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Identification of essential metabolites in metabolite networks Long, Cai 2012

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Identication of Essential Metabolites in Metabolite Networks by Cai Long B.Sc., Jilin University, 2009 Minor in B.Econ, Jilin University, 2009 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in The Faculty of Graduate Studies (Biomedical Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) October 2012 © Cai Long 2012 Abstract Metabolite essentiality is an important topic in systems biology and as such there has been increased focus on their prediction in metabolic networks. Specically, two related questions have become the focus of this eld: how do we decrease the amount of gene knock-out work loads and is it possible to predict essential metabolites in dierent growth conditions? Two dierent approaches to these questions: interaction-based method and constraints- based method, are conducted in this study to gain in depth understanding of metabolite essentiality in complex metabolic networks. In the interaction-based approach, the correlations between metabolite essentiality and the metabolite network topology are studied. With the idea of predicting essential metabolites, the topological properties of the metabolite network are studied for theMycobacterium tuberculosis model. It is found that there is strong correlation between metabolite essentiality and the degree and the number of shortest paths through the metabolite. Welch's two sample T-test is performed to help identify the statistical signicance of the dierences between groups of essential metabolites and non-essential metabolites. In the constraint-based approach, essential metabolites are identied in- ii Abstract silico. Flux Balance Analysis (known as FBA), is implemented with the most advanced in-silico model of Chlamydomonas Reinhardtii, which con- tains light usage infomation in 3 dierent growth environments: autotrophic, mixotrophic, and heterotrophic. Essential metabolites are predicted by metabolite knock out analysis, which is to set the 
ux of a certain metabo- lite to zero, and categorized into 3 types through Flux Sum Analysis. The basal 
ux-sum for metabolites is found to follow a exponential distribution, it is also found that essential metabolites tend to have larger basal 
ux-sum. iii Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xii 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Metabolite Essentiality . . . . . . . . . . . . . . . . . . . . . 1 1.2 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . 6 iv Table of Contents 2.1 Systems Biology . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.1 Basic Steps in Systems Analysis . . . . . . . . . . . . 7 2.1.2 Systems Analysis of Metabolite Essentiality . . . . . 9 2.2 Interaction-based Approach . . . . . . . . . . . . . . . . . . . 10 2.2.1 Graph Theory in Systems Biology . . . . . . . . . . . 10 2.3 Constraints-based Approach . . . . . . . . . . . . . . . . . . 12 2.3.1 Flux Balance Analysis . . . . . . . . . . . . . . . . . 13 2.4 Subjects of Applications . . . . . . . . . . . . . . . . . . . . 16 3 Metabolite Essentiality and Reaction Network Topology . 17 3.1 Graph Theory and Essential Metabolites . . . . . . . . . . . 17 3.1.1 Graph Theory . . . . . . . . . . . . . . . . . . . . . . 18 3.1.2 Categories of Metabolites . . . . . . . . . . . . . . . . 30 3.2 Application to Mycobacterium Tuberculosis . . . . . . . . . . 32 3.2.1 Mycobacterium Tuberculosis . . . . . . . . . . . . . . 32 3.2.2 Gaps in the Metabolite Network iNJ661 . . . . . . . 34 3.2.3 Metabolite Essentiality and Network Degree . . . . . 34 3.2.4 Metabolite Essentiality and the Degree of Neighbors . 36 v Table of Contents 3.2.5 Metabolite Essentiality and Clustering Coecient . . 38 3.2.6 Metabolite Essentiality and Network Betweenness. . . 38 3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4 Constraint Based Identication of Essential Metabolites . 42 4.1 Application: Microalgae . . . . . . . . . . . . . . . . . . . . . 43 4.1.1 Chlamydomonas Reinhardtii . . . . . . . . . . . . . . 44 4.1.2 Biofuel from Microalgae . . . . . . . . . . . . . . . . . 46 4.2 Flux Balance Analysis . . . . . . . . . . . . . . . . . . . . . . 49 4.2.1 Mathematical Reconstruction of a Biochemical Net- work . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.2.2 Model Validation . . . . . . . . . . . . . . . . . . . . 51 4.2.3 Mass Balance . . . . . . . . . . . . . . . . . . . . . . 52 4.2.4 Constraints . . . . . . . . . . . . . . . . . . . . . . . . 53 4.2.5 Objective Function . . . . . . . . . . . . . . . . . . . 56 4.2.6 Linear Program Solver . . . . . . . . . . . . . . . . . 58 4.2.7 Identication of Essential Metabolites . . . . . . . . . 59 4.3 Flux Sum Analysis . . . . . . . . . . . . . . . . . . . . . . . . 61 vi Table of Contents 4.3.1 Procedure for Flux Sum Analysis . . . . . . . . . . . 61 4.3.2 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 69 5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 A.1 Appendix 1: ELM in Mycobacterium Tuberculosis . . . . . . 85 A.2 Appendix 2: Universal Metabolites . . . . . . . . . . . . . . 86 A.3 Appendix 3: Root No-production Metabolites in iNJ661 . . . 92 A.4 Appendix 4: Root No-consumption Metabolites in iNJ661 . 93 A.5 Appendix 5: Common Essential Metabolites in All 3 Growth Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 A.6 Appendix 6: Biomass Function(Objective Function) for Dif- ferent Growth Conditions . . . . . . . . . . . . . . . . . . . . 98 A.7 Appendix 7: Matlab Codes . . . . . . . . . . . . . . . . . . . 102 A.7.1 Interaction-based Approach Code . . . . . . . . . . . 102 A.7.2 Constraint-based Approach Code . . . . . . . . . . . 108 vii List of Tables 4.1 Oil yield from algae and from other sources,(Chisti, 2007) . . 44 4.2 Oil content from microalgae (Chisti, 2007)(Li et al., 2010) . . 48 4.4 Constraints for dierent growth conditions . . . . . . . . . . . 55 4.5 Number of dierent types of essential metabolites in dierent growth conditions . . . . . . . . . . . . . . . . . . . . . . . . . 67 viii List of Figures 1.1 Interaction-based approach and constraints-based approach are both implemented to study metabolite essentiality. . . . . 4 2.1 Linear Programming . . . . . . . . . . . . . . . . . . . . . . . 15 3.1 Pathway diagraph from a simple biosystem consists of 7 metabo- lites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2 Examples of Orphan reaction and Gap. A: the missing re- action (Gap) creates two dead-end reactions; B: the reaction catalyzed by unknown gene product can be a orphan reac- tion (Reprinted from Orth, Jerey D, 2010(Orth and Palsson, 2010), with permission from 2010 Wiley Periodicals, Inc.) . . 27 3.3 Characterization of problem metabolites in metabolic net- works (Satish Kumar et al., 2007) . . . . . . . . . . . . . . . . 28 3.4 Probability distribution of degree of metabolites . . . . . . . 35 3.5 Probability distribution of neighbor's degree . . . . . . . . . . 36 ix List of Figures 3.6 Average sum of neighbor's degrees for EM, EUM and NEM . 37 3.7 Probability distribution of Clustering Coecient . . . . . . . 39 3.8 Average betweenness of EM, EUM and NEM . . . . . . . . . 39 3.9 Probability distribution of betweenness . . . . . . . . . . . . . 40 4.1 Reconstructed metabolic network of C. reinhardtii, (Reprinted from (Boyle and Morgan, 2009)) . . . . . . . . . . . . . . . . 46 4.2 Mathematically reconstruction of a biochemical network . . . 51 4.3 Model validation . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.4 Mass balance denition . . . . . . . . . . . . . . . . . . . . . 53 4.5 The total basal 
ux-sum for C.Reinhardtii in 3 dierent con- ditions. The blue part represents the total basal 
ux-sum for Universal Metabolites. . . . . . . . . . . . . . . . . . . . . . 63 4.6 Probability distribution of metabolites with certain basal 
ux- sum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.7 2 types of essential metabolites: Type AE and Type BE . . . 66 4.8 Number of dierent type of essential metabolites in dierent growth conditions . . . . . . . . . . . . . . . . . . . . . . . . . 67 x List of Acronyms EM: Essential Metabolite EUM: Essential Unusual Metabolite NEM: Non-Essential Metabolite ORF: Open Reading Frame EC number: Enzyme Commision number KEGG:Kyoto Encyclopedia of Genes and Genomes SBML: Systems Biology Markup Language FBA: Flux Balance Analysis FSA: Flux Sum Analysis LP: Linear Programming DFBA: Dynamic Flux Balance Analysis M.T: Mycobacterium tuberculosis C.R: Chlamydomonas Reinhardtii xi Acknowledgements I would like to express my most sincere appreciation and gratitude to my supervisor, Prof. Bhushan Gopaluni for his excellent supervision and pre- cious advice throughout the whole period of my study at the University of British Columbia. His motivation and inspiring attitude is exemplary. I learned how to conduct a research project from him, which I am sure will be a life time benecial. My thanks go to Dr. Ezra Kwok and whole Process Modeling and Con- trol lab, their ideas, experience and generously sharing help me grow. Special thanks go to Dr. Roger Chang and Dr. Nathan Lewis in Univer- sity of California, San Diego, for releasing their data from their experiments. I am also grateful for Dr. Pan-Jun Kim in University of Illinois at Urbana Champaign for his kindly help. Moreover, I would like to convey my thanks to all the faculty, sta and fellow postgraduate students in Chemical and Biological Engineering department at UBC. Last, I leave the warmest part of my heart for my beloved parents, who gave birth to me, enlightened me and educated me with their unconditional support and continuous love. xii Chapter 1 Introduction Every cell is characterized by the presence of a complex network of metabo- lites connected by chemical reactions. These reactions are catalyzed by spe- cialized proteins called enzymes. There are usually thousands of reactions inside the cell, and at the same time, there are thousands of metabolites (Samal et al., 2006). It is well-known that certain reactions are vital to the survival and maintenance of essential functions of a cell. These are called \essential" reactions. Notably, the essentiality of reactions or metabolites may change depending on the environmental conditions. 1.1 Metabolite Essentiality The metabolites involved in the reaction network can be classied into two categories: essential metabolites and nonessential metabolites. While cells are known to be quite robust to perturbations in the reaction network, the absence of essential metabolites could cause serious damage or even death. On the other hand, recent investigations have shown that non-essential metabolites cause very little or no impact on the living cells(Jeong et al., 2003). 1 1.1. Metabolite Essentiality The study of essential metabolites has received signicant interest from the systems biology community due to several reasons: First, the loss of essential metabolites will diminish cell viability. Most drugs exert therapeutic eects by binding and regulating the activity of a particular metabolite, set of proteins or nucleic acid targets in the pathogenic microbes. Therefore identication of essential metabolites will be benecial to investigate new inhibitors of disease and potential drug targets as in- hibitors, the identication and validation of essential metabolites compose an important step in drug discovery process (Samala, 2006). Second, analysis of essential metabolites will help researchers under- stand the complex metabolite networks, which may yield better predictions in in vivo cellular behavior, and have better insight into the complex re- lationship between cell components and systems-level cellular phenotypes (Jamshidi and Palsson, 2007). Third, many drugs that are highly successful in human clinical use mimic a substrate or product of essential metabolites. For example, folic acid is an essential biomolecule, which needs to be synthesized de novo by many bac- teria, and dihydropteroate synthase, an enzyme in the folic acid biosynthe- sis pathway, synthesizes dihydrofolate from p-aminobenzoate.Sulfonamide- based drugs are structural analogs of p-aminobenzoate and act by inhibiting dihydropteroate synthase. Many bacterial infections are eectively treated with sulfonamides, as they mimic an essential substrate and competitively inhibit an essential enzyme. There are lots of other examples of inhibition of essential metabolites by mimicking their substrates (Bermingham and Derrick, 2002). 2 1.2. Outline Hence, the study of metabolite essentiality will be benecial not only to the understanding of systems biology (especially with complex metabolite networks), but also is expected to play an important role in helping to identify drug targets. The systems biology approach, with its combination of computational, experimental and observational enquiry, is highly relevant to drug discovery and the optimization of medical treatment regimes. Particularly, computer simulation and analysis, along with traditional bioinformatics approaches, have frequently been proposed to signicantly increase the eciency of drug discovery (Kitano, 2002). Currently, the main drawback is due to the cost and time consumption of the approaches taken to identify essential metabolites, which is mainly gene knock-out experiments. With the objective to reduce the time and cost of determining essen- tial metabolites, we are going to study the correlation between metabolite essentiality and metabolite network topology, and try to predict essential metabolites using constraint-based modeling. 