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國 立 交 通 大 學

生 物 資 訊 研 究 所

碩 士 論 文

大腸桿菌在無氧環境下利用甘油生產酒精

的模擬與分析

Modeling and Analysis of Glycerol Anaerobic

Utilization by Escherichia coli

研 究 生:張恆毅

指導教授:黃憲達 博士

(2)

大腸桿菌在無氧環境下利用甘油生產酒精的模擬與分析

Modeling and Analysis of Glycerol Anaerobic Utilization by

Escherichia coli

研 究 生:張恆毅 Student:Heng-Yi Chang

指導教授:黃憲達 Advisor:Hsien-Da Huang

國 立 交 通 大 學

生物資訊研究所

碩 士 論 文

A Thesis

Submitted to Institute of Bioinformatics Science College of Biological Science and Technology

National Chiao Tung University in partial Fulfillment of the Requirements

for the Degree of Master

In

Bioinformatics Science

June 2009

Hsinchu, Taiwan, Republic of China

(3)

大腸桿菌在無氧環境下利用甘油生產酒精的模擬與分析

學生: 張恆毅 指導教授 : 黃憲達 教授 國立交通大學生物資訊研究所碩士班

中文摘要

世界能源危機的意識,使得利用微生物生產生質燃料如生質酒精、生質柴油 等,已被廣泛的研究。雖然過去的研究主要探討以微生物分解纖維素的議題,纖維素降 解程序仍然困難且繁鎖。相對地,甘油的化學結構簡單且能夠直接利用,而生質柴油生 產的過程會產生大量的甘油。因此甘油成為生產生質燃料的理想材料。也因此,甘油厭 氧利用的機制對於有效生成生質燃料與生物質有一定的重要性。 數學模擬應用於生物系統已有顯著的進展,這些模擬系統包含決定代謝反應的流 量、預測基因調節作用以及對於細胞行為的解讀。雙相(two-phase)研究運用基礎流量模 式(Elementary Flux Modes, EFMs)與非線性程式(nonlinear programming)分析並模擬大腸 桿菌內甘油代謝之厭氧路徑。我們的分析能夠解釋並提供細菌於甘油厭氧代謝時,其生 長問題的解決之道。此外,結合酵素動力準則與基礎流量模式能夠預測流量分布與代謝 濃度,甚至作為基因剔除之參考。 這些資訊有助於代謝工程在基因層次之修飾並藉以 提高目標物產量。

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Modeling and Analysis of Glycerol Anaerobic

Utilization by Escherichia coli

Student: Heng-Yi Chang Advisor: Hsien-Da Huang,

Institute of Bioinformatics, National Chiao Tung University

Abstract

Using microbes as the machine to produce biofuel such as bioethanol and biodiesel have

been widely investigated due to global energy crisis. While considerable attention has been

paid in the past on issues related to decompose the cellulose by microbes, the procedure of

cellulose degradation remains heavy and complicate. In contrast, the chemical structure of

glycerol is simpler and can be used directly. Thus glycerol became an ideal substrate for

biofuel generation because a mass of glycerol produced from biodiesel factory. Therefore,

mechanism of glycerol anaerobic utilization is important for efficiently biofuel synthesis and

biomass growth. Mathematical modeling for biology systems have progressed tremendously,

including determination of metabolic fluxes, prediction of gene regulations, and interpretation

of cell behaviors. A two-phase study was designed to utilizing elementary flux modes (EFMs)

and nonlinear programming for analysis and modeling glycerol metabolic anaerobic pathway

in Escherichia coli. Our analysis explains and provides solution for the growth problem of

bacteria during glycerol anaerobic metabolism. Besides, the model combining enzyme kinetic

principle and elementary flux modes (EFMs) could predict the flux distribution and

concentration of metabolites even gene deletion, which helps metabolic engineering to modify

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致謝

首先要感謝我的指導教授黃憲達老師,在我碩士班時,對於研究的啟蒙

以及技術的指導,更在平常的相處中學到的不少做人處事的道理,也在我

怠惰懶散時給了我很大的動力完成學業最後的口試以及論文,另外也很感

謝隔壁應用微生物與生物工程實驗室的曾慶平老師以及實驗室的學生,在

我缺乏生物上的知識以及見解時,給了我很多的意見和指教。

當然也要感覺實驗室的學長姐,不僅是在一開始帶領著我踏上研究的軌

道,也在遇到困難時在旁幫助,並且督促著我的研究進度,而與整個實驗

室的同仁們的相處也非常融洽,興趣也十分相投,包括棒球,籃球,出去

玩,吃東西等等,給了我碩士班生活很多的樂趣。

最後,要感謝家人的支持,因為住在家裡,所以許多大小事都麻煩家人,

卻又常常不回家,或是夜晚騎車回家,都帶給了家人一些擔心及關心,而

如期完成了碩士的學業,也是因為家人讓我無後顧之憂的專心在學校的研

究上,而完成碩士班的學業,都是因為大家的幫助,才有今天的我,謝謝

大家。

張恆毅 于 交通大學 2009

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Table of contents

中文摘要 ...i

Abstract ...ii

致謝 ...iii

Table of contents ...iv

List of Figures ...vi

List of Tables ...ix

Chapter 1 Introduction ... 1

1.1 Biological background... 1

1.1.1 World energy crisis ... 1

1.1.2 Glycerol for biofuels generation... 3

1.1.3 Microbes utilize glycerol ... 5

1.2 Motivation ... 6

1.3 Research goals ... 7

1.3.1 Mechanism of glycerol anaerobic utilizing in Escherichia coli ... 8

1.3.2 Computational prediction of glycerol anaerobic utilization ... 8

1.3.3 Verification of simulation derived from constructed model... 9

Chapter 2 Pathway investigation of glycerol anaerobic utilization by Escherichia coli 10 2.1 Introduction ... 10

2.1.1 Glycerol related reaction in Escherichia coli... 10

2.1.2 Elementary flux modes... 11

2.1.3 Different bacterium glycerol utilize pathway ... 13

2.1.4 Large- scale metabolic network... 14

2.2 Related work... 15

2.3 Motivation and the Specific aim... 16

2.4 Materials and methods... 16

2.5 Results ... 17

2.5.1 Numbers of elementary flux modes ... 18

2.5.2 Relationship between yields of biomass and ethanol ... 20

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Chapter 3 Modeling and simulation of glycerol anaerobic utilization behavior in

Escherichia coli ... 26

3.1 Introduction ... 26

3.1.1 Modeling for metabolic engineering ... 26

3.1.2 Simulation of biological systems... 27

3.2 Related work... 27

3.2.1 Flux balance analysis (FBA) ... 27

3.2.2 Enzyme kinetic ... 28

3.3 Motivation and the Specific aim... 28

3.4 Materials and methods... 28

3.4.1 Experimental data source ... 29

3.4.2 Method of hybrid model ... 29

3.5 Results ... 32

3.6 Summery... 36

Chapter 4 Model verification and validation ... 37

4.1 Introduction ... 37

4.1.1 Parameter sensitivity analysis... 37

4.1.2 Correlation of flux and parameters... 37

4.2 Results ... 38

4.2.1 Parameters analysis and correlation coefficient between EFMs ... 38

4.2.2 Case study... 51

4.3 Summery... 53

Chapter 5 Discussions... 54

5.1 Glycerol anaerobic utilization ... 54

5.2 Elementary flux mode ... 54

5.3 Modeling... 54

5.4 Compound influence cell growth and metabolite distributions... 55

5.5 Future work ... 55

Chapter 6 Conclusion ... 56

Reference ... 57

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List of Figures

Figure 1.1 World primary energy demand in the reference scenario. (International Energy

Agency, 2007)... 2

Figure 1.2 Assumed ratio of natural gas and implied relation of coal prices to oil prices to oil prices in the reference scenario. ... 2

Figure 1.3 Ratio of renewable energy from different sources. ... 2

Figure 1.4 Biodiesel production and its byproduct glycerol. ... 3

Figure 1.5 US biodiesel production and its impact on crude glycerol prices [2] ... 4

Figure 1.6 Comparison of ethanol production from corn-derived sugars[2]... 4

Figure 1.7 systems flow of Modeling and Analysis of Glycerol Anaerobic Utilization by Escherichia coli ... 7

Figure 2.1 Subset of glycerol anaerobic utilization pathway in Escherichia coli... 11

