semi-quantitative modeling for the effect of oxygen level.pdf

7/27/2019 Semi-quantitative Modeling for the Effect of Oxygen Level.pdf

1/8

Semi-quantitative Modeling for the Effect of Oxygen Level

on the Metabolism inEscherichia coli

Yu Matsuoka1, Kazuyuki Shimizu1,21Dept. of Bioscience and Bioinformatics, Kyushu Institute of Technology,

Iizuka, Fukuoka 820-8502, Japan2Institute for Advanced Biosciences, Keio University, Tsuruoka, Yamagata 997-0017, Japan

E-mail: [email protected]

Abstract

Mathematical models for the main metabolic

pathways such as glycolysis, pentose phosphate

pathway, TCA cycle, fermentation pathway etc. were

considered for the enzyme level regulation in E.coli. Itis quite important to develop a model which can

simulate the effect of oxygen level on the metabolism in

practice. For this, the effect of oxygen level on the

expressions of the global regulators such as arcA/B

and fnr was modeled based on the experimental data.

Then the effects of these gene expressions on the

metabolic pathway gene expressions were

incorporated in the model, where the effects of oxygen

levels on PDHc and Pfl fluxes as well as the

respiratory pathway flux were expressed based on the

experimental data. Thus, the model could express the

increase in the redox ratio, NADH/NAD as the oxygen

level decreases, and in turn the activation of the

fermentation pathways. The semi-quantitative modeldeveloped in the present research enables us to

simulate the effect of changing the oxygen level on the

cell growth and the production of the variety of

metabolites such as lactate, ethanol etc.

1. Introduction

One of the most challenging goals of metabolic

engineering and bioprocess engineering is to design the

cell metabolism based on metabolic regulation analysis

and to find the optimal culture condition for the cell

growth and the specific metabolite production. For this,

it is strongly desired to develop a mathematical model

which can describe the dynamic behavior of the cell

metabolism in response to culture environment and/or

genetic modifications.

Some of the kinetic models have been developed in

the past for Saccharomyces cerevisiae [1-3]. The

dynamics of the intracellular metabolite concentrations

in response to the pulse addition of glucose-limited

continuous culture have been investigated [2, 4-6].

The kinetic equations for the glycolysis and pentose

phosphate (PP) pathway in E.coli have also beendeveloped by Chassagnole et al. [7] to simulate the

dynamics of the intracellular metabolite concentrations

in response to the pulse change in the feed glucose

concentration in glucose-limited continuous culture.

This model does not contain kinetic equations for the

TCA cycle as well as fermentation pathways, and thus

cannot simulate the typical batch cultivation.

In the present investigation, we considered the

kinetic model equations for the glycolysis, PP

pathweay, TCA cycle and the fermentation pathways.

Moreover, most of the kinetic models developed so far

can express only enzyme level regulation due to the

change in the concentrations of substrate, product aswell as various effectors. Thus, the conventional model

cannot express the metabolic changes in relation to the

change in culture environment such as dissolved

oxygen and/or the genetic changes, where those affect

the cell metabolism via gene level regulation. Although

it is not easy to express gene level regulation by

mathematical equations, we considered a semi-

quantitative approach by utilizing some of the

experimental data and the knowledge on gene level

regulation.

2. Modeling

2.1. Dynamic Equations

Referring to Fig.1, the dynamic equations may be

described based on mass balances as follows:

( ) ][][ XGlcdt

Xd ex=

(1a)

Digital Object Identifier inserted by IEEE

International Conference on Complex, Intelligent and Software Intensive Systems

978-0-7695-3575-3/09 $25.00 2009 IEEE

DOI 10.1109/CISIS.2009.179

215

International Conference on Complex, Intelligent and Software Intensive Systems

978-0-7695-3575-3/09 $25.00 2009 IEEE

DOI 10.1109/CISIS.2009.179

215


2/8

][][

Xvdt

GlcdPTS

ex

=(1b)

]6[]6[

6 PGvvvdt

PGdPDHGPfkPTS =

(1c)

][][

FDPvvdt

FDPdAldPfk =

(1d)

][2

][

GAPvvdt

GAPd

GAPDHAld =

(1e)

][][

PGPvvdt

PGPdPgkGAPDH =

(1f)

]3[]3[

PGvvdt

PGdEnoPgk =

(1g)

][][

PEPvvvvvdt

PEPdPTSPpcPykPckEno +=

(1h)

][][

PYRvvvvvdt

PYRdPflLDHPDHPTSPyk +=

(1i)

][][

LACvdt

LACdLDH =

(1j)

][][

AcCoAvvvvvdt

AcCoAdCSALDHPtaPflPDH +=

(1k)