1.2 Outline In Chapter 2, we will review recent progress made on the topic of corre- lation between metabolite essentiality and network topology, the lethality- centrality rule, and other ndings. We will also discuss the importance of choosing C.Reinhardtii, which is a model organism of microalgae, as our in- 3 1.2. Outline vestigation object. Finally, the basic concepts of systems biology and linear programming will be discussed here. Figure 1.1: Interaction-based approach and constraints-based approach are both implemented to study metabolite essentiality. As indicated in Figure 1.1, two modeling approaches: interaction-based approach and constraints-based approach are both implemented to study metabolite essentiality. In Chapter 3, interaction-based approachmodel iNJ661 ofMycobac- terium tuberculosis is used to identify essential metabolites. First, we cat- egorize the essential metabolites into 3 dierent types: Essential Unusual Metabolites, Universal Metabolites, and Non-Essential Metabolites. Sec- ondly, we introduce a method based on adjacency matrix to nd the gaps in the model and ll the model with GapFill, a method developed by Orth Jerey to ll the gaps (Orth and Palsson, 2010). Finally, we study the correlations between metabolite essentiality and the topology parameter of metabolic networks. The metabolite degree, degree of neighbors, clustering 4 1.2. Outline coecient of each metabolite, and betweenness of the metabolite network is discussed, respectively. In Chapter 4, constraints-based approach model organism, Chlamy- domonas Reinhardtii, is chosen to conduct the study of predicting essential metabolites by constraints based modeling. With the light usage informa- tion, we are able to predict essential metabolites in dierent growth con- ditions, and nd the common essential metabolites. We also propose the categorization of essential metabolites by using Flux Sum Analysis. In Chapter 5, we summarize the results and discuss possible future work. 5 Chapter 2 Literature Review At the core of our understanding of biological processes and underlying sys- tems, is a characterization of function and interactions of their constituent parts. Systems biology, which takes into account the key characteristics of complex systems, including essentiality, emergence, robustness and modu- larity, is one of the essential topics. Today, systems biology is established as a fundamental interdisciplinary science that focuses on detailed studies of the complex mechanisms, which orchestrate the interactions between various biomolecules that compose life. 2.1 Systems Biology Systems biology, broadly speaking, is a subject that attempts to investi- gate the behavior and relations of all the `elements' in a given functioning biological system (Kitano, 2002). It aims at system-level understanding of biological processes and biochemical networks as a whole. This \system- oriented" new biology is shifting our focus from examining particular molec- ular details to studying the information 
ow at all biological levels: genomic DNA, mRNA, proteins, informational pathways, and regulatory networks 6 2.1. Systems Biology (Price and Lee, 2010). Systems biology approaches seek to study the com- plexity of life to help in understanding how the cellular networks work to- gether. It requires a broad interdisciplinary knowledge of molecular and cell biology, biochemistry, informatics, mathematics, computing, and engineer- ing. It provides tools to understand the various functions and properties of biological systems, and predicts systems behavior under various physiologi- cal conditions. 2.1.1 Basic Steps in Systems Analysis A widely used in silico quantitative systems biology tool to relate the geno- type to the phenotype comprises of four steps: 1. Collection of information from `omics' and literature data on the target organism Genome sequencing is the starting point for the systems analysis. Af- ter that, the genome is annotated to dene genes and transcribed elements, and open reading frame (ORF)s are delineated. The most challenging part of genome annotation, which is assigning molecular function, can be done through comparison of related genes and pro- teins with known functions, for instance, by predicting protein func- tion based on sequence similarity with proteins of previously anno- tated function in database such as Uniprot or Metacyc databases. This approach generates a genome annotated with Enzyme Commis- sion(EC) numbers which contains the catalytic information of the gene product.(Francke et al., 2005) 7 2.1. Systems Biology 2. Reaction network model After genomic sequencing,the reaction network reconstruction process are performed. This process is carried out by assigning reactions to an- notated genes using metabolic databases such as Kyoto Encyclopedia of Genes and Genomes (KEGG). Reaction properties that include re- versibility and localization to cellular compartments are also built into the network model. Incomplete reaction pathways or lack of metabolic functions are quite common in network models. Often, reorganization of reactions is required to make the model consistent with the known physiological and biochemical characteristics. 3. Mathematical description of the network model The reaction network model is described by a set of reaction rate equa- tions so as to allow quantitative analysis. Stoichiometric matrix is a popular representation of the network model and is rather straight- forward to generate. The large number of reactions in these models makes it almost impossible to develop models manually. A variety of software programs are available for automatically building the math- ematical models based on reaction network information. Antimony is one such software that generates a model in Systems Biology Markup Language (SBML) (Smith et al., 2009). 4. Evaluation and renement of the model Metabolomic and transcriptomic data from high-throughput experi- ments is used to evaluate and rene the model and iteratively improve its capacity to predict phenotypes. Dierent types of analysis can be performed on the rened model to optimize or predict the prop- 8 2.1. Systems Biology erties of the network. In this context, constraint based modeling ap- proaches such as 
ux balance analysis (FBA) have been widely studied to predict 
ux through metabolic path ways, optimal growth media, product yields, and other factors relevant to bioprocess design and optimization (Hatzimanikatis et al., 2005; Hjersted and Henson, 2009; Hucka, 2003; Kauman et al., 2003; Krieger et al., 2004; Lee et al., 2006; Meadows et al., 2010) 2.1.2 Systems Analysis of Metabolite Essentiality Serval attempts, both in vivo or in silico, have been made to study the metabolite essentiality. Among in silico methods, systems biology is the most popular one. Rigoustos states that \Systems biology is an integrated approach that brings together and leverages theoretical, experimental, and computational approaches in order to establish connections among impor- tant molecules or groups of molecules in order to aid eventual mechanistic explanation of cellular processes and systems." (Rigoutsos, 2007). Aiming at a system-level understanding of biological systems, systems biology pro- vides a tool to understand the various properties of biological systems and predict system behavior under dierent physiological conditions (Palsson, 2009). Just as theoretical and mathematical biology deal with the mathe- matical modeling of certain aspects of biology, systems biology deals with the prediction of various function from the metabolic networks and provides a mechanistic bridge between phenotype and genotypes. Flux Balance Analysis (Ghim et al., 2005; Imieliski et al., 2005; Kim et al., 2007; Li et al., 2011; Palsson, 2003) and Flux-sum analysis (Chung and Lee, 9 2.2. Interaction-based Approach 2009) are two popular systems biology approaches that are used in under- standing metabolite essentiality. Metabolite essentiality is commonly deter- mined in silico by monitoring cell growth while changing the concentration of a given metabolite to zero. An in vivo method for studying metabolite essentiality is to implement wet-lab gene knock out experiments to nd out the essential enzymes, and determine the essential metabolites based on the knock-out results. These experiments often provide more reliable models, however, there is usually missing information about reactions or mechanisms in the in silico network (Lamichhane et al., 2011). 2.2 Interaction-based Approach 2.2.1 Graph Theory in Systems Biology Graph theory has been used for analyzing data for protein interaction net- work, and is receiving more and more attention in predicting essential metabo- lites. Metabolite essentiality has gained enormous interest in the recent years. One of the most intriguing questions in the study of metabolite essentiality is to understand the connection between biological and topological impor- tance of metabolite networks. One of the rst attempts at studying this topic was made in 2001 on the S. cerevisiae protein-protein interaction network (Bro et al., 2006). It was also investigated under the topic \centrality and lethality" by Jeong and colleagues (Jeong et al., 2001). Since then, many 10 2.2. Interaction-based Approach eorts have been put into the protein-protein interaction network, the cor- relation between protein-protein network topology and protein essentiality was conrmed by many researchers (Coulomb et al., 2005; Hahn and Kern, 2005; Yu et al., 2004, 2007; Zotenko et al., 2008). The recent availability of large protein interaction databases has fueled the analysis of protein in- teraction networks and it has been demonstrated that protein essentiality could be strongly related to some topological parameters of these networks. For example, protein networks are found vulnerable when a highly con- nected \hub" is removed (He and Zhang, 2006). Computational analysis shows that removing hubs increases the proportion of unreachable pairs of nodes(metabolites) and the mean shortest path length between all pairs of reachable nodes in the network.(Albert et al., 2000) However, not much work has been reported on the correlation between metabolite essentiality and topology. Mahadevan et al(Mahadevan and Palsson, 2005) conjectured that low degree metabolites (metabolites connect with small number of other metabolites) are just as likely to be recognized as essential metabolites as high degree metabolites (metabolites connect with large number of other metabolites). Areejit Samal generated a random ma- trix to explain this phenomenon(Samal et al., 2006). Other graph driven methods to analyze complex cellular networks are emphasized by many re- searchers (Aittokallio and Schwikowski, 2006a). Traditional methods to study the essential metabolites mainly rely on creating random mutants of a gene and therefore require a large amount of work. For in silico metabolite network predictions like 
ux balance analysis, the complexity and integrity of the metabolite model would greatly aect 11 2.3. Constraints-based Approach the accuracy of the prediction. Although a lot of progress has been made in studying the topological and functional properties of metabolite networks, very little eort has been put into understanding the correlations between metabolite essentiality and topology. We are trying to involve more topo- logical parameters of the metabolite network, which would help to increase the accuracy of addressing essential metabolites, and to better understand the metabolite network structures. 2.3 Constraints-based Approach Another approach used in predicting essential metabolites is contraints- based, in which Flux Balance Analysis(FBA) and other linear programming based tools are implemented with biology mathematic models. The development of high-throughput experimental techniques in recent years has led to an explosion of genome-scale data sets for a variety of organisms. Considerable eorts have yielded complete genomic sequences and gene-annotation based metabolite models for dozens of organisms. A prudent approach to gain biological understanding from these complex data involves the development of mathematical models, simulation, and analysis and techniques (Kim et al., 2008). In these complementary eorts, many analytical tools have been developed to use these models in computational investigations of model organisms. One method in particular, Flux Balance Analysis (FBA), is a powerful mathematical approach to assess the ability of an organism to grow on a particular substrate or in particular environment and also be used to assess the eect of metabolic gene deletions under various 12 2.3. Constraints-based Approach growth conditions (Palsson, 2009). 2.3.1 Flux Balance Analysis Flux balance analysis is a widely used constraint based approach for study- ing biochemical networks (Orth et al., 2010). A reaction network is as- sumed to be at steady state in order to overcome the lack of knowledge of metabolite concentration or details of enzyme kinetics of the system (Edwards et al., 2001). It is dicult and in some cases impossible to pro- vide real time metabolite concentration or enzyme kinetics using current experimental techniques. The model of the steady state reaction network is dened by a linear matrix equation that contains reaction stoichiometric coecients. Constraints are typically of two types, one is the stoichiometry matrix, which is generated from mass balance equations (Kauman et al., 2003). These matrix-based constraints ensure the total amount of any compound being produced must be equal to the total amount being consumed at steady state. The other type of constraints are given by the reactions, which dene the maximum and minimum allowable 