Figure 2.2 Simple example of a biochemical network of elementary flux modes (O.Palsson ,systems biology :properties of reconstructed networks)... 13

Figure 2.3 Subset of glycerol fermentation pathway in Klebsiella pneumoniae. Reactions differ from Escherichia coli with red frame. ... 14

Figure 2.4 Metabolic map of E. coli central metabolic network. [13] ... 15

Figure 2.5 Yields of biomass and ethanol (A) Modes of glycerol anaerobic utilization in medium plus fumarate which relate only glycerol (B) Modes of glycerol anaerobic utilization in medium plus fumarate which relate fumarate and glycerol (C) Modes of glycerol fermentation in medium plus tryptone which relate only glycerol (D) Modes of glycerol fermentation in medium plus tryptone which relate glycerol and tryptone (E) Modes of glycerol fermentation in recombinant E.coli... 20

Figure 2.6 The mode of most high yields of ethanol in glycerol anaerobic utilization in medium plus fumarate. ... 21

Figure 2.7 The mode of most high yields of biomass in glycerol anaerobic utilization in medium plus fumarate. ... 22

Figure 2.8 The mode of average yields in glycerol anaerobic utilization in medium plus fumarate. ... 22

Figure 2.9 The mode of which most high yields of ethanol is in glycerol fermentation express foreign genes. ... 23

Figure 2.10 The mode of which most high yields of biomass is in glycerol fermentation express foreign genes. ... 23

Figure 2.11 The mode of which most high yields of ethanol is in glycerol fermentation in medium plus tryptone. ... 24 Figure 2.12 The mode of which most high yields of biomass is in glycerol fermentation in

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medium plus tryptone. ... 24

Figure 3.1 Proceed of hybrid model simulated reactions rates... 30

Figure 3.2 Schema of parameters identification... 31

Figure 3.3 Anaerobic utizilation of glycerol by E. coli supplemented with fumarate... 32

Figure 3.4 Contrast of experimental data in anaerobic utilization of glycerol by E. coli supplemented with fumarate (dark blue diamond) and simulation data (pick square) (A) formate (B) lactate (C)succinate(D)glycerol(E)fumarate consume(F)acetate(G)ethanol ... 33

Figure 3.5 Fermentation of glycerol by E. coli supplemented with tryptone... 34

Figure 3.6 Contrast of experimental data in fermentation of glycerol by E. coli supplemented with tryptone (dark blue diamond) and simulation data (pick square) (A) glycerol consume (B) ethanol (C) succinate (D) acetate. ... 34

Figure 3.7 Fermentation of glycerol by E. coli expressed foreign gene dhaB from Klebsiella pneumoniae... 35

Figure 3.8 Contrast of experimental data in fermentation of glycerol by E. coli expressed foreign gene dhaB from Klebsiella pneumoniae (dark blue diamond) and simulation data (pick square) (A) glyceorl (B) 1,3-PDO (C) succinate (D) formate (E) ethanol (F) acetate (G) lactate. ... 35

Figure 4.1 Coefficient of parameters and metabolites concentration: glycerol fermentation plus tryptone (A) tryptone (B) Ethanol (C) Succinate (D) Glycerol (E) NH3 (F) Formate (G) Biomass (H) Lactate (I) CO2... 40

Figure 4.2 Parameters distribution : glycerol fermentation plus tryptone ... 41

Figure 4.3 EFMs Correlation coefficient: glycerol fermentation plus tryptone. ... 41

Figure 4.4 The mode No.81 in glycerol fermentation in medium plus tryptone... 44

Figure 4.5 The mode No.18 in glycerol fermentation in medium plus tryptone. ... 44

Figure 4.6 The mode No.100 in glycerol fermentation in medium plus tryptone... 45

Figure 4.7 The mode No.220 in glycerol fermentation in medium plus tryptone... 45

Figure 4.8 Coefficient of parameters and metabolites concentration: glycerol fermentation plus furmarate ... 46

Figure 4.9 Parameters distribution: glycerol anaerobic utilization plus fumarate... 47

Figure 4.10 EFMs Correlation coefficient: glycerol anaerobic utilization plus fumarate... 47

Figure 4.11 The mode No.320 in glycerol fermentation in medium plus fumarate ... 48

Figure 4.12 Coefficient of parameters and metabolites concentration: glycerol fermentation plus furmarate ... 49

Figure 4.13 Parameters distribution: glycerol fermentation express foreign gene... 50

Figure 4.14 EFMs Correlation coefficient: glycerol fermentation express foreign gene. ... 50

Figure 4.15 The mode No236 in glycerol fermentation expressed foreign gene dhaB... 51

Figure 4.16 Main fermentative pathways involved in the anaerobic fermentation of glycerol in E. coli [33] ... 52

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Figure 4.17 Left is performance of strains gay bar represent FHL knock and white bar represent not. Center is Cell growth (close)and glycerol utilization(open), triangle represent FHL knock and square represent not [33]. Right is biomass simulation of FHL deletion :pink represent FHL knock ,dark blue represent not. ... 53

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List of Tables

Table 1.1 Capability of glycerol fermentation and distribution of glyDH and 1,3PD-DH in

enterbacterial species... 5

Table 1.2 Glycerol utilization pathway reactions. ... 6

Table 1.3 Microbial pathogenicity and applications which can ferment glycerol... 6

Table 2.1 Enzymes related glycerol utilization in Escherichia coli ... 11

Table 2.2 Coordination of glycerol anaerobic utilized literatures. ... 16

Table 2.3 Example of METATOOL input file‘s reactions. ... 17

Table 2.4 Pathway data about glycerol anaerobic utilization . ... 17

Table 2.5 Numbers of elementary flux modes in different carbon source and conditions. .... 19

Table 2.6 Overall reaction of glycerol fermentation... 19

Table 2.7 Numbers of elementary flux modes in different strategy for E.coli no growth problem... 19

Table 3.1 Experimental data source... 29

Table 4.1 Reaction frequency of EFMs for glycerol fermentation plus tryptone: 33~133... 39

Table 4.2 Reaction frequency of EFMs for glycerol fermentation plus tryptone: 1~32... 42

Table 4.3 Reaction frequency of EFMs for glycerol fermentation plus tryptone: 33~133... 43

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Chapter 1 Introduction

1.1 Biological background

1.1.1 World energy crisis

When we concern about the problem in our life, we’ll find that the most important source

will be exhausted and unable to regenerate in a few years. Because the resources are versatile,

it is used as primary energy source.

World energy dependence is mainly depends on limited resource such as coal, oil or

natural gas. With the economic progression, the energy demands are increasing in developed

country and under-development country. According to the report from International Energy

Agency in 2007, the demands are drastically increasing in recent ten years and will keep

surging in the following ten to twenty years, see Figure1.1 (World Energy Outlook, 2007).

Owing to mass demands and the finite resource, the supply of energy falls short of demands.

Figure 1.2 shows the different fuel prices divided by oil prices in relation to the time scale,

which implied that oil price is increasing with time in every way (World Energy Outlook,

2007). It is evident that shortage of this limited natural resource results in energy crisis in the

world. Fortunately, there are renewable energy generated from nuclear, hydro and biomass.

Figure 1.3 shows the renewable energy constitutes about 80% of bio-energy, which was

energy derived from biomass (World Energy Outlook, 2003). Thus the bio-energy may

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Figure 1.1 World primary energy demand in the reference scenario. (International Energy Agency, 2007)

Figure 1.2 Assumed ratio of natural gas and implied relation of coal prices to oil prices to oil prices in the reference scenario.

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1.1.2 Glycerol for biofuels generation

Biofuels like biodiesel and bioethanol become a biological solution for generating

renewable energy, which convert animal or vegetable oil to useful chemical compound

biodiesel. The chemical structure and the procedure of biodiesel synthesis are shown at Figure

1.4. During the biodiesel production, byproduct glycerol also produced. The glycerol

produced from biodiesel production became competitive compared with those generated from

general glycerol factory.

Glycerol is commonly called glycerine or glycerin which was used as materials for

flexible foams, serves as humectants, and as a thickening agent in liqueurs. Since 2004, the

price of glycerol was cut down dramatically for biodiesel expand vigorously that shown in

Figure 1.5. Overproduction of glycerol changed the strategy of glycerol factory such as P&G,

Uniqema, Dow Chemical and Cognis. Therefore, glycerol was developed for additional role

like sources of hydrogen gas [1] or convert to ethanol [2] for saving the energy crisis.