][

][

AcAldvvdt

AcAlddADHALDH

=(1l)

][][

ETHvdt

ETHdADH =

(1m)

][][

AcPvvdt

AcPdAckPta =

(1n)

]])[[(][

XACEvdt

ACEd exAck

ex

=(1o)

][][

CITvvdt

CITdICDHCS =

(1p)

]2[]2[

2 KGvvdt

KGdKGDHICDH =

(1q)

][][

2SUCvvv

dt

SUCdSDHFrdKGDH

+=(1r)

][

][

FUMvvvdt

FUMdFrdFumSDH

=(1s)

][][

MALvvdt

MALdMDHFum =

(1t)

][][

OAAvvvvdt

OAAdPckCSPpcMDH +=

(1u)

where [.] denotes the concentration. is the specific

growth rate, and iv are the kinetic rate equations in

mmol/gDCW.h.

As shown in Fig.1, G6P and F6P were lumped

together, since Pgi reaction is well in equilibrium. In

the same reason, GAP and DHAP were also lumped

together. A sequence of enzymatic reactions by Gpm,

and Eno may be considered to be in equilibrium, andwas assumed to be one reaction from 3PG to PEP. As

for the PP pathway, only G6PDH and PGDH were

considered in view of NADPH production.

Here, Mez, Icl, MS, Acs, Pps, Fbp etc. were not

considered in the present study, since the focus of the

current attention is fermentation under micro-aerobic

or anaerobic condition.

Fig.1 Metabolic Pathways

2.2.Kinetic equationsSome of the important kinetic equations used for the

various enzyme-catalyzed reactions are as follows:

2.2.1. Cell growth

The specific growth rate was assumed to be the

following simple Monod model:

( )][

][

,

ex

Glcm

ex

mex

GlcK

GlcGlc

ex +

=

(2a)

2.2.2. Phosphotransferase system (PTS)

The glucose transport via phosphotransferase

system (PTS) has been extensively investigated and is

catalyzed by a sequence of enzymes such as EI, HPr,

EIIAGlc and the rate-limiting step to the final step of

glucose transport and phosphorylation from PEP.

Those were encoded by such genes as ptsHI, crr and

ptsG. The kinetic rate equation for PTS may be

expressed as [7]

+

+++

=

PGPTS

n

exexaPTSaPTSaPTS

exPTS

PTS

K

PG

PYR

PEPGlcGlcKPYR

PEPKK

PYR

PEPGlcv

vPGPTS

6,

3,2,1,

max

6,]6[1][

][][][][

][

][

][][

(2b)

Fig.2a shows the effect of [PEP] onPTSv

with respect to

glucose concentration, wherePTSv

increases as [PEP]

increases.

216216


3/8

Fig.2a Effect of [PEP] on PTSv

2.2.3. PhosphofructokinaseThe phosphofructokinase (Pfk) is encoded by pfkA

and pfkB in E.coli, where Pfk-1 encoded by pfkA is

dominant, accounting for 90 % of the total activity [8].

Here, we considered only Pfk-1, where it is inhibited

by PEP [9], and its reaction rate may be expressed as

[7]

+

+

+

++

=

Pfkn

sPFPfk

Pfk

sPFPfk

cADPPfk

sATPPfk

Pfk

Pfk

AK

BPF

L

B

AKPF

K

ADPKATP

PFATPvv

,6,

,6,

,,

,,

max

]6[1

1]6[][

1][

]6][[

(2c)

where

,][][][

1,,,,, bAMPPfkbADPPfkPEPPfk K

AMP

K

ADP

K

PEPA +++=

aAMPPfkaADPPfk K

AMP

K

ADPB

,,,,

][][1 ++=

2.2.4. GAPDH

The rate equation for glyceraldehyde 3-phosphate

dehydrogenase (GAPDH) may be expressed as [7]

+

+

+

+

=

1][

][1

][

1][

][1

][

][][][

,

,

,

,

,

max

NAD

NADH

KNADKGAP

K

PGPK

NAD

NADH

K

PGPGAPv

v

NADHGAPDH

NADGAPDH

PGPGAPDH

GAPGAPDH

eqGAPDH

GAPDH

GAPDH (2d)

whereGAPDHv becomes small as [NADH] increases as

shown in Fig.2b, whereGAPDHv decreases as

[NADH]/[NAD] increases.