uxes of the reactions. However, the dynamics of the metabolic networks sometimes are too im- portant to be neglected, Dynamic Flux Balance Analysis (DFBA), a widely used approach for studying biochemical networks and phenotype optimiza- tion method, was introduced to generate dynamic prediction of substrate, biomass and concentrations in batch culture (Meadows et al., 2010). Many tools have been developed to perform FBA and DFBA, for instance, FBA- 13 2.3. Constraints-based Approach SimVis(Grafahrend-Belau et al., 2009), SurreyFBA((Gevorgyan et al., 2010), and CobraToolbox(Becker et al., 2007). With the network reconstruction data from Nanette R Boyle (Boyle and Morgan, 2009), and Kyoto Encyclopedia of Genes and Genomes (KEGG), DFBA is utilized to predict the biomass production and lipid concentration of C.Reinhardtii. (Hucka, 2003)(Becker et al., 2007), the simulation and opti- mization results will be compared with existing experimental results (Smith et al., 2009). Linear programming(LP) is used to identify single or multiple optimal solutions from constraints in constraints based modeling. Linear Programming Linear Programming (also known as LP, or Linear Optimization) is a math- ematical method to determine the optimal solution (such as maximum or minimum) in a given mathematical model with a list of constraints rep- resented as linear relationships. The linear objective function, subject to linear equality and linear inequality constraints is used to nd the optimal point. The optimal solution normally lies in a corner of the constraint poly- tope. Occasionally, the objective function has the same value along a whole edge and all the points on that edge are optimal values. In this rare case the objective function is "parallel" to the edge of the polytope. The gure below represents a simple example of linear programming problem. 14 2.3. Constraints-based Approach Solution space defined by constraints  Optimal Point Null Space Figure 2.1: Linear Programming LP problems can usually written into form: Maximize cTx subject to Ax  b and x  0 where x represents the vector of variables, c and b are vectors of co- ecients, A is the coecient matrix. Most of the metabolic engineering LP problems are convex under-determined. An under-determined system means there are less equations than variables, while an over-determined sys- tem means there are more equations than unknowns. 15 2.4. Subjects of Applications 2.4 Subjects of Applications Two modeling approaches, interaction-based and constraints-based , are ap- plied on dierent model organisms. Mycobacterium tuberculosis, model iNJ661, is used in the interaction- based approach, with a list of essential metabolites from G.Lamichhane, J.Freundlich et al. in 2011 through a wet-lab approach. The correlations between metabolite essentiality and the topology parameter of metabolic networks are being studied, to improve the accuracy of the essential metabo- lites predication. The main reason to use this model is that it's the rst organism with a full list of essential metabolites with wet-lab experiemental results. Constraints-based approach is applied on Chalmydomonas Reinhardtii, model iRC1080, as it is the latest and only model with light usage, which enable us to implement simulation under three dierent growth conditions. Flux balance analysis is utilized to identify the essential metabolites, and 
ux sum analysis is used to categorize the essential metabolites. 16 Chapter 3 Metabolite Essentiality and Reaction Network Topology One of the most interesting questions in the study of metabolite essentiality is to understand the connection between biological and topological impor- tance of metabolite networks. In this chapter, we investigated the degree, neighbor's degree, clustering coecient and betweenness of the essential metabolites and unessential metabolites, try to nd the correlation between essential metabolites and reaction network topology. 3.1 Graph Theory and Essential Metabolites Before we study the correlation between metabolite essentiality and reaction network topology properties, the basic concepts of graph theory, and the methodologies we used to classify essential metabolites are discussed. 17 3.1. Graph Theory and Essential Metabolites 3.1.1 Graph Theory Graph A graph is a mathematical abstraction of structural relationships between discrete objects. A graph usually refers to a collection of \nodes" and \edges" that connect the vertices. An edge could be either directed, meaning there is a distinction from one node to another or undirected, which means there is no direction from one node to another. Several methods or data structures can be used to describe the nodes and edges, an easy and widely used one is adjacency matrix M . An adjacency matrix is an n by n matrix, where n is the number of nodes in the graph. If there is an edge from node x (in metabolite network, metabolite X) to node y (in metabolite network, metabolite Y ), then the element M(x; y) is 1(or in general the number of edges between x and y), otherwise it would be zero. M(x; y) = n n is the number of reactions in which metabolite X acts as a reactant and metabolite Y is a product. The representation of complex cellular networks as a graph has made it possible to systematically investigate the topology and function of these networks using well-understood graph-theoretical concepts that can be used to predict the structural and dynamical properties of the underlying network (Aittokallio and Schwikowski, 2006b). 18 3.1. Graph Theory and Essential Metabolites A simple biosystem, which consists of 4 reactions and 8 metabolites, is constructed for demonstration: A! B + C B ! E +D G  C D +G! E + F While! means non-reversibility, the symbol  in the reaction indicates it's reversible. A pathway diagram representing this simple system is shown as Fig 3.1, A C E G F D B Figure 3.1: Pathway diagraph from a simple biosystem consists of 7 metabo- lites The adjacency matrix X can be derived for the above reaction system in a straightforward way. So the Figure 3.1 could be interpreted as : 19 3.1. Graph Theory and Essential Metabolites X  = 0BBBBBBBBBBBBBBB@ A B C D E F G A 0 1 1 0 0 0 0 B 0 0 0 1 1 0 0 C 0 0 0 0 0 0 1 D 0 0 0 0 1 1 0 E 0 0 0 0 0 0 0 F 0 0 0 0 0 0 0 G 0 0 1 0 1 1 0 1CCCCCCCCCCCCCCCA A very interesting and useful property of adjacency matrix is that the (i; j) element of Xk gives the number of k-step edge sequences from node i to node j (Jiang et al., 2009). For instance, element (2; 5) represents that there are two 2-step edge sequences from node b to node e; as it is clear that we can nd in the graph that there are two 2-step edge sequences from node b to node e: fb! c! eg; fb! d! eg For a digraph with N nodes and an adjacency matrix X, the following matrix R = (X +X2 +X3 +   +XN ) is dened as a connectivity matrix, the (i; j)th element of R indicates the number of directed paths from node i to node j. In our research, we only focus on two-step connections, which means, R = X +X2 +X3 20 3.1. Graph Theory and Essential Metabolites The connectivity matrix for the digraph in Fig 3.1 is X  = 0BBBBBBBBBBBBBBB@ A B C D E F G A 0 1 2 1 3 2 1 B 0 0 0 1 2 1 0 C 0 0 1 0 1 1 2 D 0 0 0 0 1 1 0 E 0 0 0 0 0 0 0 F 0 0 0 0 0 0 0 G 0 0 2 0 2 2 1 1CCCCCCCCCCCCCCCA X1; 3 = 2, it means from node A to node C, there are 2 pathways with less than 2 nodes in between. The connectivity matrix is used to nd the gaps in our study, as well as to study the nature of metabolite reaction network topology. Stoichiometric and Adjacency Matrices For large systems, especially complex metabolite networks, the adjacency matrix can be obtained from the corresponding stoichiometric matrix. The stoichiometric matrix is widely used in the computational systems biology, the matrix S stores the stoichio- metric coecients associated with each reaction 
ux in a network. In the above formulation, both internal 
uxes and boundary 
uxes, which trans- port material into or out of the system, are included in S. Typically, a number of inequalities are introduced to constrain the boundary (also called injection) 
uxes depending upon the external media (Edwards, 2000) (Beard et al., 2002). Stoichiometric matrix can be obtained from databases 21 3.1. Graph Theory and Essential Metabolites like MetaCyc(Caspi et al., 2010), CSB.DB (Kopka et al, 2005) quite easily. More details about stoichiometric matrix can be found in chapter 4. In the Stoichiometric matrix, the ith reaction A+B ! C +D showing that A and B will be consumed to produce C and D, so both A and B are adjacent to C and D. For any metabolite X in stoichiometric matrix S, jA is the row number of the metabolite X. For ith reaction, we dene the boolean equivalent of any reachability between any two metabolites A and B as follows: K(jA; jB) = 8>><>>: 0; if S(jA; i)  S(jB; i) = 0; 1; if S(jA; i)  S(jB; i) 6= 0; For a system with i reactions, the adjacency matrix would be: R(jA; jB) = X K(jA; jB)#i The MATLAB code can be found in the Appendix 6. Network Topology Denitions and Notations For a directed graph G, we shall write D(x) as the degree of a node x in V (G), which is the total number of edges (both in- or out- of the vertex) of x. 22 3.1. Graph Theory and Essential Metabolites Degree The degree of a certain metabolite in the metabolite network is equal to the number of reactions it is included, either as a reactant or prod- uct. D(X) = nX i=1 Mx;i + nX j=1 Mj;x The degree distribution of the metabolite network measures the propor- tion of nodes in the network having degree k. We have P (k) = nk n where nk is the number of nodes in the network of degree k, and n is the size of the network. Neighbor's Degree The sum of the degrees of a certain metabolite's neighbors, which reveal the numbers of metabolites connected to the metabo- lite indirectly but very still very close to that metabolite, is also very im- portant. An interesting and useful property of adjacency matrix is: (i; j) element of Xk gives the number of k-step edge sequences from node i to j. So ND(X), the number of degrees of the neighbors of metabolite X is: ND(X) = xX i=1 M2i;x + xX i=1 M2x;i 23 3.1. Graph Theory and Essential Metabolites The average of the neighbors' degrees of metabolite X Avg ND(X) is calculated as: Avg ND(X) = ND(X) D(X) Clustering Coecient Next, in graph theory, clustering coecient rep- resents how the nodes tend to cluster together. Here we study the local clustering coecient for each node, which quanties how close its neighbors are to being a clique(a complete circle), is dened as the proportion of links between the vertices within its neighborhood divided by the number of links that could possibly exist between them. For a directed graph, eij is distinct from eji and therefore for each node Ni there are ki(ki 1) links that could exist among the nodes within the neighborhood, here ki is the degree(in and out) of the node.(Mason and Verwoerd, 2007) Ci = jfejkgj ki(ki  1) Betweenness Another important topological feature of the network has received much attention - betweenness, which measures the total number of nonredundant shortest paths going through a certain node or edge (Girvan and Newman, 2002). For node k, the betweentess can be dened as following: Pk = X Nij 24 3.1. Graph Theory and Essential Metabolites Nij = 8><>: 0; if no shortest path through node k; 1; if the shortest path through node k; Missing Information in the Biological Models The genomes of several microorganisms have been completely sequenced and annotated in the past decade, however, even the most complete genomes are not perfect; they have missing information, which may lead to inaccurate predictions of the model. A key challenge in the automated generation of genome-scale reconstructions is the elucidation of the gaps and the subse- quent generation of hypotheses to bridge them. This challenge has already been recognized and a number of computational approaches have been un- der development to resolve these issues.Feist et al. (2009); Oh et al. (2007); Orth and Palsson (2010); Satish Kumar et al. (2007) There are two types of missing information (Orth and Palsson, 2010): ˆ Gaps: Gaps are created by dead-end reactions. When a reaction that consumes or produces a metabolite is missing, it creates a dead-end. For instance, experiments reveal a producing reaction but no con- suming reaction, or no producing reaction but a consuming reaction). Example A in Figure 3.2 is a common type of gap. In FBA, these reactions carry no 
uxes and therefore can lead to wrong predictions. There are several reasons for gaps in the metabolic network: 25 3.1. Graph Theory and Essential Metabolites 1. Biological: An enzyme in a completed reaction pathway is missing in the biochemical network. For example, iAF1260 for E.coli K-12 MG1655 (Edwards, 2000). 2. Scope: Metabolites produced in metabolism but then enter other systems not included in the network models like transcription and, translation may leave gaps in the models. For example, tRNAs in iAF1260 (Chavali et al., 2008). 3. Knowledge: It is not known what biochemical reaction produces or consumes a certain metabolite. A new biological discovery must be made to ll this gap. ˆ Orphan reactions: There are two dierent types of orphan reactions: 1. Reactions known to exist but are catalyzed by unknown gene product. They are the result of missing knowledge of the metabolism of an organism, (which gene or genes code for their enzymes.) 2. Reactions catalyzed by gene products with unknown functions. Even most well-studied organisms have many gene with unknown functions, eg: E.coli K-12 MG1655 has 981 partially or fully un- characterized. A database named ORENZA lists global orphan reactions recently found. Example B in Figure 3.2 shows one type of orphan reactions, which is cat- alyzed by a unknown gene product. 26 3.1. Graph Theory and Essential Metabolites Figure 3.2: Examples of Orphan reaction and Gap. A: the missing reaction (Gap) creates two dead-end reactions; B: the reaction catalyzed by unknown gene product can be a orphan reaction (Reprinted from Orth, Jerey D, 2010(Orth and Palsson, 2010), with permission from 2010 Wiley Periodicals, Inc.) Identifying the Gaps in a Reaction Network Gaps exist in almost every metabolic reaction network due to lack of in- formation. In this thesis, a novel approach to nd these gaps using what is called an adjacency matrix is proposed. The adjacency matrix contains information about interactions between metabolites. Gaps in metabolic re- 27 3.1. Graph Theory and Essential Metabolites constructions are dened as (i) metabolites which cannot be produced by any of the reactions or imported through any available uptake pathways in the model; or (ii) metabolites that cannot be consumed by any of the reactions or exported by any secretion pathways in the network. The rst kind of metabolites are recognized as root no-production metabolite (e.g.; metabolite A in Figure 3.3) and the second situation is recognized as root no-consumption metabolites(e.g.; metabolite B in Figure 3.3). There will be no 