Previous study showed a lot of research works have been done in application of cellulose

as carbon source to biofuels. But only a few recent efforts have focus on glycerol as microbial

carbon source. Compare with cellulose, glycerol economizes is not only the work of

degradation into small molecular but also cost of operation that shown in Figure 1.6. [3]

Because of its availability, low prices, and high degree of reduction[2], glycerol become

a good resource from biodiesel waste. The biofuels second generation aims to improve the

efficiency of renewable energy production.

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Figure 1.5 US biodiesel production and its impact on crude glycerol prices [2]

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1.1.3 Microbes utilize glycerol

The microbes which using glycerol as carbon source in anaerobic condition have some

characteristics in gene coding enzymes that utilizing glycerol[4]. That showed the capability

of glycerol fermentation are related with 1,3-propanediol dehydrogenase and glycerol

dehydratase. But the pathway of glycerol utilize not only use there two reaction that shown in

Table 1.1, but also have two path that convert glycerol to glycolysis intermediates for growth

biomass and produce fermentation product that shown in Table1.2.they can convert glycerol

to 1,3-propanediol, but the yield of 1,3-propanediol from glycerol is not 100%.becuase of

NADH and NAD concentration spend affected the reactions are reduction or oxidation .

Therefore, glycerol passed through different reactions to achieve chemical and redox potential

balance.

Contrast of their pathogenicity and application shown in Table 1.3, Klebsiella

pneumoniae, Clostridium butyricum, Citrobacter freundii and Enterobacter gergoviae possess intense pathogenicity, Lactobacillus reuteri is better for producing the antibiotic. Because of

them, the safely and more feasible for gene modify microbe, Escherichia coli, that can

ferment glycerol in special condition is suitable to be a biofuels synthesizer and recombinant

host.

Table 1.1 Capability of glycerol fermentation and distribution of glyDH and 1,3PD-DH in enterbacterial species.

Glycerol fermentation 1,3-PD dehydrogenase Glycerol dehydratase Citrobacter braakii

Citrobacter farmeri Citrobacter freundii Citrobacter werlamanii

YES YES YES

Enterobacter gergoviae YES YES YES

Klebsiella pneumoniae YES YES YES

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Table 1.2 Glycerol utilization pathway reactions.

Glycerol utilization pathway reactions Aerobic Anaerobic(have

electron acceptor)

Fermentation

glycerol→sn-glycerol-3-p→DHAP→glycolytic intermediates

YES YES NO

glycerol→DHA→DHAP→glycolytic intermediates NO NO YES

glycerol→3-HPA→DHAP→,3-propanediol YES YES YES

Table 1.3 Microbial pathogenicity and applications which can ferment glycerol.

Species Pathogenicity Applications

Klebsiella pneumoniae Pulmonary disease, enteric pathogenicity, nasal mucosa atrophy, and rhinoscleroma

Lactose fermenting, facultative anaerobic

Clostridium butyricum Botulism, tetanus and gas gangrene Toxic chemicals and detergents

Lactobacillus reuteri Anti-microbial agent

Citrobacter freundii In clinical specimens as an opportunistic or secondary pathogen

Ability to convert tryptophan to indole, ferment lactose, and utilize malonate

Enterobacter gergoviae Nosocomial (hospital-acquired) urinary tract infections

1.2 Motivation

In the past, considerable attentions have been paid on issues related to decompose the

cellulose by microbes. However, the procedure of cellulose degradation is complex and

inefficient. Since biodiesel became more and more popular, the major byproduct during

biodiesel production, glycerol, also produced with a large amount. Unlike cellulose, the

structure of glycerol is more ordinary and can be used directly. Therefore glycerol came out to

be an ideal substrate to generate biofuels.

There are many studies on glycerol fermentation in Escherichia coli, previous study

described that glycerol was not fermented in the absent of external electron acceptor. However,

Dharmadi [3]proposeda framework for glycerol fermentation by Escherichia coli which showed using tryptone could affect cell growth, yet tryptone is not electron acceptor and the

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mechanism of its effectiveness remains unknown.

Recently, the metabolic engineering began to involve with metabolic pathways and gene

networks to optimize the yield of metabolites required. However, efforts in experiments to

find the beneficial gene for production are too heavy and complicated to execute. Therefore,

we need the mathematical method, especially modeling, to facilitate the metabolic

engineering implementation. Constructing models using the experimental data combined with

chemical and physical knowledge could simulate the behavior of cell and even economize on

complicated experiments by reasonable gene selection. Besides, studies on gene expression

and enzyme activity dominating metabolites synthesis usually focus on only one enzyme or

metabolites, which may overlook the complexity within a cell. Systematic analysis has

gathered great importance in recent years. Integrating all its aspects into glycerol anaerobic

utilization by Escherichia coli could verify the results more correctly.

Figure 1.7 systems flow of Modeling and Analysis of Glycerol Anaerobic Utilization by Escherichia coli

1.3 Research goals

The purpose of this study was to investigate the mechanism of glycerol anaerobic

utilizing in Escherichia coli, computational anticipation of glycerol anaerobic utilization, and

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1.3.1 Mechanism of glycerol anaerobic utilizing in Escherichia coli

The specific research question in this study addressed concerns on why Escherichia coli

couldn’t immediately ferment glycerol in anaerobic condition and how to solve the problem

with different strategies such as replenish tryptone, fumarate, or foreign gene transformation.

The methods in previous projects for different objective exists some disadvantages when

producing ethanol. Besides, the purpose of those experiments is not for ethanol production.

However, the strategies have been proved by many literatures that they actually work in

Escherichia coli.

Elementary flux modes (EFM) analysis was used to count the possible way of metabolic

systems in the metabolic analysis of central carbon. The EFM analysis obeyed the

physiological rule, such as the law of conservation of mass. Using elementary flux modes

(EFM) analysis can indicate the different condition of possible routes from the external

carbon source to the end product. Compared with high yield modes, low yield modes can

clearly illustrate the relation between metabolic flux distribution and products yield.

1.3.2 Computational prediction of glycerol anaerobic utilization

The next part of the analysis used hybrid model to extend elementary flux modes

usability and can be differ from previous study about elementary flux modes. Previous studies

calculate elementary flux modes to represent the whole systems reaction flux distribution, in

which each mode will multiply one independent parameter. This did not express metabolic

systems characteristics such as the fluctuation of time scale dependant metabolites

concentration. The hybrid model methods not only contain the time dependant parameters but

also reveal enzyme kinetic based knowledge like Michaelis–Menten kinetics [5].

The parameters have to fit experimental data to construct the computational model that

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compared with general data are similar, it can be told that parameters fitted correctly and

reflected the real experiment.

1.3.3 Verification of simulation derived from constructed model

The model accuracy is of importance when used to predict cell behavior in real system.

The process of verifying the model makes it reliable with biologist. When models are used to

evaluate strategies in experiments, the results of evaluation is usually made to a fundamental

model representing a cellular system, from which systems could be modified and work.

Sensitivity of parameters quantified the correlation between parameters and model’s

variables. The significance of parameters affecting whole systems can be found. Besides, the

parameters distribution also implied the tendency of model system. For example, the specific

reaction became momentous role when condition changed. The analysis of parameters

accompanied with the evidence of gene modification experiments together demonstrate the

anaerobic condition of Escherichia coli system utilizing glycerol is an authentic way when

predicting the work of Escherichia coli behaviors.

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Chapter 2 Pathway investigation of glycerol

anaerobic utilization by Escherichia coli

2.1 Introduction

2.1.1 Glycerol related reaction in Escherichia coli

Using glycerol for generating biofuels is a new strategy differs from cellulose as carbon

source in Escherichia coli last three years. The major variation of these two carbon source is

the reactions of convert substrate to glycolytic intermediate. Glycerol was through glycerol

kinase or glycerol dehydrogenase in different conditions. When the environment presents

electron acceptor, glycerol converted to sn-glycerol -3-phosphate. After then, sn-glycerol

-3-phosphate transferred to dihydroxyacetone phosphate by glycerol-3-phosphate

dehydrogenase, which only express in anaerobic condition shown in Table 2.1.

Previous study showed glycerol fermentation can not take place in Escherichia coli.