Fig.2b Effect of NADH/NAD on GAPDHv

2.2.5. Pyruvate kinaseThe pyruvate kinase (Pyk) reaction is catalyzed by

two isoenzymes such as PykI and PykII each encoded

by pykF and pykA, respectively. PykI is dominant and

activated by FDP and inhibited by ATP, whereas

minor PykII is activated by AMP. Here, we lumped

these together, and the rate equation may be expressed

as [7]

( )ADPPyk

n

PEPPyk

n

AMPPykFDPPyk

ATPPyk

PykPEPPyk

n

PEPPyk

Pyk

Pyk

KADPK

PEP

K

AMP

K

FDP

K

ATP

LK

ADPK

PEPPEPv

v

Pyk

Pyk

Pyk

,

,

,,

,

,

1

,

max

][1][

1][][

][1

][1][

][

+

++

++

+

+

=

(2e)

wherePykv increases as [FDP] increases. Fig.2c shows

the effect of [FDP] on Pykv with respect to [PEP] at theconstant value of [ATP], [ADP] and [AMP], where

Pykv increases little as [FDP] increases in the range of

concern.

Fig.2c Effect of [FDP] on Pykv

2.2.6. PEP carboxylase

It is quite important to correctly simulate the fluxes

at the branch point of PEP, where the enzyme activities

of Pyk and Ppc determine the fluxes. It has been

known that Ppc exhibits a hyperbolic function with

respect to PEP, and that the reaction rate is usually low

without any activator, where AcCoA is a very potent

activator, and FDP alone exhibits no activation, but it

gives strong synergistic activation with AcCoA [10].

Those may be taken into account for the rate equation

[11] as

+++

+++=

][

][

][][1

]][[][][

65

4321

PEPK

PEP

FDPKAcCoAK

FDPAcCoAKFDPKAcCoAKKv

m

Ppc (2f)

Although CO2 is the cosubstrate in Ppc reaction, the

effect of CO2 was not considered in Ppcv . Fig.2e shows

the effect of [AcCoA] onPpcv with respect to [PEP],

where it shows thatPpcv increases as [AcCoA]

increases.

The reverse reaction to Ppc, Pck may be considered

[12, 13], but not shown here.

2.2.7. PDHFor the rate equation of pyruvate dehydrogenase

complex (PDHc) encoded by aceE, F and lpdA, the

hyperbolic function with respect to PYR was

considered, and the inhibition by NADH/NAD was

also taken into account [14]

217217


4/8

++

++

+

+

=

AcCoAmCoAmNADHmNADmPYRm

CoAmNADmPYRmi

PDH

PDH

K

AcCoA

K

CoA

NAD

NADH

KKNADK

PYR

K

CoA

KK

PYR

NAD

NADHK

v

v

,,,,,

,,,

max

][][1

][

][11

][

1][1

][1][

][

][1

1

(2g)

2.2.8. Acetate formation

The acetate formation is of important concern in thecell growth and the specific metabolite production in

E.coli. The main pathway for acetate production is Pta-

Ack pathway, where the reaction catalyzed by Pta and

Ack proceeds through an unstable, high energy acetyl

phosphate (Ace-P). For Pta reaction, the following

equation was considered [14] based on Hankin and

Abales [15]:

++++++

=

CoAiACPmPmAcCoAiCoAiACPiPiAcCoAi

eqpmAcCoAi

Pta

Pta

KK

CAOACP

KK

PAcCoA

K

CoA

K

ACP

K

P

K

AcCoA

K

CoAACPPAcCoA

KKv

v

,,,,,,,,

,,

max

]][[]][[][][][][1

]][[]][[

1

(2h)

The rate equation for Ack reaction was assumed to be

expressed as follows [14]:

++

++

=

ATPmADPmACmACPm

eqACPmADPm

Ack

Ack

K

ATP

K

ADP

K

AC

K

ACP

K

ATPACADPACP

KKv

v

,,,,

,,

max

][][1

][][1

]][[]][[

1

(2i)

2.2.9. ICDH

In E.coli, NADPH is formed in ICDH reaction, and

the activity is inhibited by NADPH. The following

equation was considered [16] in the present study:

1

][

2,

,

][]][2][[]][[

A

ICDHK

COKGNADPHNADPICIK

K

k

v

ICDH

eq

NADPd

ICIm

f

ICDH

=

(2j)

where

2

2

2

22

2

2

2

2

22

2

,

2

,,

,,,,

,,

,,,

,2

,

2

,

,,

,

,,,,

,,

,

2

,,,

,,

,,,

,

,,,,,,

,

1

][][][

][][]][[][][

][][][][][

][][]][[][][1

COdKGmNADPHenhe

NADPeknCOdNADPHenheKGm

COekeNADPHm

COdNADPHenheKGm

NADPHm

COdNADPHenhe

COdNADPHenhe

COm

KGmCOdNADPHenheKGm

COekeNADPHm

COdCOdNADPHenheKGm

COmKGeknh

NADPHemhNADPdICIm

NADPm

ICIdNADPdICImNADPdNADPdICIm

NADPm

K

CO

K

KG

K

NADPH

K

NADPH

KKK

KKKG

KKK

KCOKG

K

CO

K

NADPH

KK

KNADPH

K

KG

KKK

KKKG

K

CO

KKK

KKNADPH

KKK

KNADPH

K

ICI

KK

NADPICI

K

NADP

KK

KICIA

+

+++

++++

++++=

2.2.10. Fermentative pathway

The following equation was used for LDH reaction

[14]:

++

++

=

NADmNADHmLACmPYRm

eqNADHmPYRm

LDH

LDH

KNAD

NADH

KNADK

LAC

K

PYR

K

LAC

NAD

NADHPYR

KKV

v

,,,,

,,

max

1

][

][1

][

1][][1

][

][

][][

1

(2k)

whereLDHv iscreases as NADH/NAD increases. Fig.2d

shows the effect of NADH/NAD onLDHv with respect

to [PYR], whereLDHv increases as NADH/NAD

increases.

Fig.2d Effect of NADH/NAD on LDHv

The equations for ethanol formation from AcCoA

was expressed as [14]

++++

++

=

CoAmAcAldmAcAldmCoAmAcCoAmNADHmNADm

eqNADHmAcCoAm

AALDH

AALDH

KK

CoAAcAld

K

AcAld

K

CoA

K

AcCoA

NAD

NADH

KKNAD

K

AcAldCoA

NAD

NADHAcCoA

KKV

v

,,,,,,,

,,

max

]][[][][][1

][

][11

][

1

]][[

][

][][

1

(2l)

and

++

++

=

ETHmAcAldmNADHmNADm

eqNADHmAcAldm

ADH

ADH

K

ETH

K

AcAld

NAD

NADH

KKNAD

K

ETH

NAD

NADHAcAld

KKV

v

,,,,

,,

max

][][1

][

][11

][

1

][

][

][][

1

(2m)

where those increase as NADH/NAD increases. Fig.2eshows the effect of NADH/NAD on

ADHv with respect

to [AcAld], whereADHv increases as NADH/NAD

increases.

Fig.2e Effect of NADH/NAD on ADHv

2.2.11. PP pathway

For G6PDH and PGDH in the PP pathway, the

following equations [7] were employed:

( )

+

+

++

=

][][

1][

1]6[

]][6[

,,6

,6

6,,6

6,6

max

66

NADPK

NADPHK

K

NADPHKPG

NADPPGVv

NADPHinhNADPHPDHG

NADPPDHG

PinhGNADPHPDHG

PGPDHG

PDHGPDHG

(2n)

and

( )

+

+++

=

ATPinhPGDHNADPHinhPGDH

NADPPGDHPGPGDH

PGDHPGDH

K

ATP

K

NADPHKNADPKPG

NADPPGVv

,,

,6,

max

][1

][1][]6[

]][6[

(2o)

2.2.12. Other rate equationsOther rate equations for Ald, Pgk, CS, 2KGDH,

SDH, Fum, MDH were also considered but not shown

here due to space limitation.

2.3. Effect of oxygen level on the metabolism

It is quite important to grasp the relationship

between oxygen level and the metabolism, since the

oxygen level affects both cell growth and the specific

metabolite production. For example, the following

218218


5/8

strategy is often employed in practice: Initially aerobic

condition was employed to enhance the cell growth,

and then changed to micro-aerobic or anaerobic

condition for the efficient metabolite production. It is,

therefore, desired to simulate the effect of oxygen level

on the metabolism. Escherichia coli possesses the

specific sensing/regulation systems for the rapidresponse to the availability of oxygen and the presence

of other electron acceptors [17-22]. The adaptive

responses are coordinated by a group of global

regulators, which includes two-component ArcA

(anoxic redox control) system and one-component Fnr

(fumarate, nitrate reduction). It has been known that

although the concentration of Fnr protein is similar in

both aerobic and anaerobic conditions [18, 23], it

becomes active only in the anaerobic growth condition.

On the other hand, ArcA/B system works at micro-

aerobic condition. The cytoplasmic ArcA regulator

with its cognate sensor kinase ArcB regulates such

genes that encode several dehydrogenases of theflavoprotein, terminal oxidases, TCA cycle enzymes,

glyoxylate enzymes etc. in response to deprivation of

oxygen [24-26].

Under micro-aerobic or anaerobic condition, PYR is

the important branch point, where LDH, PDHc, and Pfl

compete for it. As the oxygen level decreases, the

redox ratio NADH/NAD increases, and it affects the

flux through LDH and PDH by enzyme level

regulation. Since PDHc is repressed whereas Pfl is

activated by both ArcA and Fnr as the oxygen level

decreases, the effect of oxygen level on these fluxes

may be expresses by the relationship as given in Fig.3a,

where it indicates gene level regulation [27].