ow through these metabolites at steady state due to their inability to connect with the rest of the network. Consequently, the metabolites directly related to them will be aected as well, which are dened as downstream no-production metabolites (e.g.; metabolite C in Figure 3.3) and upstream no-consumption metabolite (e.g.; metabolite D in Figure 3.3) respectively (Satish Kumar et al., 2007). Figure 3.3: Characterization of problem metabolites in metabolic networks (Satish Kumar et al., 2007) The root no-production metabolites and root no-consumption metabo- lites are caused by the gaps in the system, while they introduce more down- stream or upstream no 
ux metabolites simultaneously. In the connectivity matrix, the value of elementX(i; j) shows the number of pathways from node i to node j, if X(i; j) = 0, there is no 
ux from metabolite i to metabolite j. Set 28 3.1. Graph Theory and Essential Metabolites Kj = i=1;2:::nX X(i; j) Clearly, ifKj = 0, the jth metabolite is a root no-production metabolite. Similarly, set Ci = j=1;2:::nX X(i; j) Ci represent the number of pathways producing metabolite i, so if Ci = 0, it would be a root no-consumption metabolite. Gaps could be lled by dierent methods like BNICE (Hatzimanikatis et al., 2005), GapFill (Satish Kumar et al., 2007) , SMILY (Reed et al., 2006), etc. Current gap-lling methods: In computational biology, gap-lling meth- ods are quite useful as they improve the predictive capabilities of models by making them more realistic by characterizing a previously unknown gene, a model renement tool. ˆ a) Computational methods: (to lling the gaps, reactions from database , KEGG, etc are used) 1. GapFind and GapFill: minimize the total number of gaps in a metabolic network model. Gapnd: a mixed integer linear pro- gramming algorithm that can identify every gap in a network by identifying blocked metabolites (cannot be produced or consumed at steady-state under any conditions) GapFill: another mixed integer linear programming(MILP) method 29 3.1. Graph Theory and Essential Metabolites to minimizing the gaps by reversing the existing reactions, adding new reactions or transport reactions, or reactions between com- partments, with minimal number of model modications. 2. SMILEY: predicts reactions that are likely missing from a net- work when the model predicts no growth but experiment predicts growth (based on the OptStrain algorithm). 3. GROWMATCH: uses experimentally determined gene essential- ity data to identify incorrect model predictions. 4. other methods. OMNI, for example. ˆ b) Experimental methods. Several experimental methods could also be introduced to lling the gaps. After rening the model by nd and ll the gaps, we categorize metabo- lites into 3 dierent types novelly: Universal Metabolites, Essential Unusual Metabolites, and Non-Essential Metabolites. 3.1.2 Categories of Metabolites In this study, the metabolites are divided into three groups: Universal Metabolites (UM): Some inorganic or cofactor metabo- lites, such as H2O, ATP, or NADP+, have been found to exist universally more than 90% organisms whether they are prokaryotes or eukaryotes. These metabolites are called universal metabolites. Essential Unusual Metabolites (EUM): The metabolites whose ab- sence will cause cell death, but are not UM are called Essential Unusual 30 3.1. Graph Theory and Essential Metabolites Metabolites. In order to nd out the essential metabolites, a large amount of transposon insertion mutants are created to represent the disruption and therefore the loss of function of more than 2000 genes. UM and EUM are usually seen as essential metabolites together, in most of the studies. The list of EUM in M.Tuberculosis can be nd in Appendix 1. Non-Essential Metabolites(NEM): All other metabolites are called non-essential metabolites. The universal metabolites are usually treated as essential metabolites be- cause most living matter cannot survive without the metabolites like H2O and ATP. However, this denition could bring confusion and misunderstand- ing in the research, especially in the drug target studies. For example, metabolites as H2O and ATP are to be recognized as essential because very few living cell can live without H2O and ATP, but they can hardly be used as a drug target. (Martelli et al., 2009) We are trying to nd a method to predict the metabolites which are not common metabolites, but still, the fact without them will signicantly eliminate the cell growth. A innovative idea is to lter all the common seen metabolites, in other words, to pick out the Essential Unusual Metabolites (EUMs). Obtain EUM and UM With a database of 250 species of organism, we dene metabolites those could be found in more than 90% of the organisms are universal metabolites. Some of the list of metabolites in dierent species are obtained from a database investigated by Kim (Kim et al., 2007), other 31 3.2. Application to Mycobacterium Tuberculosis are from KEGG pathway database. The comprehensive list of the universal metabolites are listed in Appendix 2. All the UM metabolite are found to be essential metabolites in most of the recent studies about essential metabolites in dierent organisms (Martelli et al., 2009). The next main step is to study the correlation between the topol- ogy of the metabolite network and the metabolite essentiality for each type. Before that, it's very important to rene the model we are going to use, as there are missing information as gaps and orphan reactions. 3.2 Application to Mycobacterium Tuberculosis A list of essential metabolites for Mycobacterium Tuberculosis(MTB) was obtained from G.Lamichhane, J.Freundlich et al., (Lamichhane et al., 2011) from a in vivo approach. 5126 independent, genotyped and archived mu- tants with disruption in both intra- and intergenic regions were created, followed by a statistical analysis to predict the essentiality of the genes. The molecules produced by reactions encoded by essential enzymes are clas- sied as essential metabolites. This is also the rst comprehensive report of a large number of essential molecules so far.(Duarte et al., 2004) 3.2.1 Mycobacterium Tuberculosis Mycobacterium tuberculosis(MTB) is a pathogenic bacterial species in the genus Mycobacterium and the causative agent of most cases of tuberculosis, it was rst discovered in 1882 by Robert Koch. However, with 1.77 million 32 3.2. Application to Mycobacterium Tuberculosis deaths from TB in 2007, this disease ranks second only to human immun- odeciency virus as a cause of death from an infectious agent. The estimate that more lives may be lost in 2011 due to tuberculosis than in any year in history is alarming. In 1993, the gravity of the situation led the World Health Organisation (WHO) to declare tuberculosis a global emergency in an attempt to heighten public and political awareness. Complete genome sequence of the best-characterized strain of Mycobacterium tuberculosis has been determined in 1998 by S.T. Cole, R.Brosch et al, (Cole et al., 1998a) to enhance the understanding of the biology of the slow-growing pathogen and to help the conception of new prophylactic and therapeutic interven- tions. New-resistant tuberculosis appear almost every year, so new drugs are needed to treat the infections caused, the attempt to determine essential metabolites would benet the drug target ltration. Gyanu, Joel, et al, iden- tied essential metabolites and enzymes for M.tuberculosis using a genetics- based approach,(Lamichhane et al., 2011) which provide a new blueprint for developing eective chemical probes of M. tuberculosis metabolism. The cell envelope of M. tuberculosis, contains an additional layer beyond the peptidoglycan that is exceptionally rich in unusual lipids, glycolipids and polysaccharides. Cell-wall components such as mycolic acids, myco- cerosic acid, phenolthiocerol, lipoarabinomannan and arabinogalactan, are generated by novel biosynthetic pathways, and several of these may con- tribute to mycobacterial longevity, trigger in
ammatory host reactions and act in pathogenesis. Little is known about the mechanisms involved in life within the macrophage, or the extent and nature of the virulence factors pro- duced by the bacillus and their contribution to disease.(Cole et al., 1998b) In addition to the mycolic acids, the cell envelope contains a wide array of 33 3.2. Application to Mycobacterium Tuberculosis distinctive lipids and glycolipids that confers extreme hydrophobicity to the outer surface of the organism.(Sibley et al., 1988, 1990) The model of Tuberculosis we used is iNJ661 for Mycobacterium tuber- culosis H37Rv, developed by N. Jamshidi. (Jamshidi and Palsson, 2007) 3.2.2 Gaps in the Metabolite Network iNJ661 Using graph theory stated in 3.1, there are two dierent types of gaps found in iNJ661 model for MTB. For the list of root no-production metabolites, please see Appendix 3. For a comprehensive list of root no-consumption metabolites, please see Appendix 4. 3.2.3 Metabolite Essentiality and Network Degree It has been found that essential metabolites have higher degree than non- essential metabolites in E.coli (He and Zhang, 2006). However, inM.tuberculosis, we calculated the average degree of essential metabolites and non-essential metabolites, respectively. The average degree of essential metabolites is found to be 83, much higher than the non-essential ones, which is just 9. It is mainly because the universal metabolites, which are counted as essen- tial metabolites, usually have much higher degree than the others with a noticeably average degree of 95:89. In order to nd out if there is statistically signicant dierence between essential metabolites and non-essential metabolites, Welch two sample test is implemented on the essential metabolites and non-essential metabolites, 34 3.2. Application to Mycobacterium Tuberculosis Figure 3.4: Probability distribution of degree of metabolites with a p value of 0:00066. When comparing with the t-test result of EUMs and NEMs, which has a p value of 0:1588 shows there is no statistically signicant dierence existing if UMs are not included. It is concluded that the the higher degree of UMs is the reason for the dierence between EMs and NEMs, and this supports He's nding. Another interesting fact is the fraction of essential metabolites among the 10% most connected is 64:8% and there is no essential metabolites in the least connected. However, it is interesting to see that the t-test shows there is a signicant dierence between the downstream degree of EUMs and NEMs, with a p-value of 0:00014, it means usually EUMs has smaller downstream degree, so there is a higher possibility that a metabolite with fewer products is EUM. 35 3.2. Application to Mycobacterium Tuberculosis Figure 3.4 is the degree distribution of iNJ661. The horizontal axis is the degree of the metabolite, while the vertical axis is the probability of the metabolite, so for any given spot, it shows the probability of metabolites with a certain degree. It shows that essential metabolites have a higher probability with higher degrees, especially larger than 20. It also shows that most of the non-essential metabolites have degrees under 20, and barely any NEMs larger than 20. 3.2.4 Metabolite Essentiality and the Degree of Neighbors Figure 3.5: Probability distribution of neighbor's degree Here we examine the total degree of neighbors and the average degree of neighbors for EM, EUM, NEM, respectively. The average sum of the neighbor's degrees for EM, EUM and NEM are shown in Figure 3.5. With a Welch's two sample t-test, it is clear that both EM and EUM 36 3.2. Application to Mycobacterium Tuberculosis Figure 3.6: Average sum of neighbor's degrees for EM, EUM and NEM have a distribution with larger degree of their neighbors compared to NEMs, with p values of 0:0206 and 0:0003. The mean of EM is 12108, 8 times larger than that of NEM, which has a mean of 1416. The main reason is that UM has incredibly high indirectly-connected neighbors. The mean of EUM is 852, and we can see from Figure 3.6 that they have much higher probability with neighbor's degree larger than 10, and almost all the NEMs's neighbor's degrees are under 20. Interestingly, we found there is no signicant statistical dierence be- tween both the average degrees of EM and NEM (p value = 0:3952), EUM and NEM(p value = 0:9455), which means for all the metabolites, the av- erage degrees of their neighbors are not related to the fact it's essential or not, statistically. 37 3.2. Application to Mycobacterium Tuberculosis 3.2.5 Metabolite Essentiality and Clustering Coecient With the model of iNJ661, when it comes to clustering coecient, we found that there is no true dierence between EM and NEMs (p value = 0:256), the averages of them are also quite close, 0:272 for EM and 0:234 for NEM . We observed that EUMs, the means of which is only 0:07, shows a visible dierence from the NEMs. t-test results show the EUMs do have a smaller clustering coecient, with a p-value of 0.0051. The fraction of metabolites with 0 clustering coecient is much higher in the EUMs than other 2 groups. Figure 3.7 shows the prolixity distribution of clustering coecient for all 3 type of metabolites, in which more EUMs have a clustering coecient of 0. This interesting result shows that we can reliably associate metabolite essentiality with this parameter, but is just limited to EUMs, which is useful as the UMs can be derived from the database straightforwardly. Small clustering coecient could be used as an indicator for the EUMs. 3.2.6 Metabolite Essentiality and Network Betweenness. According to our investigation, both UMs and EUMs are shown to have shortest path through, the means of which are 8924 and 1310, respectively, while the average of NEMs is just 666, the p value for Welch's two sample t-test is 0.001 for UMs and NEMs. There is a signicant dierence between UMs and NEMs. It's important to note that NEMs have more shortest path through them. According to Figure 3.8, it can be concluded that EM and EUMs have great probability with higher betweenness. So the network 38 3.2. Application to Mycobacterium Tuberculosis Figure 3.7: Probability distribution of Clustering Coecient betweenness could also be used as an indicator for the metabolite essentiality. Figure 3.8: Average betweenness of EM, EUM and NEM Figure 3.9 is about the probability distribution of betweenness, we could 39 3.3. Conclusion Figure 3.9: Probability distribution of betweenness nd the distribution follows a exponential distribution, and when the be- tweenness is larger than 3000, only probabilities of EM and EUM are above 0, and NEMs are all 0. 