Escherichia coli grow under anaerobic conditions in a mixture of glycerol together with nitrate or fumarate. However, recent research [3] showed that Escherichia coli undergo

glycerol fermentation when tryptone added and they prove that tryptone is not electron

acceptor by NMR spectra. Yet if tryptone is absent, Escherichia coli can not grow in this

condition. According to these studies, we proposed that the tryptone is taken as a cell’s

biomass growing source, from which some redox compounds was provided to push metabolic

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Table 2.1 Enzymes related glycerol utilization in Escherichia coli Condition Glycerol kinase Glycerol dehydrogenase Glycerol-3-phosphate dehydrogenase(GlpABC) Glycerol-3-phosphate dehydrogenase(GlpD)

Aerobic YES NO NO YES

Anaerobic(have electron acceptor ) YES NO YES NO Anaerobic(no electron acceptor ) YES YES NO NO

Figure 2.1 Subset of glycerol anaerobic utilization pathway in Escherichia coli.

2.1.2 Elementary flux modes

Because of detailed investigation of genome and enzyme in Escherichia coli, the

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and survival[6]. When intracellular substrates and enzymes presented under suitable condition,

the enzyme catalyzed reaction is not restricted by simple decisions. Few routes in metabolic

pathway couldn’t represent the whole metabolic pathway. Leiser and Blum [7] proposed the

“fundamental modes ”can be decomposed to a linear structure as a model of elementary flux

modes. In a biochemical reaction systems distinguish between border reactions and internal

reactions. Border reactions and internal reactions can be distinguished in a biochemical

reaction system such as glucose that be feed on E.coli, or ethanol flow from E.coli. A

chemical reaction possess two direct that called the reversible reaction because of enzyme

capability, free energy of reactions, and push form the environment. If the reaction is

reversible, the numbers of path that elementary mode analyses calculated will be increase.

The principle of elementary flux mode is finding the immediate path from substrate to end

product, and the numbers of elementary flux mode represent all of possible cell behavior in

metabolic pathway. Which elementary flux mode related to different end product in metabolic

pathway such as biomass, ethanol, acetate and lactate, is commentated by biological

knowledge.

The route from external metabolite go through the direct reactions to the end product

shown in Figure 2.1, and every elementary flux modes that is not cyclic have at least one

input and one output flux, which allowed multiple compounds in one reaction. The possible,

complex pathways in a cell were thought to indicate cell flexibility and robustness to adapt

with optima fitness to the environmental conditions by integrating the use of preferable

pathways. One of the aims for elementary flux modes was to assign anabolic and catabolic

costs to make benefits in different environments[8]. Another aim was to reduce the intricate

metabolism to a simple linear path with different properties[9].

Besides, there are various extensions of the elementary flux modes such as

thermodynamics rules[9], optimal conversion yields[10] and simulation by multiplying an

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Reaction Network

EM 1 EM 2

EM 3 It’s not EM

Need to define

the reaction reversibility, and metabolite position in or out of cell

: External metabolite : internal metabolite

Figure 2.2 Simple example of a biochemical network of elementary flux modes (O.Palsson ,systems biology :properties of reconstructed networks).

2.1.3 Different bacterium glycerol utilize pathway

The reactions of microbes shown in Table 1.1 compare to Escherichia coli are something

different. Figure 2.3 and Figure 2.4 show major reactions of glycerol utilization in

Escherichia coli and Klebsiella pneumoniae. The reactions in red frame are crucial role for glycerol fermentation, which involves two enzymes as glycerol dehydratase and

1,3-propanediol dehydrogenase. Glycerol dehydratase convert glycerol to

3-hydroxypropionaldehyde and liberate water as electron acceptor that could make up for the

lack of electron acceptor in Escherichia col. By genetic engineering, these two foreign genes

imported from Klebsiella pneumoniae to Escherichia coli could make the latter one ferment

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ISBLab - Integrative Systems Biology Laboratory

Glycerol 3-HPA 1,3-PDO

Dihydroxyactone Biomass Dihydroxyactonephosphate ATP ADP PEP Pyruvate Acetyl-CoA Acetaldehyde Acetyl-P Acetoin 2,3-Butanediol Formate H2 CO2

Acetic acid Ethanol

Lactic acid CoA Succinic acid H2O NADH2NAD+ NAD+ NADH2 NAD+ NADH2 NAD+ NADH2 NAD+ NADH2 2NAD+ 2NADH2 Pyruvate 2CO2 NADH2 NAD+ NADH2 NAD+ CoA Pi NAD+ NADH2 H2 CO2 CO2 NAD+ NADH2 ATP ADP ATP ADP ATP ADP ADP ATP NADH2 NAD+ p

Figure 2.3 Subset of glycerol fermentation pathway in Klebsiella pneumoniae. Reactions differ from Escherichia coli with red frame.

2.1.4 Large- scale metabolic network

In microbes, the arrangement of cell is intricate and complicated. Although the key

section could explain specific movement, their large-scale structure remains unknown[12].

Trinh’s[13] E. coli central metabolic network shown in Figure 2.4, which includes

glycolysis, gluconeogenesis, pentose phosphate pathway, tricarboxylic acid cycle,

fermentative acid pathway, anapleurotic pathway, entner-doudoroff pathway, degradation

pathways of pentoses and hexoses, oxidative phosphorylation, maintenance energy,

membrane transport, and biomass synthesis. About 70 reactions that can describe major

(26)

Figure 2.4 Metabolic map of E. coli central metabolic network. [13]

2.2 Related work

Early research developed process shown in Table 2.2. At first, researchers proposed that

E.coli can not ferment glycerol as external electron acceptor to grow unless fumarate of nitrate was used as an exogenous hydrogen acceptor[4].

Later, other species such as K. pneumoniae, C. butyricum and C. freundii expand

glycerol fermentation to 1,3-propanediol, and the major products are 1,3-propanediol and

ethanol. Besides, researchers studied on how to improve the yields of 1,3-propanediol. They

also found that K. pneumoniae couldn’t produce 1,3-propanediol only, because of the balance

between biomass growth and reduction potential.

(27)

pneumoniae to wild-type Escherichia coli. They successfully construct a recombinant E.coli by importing dha regulon, and found that the growth is not luxuriant. Later, researchers

cloned dhaB from Citrobacter freundii and used it to improve E.coli growth[15].

Last three years, Dharmadi used a medium containing high concentration of yeast

extracts and tryptone, on which E.coli can grow with glycerol under anaerobic condition [3].

Table 2.2 Coordination of glycerol anaerobic utilized literatures.

Condition Description Ref.

No growth Requires electron acceptors [4]

Plus fumarate Fumarate, as an exogenous hydrogen acceptor. [4]

Plus tryptone Using a medium containing high concentrations of yeast extract and tryptone.

[3]

Other species Ability to grow fermentatively on glycerol without an exogenous hydrogen acceptor

[16, 17]

Foreign gene express in E.coli

Their purpose for clone dha regulon genes to E.coli producing 1,3-propanediol

[14, 15, 18]

Plus glucose Glucose will be uptake first and become major carbon source

2.3 Motivation and the Specific aim

With previous study on glycerol anaerobic utilization in Escherichia coli, we use

elementary flux modes analysis to explain why Escherichia coli can not grow in glycerol

under anaerobic condition. And then we calculate the possible yields in each mode using

different strategy for Escherichia coli glycerol anaerobic utilization.

2.4 Materials and methods

That calculated all EFMs using METATOOL 5.0, Matlab-based software package for fast

and flexible elementary modes analysis. [19]

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metabolic network we concerned like Table 2.3. The second is reversibility of enzymes of

reactions, express which reaction can react in reverse directly. And the final part is position of

metabolite, which described which metabolite was used as end product and initial substrate.

To construct three METATOOL file for calculate elementary flux mode, there are glycerol

fermentation with tryptone added medium, glycerol anaerobic utilization with fumarate added

medium, and glycerol fermentation in E.coli which expressed foreign gene dhaB. The

knowledge of reactions and enzymes was shown in Table 2.4.

Table 2.3 Example of METATOOL input file‘s reactions.

No. Reaction

GG1 GLC_external + PEP = G6P + PYR GG2r G6P = F6P

GG3 F6P + ATP = F16BP + ADP

Table 2.4 Pathway data about glycerol anaerobic utilization .

Data description Ref.