0 10 20 30 40

0

2

4

6

8

10

12

[m

m

olg-

1h-

1]

% of aerobiosis

PFL flux

PD H flux

Fig.3a Effect of oxygen level on PDH and Pfl fluxes

(symbols are the experimental data)

The effect of oxygen level on arcA and fnr gene

expressions may be obtained as given in Fig.3b [28].

The effects of ArcA and Fnr on the metabolic pathway

genes such asgltA, acnA,B, icdA, sucABCD, sdhCDAB,

fumA,C, mdh, cyo, cydetc. may be obtained (data not

shown). Those relationships were reflected to modulate

maxv in the reaction rate equations.

0 2 4 6 8 10

100

150

200

250

300

350

0

50

100

150

200

250

300

arcA

expression

relative

to

10

%

O

2

% of aerobiosis

fnrexpression

relative

to

10

%

O

2

Fig.3b Effect of oxygen level on arcA and fnrgene

ecpressions

In order to simulate the effect of oxygen level on

the TCA cycle activation, it is critical to model the

respiratory chain reactions. It may be able to calculate

the distributions of the respiratory flux for the

cytochrome bd and bo terminal oxidases. The kinetic

parameters for Cyd is as follows: Km=0.024 MO2,

vm=42 mol of O2.nmol of Cyd-1.h-1, while those of

Cyo is as follows: Km=0.2 MO2, vm=66 mol of

O2.nmol of Cyo-1.h-1 [29]. Then the flux of electrons to

oxygen (qO2) may be estimated as given in Fig.4 [24],

where qO2 decreases as the oxygen level decreases, and

the amount of NADH utilized for ATP production

reduces. Thus NADH/NAD ratio tends to increase as

the oxygen level decreases, which in turn forces the

fermentative pathways to be activated.

0 20 40 60 80 100

0

1

2

3

4

5

6

qO

2

[m

m

olg-

1h-

1]

% of aerobiosis

Fig.4 Effect of oxygen level on qO2

3. Result

Figure 5 shows part of the simulation result for the

batch culture ofE.coli, where the parameter values

used for the simulation is listed in Table 1. The kinetic

parameter values were employed from the literature as

given in Table 1 exceptmax

v , where denotes the

enzyme name.

max

v was estimated from the flux dataand the measured intracellular metabolite concentration

in the chemostat culture [7,30-33].

219219


6/8

Table 1 Model Parameters

Enzyme Kinetic parameter valuesOriginalsource

Cell

growth1

max 25.0

= h , mMKs 0.1=

PTShgDCWmolmv

PTS./739.25max = mMK aPTS 11, =

mMK aPTS 01.02, = 13, =aPTSK

46, =PGPTSn

mMK PGPTS 5.06, =

[7]

G6PDH

hgDCWmolmv PDHG ./979.0max

6 =

mMK PGPDHG 07.06,6 =

mMK NADPPDHG 015.0,6 =

mMK NADPHinhNADPHPDHG 01.0,,6 =

mMK PinhGNADPHPDHG 18.06,,6 =

[7]

PGDHhgDCWmolmvPGDH ./81.1

max=

mMK PGPGDH 1.06, = mMK NADPPGDH 028.0, = mMK NADPHinhPGDH 01.0, =

mMK ATPinhPGDH 3, = [7]

PfkhgDCWmolmv

Pfk./936.26max =

mMK sPFPfk 14.0,6, = mMK sATPPfk 16.0,, =

mMK aADPPfk 239,, = mMK bADPPfk 25.0,, =

mMK cADPPfk 36.0,, =

mMK aAMPPfk 74.8,, =

mMKbAMPPfk

01.0,, =

mMKPEPPfk

25.0, =

4000000=Pfk

L 4=Pfkn

[7]

AldhgDCWmolmvAld ./461.64

max=

mMK FDPAld 133.0, = mMK DHAPAld 088.0, =

mMK GAPAld 088.0, = mMK GAPinhAld 6.0, =

2, =blfAldV mMK eqAld 1.0, =

[7]

GAPDH

hgDCWmolmvGAPDH ./582.10max

=

mMK GAPGAPDH 15.0, = mMK PGPGAPDH 1.0, =

mMK NADGAPDH 45.0, = mMK NADHGAPDH 02.0, =

63.0, =eqGAPDHK

[7]