3.3 Conclusion We looked systematically for correlations between the essentiality of genes and their topological characteristics in interaction networks. We have found that the metabolite essentiality is signicantly related to the parameter of the metabolite in the metabolic network. The EMs are usually with larger degree, more neighbors' degree and more shortest path through, notably, the EUMs have smaller clustering coecient. While the essential metabolites are derived from the essential genes and 40 3.3. Conclusion approved by the experiments, it is possible that gene essentiality is also related to metabolite topology parameters, this could be evaluated by future studies. 41 Chapter 4 Constraint Based Identication of Essential Metabolites Flux Balance Analysis and Flux Sum Analysis are two alternate approaches to graph theory that are often used to identify the essential metabolites. Unlike graph theory, which is a generic statistical predication, the constraint based approaches (Flux Balance Analysis and Flux Sum Analysis) identify the essential metabolites in-silico, and would further decrease the amount of wet-lab experiments for validating essential metabolites. With the most advanced model of C. Reinhardtii, we identied essential metabolites under three dierent growth conditions, and categorized the essential metabolites using Flux Sum Analysis. 42 4.1. Application: Microalgae 4.1 Application: Microalgae Microalgae are ubiquitous sunlight driven cell factories in fresh water or ma- rine systems, they convert CO2 to food, biofuels or other high value bioactive products, and even cosmetic products (Spolaore et al., 2006). The number of algal species have been estimated to be more than one million with a ma- jority being microalgae (Metting, 1996). Among all the potential sources, microalgae are now recognized as the only source of renewable biodiesel that is capable of meeting the global demand for transport fuels. Compared to the rst generation sources of biofuel, microalgae have greater potential as a reliable alternate energy source.Table 4.1 about oil yield from algae and other sources below demonstrates the advantage of cul- tivating microalgae. The higher concentration of lipid content in microalgae is one reason for this, as lipid contains quite high energy. The lipid concen- tration can often exceed 80% while 20%-50% are quite common.(Beer et al., 2009) Moreover, the fast doubling time of microalgae makes it possible to generate large quantities of biomass, which could be further processed to get dierent types of biofuels. Currently, several species of microalgae have gained public and scientic attraction. However, for the following reasons there is still enormous scope for engineering micro algae to increase their production: 1. Little experience with the development of closed large scale photo- bioreactors. 2. High material costs for closed, highly ecient bioreactor systems. 43 4.1. Application: Microalgae Crop Oil Yield(L/ha) Corn 172 Soybeans 446 Jatropha 1892 Coconut 2689 Oilpalm 5950 Microalgae 5000-15000 Table 4.1: Oil yield from algae and from other sources,(Chisti, 2007) 3. High energy requirement for cultivation (e.g. mixing). Expensive har- vesting (cells need to be separated from medium which is time and/or energy consuming) (Metting, 1996). 4.1.1 Chlamydomonas Reinhardtii Among many types of microalgae, green algae C. Reinhardtii is selected for this study for the following reasons: ˆ C.Reinhardtii is a model organsim for the process of photosynthesis in plants (Harris, 2001), and a model for photosynthetic hydrogen production (Melis and Happe, 2004). Model organisms are simplied representative systems whose study enables researchers to extrapo- late their understanding to other complex organisms. A number of eorts have been made on studying C.Reinhardtii and full nuclear genome sequence has been assembled in 2007 (Merchant et al., 2007) (Maul et al., 2002) (Vahrenholz et al., 1993) (Boer et al., 1985). 44 4.1. Application: Microalgae ˆ C.Reinhardtii can be cultivated under dierent conditions, either au- totrophic (from simple inorganic molecular and using energy from light), auxotrophic (relying on organic acid and light) or heterotrophic (with organic acids only). ˆ In addition, the time for C.Reinhardtii to grow to a mature individual is 5 to 6 hours under laboratory conditions, with a total fatty acid content of the isolated strain of 25%. The composition of fatty acids in the species of microalgae was mainly docosanoic acid methyl ester, tetradecanoic acid methyl ester, hexadecanoic acid methyl ester and nonanoic acid methyl ester. Cells of C. reinhardtii are oval-shaped, typically 10  m in length and 3  m in width with two 
agella at their anterior end. This algae contains several mitochondria and a unique chloroplast which occupies 40% of the cell volume and partly surrounds the nucleus(May et al., 2008). Figure 4.1 shows the reconstructed metabolic network of C.Reinhardtii. This unicellular green algae, closely related to photoreceptors of multicellular organisms, oers a simple life cycle, easy isolation of mutants, and a growing array of tool and techniques for molecular genetic studies (Li et al., 2010; Rupprecht, 2009). Recently, C. Reinhardtii have received more attention, because of its potential to generate biofuel to meet the growing clean energy demands. In our study, model iRC1080, the newly reconstructed genome-scale metabolic network for C.Reinhardtii with a novel light-modelling approach that enables quantitative growth prediction for a given light source, is chosen to investigate the essential metabolites in C.Reinhardtii. 45 4.1. Application: Microalgae Figure 4.1: Reconstructed metabolic network of C. reinhardtii, (Reprinted from (Boyle and Morgan, 2009)) 4.1.2 Biofuel from Microalgae A biofuel is a solid, liquid or gaseous fuel derived from any biological carbon source including treated municipal and industrial wastes. Biofuels can be derived either from land-based crops or marina plants as microalgae. Three main types of biofuels are now produced from microalgae: biohydrogen, biodiesel, ethanol from fermentation of biomass. Biohydrogen from Microalgae As a fuel, hydrogen causes less environ- mental impact whether in stationary engines, gas turbines or automotive vehicles. Microalgae have the genetic, metabolic and enzymatic charac- 46 4.1. Application: Microalgae teristics for hydrogen which cannot be provided by any land-based plants. During photosynthesis, the microalgae convert water molecules into hydro- gen ions H+ and oxygen. The hydrogen ions are then converted into H2 by the enzyme hydrogenase (Hahn et al., 2004). The photosynthetic pro- duction of O2 results in rapid inhibition of the enzyme hydrogenase and the production of H2 is inhibited. Therefore, cultivation of microalgae for the production of hydrogen must take place under anaerobic conditions (Brennan and Owende, 2010). Hydrogen production in Chlamydomonas has to take place at an e- ciency of 7% under outdoor conditions to be commercially viable. While maximum eciency for this process has been calculated to be between 6% to 10%. (Rupprecht et al., 2006) Biodiesel from Microalgae Microalgae has shown great potential in the economical biodiesel production. Microalgae commonly double their biomass within 24h, which makes it possible to produce enough biomass for production of oil. There are two main large producing methods for the biomass: raceway pond and photobioreactors. Photobioreactors provide much greater oil yield compared with raceway ponds, but raceways ponds are cheaper. Both are technically feasible. Currently, some naturally isolated microalga Chlamydomonas (for in- stance, sp MCCS 026) have been proven to be valuable candidates for biodiesel production as they have high growth rate and lipid content. They require a simple and comparatively low cost culture medium(Morowvat et al., 2010). The oil content in dierent kinds of microalgae can be found in the 47 4.1. Application: Microalgae Microalga Lipid content (%dry weight) Botryococcus braunii 25-75 Chlorella sp. 28-32 Crypthecodinium cohnii 20 Cylindrotheca sp. 16-37 Dunaliella primolecta 23 Isochrysis sp. 25-33 Monallanthus salina N 20 Nannochloris sp. 20-35 Phaeodactylum tricornutum 20-30 Chlamydomonas Reinhardtii 30 - 60 Schizochytrium sp. 50-77 Table 4.2: Oil content from microalgae (Chisti, 2007)(Li et al., 2010) table below: Biomethane from Microalgae Microalgae has been investigated for biomethane production for a long time, it can be grown in large amounts (150 -300 tons per ha per year (Degen, 2001)), which leads to a theoretical yield of 200; 000 - 400; 000 m3 of methane per ha per year. However, due to the high cost of biomass, and the low production capacity compared to the high demand of commercial gas, biogas is now usually a mixture of carbon dioxide gas and biomethane (Schenk et al., 2008). Despite the advantages of algae as a source of biofuels, there are still signicant challenges that must be addressed before algal biofuels can be 48 4.2. Flux Balance Analysis widely used. One of the main concerns is the biodiesel from algae is not yet economically competitive with fossil fuels or corn ethanol: the cost to producing gasoline is about $ 1:86 per gallon (according to retail price in 2009 ), while for algal biodiesel, it will be $2:5 -$25( range depends on algae productivity ) (Schmidt et al., 2010). 4.2 Flux Balance Analysis Flux Balance Analysis(FBA) calculates the 
ow of metabolites (also known as 
ux), and is widely used as a tool to predict metabolite behavior such as growth rate of an organism or the rate of production of a bio-technologically important metabolite. With the assumption that the system will reach a steady state under any given environmental condition, the regulated metabo- lite network is set to satisfy a set of feasible constraints. Once the constraints and 
uxes are identied, optimization techniques could be used to evaluate the performance of the biological system under dierent conditions, such as varying objective functions or bounds on certain reactions, growth on dier- ent media, or of bacteria with dierent gene knockouts. FBA can be further used to predict the yields of important cofactors such as ATP, NADH or NADPH (Kauman et al., 2003; Lee et al., 2006). Flux Balance Analysis can be divided into 4 steps as follows: 49 4.2. Flux Balance Analysis 4.2.1 Mathematical Reconstruction of a Biochemical Network Metabolite network reconstruction is the fundamental step in FBA, it in- volves generating a model that describes the system of interest. This process can be further decomposed into three parts typically performed simultane- ously during model construction: data collection, metabolic reaction list generation, and gene-protein relationship determination . After genome-scale metabolic reconstruction, a stoichiometric matrix S could be generated from the metabolic reactions, S is an m  n matrix of stoichiometric coecients that captures the underlying reaction of the biochemical network. The rows of S correspond to the compounds, while the columns of S correspond to reactions. The entries in each column are the stoichiometric coecients of the metabolites participating in a reaction. Negative elements of the matrix represent the consumption of compounds and positives elements denote production, for the metabolites not participat- ing in a particular reaction, the coecient is zero (Palsson, 2003). Figure 4.2 shows the basic procedures for mathematically reconstruction of a biochem- ical network. The reactions are obtained from the complex gene annotation database, and then converted into stoichiometric matrix. The genome-scale C:reinhardtii metabolic network used in this study consists of 1080 genes, associated with 2190 reactions and 1068 unique metabolites, and encompasses 83 subsystems distributed across 10 compart- ments (Chang et al., 2011). 50 4.2. Flux Balance Analysis Figure 4.2: Mathematically reconstruction of a biochemical network 4.2.2 Model Validation Even the most complete models are not perfect; they might contain missing information, which are called "gaps", the incomplete reconstructions may lead to prediction of erroneous genetic interventions for a targeted over- production or the elucidation of misleading organizational principles and properties of the metabolic network. Several computational and experimen- tal methods can be used to address the gaps to help make more realistic predictions. As Figure 4.3 shows, the dead-end metabolites are identied. 51 4.2. Flux Balance Analysis Figure 4.3: Model validation 4.2.3 Mass Balance After the network matrix is reconstructed, mass balance can be dened in terms of the 
ux through each reaction and the stoichiometry of that reaction in the following form @x @t = Sv v is the vector of 
uxes with elements corresponding to the 
uxes in given reactions. In steady state, the change amount of a metabolite x over time t within the whole system becomes zero, yielding : 52 4.2. Flux Balance Analysis Sv = 0 Figure 4.3 explains the basic mechanism of mass balance denition. Figure 4.4: Mass balance denition 4.2.4 Constraints One way to add additional constraints to the metabolic network and cal- culate the 
uxes in the network is to measure 
uxes in the metabolite net- work. Usually, it's hard to measure the exact 
ux values, so ranges of al- lowable 