Metabolic map of E. coli central metabolic network [13]

Glycerol degradation pathway [3, 6]

1,3-propanediol production pathway [14, 15]

.

2.5 Results

In this section, explanations of cell growth condition are investigated by elementary flux

modes analysis. The ideality yields of each condition are discussed for high yields mode and

low yields mode. Finally, the selected mode with both high biomass and high ethanol yields

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2.5.1 Numbers of elementary flux modes

Verifying to previous study find that E.coli can not directly grow in anaerobic condition

that absence external electron acceptor. Compare to other carbon source, numbers of EFMs

shown in Table 2.5.the numbers of Glucose is more than the others, obviously E.coli had

place importance on digest glucose. See the glycerol part , the numbers of EFMs is very few

and the EFMs related biomass is zero ,that show E.coli can not grow in this condition , it

correspond to previous study.

This analysis used EFMs in glycerol fermentation in E.coli is directly explain that only

glycerol as carbon source would not be utilized to generate biomass. Compare to E.coli,

Klebsiella pneumoniae only add two reactions, but its numbers of EFMs are 1762.

The biological significant of each carbon source in anaerobic condition is present in the

numbers of EFMs, which E.coli feed on glucose contain 5010 EFMs more than feed on other

carbon source ,because of preferable import channel such as phosphoenolpyruvate

phosphotransferase system provide more efficiently and more important with carbon source.

Because of the coenzyme NADH and NAD+ are key role of some reactions that include

in biomass growing , if NADH had not generate from reactions ,the biomass reactions can not

obtain the require compound, that didn’t grow biomass at all.

The different strategies of glycerol anaerobic utilization have a common ground about

electrons transformation, first is tryptone provide biomass growing factor: NADH generated

to push glycerol dehydrogenase activate, second is fumarate convert to succinate and accept

(30)

Table 2.5 Numbers of elementary flux modes in different carbon source and conditions. Xylose or

Arabinose Glucose Mannose Galactose Glycerol

Glycerol in K.pneumoniae Anaerobic EFMs 1004 5010 2841 1620 18 1762 ETOH 964 4913 2745 1580 18 406 Biomass 443 4157 2134 1297 0 1357 ETOH and Biomass 415 4080 2064 1269 0 326 Ethanol yield 0~0.51 0~0.51 0~0.51 0~0.51 0.25~0.5 0~0.5 Biomass yield 0~0.19 0~0.31 0~0.31 0~0.21 0 0~0.3

Reference Trinh et al. 2008 Trinh et al. 2008 Trinh et al. 2008 Trinh et al.

2008 This study This study

Expect the biomass reactions part, the EFMs’s overall reaction descript that glycerol

fermentation is inclined to produce ethanol shown in Table 2.6.

The preliminary elementary flux modes for three part of glycerol utilization in E.coli

presented in Table 2.7, that depicted the three condition for E.coli are more likely to produce

ethanol or grow more biomass such as glycerol + tryptone the ratio of EFMs of

biomass/anaerobic are very high, that obviously said grow in glycerol + tryptone exuberant.

Table 2.6 Overall reaction of glycerol fermentation.

EFMs ratio Overall reaction

6/18 GLYCEROL_ext = H2_ext + ETOH_ext + CO2_ext

6/18 2 GLYCEROL_ext = H2_ext + ETOH_ext + SUCC_ext

6/18 GLYCEROL_ext = ETOH_ext + FOR_ext

Table 2.7 Numbers of elementary flux modes in different strategy for E.coli no growth problem

Glycerol + tryptone Glycerol + fumarate Glycerol +1,3 PDO pathway

Anaerobic EFMs 442 1952 1762

Ethanol 114 940 406

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2.5.2 Relationship between yields of biomass and ethanol

That detail concern the yields of each modes, we can see Figure 2.5 (B), that three of

blots descript the best ethanol produce mode, best biomass grow mode, and blank mode to

compare to others. The modes include what reaction shown in Figure 2.6 ~ Figure 2.8, those

reactions different in obviously in Figure 2.6 and Figure 2.7 are Entner-Doudoroff pathway,

and different in Figure 2.8 are respiration (anaerobic) pathway and produce acetate acid. It

shows a relationship of biomass and Entner-Doudoroff pathway.

0 0.2 0.4 0.6 0.8 1 1.2 0 0.2 0.4 0.6 0.8 1

Biomass mmol / Carbon source mmol

E tha no l m m ol / Ca rbo n s o ur c e mm o l 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.00E+00 5.00E-06 1.00E-05 1.50E-05 2.00E-05 Biomass mmol / Carbon source mmol

E tha no l m m ol / Ca rbo n s o ur c e mm o l 0 0.2 0.4 0.6 0.8 1 1.2

0.00E+00 1.00E-05 2.00E-05 3.00E-05 4.00E-05 5.00E-05 Biomass mmol / Carbon source mmol

E tha nol m m ol / Ca rbon s o ur c e mm o l 0 1 2 3 4 5 6 0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 Biomass mmol / Carbon source mmol

E tha nol m m ol / Ca rbon s o ur c e mm o l (A) (B) (C) (D) 0 0.2 0.4 0.6 0.8 1 1.2 0.00E+0 0

2.00E-06 4.00E-06 6.00E-06 8.00E-06 1.00E-05 1.20E-05 1.40E-05 1.60E-05

Biomass mmol / Carbon source mmol

E tha nol m m ol / C ar bon s our c e mmo l (E)

Figure 2.5 Yields of biomass and ethanol (A) Modes of glycerol anaerobic utilization in medium plus fumarate which relate only glycerol (B) Modes of glycerol anaerobic utilization in medium plus fumarate which relate fumarate and glycerol (C) Modes of glycerol fermentation in medium plus tryptone which relate only glycerol (D) Modes of glycerol fermentation in medium plus tryptone which relate glycerol and tryptone (E) Modes of glycerol fermentation in recombinant E.coli.

(32)

Compare the others condition, the modes of most high ethanol yields and most biomass

growing are similar to above conditions. Correspond to our purpose, that Entner-Doudoroff

pathway is related with biomass growing.

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Figure 2.7 The mode of most high yields of biomass in glycerol anaerobic utilization in medium plus fumarate.

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Figure 2.9 The mode of which most high yields of ethanol is in glycerol fermentation express foreign genes.

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Figure 2.11 The mode of which most high yields of ethanol is in glycerol fermentation in medium plus tryptone.

(36)

2.6 Summery

The yields of product are important for factory to produce a large amount, investigating

possible yields use elementary flux mode that provide valuable information.

Above all, the analysis indicated the reason about E.coli glycerol fermentation absence

electron acceptor problem, no any biomass growing mode in elementary flux mode analysis,

so we can correspond to previous study, and them which reason about biomass no growth may

be some redox factor like NADH is scanty, so we find the solution strategy from previous

research that consist three part, first is cultivating E.coli in medium plus electron acceptor like

fumarate , second is cultivating E.coli in medium plus tryptone for biomass growing , third is

cultivating E.coli express foreign gene dhaB from Klebsiella pneumoniae.

The analysis of elementary flux mode about the glycerol pathway shown the mold of

high yields pathway, and we show the pathway that is most high yields, descript the possible

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Chapter 3 Modeling and simulation of glycerol

anaerobic utilization behavior in Escherichia coli

3.1 Introduction

3.1.1 Modeling for metabolic engineering

Metabolic engineering consist of two parts. One is the development of strategies for

control pathways in microbes, and the other use actual biotechnological experiments to

complete such strategies [20]. In other words, there are theories and execution involve in

metabolic engineering. This study is critically important in considerable decision for

implementation of efficient experiments.

Besides, metabolic engineering has a large amount experiment for change expression

level of gene, or the different condition for specific enzyme activity. Prediction not only

implies the result of experiments, but also explains the biological significant for complex

biochemical experiments.

The relationship between substrates in a chemical reaction can be summarized

quantitatively by stoichiometry [21]. When breaking metabolic network down into a

stoichiometric matrix, the rows and columns in the matrix represent participated chemicals

and reactions themselves, respectively. To infer the possibilities from the metabolic network,

recent study work on two approaches, that is extreme pathways and elementary mode analysis

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3.1.2 Simulation of biological systems

The simulations of biological systems contain three aspects such as gene regulatory

network, metabolic pathway, and signal transduction pathway. Three parts represent

intracellular behavior fundamental elements that are gene, protein, and metabolite.