Pgk

hgDCWmolmvPgk ./84.158max

= 1800, =eqPgkK

mMK PGPPgk 006.0, = mMK PGPgk 17.03, =

mMK ADPPgk 18.0, = mMK ATPPgk 24.0, =

[7]

EnohgDCWmolmvEno ./439.12

max=

4, =eqEnoK

mMK PGEno 1.02, = mMK PEPEno 135.0, =

[7]

Pyk

hgDCWmolmvPyk ./085.1max

= 1000=PykL

mMK PEPPyk 31.0, = mMK ADPPyk 26.0, =

mMK ATPPyk 5.22, = mMK FDPPyk 19.0, =

mMKAMPPyk

2.0, =

4=Pykn

[7]

PDHhgDCWmolmvPDH ./

max= mMK PYRm 1, =

mMK NADm 4.0, = mMK CoAm 014.0, =

mMK AcCoAm 008.0, = mMK

NADHm1.0, =

mMKi 4.46=

[14]

LDH

hgDCWmolmvLDH ./762.7max

= 7.21120=eqK

mMK NADHm 08.0, = mMK PYRm 5.1, = mMK NADm 4.2, =

mMK LACm 100, =

[14]

Pta

hgDCWmolmvPta ./665.45max

= 0281.0=eqK

mMK AcCoAi 2.0, =

mMK Pm 6.2, =

mMK Pi 6.2, =

mMK AcPm 7.0, = mMK AcPi 2.0, =

mMK CoAi 029.0, = mMK CoAm 12.0, =

[14]

AckhgDCWmolmvAck ./36.875

max=

mMK AcPm 16.0, = mMK ADPm 5.0, =

[14]

mMK ACm 7, = mMK ATPm 07.0, =

2.174=eqK

ALDH

hgDCWmolmvALDH ./69001.0max

=

mMK AcCoAm 007.0, = mMK NADHm 025.0, =

mMK NADm 08.0, = mMK CoAm 008.0, =

mMK AcAldm 10, = 1=eqK

[14]

ADHhgDCWmolmvADH ./928.12

max=

mMK AcAldm 03.0, = mMK NADHm 05.0, =

mMK NADm 08.0, = mMK ETHm 1, = 9.12354=eqK

[14]

CShgDCWmolmvCS ./0675.1

max=

mMK AcCoACS 01.0, = mMK OAACS 007.0, =

mMK CoAi 11.0, =

[33]

ICDH

mMKeq 1000=1min4830 =fk

mMKiCiT

m0059.0= mMK

NADP

d0013.0=

mMKNADPm

0227.0= mMKNADPH

d12.0=

mMKiCITd 03.0= mMK

KG

m038.02 =

mMKiCiTm

0059.0= mMKKG

eknh5.52 =

mMKCO

d6.12 = mMK

CO

eke6.12 =

mMKNADPekn

00016.0= mMKNADPH

m0036.0=

mMKNADPH

enhe 028.0=

[16]

2KGDH

hgDCWmolmv KGDH ./3677.2max

2 = 5.1=KZ

mMK KGKGDH 00.12,2 = mMK CoAKGDH 002.0,2 =

mMK NADKGDH 07.0,2 = mMK KGi 75.02, =

mMK SUCi 0.1, = mMK NADHi 018.0, =

[33]

SDHhgDCWmolmVSDH ./5622.1

max

1 =

hgDCWmolmVSDH ./max

2 =

mMK SUCSDH 10.0, = 0.10, =eqSDHK

[33]

FumhgDCWmolmVFum ./98636.0

max

1 =

hgDCWmolmVFum ./max

2 =

mMK FUMFum 10.0, = 0.10, =eqFumK

[33]

MDH

hgDCWmolmVMDH ./444.62max

1 =

hgDCWmolmVMDH ./max

2 =

mMK NADMDH 10.0, = mMK MALMDH 33.1, = mMK NADHMDH 04.0, =

mMK OAAMDH 27.0, =

mMK NADi 31.0, = mMK MALi 30.3, =

mMK NADHi 04.0, = mMK OAAi 27.0, =

31.0, =lAiK 17.0, =lQiK

0.1, =eqMDHK

[33]

Ppc

hgDCWmolmvPpc ./max

=mMK

PEP

m3231.0=

03176.01 =k mMk 2878.12 =

mMk 05425.03= mMk 8139.0

4=

mMk 0939.05= mMk 2693.0

6=

[11]

Fig.5 shows that cells grow exponentially in

response to the glucose consumption, and how the

intracellular metabolite concentrations change. Fig.5indicates that [PEP] is low throughout batch culture

due to its utilization in PTS. Moreover, all the

intracellular metabolite concentrations were on the

order of 0.1~2.5, which are quite reasonable from the

view point of experimental data. Although the

changing alters of intracellular metabolite

concentration in the glycolysis are reasonable, those in

220220


7/8

the TCA cycle may be somewhat different from the

real behavior. This has to be refined in the near future.