ux values are incorporated as additional constraints. Constraints could be physicochemical, topological or environmental. Physicochemical constraints are physical laws like conservation of energy and mass; topolog- ical constraints contains information of metabolites within dierent cellular compartments; and environmental constraints include nutrient availability, 53 4.2. Flux Balance Analysis pH and temperature that vary over time and space. The constraints im- posed by the thermodynamics (e.g.eective reversibility or irreversibility of reactions) and enzyme or transporter capabilities (e.g. maximum uptake or reaction rates) are considered and incorporated into the model. It should be emphasized that these constraints are based on what may be considered \hard-wired" constraints the metabolic system must obey. i  vi  i The following constraints several of which are obtained from Roger Chang and Nanette Boyle (Boyle and Morgan, 2009; Chang et al., 2011) are often used: 1. Fluxes of all reversible reactions are left unbounded. 2. Irreversible reactions are given a lower bound of zero to preserve di- rectionality. 3. Dierent environmental conditions are modeled by appropriately set- ting reaction 
ux constraints in iRC1080. These reactions consist of environmental exchanges, non-growth associated ATP maintenance, O2 photoevolution, starch degradation, and light or dark-regulated enzymatic reactions (Table 4.4). 4. Constraint values are derived from published sources unless otherwise noted and imposed only under appropriate environmental conditions. 5. Minimal condition signies a constraint that is used under all envi- ronmental conditions. The appropriate biomass reaction was set as 54 4.2. Flux Balance Analysis Metabolite A B C Ex photonVis 0 lb Ex CO2 0 lb EX Oxygen(e) -10 lb -10 lb -10 lb EX ac(e ) 0 lb -10 lb EX starch(h) 0 both 0 both PCHLDR 0 both 0 both PFKh 0 both 0 both G6PADHh 0 both 0 both G6PBDHh 0 both 0 both FBAh 0 both 0 both H2Oth 0 ub 0 ub 0 lb BIOMASS Chlamy auto 1.00 BIOMASS Chlamy hetero 1.00 BIOMASS Chlamy mixo 1.00 Table 4.4: Constraints for dierent growth conditions the objective function for optimization depending on environmental conditions. For the list of constraints, please see below: A(Autotrophic):light, aerobic, no acetate B(Mixotrophic):light, aerobic with acetate C(Heterotrophic):dark, aerobic, with acetate 55 4.2. Flux Balance Analysis In addition, GLPThi, ATPSh, BFBPh, GAPDH(nadp), MDH(nadp)hi, MDHC(nadp)hi, PPDKh, IDPh, PRUK, RBPCh, rRBCh, SBP are set to be zero 
ux in the heterotrophic growth condition, as there are no photo- synthesis reaction in this growth condition. In the light growth conditions (autotrophic and mixotrophic), the light is assumed to have the same compo- sition as solar light when measured from the surface of the earth. According to the literature, the conversion rate from emitted energy (Em2s) to incident (mmolgDWhr) is found to be 3:83.(Costa and de Morais, 2010) 4.2.5 Objective Function The model is under-determined as the number of linear equations is far less than the number of unknown reaction 
uxes. Therefore, additional constraints should be incorporated into FBA so as to optimize a particular cellular objective. Objective functions usually take on a linear form Z = cv where c denotes the coecient for weights indicating how much each re- action (v) contributes to the objective. In practice, when only one reaction, such as biomass production, is desired for maximization or minimization, c is a vector of zeros with a value of 1 at the position of the reaction of inter- est. Objective functions can take on many forms, commonly used objective functions include: Maximizing biomass: the objective is to simulate the optimal cell growth. 56 4.2. Flux Balance Analysis Minimize ATP production: the objective is to deter mine conditions of optimal metabolic energy eciency. Maximize metabolite production: this objective function has been used to determine the biochemical production capabilities of Escherichiacoli: In this analysis, the objective function was dened to maximize the production of a chosen metabolite or desired product (e.g: lysine or phenylalanine) According to the literature, the in silico predictions of the maximizing biomass production are consistent 86% of the time for E.coli, and approx- imately 60% of the time for Helicobacter pylori, approximately 91% for the E.coli when transcriptional regulation was accounted for (Ibarra et al., 2002)(Edwards et al., 2001). Biomass Objective Function for C. Reinhardtii The biomass for- mation equations used for Flux Balance Analysis were derived according to previous methods (Chavali et al., 2008). The idea is to estimate the proportion of dry weight biomass composed of protein, DNA, RNA, carbo- hydrate, fatty acid, glycerol, lipids, chlorophyll, etc., using available liter- ature. At rst, concentration of DNA, RNA, retinal, chlorophyll and xan- thophylls in the cell have been found in the literature to be about 0:40% (Valle et al., 1981), 11.1%, 0.00002795%(Beckmann and Hegemann, 1991), 2.4% and 0.37%(Niyogi, 1997). Then composition of the remaining cellular components was estimated from previously published data, components reported at less than 0.1g/L are omitted, the remaining components (carbohydrates, including starch; 57 4.2. Flux Balance Analysis glycerol; lipid, including triglyceride; protein; and volatile fatty acids, repre- senting the sum of acetic, propionic, butyric, and valeric acids) are obtained from R.Chang in UCSD. Finally, the data above are integrated into dierent full biomass equa- tions for each growth condition. All the values are converted intommol=gDW The biomass function for 3 dierent growth conditions can be found in the Appendix 6. 4.2.6 Linear Program Solver Linear programming is used to nd the optimal solution derived from the ob- jective function within the space dened by the mass balance equations and reaction bounds and other constraints. Due to the under-determined nature of the stoichiometric equations, the solution to the above optimization prob- lem maybe non-unique (i.e, the optimal solution lies along an edge, plane, or hyperplane, rather than simply lying at a vertex); thus, several dierent sets of 
uxes may achieve the same optimal objective. Please see Figure 2.1 for Linear Programming.) In general, lots of computational tools can be implemented to solve the LP problem that arises in FBA, even for large-scale systems. 58 4.2. Flux Balance Analysis 4.2.7 Identication of Essential Metabolites With the 
ux distribution obtained from the initial Flux Balance Analysis, essential metabolites are distinguished from a total of 1215 metabolites. The metabolite essentiality can be found by metabolite knock-out analysis, which is dened as the phenotypic eect on cell growth when the consumption rate of a given metabolite M is set to zero.Only 
uxes producing M are allowed, so the constraints are applicable to all the outgoing 
uxes that are set to zero. The essentiality of metabolite is dened by the change in scale of cell growth rate compared to the growth rate of wild type, ME = (BasegrowthOptimal Growth)=Base Growth In this study, an essential metabolite is recognized when its absence leads to decrease in cell growth rate that is at least half of that of the wild type, which means, ME > 90%. We calculated the elimination caused by the reduction of the 
ux of each metabolite to zero. With the model iRC1080, which creatively contains metabolic light usage, we can simulate the growth in three dierent conditions. The growth conditions includes: Condition A (Autotrophic) : light, aerobic, no acetate, biomass as ob- jective function. Condition B (Mixotrophic): light, aerobic, with acetate, biomass as ob- jective function. Condition C (Heterotrophic): dark, aerobic, with acetate, biomass as objective function. 59 4.2. Flux Balance Analysis The same metabolite could exist in seven dierent compartments in this model, including cytosol, chloroplast, mitochondria, glyoxysome, 
agellum, nucleus and extra-cellular. The metabolite essentiality are calculated sepa- rately in dierent compartments. In other words, if a metabolite participates in reactions in dierent compartments, the 
ux of that particular metabolite is treated as two dierent 
uxes in their respective compartments. When it comes to analyzing the overall metabolite essentiality, we ignore the com- partment dierence, it is recognized to be essential as long as it is found to be essential in any one of the compartments. There are 1215 metabolites in total in C.R, in model iRC1080. Among all the 1215 metabolites, 426 are found to be essential in Condition A , and 247 are found to be essential in Condition B , while 260 in Condition C , this demonstrates for dierent growth conditions, the microalgae use dierent metabolite pathways to fulll the basic growth requirements. 189 metabolites show essentiality in all 3 growth conditions (Appendix 5), 38 metabolites are found to be essential in 2 growth conditions, 419 metabolites show essentiality in 1 growth conditions. Less than 15% of metabolites are found to be essential in all three growth conditions, this might be because of the high robustness of biosystems because in dierent growth conditions dierent pathways are activated to ensure cell growth. Although essential metabolites have been identied, it is not yet clear if all the essential metabolites exert the same in
uence on the biological sys- tem. We are going to categorize essential metabolites by Flux Sum Analysis, to better understand how essential metabolites in
uence the total growth rate of biological systems. 60 4.3. Flux Sum Analysis 4.3 Flux Sum Analysis A new variable "
ux-sum" is introduced by Bevan Kai Sheng Chung and Dong-yup Lee in 2009 (Chung and Lee, 2009) to describe the absolute rate of consumption and production of each metabolite. For a steady state system, which is also the fundamental assumption of Flux Balance Analysis, 
ux- sum i of the metabolite i can be derived from summing up all the incoming and outgoing 
uxes around the metabolite (Kim et al., 2007): i = X j"Pi Sijvj =  X j"Ci Sijvj = 1 2 j X j Sijvj j where Sij is the stoichiometric matrix, and Vj is the 
ux of reaction j. Pi denotes the set of reactions producing metabolite i, while Ci represents the set of reactions consuming metabolie i. For a system in steady state, in order to maintain a constant concentration of a certain metabolite, the sum of outgoing 
uxes should be equal to the sum of incoming 
uxes. Flux sum analysis is known for its capability to help study the dierences among essential metabolites, a two-step approach is employed to carry out the 
ux sum attenuation. 4.3.1 Procedure for Flux Sum Analysis Step 1 : Evaluate basal 
ux-sum distribution The wild-type 
ux distribution is dened as the 
ux distribution in the wild-type metabolite model (without changing any elements of the mathematic model.) The 61 4.3. Flux Sum Analysis basal 
ux-sum distribution is calculated from the wild-type 
ux distribution out of FBA, under unperturbed condition. In this case, 3 dierent growth conditions are simulated, respectively. max vbiomass s:tX j Sijvj = 0 j  vj  j The basal 
ux-sum distribution for metabolite i is achieved after solving the above linear programming question: Bi == 1 2 j X j Sijvj j The basal 
ux-sum distribution for Chalmydomonas is listed in the Ap- pendix V. We calculate the total basal 
ux-sum for the systems in 3 dierent growth conditions same as Flux Balance Analysis. The total basal 
ux-sum for mixotrophic growth (with light, with acetate) is found to be larger than other 2 growth conditions. This result is consistent with current studies. The total basal 
ux-sum for all the Universal Metabolites are also calcu- lated, it's found that the Universal Metabolites contributes to a very large percentage of the system 
ux-sum (about 80% - 85%)(Figure 4.5). It is also noticed that the probability of the basal 
ux-sum generically 62 4.3. Flux Sum Analysis Figure 4.5: The total basal 
ux-sum for C.Reinhardtii in 3 dierent con- ditions. The blue part represents the total basal 
ux-sum for Universal Metabolites. follows an exponential distribution (as shown in Figure 4.6). y = ea+bx+cx 2 y is the probability of a metabolite with basal 
ux-sum of 10x. With R2 larger than 0.99. Step 2 : Manipulate 
ux-sum by attenuation Flux-sum of each metabolite is manipulated to evaluate the corresponding metabolite essen- 63 4.3. Flux Sum Analysis -3 -2 -1 0 1 2 3 0.0 0.2 0.4 0.6 0.8  Condition A  Condition B  Condition C P ro ba bi lit y Metabolite Basal Flux-Sum (logX) Figure 4.6: Probability distribution of metabolites with certain basal 
ux- sum. tiality: the basal 
ux-sum is considered as a starting point, followed by examining the eects of decreasing the metabolite 
ux-sum. Same as above, we simulated 3 dierent growth conditions for each metabolite. max vbiomass s:t 1 2 j X j Sijvj j kattBi 64 4.3. Flux Sum Analysis X j Sijvj = 0 j  vj  j Biomass production values for dierent levels of 
ux-sum attenuation can be obtained by solving this LP problem. katt control the levels of attenuation of the 
ux-sum, we set katt = 1 initially and then decrease the value of it until katt = 0. While essential metabolites are usually associated with lethal reactions, 3 dierent types of essential metabolites are determined through the 
ux- sum attenuation analysis according to the curve trend when we manipulate the 
ux-sum of dierent metabolites in Figure 4.7. Type AE: the most common essential metabolites found in the metabo- lite network, the biomass production rate varies linearly to the 
ux-sum of the metabolite. Type BE: these type of metabolites are attributed to the existence of alternate optimal solutions, which also demonstrates the highly robustness of the bio-system, a small reduction of 
ux-sum can be compensated by other "equivalent" 
uxes. Type CE: these metabolites showed a rapid drop when the 
ux-sum was attenuated and reach the 0 
ux earlier than other essential metabolites. With a relatively high threshold, the organism would not be able to pro- duce any biomass under the threshold. These metabolites were found to be involved in non-growth associated maintenance. 65 4.3. Flux Sum Analysis 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 B io m as s Le ve l ( 0. 2) Flux Sum Level (0.2) AE BE Figure 4.7: 2 types of essential metabolites: Type AE and Type BE With the model iNJ1080 for C.Reinhardtii, we carried out Flux Sum Attenuation Analysis to study the type of all the essential metabolites in 3 dierent growth conditions. The table below show the number of dierent type of essential metabolites in dierent growth conditions. We could see from Table 4.5 and in Figure 4.8 that here are much more Type A essential metabolites than Type B essential metabolites, and very a few Type C metabolites. The two essential types, AE and CE, may serve as promising drug targets since the attenuation of their 