Large-scale simulations regenerate gene expression and how many genes are regulated, genes

possessed translation to protein that will bind to other protein or react with chemical

compounds, called protein-protein interaction and metabolic pathway. But the transition of

each fundamental element is difficult problem for scaling the heterogeneous data and

parameters. Therefore, the research focus on one part of aspect ignored other part’s influence.

The usage of simulation are confirming the corresponding of mathematical model with a

set of experimental data, predicting the behavior that experiments didn’t prove , and the

biological significant of cell behaviors[23].

3.2 Related work

3.2.1 Flux balance analysis (FBA)

Flux balance analysis is a different way to simulate the metabolic network using linear

programming. There’s only single solution resulted from flux balance analysis, which differs

from elementary mode analysis and extreme pathways. Because linear programming is

usually used to get the maximum potential from the objective function investigated, single

solution became ideal for the optimization problem when using flux balance analysis [24].

When approaching flux balance analysis, only metabolites entering or leaving particular

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fluxes along with the enzymes ranging from negative to positive value.

3.2.2 Enzyme kinetic

Enzyme kinetic is research of relation of enzyme and substrate. When substrate bond to

enzyme, the protein structure of enzyme were changed and the activity of enzyme responded

binding affinity.

The Michaelis–Menten equation relates the initial reaction rate v0 to the substrate

concentration. The corresponding graph is a hyperbolic function; the maximum rate is

symbolized as Vmax.

The number of reactions per second catalyzed per mole of the enzyme was defined as

reaction rate and symbolized as V. According to Michaelis–Menten equation, the reaction rate

increases when substrate concentration increasing and the maximum rate may approach to

Vmax.

3.3 Motivation and the Specific aim

Simple elementary flux modes is topological analysis of metabolic network, it doesn’t

realize the cell behavior such as time dependant metabolite concentration. And the simulation

of metabolite concentration is vital to the biologist because of cell dynamic change can tell us

much valuable information. So we expand the elementary flux modes using hybrid method

which Kim[25]develop, correctly simulate time series data similar to experiments.

3.4 Materials and methods

There are result of elementary flux mode analysis, and experimental data from literatures,

using the hybrid model that combined EFMs and enzyme kinetic base parameters of

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3.4.1 Experimental data source

Experimental data were collected from literature, shown in Table3.1, include Glycerol

fermentation in medium add tryptone, express foreign gene dhaB from Klebsiella pneumoniae,

and cultivate in medium which contain fumarate.

Table 3.1 Experimental data source.

3.4.2 Method of hybrid model

Kim and his group [25] used the elementary flux mode decomposition to express the

reaction rate vector by

Z is the matrix represents all of elementary flux modes. For example, when we have 4

reactions that contain 8 elementary flux modes, Z is a 4 X 8 matrix. then rM is each EFMs

regulated uptake rate vector, that represent each of EFMs multiply regulated uptake rate

vector will get each reactions rate depend times. And metabolite concentration can be

calculated by each reaction rate.

rM defined in Figure 3.1,that show rM is similar to enzyme kinetic model:

Michaelis–Menten kinetics [5].

Data description Reference

Glycerol fermentation add tryptone [26]

Recombinant E.coli which can produce 1,3 PDO [27]

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Ki is the saturation constant,

e

i is the enzyme level for elementary flux mode, and kmax is

maximum uptake rate of elementary flux mode. Detailed explain shown in Figure 3.1, first we

got the EFMs like matrix contain amount of EFMs and the reactions in this network, second

we generated transposed matrix and use initial parameters for calculate the regulated flux

vector rM, third carried matrix multiplication out .finally we can get the reaction rate in

procession .Reaction rate provide how fast of substrate transform to product, that were

influenced by temperature, pH value, cofactor, inhibitor and other environment variables. The

end product concentration can be calculated by reactions rate of each reactions. For example,

the reaction rate V0 that dependant times, and the product B initial concentration x. when next

time step B concentration is x +V0.

1 2 3 = 1 2 3 1 2 3 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 = > 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 2 3 4 5 6 EFM1 EFM2 EFM3

rm: the regulated uptake rate vector

1 2 3

4

5 6

r: the reaction rate vector

T

EFM3 EFM2 EFM1

(42)

Experiment data

Simulation data

Compare the residual

between simulation

and experiment data

if

residual >desirable value

Yes

NO

Revise parameters

model

Parameters successfully

identify

Figure 3.2 Schema of parameters identification.

But this result of simulation is worse because of parameters didn’t match with

experimental data. Therefore, we have to train the parameters of model shown in Figure 3.2,

because of the parameters involve in the kinetic base, that need the solver for nonlinear least

square problem, using Tomlab ,matlab package software that is powerful optimization

platform and modeling language for solving applied optimization problems in Matlab.

The training flow need a threshold residual for confirm the parameters quality, the

residual represent the distance different with simulation and experimental data. If residual

value bigger than threshold value, parameters will alter for decrease residual. When

parameters smaller than threshold value, that we can called the parameters successfully

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3.5 Results

The results show experimental data in different conditions that contain of metabolite

concentration disputant times, which include formate, succinate, glycerol, fumarate, biomass,

lactate, and ethanol. Figure 3.3 ,Figure3.5 and Figure3.7 illustrate the experimental data from

literature that rough descript the yields of each metabolite .and them Figure 3.4 ,Figure3.6 and

Figure3.8 depicts the comparisons of metabolite experimental data and simulation data from

our model generated, which the variation of predict data and real data was small when the

metabolite concentration is not too small to calculate, and see the Figure 3.4 (B), the variation

seem very large , but the real variation compare with others is very small.

In this study, the model construction fit to experimental data was successful to simulate

the quality data.

lactate lactate formate formate succinate succinate glycerol glycerol fumarate fumarate ethanol ethanol biomass biomass mM /g cell dr y w e ight Time (m) 0 50 100 150 200 250 300 350 400 450 500 0 20 40 60 80 100 120 140

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0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0 0.5 1 1.5 2 2.5 0 50 100 150 200 250 300 350 400 450 500 0 0.5 1 1.5 2 2.5 0 50 100 150 200 250 300 0 0.5 1 1.5 2 2.5 0 50 100 150 200 250 300 0 0.5 1 1.5 2 2.5 0 50 100 150 200 250 300 350 400 0 0.5 1 1.5 2 2.5 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 5.6 5.8 6 6.2 6.4 6.6 6.8 0 0.5 1 1.5 2 2.5 (A) (D) (B) (C) (E) (F) (G)

Figure 3.4 Contrast of experimental data in anaerobic utilization of glycerol by E. coli supplemented with fumarate (dark blue diamond) and simulation data (pick square) (A) formate (B) lactate

(C)succinate(D)glycerol(E)fumarate consume(F)acetate(G)ethanol

In Figure 3.3, formate and succinate are major end product, and the concentrations of

glycerol decrease parallel with fumarate. Moreover, fumarate respiration net reactions contain

H2 + Fumarate --, Succinate and HCO2- + Fumarate + H + ~ CO2 + Succinate, that two

reactions end product agreement with experimental data [31].

The simulation shown in Figure 3.4, the direct comparisons experimental data

perturbation more than simulation because of the simulation prefer the linear values than large

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0 5 10 15 20 25 0 20 40 60 80 100 120 glycerol glycerol ethanol ethanol succinate succinate acetate acetate M /g cell dr y w e ight Time (h)

Figure 3.5 Fermentation of glycerol by E. coli supplemented with tryptone

0 50000 100000 150000 200000 250000 300000 350000 0 20 40 60 80 100 120 0 50000 100000 150000 200000 250000 300000 350000 0 20 40 60 80 100 120 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 0 20 40 60 80 100 120 0 1000 2000 3000 4000 5000 6000 7000 8000 0 20 40 60 80 100 120 (A) (C) (D) (B)

Figure 3.6 Contrast of experimental data in fermentation of glycerol by E. coli supplemented with tryptone (dark blue diamond) and simulation data (pick square) (A) glycerol consume (B) ethanol (C) succinate (D) acetate.

(46)

0 1 2 3 4 5 6 7 8 9 10 0 5 10 15 20 25 30 acetate ethanol lactate succinate formate 1,3 -PDO mM /g ce ll dr y w e igh t Time (h)

Figure 3.7 Fermentation of glycerol by E. coli expressed foreign gene dhaB from Klebsiella pneumoniae.