Fig.5 Simulation result for the batch culture

4. Discussion

Although semi-quantitative models were considered

using some experimental data, the developed model

could simulate how the decrease in oxygen level

affects the fermentation patterns in view of

NADH/NAD ratio. Moreover, the overall ATP

produced can be also computed and this can be used to

estimate the cell growth rate by taking into account the

biosynthetic equation as well. The present modeling

approach is new and can be used in practice for

performance improvement and the design of cell

metabolism.

5. Conclusion

It was shown that the kinetic models considered in

the present research can be used for the simulation of

the batch culture of both aerobic and anaerobic

conditions.

6. References

[1] M. Rizzi, M. Baltes, U. Theobald, M. Reuss, In vivoanalysis of metabolic dynamic in Saccharomyces cerevisiae:II. Mathematical model, Biotechnol. Bioeng. 55, pp.592-

608, 1997.

[2] U. Theobald, W. Mailinger, M. Baltes, M. Rizzi, M.Reuss, In vivo analysis of metabolic dynamic inSaccharomyces cerevisiae: I. Experimental observations,Biotechnol. Bioeng. pp.305-316, 1997.

[3] S. Vaseghi, A. Baumeister, M. Rizzi, M. Reuss, In vivodynamics of the pentose phosphate pathway inSaccharomyces cerevisiae, Metabolic Eng. 1, pp.128-140,1999.

[4] S. Buziol, I. Bashir, A. Baumeister, W. Claassen, M.

Rizzi, W. Mailinger, M. Reuss, A new bioreactor coupledrapid stopped-flow sampling technique for measurement oftransient metabolites in time windows of milliseconds, InProceeding of the Fourth International Congress on

Biochemical Engineering. Stuggart: Fraunhofer IRB, pp.79-83, 2000.

[5] S. Buziol, I. Bashir, A. Baumeister, W. Claassen, N.Noisommit-Rizzi, W. Mailinger, M. Reuss, A newbioreactor coupled rapid stopped-flow sampling techmique

for measurement of metabolite dynamics on a subsecondtime scale, Biotechnol. Bioeng. 80, pp.632-636, 2001.

[6] U. Theobald, W. Mailinger, M.Reuss, M. Rizzi, In vivoanalysis of glucose induced fast changes in yeast adeninenucleotide pool applying a rapid sampling technique, Anal.

Biochem. 214, pp.31-37, 1993.

[7] C. Chassagnole, N. Noisommit-Rizzi, J. W. Schmid, K.Mauch, M. Reuss, Dynamic modeling of the central carbonmetabolism of Eschrichia coli, Biotechnol. Bioeng. 79,

pp.53-73, 2002.

[8] P. Karp, M. Riley, S. Paley, A. Pellegrini-Toole, M.Krummenacker, EcoCyc: Electronic encyclopedia ofE-coli

genes and metabolism, Nucl. Acids Res. pp.27-55, 1999.

[9] D. Kotlarz, H. Garreau, H. Buc, Regulation of theamount and of the activity of phosphofructokinase and

pyruvate kinase in Escherichia coli , Biochem. Biophys.

Acta. pp.257-268, 1975.

[10] K. Izui, M. Taguchi, M. Morioka, H. Katsuki,

Regulation of Escherichia coli phosphoenolpyruvate

221221


8/8

carboxylase by multiple effectors in vivo. Kinetic studieswith a reaction system containing physiologicalconcentrations of ligands, J. Biochem. 90, pp.1321-1331,

1981.

[11] B. Lee, J. Yen, L. Yang, J. C. Liao, Incorporatingqualitative knowledge in enzyme kinetic models using fuzzy

logic, Biotechnol. Bioeng. 62, pp.722-729, 1999.

[12] A. Krebs, W. A. Bridger, The kinetic properties ofphosphoenolpyruvate calboxykinase ofEscherichia coli , J.Biochem. 58, pp.309-318, 1980.

[13] C. Yang, Q. Hua, T. Baba, H. Mori, K. Shimizu,Analysis ofEscherichia coli anaplerotic metabolism and its

regulation mechanisms from the metabolic responses toaltered dilution rates and phosphoenolpyruvatecalboxykinase knockout, Biotechnol. Bioeng. 84, pp.129-144, 2003.

[14] M. N. Hoefnagel, M. J. C. Starrenburg, D. E. Martens, J.Hugenholtz, M. Kleerebezem, I. V. Swam, R. Bongers, H. V.