ux-sum will lead 66 4.3. Flux Sum Analysis Lna Lwac Da Type AE 301 182 179 Type BE 122 65 79 Type CE 3 1 2 Total 426 248 260 Table 4.5: Number of dierent types of essential metabolites in dierent growth conditions to signicant reduction in cell growth. Figure 4.8: Number of dierent type of essential metabolites in dierent growth conditions 67 4.3. Flux Sum Analysis Biological Discussion The result shows great consistency with B. Chung's hypothesis that most of the essential metabolites in the cell are type AE (Chung and Lee, 2009). There are 189 metabolites found to be essential in all three dierent kind of growth conditions, it demonstrated the high robustness of the bio- logical systems. In dierent growth conditions, the mircroalgae will change the metabolite pathway to meet the living requirements. We have found that in autotrophic condition, photosynthesis, porphyrin and chlorophyll metatabolism,phenylalanine, tyrosine, and tryptophan biosynthesis were the most essential subsystems, and had most of the essential metabolites. While for mixotrophic condition, phenylalanine, tyrosine, tryptophan biosynthesis, porphyrin and chlorophyll metabolite pathways showed more essentiality than other pathways. When the simulation is running under the heterotrophic condition, in the dark environment with acetate, photosynthesis pathway does not show essentiality any more.Instead, glycolysis, starch metabolism, amino acids, chlorophyll, and nucleotides still make up a high proportion of required metabolites. Expectedly, the fact that most of the essential metabolites are Type AE, demonstrates that most of the essential metabolites contribute crucially to the cell growth without any substitute. However, there are still some essential metabolites(BE) that can nd a alternative pathway to sustain cell growth for a short period of time. 68 4.3. Flux Sum Analysis 4.3.2 Conclusion In this chapter, we implement Flux Balance Analysis as the constraint based modeling tool to identify the essential metabolites, the constraints and biomass formation are conducted from literatures and other resources. 183 metabolites are found to be essential in all 3 growth conditions. This is also the rst comprehensive essential metabolites list for C. Reinhardtii under all 3 growth conditions. By using Flux Sum Analysis, we categorized all the essential metabolites into 3 dierent types according to the type of impact when the total 
ux of a certain metabolite is decreasing. We found that Type AE is the most common essential metabolites. This study reveals that most of the essential metabolites exert equally in
uence on the cell growth. 69 Chapter 5 Conclusion Understanding and identifying the essential metabolites is important as their absence leads to cell death. The main objective of this study is to identify the metabolite essentiality through two dierent approaches: an interaction- based and a constraints-based. In the interaction-based approach, a latest model with essential metabo- lites from Lamichhane et al. (2011) for Mycobacterium tuberculosis is used to study the correlations between metabolite essentiality and the metabolite network topology. The metabolite degree, the degree of neighbors, the clus- tering coecient of each metabolite, and the betweenness of the metabolite network is calculated, separately. Based on the statistical tests, we found that the metabolite essentiality is signicantly related to the topological characteristics. The essential metabolites usually have larger degree, larger sum of neighbors' degree and smaller shortest path and the essential lite metabolites have smaller clustering coecient. In the constraint-based approach, Flux Balance Analysis (known as FBA) is implemented on the most advanced in-silico model of C. Reinhardtii, which contains light usage reactions to make it possible to predict essential 70 Chapter 5. Conclusion metabolites in 3 dierent growth environments: autotrophic, mixotrophic, and heterotrophic. 403, 223 and 206 essential metabolites were found in these three growth conditions. Flux Sum Analysis is used afterward to clas- sify the essential metabolites, it's found that most of the essential metabo- lites are Type A, and the distribution of 
ux sum for all the metabolites tends to follow an exponential distribution and essential metabolites are likely to have larger 
ux sum. This work provides a good understanding of essential metabolites through two dierent approaches. Future work could focus on ˆ experimental validation, to illustrate the prediction of essential metabo- lites in C. Reinhardtii, the list of essential metabolites can be obtained through gene-knockout experiments. ˆ further study of the correlations between metabolite topology and metabolite essentiality in more model organisms. ˆ incorporating dynamic 
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Appendix 2: Universal Metabolites 10 glu-L L-Glutamate 11 glu1sa L-Glutamate 1-semialdehyde 12 hmbil Hydroxymethylbilane 13 ppbng Porphobilinogen 14 skm5p Shikimate 5-phosphate 15 sl2a6o N-Succinyl-2-L-amino-6-oxoheptanedioate 16 uaagmda Undecaprenyl-diphospho-N-acetylmuramoyl- (N-acetylglucosamine)-L-ala-D-glu-meso-2,6-diaminopimeloyl-D-ala-D-ala 17 uaccg UDP-N-acetyl-3-O-(1-carboxyvinyl)-D-glucosamine 18 ugmda UDP-N-acetylmuramoyl-L-alanyl-D-glutamyl-meso-2,6- diaminopimeloyl-D-alanyl-D-alanine A.2 Appendix 2: Universal Metabolites No. Abbrev. Universal Metabolite Name 1 utp UTP 2 ump UMP 86 A.2. Appendix 2: Universal Metabolites 3 udp UDP 4 tyr-L L-Tyrosine 5 trdrd Reduced thioredoxin 6 trdox Oxidized thioredoxin 7 thf 5,6,7,8-Tetrahydrofolate 8 ser-L L-Serine 9 pyr Pyruvate 10 pi Phosphate 11 phe-L L-Phenylalanine 12 nadph Nicotinamide adenine dinucleotide phosphate - reduced 13 nadp Nicotinamide adenine dinucleotide phosphate 14 nadh Nicotinamide adenine dinucleotide - reduced 15 nad Nicotinamide adenine dinucleotide 16 mlthf 5,10-Methylenetetrahydrofolate 17 his-L L-Histidine 18 h2o H2O 19 h H+ 87 A.2. Appendix 2: Universal Metabolites 20 gtp GTP 21 gly Glycine 22 glu-L L-Glutamate 23 gln-L L-Glutamine 24 gdp GDP 25 dttp dTTP 26 dgtp dGTP 27 dctp dCTP 28 datp dATP 29 ctp CTP 30 coa Coenzyme A 31 co2 CO2 32 atp ATP 33 asp-L L-Aspartate 34 amp AMP 35 adp ADP 36 accoa Acetyl-CoA 88 A.2. Appendix 2: Universal Metabolites 37 val-L L-Valine 38 trp-L L-Tryptophan 39 thr-L L-Threonine 40 pro-L L-Proline 41 pep Phosphoenolpyruvate 42 met-L L-Methionine 43 ile-L L-Isoleucine 44 dump dUMP 45 dtdp dTDP 46 cys-L L-Cysteine 47 cmp CMP 48 arg-L L-Arginine 49 ala-L L-Alanine 50 lys-L L-Lysine 51 leu-L L-Leucine 52 gmp GMP 53 dhap Dihydroxyacetone phosphate 89 A.2. Appendix 2: Universal Metabolites 54 amet S-Adenosyl-L-methionine 55 f6p D-Fructose 6-phosphate 56 dtmp dTMP 57 3pg 3-Phospho-D-glycerate 58 ru5p-D D-Ribulose 5-phosphate 59 3dhsk 3-Dehydroshikimate 60 3dhq 3-Dehydroquinate 61 13dpg 3-Phospho-D-glyceroyl phosphate 62 glyc3p Glycerol 3-phosphate 63 fad FAD 64 cdpc16c19g CDPdiacylglycerol (E coli) ** 65 ACP acyl carrier protein 66 prpp 5-Phospho-alpha-D-ribose 1-diphosphate 67 e4p D-Erythrose 4-phosphate 68 gam6p D-Glucosamine 6-phosphate 69 g6p D-Glucose 6-phosphate 70 xmp Xanthosine 5'-phosphate 90 A.2. Appendix 2: Universal Metabolites 71 imp IMP 72 dhpt Dihydropteroate 73 g1p D-Glucose 1-phosphate 74 dhf 7,8-Dihydrofolate 75 rib
v Ribo
avin 76 o2 O2 77 oaa Oxaloacetate 78 akg 2-Oxoglutarate 79 aicar 5-Amino-1-(5-Phospho-D-ribosyl)imidazole-4-carboxamide 80 10fthf 10-Formyltetrahydrofolate 81 dpcoa Dephospho-CoA 82 aacoa Acetoacetyl-ACP 83 phpyr Phenylpyruvate 84 fmn FMN 85 34hpp 3-(4-Hydroxyphenyl)pyruvate 86 34hpp Phosphatidylglycerophosphate (Ecoli) ** 87 hco3 Bicarbonate 91 A.3. Appendix 3: Root No-production Metabolites in iNJ661 88 uacgam UDP-N-acetyl-D-glucosamine 89 tdeACP Tetradecenoyl-ACP (n-C14:1ACP) 90 malACP Malonyl-[acyl-carrier protein] 91 dnad Deamino-NAD+ 92 ddca Dodecanoyl-ACP (n-C12:0ACP) 93 2obut 2-Oxobutanoate A.3 Appendix 3: Root No-production Metabolites in iNJ661 a23dhba c bmn c xyluD c pmcoa c a2c25dho c cbi c fdxrd c ppal c a2dglcn c cbl1 c fol c pre2 c a2dr5p c cdpdodecg c glcn c psd5p c a2mop c cl c glutrna c ptcys c a2pglyc c clpn160190 c glyc-R c pyam5p c a4h2opntn c cobalt2 c lald-L c pydam c 92 A.4. Appendix 4: Root No-consumption Metabolites in iNJ661 a5dglcn c cobya c meoh c pydxn c a5odhf2a c copre2 c mettrna c ru5p-L c acgam c copre6 c mhpglu c s c achms c dmbzid c mi3p-D c sdhlam c ad c dtt c mi4p-D c selcys c alpam c dttOX c mppp9 c seln c amob c dxyl c mshfald c seramp c apoACP c enter c ncam c thfglu c appl c fc1p c no c thym c applp c fdxox c pdx5p c trnaala c uppg1 c A.4 Appendix 4: Root No-consumption Metabolites in iNJ661 a3ddgc c copre8 c omdtria c spmd c a4hba c cpppg1 c pat c tat c 93 A.4. Appendix 4: Root No-consumption Metabolites in iNJ661 a4hthr c crn c pdima c tmha1 c a4mhetz c dttOX c peptido-EC c tmha2 c a5mtr c enter c peptido-TB1 c tmha3 c a5odhf2a c etha c peptido-TB2 c tmha4 c Ac1PIM4 c fmettrna c pg160 c tmha5 c Ac2PIM2 c gcald c pg190 c tmha6 c acysbmn c gdptp c pheme c triat c alatrna c glyb c PIM6 c trnaglu c arabinanagalfragund c homtta c ptth c uaaAgtla c btamp c hpglu c rhcys c uaaGgtla c cl c maltpt c rmyc c uaagtmda c cobya c man c seln c udpglcur c copre5 c mcbts c sheme c ugagmda c mfrrppdima c sl1 c xylD c 94 A.5. Appendix 5: Common Essential Metabolites in All 3 Growth Conditions A.5 Appendix 5: Common Essential Metabolites in All 3 Growth Conditions 12dmpo argsuc glyc3p pgp1819Z160 1hdecg3p aspsa h2mb4p phpyr 1odec11eg3p B-DASH-ara1p h2o2 phyt 1odec9eg3p ca hco3 phyto 1odecg3p cacoa hcys-DASH-L pi 1pyr5c caro hdeACP ppa 23dhdp cbasp hisp ppad 23dhmb cdp12dgr18111Z160 histd ppbng 23dhmp cdp12dgr1819Z160 hmppp9me ppgpp 25aics cdpea hom-DASH-L pphn 26dap-DASH-LL chlda hso3 ppi 26dap-DASH-M chldb imacp pppg9 2ahbut cmp lyc pq 2cpr5p coa malcoa pqh2 2dda7p ctp methf pram 2h3kmtp cys-DASH-L mg2 pran 95 A.5. Appendix 5: Common Essential Metabolites in All 3 Growth Conditions 2ippm cyst-DASH-L mgdg1819Z160 prbamp 2kmb dcamp mgdg1819Z1619Z prbatp 2me4p dcaro mi3p-DASH-D prfp 2mecdp dghs16018111Z mlthf prlp 34hpp dghs1601819Z mppp9 protdt 3c2hmp dghs18111Z18111Z mppp9me pyr 3c4mop dghs18111Z1819Z nadp r5p 3dhq dghs1819Z18111Z norsp retinal 3dhsk dghs1819Z1819Z o2 retinal-DASH-11-DASH-cis 3hcvac11eACP dhor-DASH-S ocdca s7p 3hmop dkmpp ocdccoa skm 3mob dtmp ocdcea skm5p 3ocvac11eACP dump octeACP so4 3psme dxyl5p omppp9me sqdg18111Z160 4c2me eig3p orot5p sqdg1819Z160 4pasp etha pa succ 5aizc ethamp pa160 thdp 96 A.5. Appendix 5: Common Essential Metabolites in All 3 Growth Conditions 5aop fdxox pa16018111Z thf 5mdr1p fgam pa1601819Z thmpp 5mdru1p fpram pa1801819Z trdox 5mthf fprica pa18111Z160 trnaglu acg5p fum pa18111Z18111Z trp-DASH-L acg5sa g3p pa18111Z1819Z tyr-DASH-L acglu gal pa1819Z160 udp ade gar pa1819Z1619Z udpg adn gcaro pa1819Z18111Z udpgal ahcys gdptp pa1819Z1819Z udpsq aicar glu1sa pacoa udpxyl amet glu5p pcdme ump anth glu5sa pep val-DASH-L aps glutrna pgp18111Z160 xu5p-DASH-D zcaro 97 A.6. Appendix 6: Biomass Function(Objective Function) for Dierent Growth Conditions A.6 Appendix 6: Biomass Function(Objective Function) for Dierent Growth Conditions The biomass function for autotropic: Biomass = 273:7E3  ala-L[c] + 150:2E3  arg-L[c] + 67:8E3  asn-L[c] + 67:8E3  asp-L[c] + 2:4E3  cys-L[c] + 81:2E3  gln-L[c] + 81:2E3  glu-L[c] + 103:0E3  gly[c] + 1:2E3  his-L[c] + 32:7E3  ile-L[c] + 82:4E3  leu-L[c] + 18:2E3  lys-L[c] + 2:4E3 met-L[c] + 33:9E3  phe-L[c] + 47:2E3  pro-L[c] + 20:6E3  ser-L[c] + 82:4E3  thr-L[c] + 1:2E3  trp-L[c] + 1:2E3  tyr-L[c] + 59:4E3  val-L[c] + 2:2E3  datp[c] + 3:9E3  dctp[c] + 3:9E3  dgtp[c] + 2:2E3  dttp[c] + 58:6E3  atp[c] + 104:2E3  ctp[c] + 104:2E3  gtp[c] + 58:6E3  utp[c] + 6:4E3  starch300[h] + 328:4E3 man[c] + 524:1E3  arab-L[c] + 697:0E3  gal[c] + 28:4E3 mgdg1839Z12Z15Z1644Z7Z10Z13Z[h] + 3:2E3 mgdg1839Z12Z15Z1637Z10Z13Z[h] + 3:2E3 mgdg1839Z12Z15Z1634Z7Z10Z[h] + 269:4E6  dgdg1839Z12Z15Z1644Z7Z10Z13Z[h] + 739:2E6  dgdg1839Z12Z15Z1637Z10Z13Z[h] + 739:2E6  dgdg1839Z12Z15Z1634Z7Z10Z[h] + 74:3E6  dgts18111Z1819Z[c] + 74:3E6  dgts18111Z18111Z[c] + 1:1E3  dgts1601829Z12Z[c] + 98 A.6. Appendix 6: Biomass Function(Objective Function) for Dierent Growth Conditions 1:2E3  asqdpa1819Z160[c] + 1:2E3  asqdpa18111Z160[c] + 1:3E3  tag16018111Z160[c] + 1:3E3  tag1601819Z160[c] + 1:3E3  tag1801819Z160[c] + 1:3E3  tag18111Z18111Z160[c] + 1:3E3  tag18111Z1819Z160[c] + 1:3E3  tag1819Z18111Z160[c] + 37:1E3  ac[c] + 30:0E3  ppa[c] + 25:3E3  but[c] + 12:1E3  glyc[c] + 10:1E3  chla[u] + 16:5E3  chlb[u] + 1:0E6  rhodopsin[s] + 504:2E6  acaro[h] + 100:8E6  anxan[u] + 1:4E3  caro[u] + 655:4E6  loroxan[u] + 1:3E3  lut[u] + 554:6E6  neoxan[u] + 352:9E6  vioxan[u] + 302:5E6  zaxan[u] + 29:9 ATP maintainance + 2:3E3  pe1801835Z9Z12Z[c] + 1:9E3  pail18111Z160[c] + 258:4E6  pail1819Z160[c] The biomass function for Mixotrophic: Biomass = 279:3E3  ala-L[c] + 93:7E3  arg-L[c] + 69:5E3  asn-L[c] + 69:5E3  asp-L[c] + 12:2E3  cys-L[c] + 91:8E3  gln-L[c] + 91:8E3  glu-L[c] + 113:9E3  gly[c] + 12:7E3  his-L[c] + 38:0E3  ile-L[c] + 93:0E3  leu-L[c] + 30:6E3  lys-L[c] + 12:7E3 met-L[c] + 40:0E3  phe-L[c] + 51:9E3  pro-L[c] + 20:8E3  ser-L[c] + 34:5E3  thr-L[c] + 1:6E3  trp-L[c] + 1:6E3  tyr-L[c] + 64:3E3  val-L[c] + 2:2E3  datp[c] + 99 A.6. Appendix 6: Biomass Function(Objective Function) for Dierent Growth Conditions 3:9E3  dctp[c] + 3:9E3  dgtp[c] + 2:2E3  dttp[c] + 58:6E3  atp[c] + 104:2E3  ctp[c] + 104:2E3  gtp[c] + 58:6E3  utp[c] + 6:4E3  starch300[h] + 328:4E3 man[c] + 524:1E3  arab-L[c] + 697:0E3  gal[c] + 28:4E3 mgdg1839Z12Z15Z1644Z7Z10Z13Z[h] + 3:2E3 mgdg1839Z12Z15Z1637Z10Z13Z[h] + 3:2E3 mgdg1839Z12Z15Z1634Z7Z10Z[h] + 269:4E6  dgdg1839Z12Z15Z1644Z7Z10Z13Z[h] + 