0 20 40 60 80 100 120 0 10 20 30 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 10 20 30 0 1 2 3 4 5 6 7 0 10 20 30 0 0.5 1 1.5 2 2.5 3 3.5 0 10 20 30 0 0.5 1 1.5 2 2.5 3 3.5 0 10 20 30 0 1 2 3 4 5 6 7 8 9 10 0 10 20 30 0 1 2 3 4 5 6 7 8 9 0 10 20 30 (A) (B) (C) (D) (E) (F) (G)

Figure 3.8 Contrast of experimental data in fermentation of glycerol by E. coli expressed foreign gene dhaB from

Klebsiella pneumoniae (dark blue diamond) and simulation data (pick square) (A) glyceorl (B) 1,3-PDO (C) succinate (D) formate (E) ethanol (F) acetate (G) lactate.

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3.6 Summery

This section extends above part of elementary flux mode, and we construct the dynamic

model. This model contains the previous study method called hybrid method combine the

elementary flux mode and enzyme kinetic base equation. Let the model work, we have to

identify parameters in kinetic equation. Therefore the experimental data for glycerol

anaerobic utilization in different condition was used to test the parameters can successfully

push the model to simulate data that similar to experimental data.

The results of simulation are very similar to experimental data, the model we construct

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Chapter 4 Model verification and validation

4.1 Introduction

4.1.1 Parameter sensitivity analysis

The study about how to assign the uncertainty in the output of a mathematical model to

different sources of variation in the input of a mathematical model either qualitatively or

quantitatively is called sensitivity analysis (SA).[32]

Generally, when studies include some form of mathematical modeling, uncertainty and

sensitivity analyses was usually used to check the robustness of a study. Uncertainty analysis

studies the overall uncertainty in the conclusions of the studies, while sensitivity analysis

identifies which source of uncertainty weights more in the conclusions. Several guidelines for

impact assessment or for modeling have used sensitivity analysis as a tool to make sure the

reliability of the modeling or assessment. [32]

4.1.2 Correlation of flux and parameters

The correlation between two homogenous or heterogenous data indicated the

perturbation of one part, the effect affect to others. This information can tell us the intensity of

factory we concern, for example, hair style and gender are related; long hair people tend to be

girl than short hair people. But the relation is not 100 percentages.

Correlation applies for quantifiable data that numbers contain significant, usually

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4.2 Results

In this section, we demonstrate the verification of model’s parameters and provide one

case study to promote creditability of glycerol fermentation model. It can be seen that each

parameters how much of strength influence the metabolites concentration. Because of values

disproportion, parameters distributions incline to distinguish into confusion part and

limitation part. More specifically, the similarity of EFMs affect the strength is worth while to

discussion.

4.2.1 Parameters analysis and correlation coefficient between EFMs

The parameters have a primary role in mathematical model and greatly influence how the

cell behavior be simulated.

About the control effect of parameters, Figure 4.1 illustrate the strange of parameters can

be separated to a subset that has high coefficient, although the parameters didn’t have high

coefficient for every metabolite, tend to prefer high coefficient. Because of the trend, select

one of mode that correspond high coefficient parameter’s shown in Figure 4.4.Compare with

Figure 2.11 and Figure 2.12, the reactions are a lot of different such as produce acetate and

succinate ,and no ethanol produce. Studies should be undertaken to determine the frequency

of each reactions operating shown in Table 4.1.the high frequency reactions such as F16BP =

F6P, GL6P = 6PG, 6PG + NADP = R5P + CO2 + NADPH, and glycolysis pathway are more

consistent than the fermentative pathway , that explain the major trunk pathway and branch

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Table 4.1 Reaction frequency of EFMs for glycerol fermentation plus tryptone: 33~133

GG1 GG3 GG4 GG11 GG12 GG13 PPP2 PPP3 TCA1 TCA2r FR1

0 0 1 0.87 0 0.48 1 1 0.95 0.95 0.58

FR2 FR3 ANA1 ANA2 ANA3 FEM1 FEM2 FEM7 FEM8 FEM3 FEM5

0.63 0.63 1 0.19 0 0.49 0.19 0.25 0.25 0.13 0.12

FEM6 FEM4 FEM9 EDP1 EDP2 XYL1 XYL2 GAL1 MAN1 MAN2 ARA1

0.25 0.49 0.13 0 0 0 0 0 0 0 0

BIO OPM4r FC2 TRA1 TRA2 TRA3 TRA4 TRA5 TRA6 TRA7 GLB1

0.95 0.51 0 0.25 0.44 0.95 0.13 0.69 0 0.55 0.24

GLB2 TRA8 TRA9 TRA10 GLYD1 GLYD2 GLYD3 GLYD4 OPM3 TRYP GG2r

0.24 0 0 0 1 0 1 1 0 1 1

GG5r GG6r GG7r GG8r GG9r GG10r PPP1 PPP4r PPP5r PPP6r PPP7r

1 1 1 1 1 1 1 0.69 1 0.68 0.68

PPP8r TCA3r TCA4 FC1r

0.68 0.95 0.95 1

Moreover, the reaction rate is equal to parameters multiply elementary flux mode, the

parameter value is an important characteristic of reaction rate. Figure 4.2 depict the

parameters value express in logarithm and normal bar chart. It alteration of parameters in low

coefficient part is small compare with high coefficient part in logarithm bar chart, and the

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0.00E+00 1.00E-02 2.00E-02 3.00E-02 4.00E-02 5.00E-02 6.00E-02 7.00E-02 8.00E-02 9.00E-02 1 23 45 67 89 111 133 155 177 199 221 243 265 287 309 331 353 375 397 419 441 0 200 400 600 800 1000 1 22 43 64 85 106 127 148 169 190 211 232 253 274 295 316 337 358 379 400 421 442 0 50 100 150 200 250 300 350 400 1 22 43 64 85 106 127 148 169 190 211 232 253 274 295 316 337 358 379 400 421 442 0 20 40 60 80 100 120 1 22 43 64 85 106 127 148 169 190 211 232 253 274 295 316 337 358 379 400 421 442 0.00E+00 1.00E-02 2.00E-02 3.00E-02 4.00E-02 5.00E-02 6.00E-02 7.00E-02 8.00E-02 1 23 45 67 89 111 133 155 177 199 221 243 265 287 309 331 353 375 397 419 441 0 50 100 150 200 250 300 350 1 22 43 64 85 106 127 148 169 190 211 232 253 274 295 316 337 358 379 400 421 442 0 100 200 300 400 500 600 1 22 43 64 85 106 127 148 169 190 211 232 253 274 295 316 337 358 379 400 421 442 0 0.2 0.4 0.6 0.8 1 1 22 43 64 85 106 127 148 169 190 211 232 253 274 295 316 337 358 379 400 421 442 0 100 200 300 400 500 600 700 1 22 43 64 85 106 127 148 169 190 211 232 253 274 295 316 337 358 379 400 421 442 (A) (B) (C) (E) (D) (F) (G) (H) (I)

Figure 4.1 Coefficient of parameters and metabolites concentration: glycerol fermentation plus tryptone (A) tryptone (B) Ethanol (C) Succinate (D) Glycerol (E) NH3 (F) Formate (G) Biomass (H) Lactate (I) CO2.

Furthermore, we investigate the correlation coefficient of each EFMs, that can realize

that every EFMs are similar or not. Figure 4.3 shows the correlation coefficient in glycerol

fermentation plus tryptone, the red point represent high correlation coefficient, yellow point

represent low correlation coefficient, and green represent negative correlation coefficient.

There are many red square that reveal this part of EFMs is similar shown in Figure 4.3, and

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(A) (B) 0 0.02 0.04 0.06 0.08 0.1 0.12 1 17 33 49 65 81 97 113 129 145 161 177 193 209 225 241 257 273 289 305 321 337 353 369 385 401 417 433 0.00000001 0.0000001 0.000001 0.00001 0.0001 0.001 0.01 0.1 1 1 18 35 52 69 86 103 120 137 154 171 188 205 222 239 256 273 290 307 324 341 358 375 392 409 426

Figure 4.2 Parameters distribution : glycerol fermentation plus tryptone .