Westerhoff, J. L. Snoep, Metabolic engineering of lacticacid bacteria, the combined approach: kinetic modeling,metabolic control and experimental analysis, Microbiology.148, pp.1003-1013, 2002.

[15] J. Henkin, R. H. Abales, Evidence against an acyl-enzyme intermediate in the reaction catalyzed by clostridial

phosphotransacetylase, Biochemistry. 15, pp.3475-3479,1976.

[16] E. A. Mogilevskaya, G. V. Lebedeva, I. I. Goryanin,O.V. Demin, Kinetic model of functioning and regulation of

Escherichia coli isocitrate dehydrogenase, Biophysics, 52,pp.30-39, 2007.

[17] J. R. Guest, J. Green, A. S. Irvine, S. Spiro, The FNRmodulon and FNR-regulated gene expression, Chapman andHall, New York, pp.317-342, 1996.

[18] R. P. Gunsalus, Control of electron flow inEscherichiacoli: coordinated transcription of respiratory pathway genes,J. Bacteriol. 174, pp.7069-7074, 1992.

[19] E. C. C. Lin, S. Iuchi, Regulation of gene expression infermentative and respiratory systems inEscherichia coli andrelated bacteria, Annu. Rev.Genet. 25, pp.361-387, 1991.

[20] A. S. Lynch, E. C. C. Lin, Transcriptional controlmediated by the ArcA two-component response regulator

protein ofEscherichia coli: characterization of DNA bindingat target promoters, J. Bacteriol. 178, pp.6238-6249, 1996.

[21] S. J. Park, C. P. Tseng, R. P. Gunsalus, Regulation of

succinate dehydrogenase (sdhCDAB) operon expression inEscherichia coli in response to carbon supply andanaerobiosis: role of ArcA and Fnr, Mol. Microbiol. 15,

pp.473-482, 1995.

[22] G. Unden, S. Becker, J. Bongaerts, J. Holighaus, J.Schirawski, S. Six, O2-sensing and O2-dependent generegulation in facultatively anaerobic bacteria, Arch.

Microbiol. 164, pp.81-90, 1995.

[23] S. Becker, U. Holighaus, T. Gabrielczyk, G. Unden, O2as the regulatory signal for FNR-dependent gene regulation

inEscherichia coli , J. Bacteriol. 178, pp.4515-4521, 1996.

[24] S. Alexeeva, K. J. Hellingwerf, M. J. T.Mattos, Requirement of ArcA for redox regulation in

Escherichia coli under microaerobic but not anaerobic or

aerobic conditions, J. Bacteriol. 185, pp.204-209, 2003.

[25] B. J. Bachmann, Linkage map ofEscherichia coli K-

12, Microbiol. 47, pp.180-230, 1983.

[26] R. S. Buxton, L. S. Drury, Cloning and insertionalinactivation of the dye (sfrA) gene, mutation of which affectssex factor F expression and dye sensitivity ofEscherichia

coli K-12, J. Bacteriol. 154, pp.1309-1314, 1983.

[27] S. Alexeeva, B. Kort, G. Sawers, K. J. Hellingwerf, M. J.T. Mattos, Effects of limited aeration and of the ArcABsystem on intermediary pyruvate catabolism in Escherichiacoli , J. Bacteriol. 182, pp.4934-4940, 2000.

[28] S. Shalel-Levanon, K. San, G. N. Bennett, Effect ofArcA and FNR on the expression of genes related to theoxygen regulation and the glycolysis pathway in Escherichiacoli under microaerobic growth conditions, Biotechnol.Bioeng. 92, pp.147-159, 2005.

[29] C. W. Rice, W. P. Hempfling, Oxygen-limitedcontinuous culture and respiratory energy conservation in

Escherichia coli , J. Bacteriol. 134, pp.115-124, 1978.

[30] N. Ishii et al, Multiple high-throughput analysesmonitor the response ofE.coli to perturbations, Science. 316,

pp.593-597, 2007.

[31] J. Zhu, K. Shimizu, Effect of a single-gene knockout

on the metabolic regulation in Escherichia coli for D-lactateproduction under microaerobic condition, Metabolic Eng. 7,

pp.104-115, 2005.

[32] S. J. Berrios-Rivera, G. N. Bennett, K. San, The effectof increasing NADH availability on the redistribution ofmetabolic fluxes in Escherichia coli chemostat cultures,

Metabolic Eng. 4, pp.230-237, 2002.

[33] B. E. Wright, M. H. Butler, K. R. Albe, Systemsanalysis of the Tricarboxylic acid cycle in Dictyosteliumdiscoideum, J. Biochem. 267, pp.3101-3105, 1992.

222222

semi-quantitative modeling for the effect of oxygen level.pdf

Documents