth: Taiwan Academic Record:

B.S: 2007~2011

Department of Aerospace Engineering Tamkang University

Tamshui, New Taipei, Taiwan, ROC.

M.S: 2011~2013

Department of Aeronautics and Astronautics National Cheng Kung University

Tainan, Taiwan, ROC.

在文檔中出血性大腸桿菌之建模與模擬驗證 (頁 80-107)