EF M1 EF M2 EF M3 EF M4 EF M5 EF M6 EF M7 EF M8 EF M9 EF M1 0 EF M1 1 EF M1 2 EF M1 3 EF M1 4 EF M1 5 EF M1 6 EF M1 7 . . . . E FM 442 EFM1 EFM2 EFM3 EFM4 EFM5 EFM6 EFM7 EFM8 EFM9 EFM10 EFM11 EFM12 EFM13 EFM14 EFM15 EFM16 EFM17 . . . . . . . . . . . . . . . . . . . . . . . . EFM442

(53)

Each of the three parts EFMs that we select one to compare with early work shown in

Figure 4.5, Figure 4.6, and Figure 4.7. In Figure 4.5, the major product is acetate. In Figure

4.6, the major products are ethanol, biomass, and succinate. In Figure 4.7, it have the most

less reaction that only convert glycerol to succinate and ethanol ,but this EFMs didn’t growing

biomass. Above all, the cluster of EFMs matrix provides a possible thinking that performs the

a few EFMs to stand for whole systems EFMs.

The frequency of high correlation coefficient part shown in Table 4.2-4.4, focus on mode

151 – mode 282, there is none of the reaction about biomass growing, and the less flow in

pentose phosphate pathway and ratio of ethanol in fermentative produce is increased. That

cluster of EFMs stand for high yields EFMs lead us to further research on the question of how

to balance the cell growing and increase the ethanol yields.

Table 4.2 Reaction frequency of EFMs for glycerol fermentation plus tryptone: 1~32

GG1 GG3 GG4 GG11 GG12 GG13 PPP2 PPP3 TCA1 TCA2r FR1

0 0 1 0.87 0 0.47 0 0 1 1 0.57

FR2 FR3 ANA1 ANA2 ANA3 FEM1 FEM2 FEM7 FEM8 FEM3 FEM5

0.63 0.63 1 0.2 0 0.53 0.17 0.23 0.23 0.13 0.13

FEM6 FEM4 FEM9 EDP1 EDP2 XYL1 XYL2 GAL1 MAN1 MAN2 ARA1

0.27 0.53 0.13 0 0 0 0 0 0 0 0

BIO OPM4r FC2 TRA1 TRA2 TRA3 TRA4 TRA5 TRA6 TRA7 GLB1

1 0.53 0 0.27 0.4 1 0.13 0.7 0 0.53 0.27

GLB2 TRA8 TRA9 TRA10 GLYD1 GLYD2 GLYD3 GLYD4 OPM3 TRYP GG2r

0.27 0 0 0 1 0 1 1 0 1 1

GG5r GG6r GG7r GG8r GG9r GG10r PPP1 PPP4r PPP5r PPP6r PPP7r

1 1 1 1 1 1 0 1 1 1 1

PPP8r TCA3r TCA4 FC1r

(54)

Table 4.3 Reaction frequency of EFMs for glycerol fermentation plus tryptone: 33~133

GG1 GG3 GG4 GG11 GG12 GG13 PPP2 PPP3 TCA1 TCA2r FR1

0 0 1 0.87 0 0.48 1 1 0.95 0.95 0.58

FR2 FR3 ANA1 ANA2 ANA3 FEM1 FEM2 FEM7 FEM8 FEM3 FEM5

0.63 0.63 1 0.19 0 0.49 0.19 0.25 0.25 0.13 0.12

FEM6 FEM4 FEM9 EDP1 EDP2 XYL1 XYL2 GAL1 MAN1 MAN2 ARA1

0.25 0.49 0.13 0 0 0 0 0 0 0 0

BIO OPM4r FC2 TRA1 TRA2 TRA3 TRA4 TRA5 TRA6 TRA7 GLB1

0.95 0.51 0 0.25 0.44 0.95 0.13 0.69 0 0.55 0.24

GLB2 TRA8 TRA9 TRA10 GLYD1 GLYD2 GLYD3 GLYD4 OPM3 TRYP GG2r

0.24 0 0 0 1 0 1 1 0 1 1

GG5r GG6r GG7r GG8r GG9r GG10r PPP1 PPP4r PPP5r PPP6r PPP7r

1 1 1 1 1 1 1 0.69 1 0.68 0.68

PPP8r TCA3r TCA4 FC1r

0.68 0.95 0.95 1

Table 4.4 Reaction frequency of EFMs for glycerol fermentation plus tryptone: 151~282

GG1 GG3 GG4 GG11 GG12 GG13 PPP2 PPP3 TCA1 TCA2r FR1

0 0.19 0.34 0.76 0.19 0.4 0.15 0 0.35 0.35 0.53

FR2 FR3 ANA1 ANA2 ANA3 FEM1 FEM2 FEM7 FEM8 FEM3 FEM5

0.57 0.57 0.81 0.3 0.19 0.41 0.13 0.28 0.28 0.05 0.19

FEM6 FEM4 FEM9 EDP1 EDP2 XYL1 XYL2 GAL1 MAN1 MAN2 ARA1

0.28 0.41 0.09 0.15 0.15 0 0 0 0 0 0

BIO OPM4r FC2 TRA1 TRA2 TRA3 TRA4 TRA5 TRA6 TRA7 GLB1

0 0.45 0.19 0.28 0.4 0 0.05 0.67 0 0.54 0.35

GLB2 TRA8 TRA9 TRA10 GLYD1 GLYD2 GLYD3 GLYD4 OPM3 TRYP GG2r

0.35 0 0 0 1 0 1 1 0.19 0.91 0.15

GG5r GG6r GG7r GG8r GG9r GG10r PPP1 PPP4r PPP5r PPP6r PPP7r

0.15 0.98 0.98 0.98 0.98 0.98 0.15 0 0 0 0

PPP8r TCA3r TCA4 FC1r

(55)

Figure 4.4 The mode No.81 in glycerol fermentation in medium plus tryptone.

(56)
(57)

In other condition, glycerol fermentation plus furmarate, there are also high coefficient

subset and low high coefficient subset parameters with metabolites concentration.. Although

the high coefficient parameters modes influence averagely, it have less effect to the exception

metabolite. Using these variations, the extreme condition and phenomenon can be revealed.

So the cluster of similar EFMs can not use few amounts of EFMs to represent the whole

systems. (A) (B) (C) (E) (D) (F) (G) (H) (I) 0 20 40 60 80 100 120 140 1 115 229 343 457 571 685 799 913 1027 1141 1255 1369 1483 1597 1711 1825 1939 0 50 100 150 200 250 300 350 400 1 115 229 343 457 571 685 799 913 1027 1141 1255 1369 1483 1597 1711 1825 1939 0 500 1000 1500 2000 2500 3000 1 117 233 349 465 581 697 813 929 1045 1161 1277 1393 1509 1625 1741 1857 0 200 400 600 800 1000 1 117 233 349 465 581 697 813 929 1045 1161 1277 1393 1509 1625 1741 1857 0 500 1000 1500 2000 2500 1 117 233 349 465 581 697 813 929 1045 1161 1277 1393 1509 1625 1741 1857 0 200 400 600 800 1000 1200 1400 1600 1800 1 117 233 349 465 581 697 813 929 1045 1161 1277 1393 1509 1625 1741 1857 0 0.002 0.004 0.006 0.008 0.01 0.012 1 118 235 352 469 586 703 820 937 1054 1171 1288 1405 1522 1639 1756 1873 0 100 200 300 400 500 1 115 229 343 457 571 685 799 913 1027 1141 1255 1369 1483 1597 1711 1825 1939 0 20 40 60 80 100 120 140 1 115 229 343 457 571 685 799 913 1027 1141 1255 1369 1483 1597 1711 1825 1939

Figure 4.8 Coefficient of parameters and metabolites concentration: glycerol fermentation plus furmarate (A) Furmarate (B) Ethanol (C) Succinate (D) Glycerol (E) NH3 (F) Formate (G) Biomass (H) Lactate (I) CO2.

數據

Figure 1.5 US biodiesel production and its impact on crude glycerol prices [2]
Table 1.1 Capability of glycerol fermentation and distribution of glyDH and 1,3PD-DH in enterbacterial species
Figure 1.7 systems flow of Modeling and Analysis of Glycerol Anaerobic Utilization by Escherichia coli
Table 2.1 Enzymes related glycerol utilization in Escherichia coli  Condition   Glycerol  kinase  Glycerol  dehydrogenase Glycerol-3-phosphate  dehydrogenase(GlpABC)  Glycerol-3-phosphate dehydrogenase(GlpD)
+7

參考文獻

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