739:2E6  dgdg1839Z12Z15Z1637Z10Z13Z[h] + 739:2E6  dgdg1839Z12Z15Z1634Z7Z10Z[h] + 74:3E6  dgts18111Z1819Z[c] + 74:3E6  dgts18111Z18111Z[c] + 1:1E3  dgts1601829Z12Z[c] + 1:2E3  asqdpa1819Z160[c] + 1:2E3  asqdpa18111Z160[c] + 1:3E3  tag16018111Z160[c] + 1:3E3  tag1601819Z160[c] + 1:3E3  tag1801819Z160[c] + 1:3E3  tag18111Z18111Z160[c] + 1:3E3  tag18111Z1819Z160[c] + 1:3E3  tag1819Z18111Z160[c] + 37:1E3  ac[c] + 30:0E3  ppa[c] + 25:3E3  but[c] + 12:1E3  glyc[c] + 7:8E3  chla[u] + 14:3E3  chlb[u] + 1:0E6  rhodopsin[s] + 4:0E6  acaro[h] + 790:8E9  anxan[u] + 11:1E6  caro[u] + 5:1E6  loroxan[u] + 9:9E6  lut[u] + 4:3E6  neoxan[u] + 2:8E6  vioxan[u] + 2:4E6  zaxan[u] + 29:9 ATP maintainance + 2:3E3  pe1801835Z9Z12Z[c] + 1:9E3  pail18111Z160[c] + 258:4E6  pail1819Z160[c] 100 A.6. Appendix 6: Biomass Function(Objective Function) for Dierent Growth Conditions The biomass objective function for Heterotrophic: Biomass = 309:1E3  ala-L[c] + 95:0E3  arg-L[c] + 65:2E3  asn-L[c] + 65:2E3  asp-L[c] + 11:1E3  cys-L[c] + 82:5E3  gln-L[c] + 82:5E3  glu-L[c] + 99:8E3  gly[c] + 10:6E3  his-L[c] + 33:3E3  ile-L[c] + 81:3E3  leu-L[c] + 19:7E3  lys-L[c] + 10:6E3 met-L[c] + 35:4E3  phe-L[c] + 46:9E3  pro-L[c] + 23:0E3  ser-L[c] + 92:9E3  thr-L[c] + 6:0E3  trp-L[c] + 6:0E3  tyr-L[c] + 56:0E3  val-L[c] + 2:2E3  datp[c] + 3:9E3  dctp[c] + 3:9E3  dgtp[c] + 2:2E3  dttp[c] + 58:6E3  atp[c] + 104:2E3  ctp[c] + 104:2E3  gtp[c] + 58:6E3  utp[c] + 328:4E3 man[c] + 524:1E3  arab-L[c] + 697:0E3  gal[c] + 28:4E3 mgdg1839Z12Z15Z1644Z7Z10Z13Z[h] + 3:2E3 mgdg1839Z12Z15Z1637Z10Z13Z[h] + 3:2E3 mgdg1839Z12Z15Z1634Z7Z10Z[h] + 269:4E6  dgdg1839Z12Z15Z1644Z7Z10Z13Z[h] + 739:2E6  dgdg1839Z12Z15Z1637Z10Z13Z[h] + 739:2E6  dgdg1839Z12Z15Z1634Z7Z10Z[h] + 74:3E6  dgts18111Z1819Z[c] + 74:3E6  dgts18111Z18111Z[c] + 1:1E3  dgts1601829Z12Z[c] + 1:2E3  asqdpa1819Z160[c] + 101 A.7. Appendix 7: Matlab Codes 1:2E3  asqdpa18111Z160[c] + 1:3E3  tag16018111Z160[c] + 1:3E3  tag1601819Z160[c] + 1:3E3  tag1801819Z160[c] + 1:3E3  tag18111Z18111Z160[c] + 1:3E3  tag18111Z1819Z160[c] + 1:3E3  tag1819Z18111Z160[c] + 37:1E3  ac[c] + 30:0E3  ppa[c] + 25:3E3  but[c] + 12:1E3  glyc[c] + 20:2E3  chla[u] + 8:8E3  chlb[u] + 1:0E6  rhodopsin[s] + 79:7E9  acaro[h] + 15:9E9  anxan[u] + 223:3E9  caro[u] + 103:7E9  loroxan[u] + 199:4E9  lut[u] + 87:7E9  neoxan[u] + 55:8E9  vioxan[u] + 47:8E9  zaxan[u] + 29:9 ATP maintainance + 2:3E3  pe1801835Z9Z12Z[c] + 1:9E3  pail18111Z160[c] + 258:4E6  pail1819Z160[c] A.7 Appendix 7: Matlab Codes A.7.1 Interaction-based Approach Code Convert stoichiometric matrix to adjacency matrix and Determine topology property of metabolites 1 %% Reachibility analysis and convert stoichiometric matrix to 2 % adjacency matrix get the stoichiometric matrix (which is 3 % saved as a .mat file),and get the 4 % varible stoi (double) 102 A.7. Appendix 7: Matlab Codes 5 % read a file, and load a file. 6 [filename, filepath] = uigetfile; 7 fullpath = [filepath filename]; 8 load(fullpath); 9 siz = size(stoi.s); 10 % construct a reachiability matrix "Rm",and convert 11 % stoichiometric matrix to adjacency matrix. 12 Rm.m = zeros(siz(2), siz(2)); 13 Rm.met = stoi.mets; 14 for i = 1:siz(1) 15 a=0;b=0; 16 for j = 1:siz(2) 17 if stoi.s(i,j) < 0 18 a = a+1; 19 met.reactant(a) = j; % get the reactant 20 else if stoi.s(i,j) > 0 21 b = b+1; 22 met.product(b) = j; 23 end 24 end 25 end 26 if stoi.rev(i) == 1 27 met.reactant =[met.reactant met.product]; 28 met.product = met.reactant; 29 a = a +b; 30 b = a; 31 end 32 for k = 1:a 33 for m = 1:b 34 Rm.m(met.reactant(k),met.product(m)) = 1; 35 end 36 end 37 met.reactant = zeros; 103 A.7. Appendix 7: Matlab Codes 38 met.product = zeros; 39 end 40 % clear the selflinked reachibility error. and 41 % get the Rmˆ2, Rmˆ3 42 for i = 1:size(Rm.m) 43 Rm.m(i,i) = 0; 44 end 45 Rm.m2 = Rm.m * Rm.m; 46 for i = 1:size(Rm.m) 47 Rm.m2(i,i) = 0; 48 end 49 Rm.m3 = Rm.mˆ3; 50 for i = 1:size(Rm.m) 51 Rm.m3(i,i) = 0; 52 end Find gaps in the metabolite networks 1 %% Find gaps in the metabolite networks. 2 % this program is to convert the matrix from SBML into double 3 % stoichimometric matrix. 761 and 932 and be replaced by the actual 4 % size of the model. 5 initCobratoolbox; 6 sto = model.S; 7 stoi = model; 8 stoi.s = zeros (size(sto)); 9 stoi.s = full(sto); 10 stoi.rev = model.rev; 11 stoi.s = stoi.s'; %need to get a matrix with same row same reaction. 12 %% 104 A.7. Appendix 7: Matlab Codes 13 14 % get the stoichiometric matrix (which is saved as a .mat file), 15 %and get the varible stoi (double) 16 % read a file, and load a file. 17 % [filename, filepath] = uigetfile; 18 % fullpath = [filepath filename]; 19 % load(fullpath); 20 siz = size(stoi.s); 21 % construct a reachiability matrix "Rm", 22 Rm.m = zeros(siz(2), siz(2)); 23 Rm.met = stoi.mets; 24 Rm.count = zeros(siz(2)); 25 Rm.revmet = zeros(siz(2)); 26 for i = 1:siz(1) 27 a=0;b=0; 28 for j = 1:siz(2) 29 if stoi.s(i,j) < 0 30 a = a+1; 31 met.reactant(a) = j; % get the reactant 32 Rm.count(j)= Rm.count(j)+1; 33 else if stoi.s(i,j) > 0 34 b = b+1; 35 met.product(b) = j; 36 Rm.count(j)= Rm.count(j)+1; 37 end 38 end 39 end 40 41 for k = 1:a 42 for m = 1:b 43 Rm.m(met.reactant(k),met.product(m)) = 44 Rm.m(met.reactant(k),met.product(m))+1; 45 end 105 A.7. Appendix 7: Matlab Codes 46 end 47 met.reactant = zeros; 48 met.product = zeros; 49 end 50 % if it's a reversible reaction. 51 for i = 1:siz(1) 52 a=0; b = 0; 53 if stoi.rev(i) ˜= 0 54 for j = 1:siz(2) 55 if stoi.s(i,j) > 0 56 a = a+1; 57 Rm.revmet(j) = 1; 58 % revmet counts the metabolites in the reversible rxns. 59 met.reactant(a) = j; % get the reactant 60 else if stoi.s(i,j) < 0 61 b = b+1; 62 met.product(b) = j; 63 Rm.revmet(j) = 1; 64 end 65 end 66 end 67 for k = 1:a 68 for m = 1:b 69 Rm.m(met.reactant(k),met.product(m)) = 70 Rm.m(met.reactant(k),met.product(m))+1; 71 end 72 end 73 end 74 met.reactant = zeros; 75 met.product = zeros; 76 end 77 78 % clear the selflinked reachibility error. and get the Rmˆ2, Rmˆ3 106 A.7. Appendix 7: Matlab Codes 79 for i = 1:size(Rm.m) 80 Rm.m(i,i) = 0; 81 end 82 Rm.m2 = Rm.m * Rm.m; 83 for i = 1:size(Rm.m) 84 Rm.m2(i,i) = 0; 85 end 86 Rm.m3 = Rm.mˆ3; 87 for i = 1:size(Rm.m) 88 Rm.m3(i,i) = 0; 89 end 90 91 % find out the deadend in the reversible reactions. Determine clustering coecient 1 %% Determine clustering coefficient for each metabolite. 2 % Bioinformatics toolbox is used here. 3 siz = 8; 4 Rm.m = sparse(Rm.m); 5 Rm.pcount = zeros(1,siz); 6 Rm.path = num2cell(zeros(siz,siz)); 7 for i = 1: siz; 8 [Rm.dist(i,:),Rm.path(i,:),PRED] = GRAPHSHORTESTPATH(Rm.m,i); 9 end; 10 for i = 1: siz; 11 for k= 1: siz; 12 if ˜isempty(Rm.pathfi,kg); 13 n = length(Rm.pathfi,kg); 14 for ks = 2 : n1; 107 A.7. Appendix 7: Matlab Codes 15 r = Rm.pathfi,kg(ks); 16 Rm.pcount(1,r) = Rm.pcount(1,r)+1; 17 end; 18 end; 19 end; 20 end; 21 Rm.pcount = Rm.pcount  1; A.7.2 Constraint-based Approach Code Flux Balance Analysis to determine the metabolite essentiality 1 %% Flux Balance Analysis to determine the metabolite essentiality. 2 % Note: To use this code, first load iRC1080 into the COBRA 3 % toolbox in Matlab as a variable named "model". 4 % Then this code can work. 5 6 7 % Measures and constants. 8 DW = 48*10ˆ(12); 9 % avg. dry weight of log phase chlamy cell = 48 pg (Mitchell 1992) 10 CPerStarch300 = 1800; 11 % derived from starch300 chemical formula 12 ChlPerCell = (13.9+4)/(10ˆ7); 13 % 13.9 + 4 micrograms Chl/10ˆ7 cells (Gfeller 1984) 14 starchDegAnLight = (4.95+1.35)*(1/1000)*(1/CPerStarch300)* 15 (ChlPerCell/1000)*(1/DW); 16 % approx. SS rate of anaerobic starch degradation in light 17 = 4.95 + 1.35 micromol C/mg Chl/hr (Gfeller 1984) 18 starchDegAerLight = (2/3)*starchDegAnLight; 108 A.7. Appendix 7: Matlab Codes 19 % approx. SS rate of aerobic starch degradation in light = 20 2/3 of anaerobic rate (Gfeller 1984) 21 starchDegAnDark = (13.1+3.5)*(1/1000)*(1/CPerStarch300)* 22 (ChlPerCell/1000)*(1/DW); 23 % approx. SS rate of anaerobic starch degradation in dark = 24 13.1 + 3.5 micromol C/mg Chl/hr (Gfeller 1984) 25 starchDegAerDark = (2/3)*starchDegAnDark; 26 % approx. SS rate of aerobic starch degradation in dark = 27 % 2/3 of anaerobic rate (Gfeller 1984) 28 dimensionalConversion = 3.836473679; 29 % from emitted microE/mˆ2/s to incident mmol/gDW/hr 30 effectiveConversion = 0.037532398; 31 % from incident mmol/gDw/hr to effective mmol/gDw/hr 32 33 34 %% set constraints. 35 % %%% light, aerobic, no acetate, biomass objective 36 modelLna = model; 37 % The single PRISM reaction being used has to be commentedout 38 %below. 39 modelLna = changeRxnBounds(modelLna,f... 40 % 'PRISM solar litho',... 41 'PRISM solar exo',... 42 'PRISM incandescent 60W',... 43 'PRISM fluorescent warm 18W',... 44 'PRISM fluorescent cool 215W',... 45 'PRISM metal halide',... 46 'PRISM high pressure sodium',... 47 'PRISM growth room',... 48 'PRISM white LED',... 49 'PRISM red LED array 653nm',... 50 'PRISM red LED 674nm',... 51 'PRISM design growth',... 109 A.7. Appendix 7: Matlab Codes 52 g,0,'b'); 53 modelLna = changeRxnBounds(modelLna,f'EX o2(e)'g,10,'l'); 54 modelLna = changeRxnBounds(modelLna,f'EX ac(e)'g,0,'l'); 55 modelLna = changeRxnBounds(modelLna,f'EX starch(h)'g,0,'b'); 56 modelLna = changeRxnBounds(modelLna,'STARCH300DEGRA', 57 starchDegAerLight/2,'u'); 58 modelLna = changeRxnBounds(modelLna, 59 'STARCH300DEGR2A',0,'u'); 60 modelLna = changeRxnBounds(modelLna, 61 'STARCH300DEGRB',starchDegAerLight/2,'u'); 62 modelLna = changeRxnBounds(modelLna 63 ,'STARCH300DEGR2B',0,'u'); 64 modelLna = changeRxnBounds(modelLna, 65 f'PCHLDR'g,0,'b'); 66 % the lightindependent protochlorophyllide reductase is not 67 % expressed in light due to translational inhibition caused by 68 % chloroplast redox state [Cahoon 2000] 69 modelLna = changeRxnBounds(modelLna,f'PFKh'g,0,'b'); 70 % plastidic PFKh inactivated by light (Plaxton 1996) 71 modelLna = changeRxnBounds(modelLna,f'G6PADHh','G6PBDHh'g,0,'b'); 72 % light inhibits G6PDHh of oxidative pentose phosphate 73 % pathway (Plaxton 1996) 74 modelLna = changeRxnBounds(modelLna,f'FBAh'g,0,'b'); 75 % light inactivates FBAh (Lemaire 2004; Matsumoto 2008) 76 modelLna = changeRxnBounds(modelLna,f'H2Oth'g,0,'u'); 77 % there is a high h2o requirement in [h]; however, 78 % experiments show that h2o in general goes from [h] to 79 % [c] in light and from [c] to [h] in dark (Packer 1970) 80 modelLna = changeRxnBounds(modelLna, 81 f'Biomass Chlamy mixo','Biomass Chlamy hetero'g,0,'b'); 82 modelLna = changeObjective(modelLna,'Biomass Chlamy auto'); 83 84 % Base growth. 110 A.7. Appendix 7: Matlab Codes 85 solutionLna = optimizeCbModel(modelLna,'max','one'); 86 87 88 %% to get the flux sum. 89 solution = solutionLna; 90 siz = size(model.S); 91 sizem = siz(1); % number of mets. 92 sizer = siz(2); % to get the number of rxns. 93 94 %% Identify the essential Metabolites. 95 % find the rxn in which metabolite i is a reactant. r : reactant, p: 96 % product. 97 modeld = modelLna; 98 for i = 1 : sizem; 99 for j = 1: sizer; 100 if modeld.S(i,j) > 0; 101,1)= 0; 102 modeld.ub(j,1) =0; 103 elseif modeld.S(i,j) < 0; 104 modeld.ub(j,1) =0; 105,1)= 0; 106 end 107 end 108 solution x = optimizeCbModel(modeld,'max','one'); 109 s effectr(i,1) = solution x.f  solutionLna.f; 110 s effectr(i,2) = s effect(i,1)/solution.f; 111 end Obtain basal 
ux-sum in dierent growth conditions 111 A.7. Appendix 7: Matlab Codes 1 % To obtain basal fluxsum in different growth conditions. 2 % Note: To use this code, first load iRC1080 into the COBRA 3 % toolbox in Matlab as a variable named "model". Then this code can be run. 4 5 6 % Measures and constants. 7 DW = 48*10ˆ(12); 8 % avg. dry weight of log phase chlamy cell = 48 pg (Mitchell 1992) 9 CPerStarch300 = 1800; 10 % derived from starch300 chemical formula 11 ChlPerCell = (13.9+4)/(10ˆ7); 12 % 13.9 + 4 micrograms Chl/10ˆ7 cells (Gfeller 1984) 13 starchDegAnLight = (4.95+1.35)*(1/1000)*(1/CPerStarch300)* 14 (ChlPerCell/1000)*(1/DW); 15 % approx. SS rate of anaerobic starch degradation in light 16 = 4.95 + 1.35 micromol C/mg Chl/hr (Gfeller 1984) 17 starchDegAerLight = (2/3)*starchDegAnLight; 18 % approx. SS rate of aerobic starch degradation in light 19 = 2/3 of anaerobic rate (Gfeller 1984) 20 starchDegAnDark = (13.1+3.5)*(1/1000)*(1/CPerStarch300) 21 *(ChlPerCell/1000)*(1/DW); 22 % approx. SS rate of anaerobic starch degradation in 23 dark = 13.1 + 3.5 micromol C/mg Chl/hr (Gfeller 1984) 24 starchDegAerDark = (2/3)*starchDegAnDark; 25 % approx. SS rate of aerobic starch degradation in dark 26 = 2/3 of anaerobic rate (Gfeller 1984) 27 dimensionalConversion = 3.836473679; 28 % from emitted microE/mˆ2/s to incident mmol/gDW/hr 29 effectiveConversion = 0.037532398; 30 % from incident mmol/gDw/hr to effective mmol/gDw/hr 31 32 33 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 112 A.7. Appendix 7: Matlab Codes 34 % %%% light, aerobic, no acetate, biomass objective 35 modelLna = model; 36 % The single PRISM reaction being used has to be commentedout below. 37 modelLna = changeRxnBounds(modelLna,f... 38 % 'PRISM solar litho',... 39 'PRISM solar exo',... 40 'PRISM incandescent 60W',... 41 'PRISM fluorescent warm 18W',... 42 'PRISM fluorescent cool 215W',... 43 'PRISM metal halide',... 44 'PRISM high pressure sodium',... 45 'PRISM growth room',... 46 'PRISM white LED',... 47 'PRISM red LED array 653nm',... 48 'PRISM red LED 674nm',... 49 'PRISM design growth',... 50 g,0,'b'); 51 modelLna = changeRxnBounds(modelLna,f'EX o2(e)'g,10,'l'); 52 modelLna = changeRxnBounds(modelLna,f'EX ac(e)'g,0,'l'); 53 modelLna = changeRxnBounds(modelLna,f'EX starch(h)'g,0,'b'); 54 modelLna = changeRxnBounds(modelLna,'STARCH300DEGRA' 55 ,starchDegAerLight/2,'u'); 56 modelLna = changeRxnBounds(modelLna,'STARCH300DEGR2A',0,'u'); 57 modelLna = changeRxnBounds(modelLna,'STARCH300DEGRB 58 ',starchDegAerLight/2,'u'); 59 modelLna = changeRxnBounds(modelLna,'STARCH300DEGR2B',0,'u'); 60 modelLna = changeRxnBounds(modelLna,f'PCHLDR'g,0,'b'); 61 modelLna = changeRxnBounds(modelLna,f'PFKh'g,0,'b'); 62 modelLna = changeRxnBounds(modelLna,f'G6PADHh','G6PBDHh'g,0,'b'); ) 63 modelLna = changeRxnBounds(modelLna,f'FBAh'g,0,'b'); 64 modelLna = changeRxnBounds(modelLna,f'H2Oth'g,0,'u'); 65 modelLna = changeRxnBounds(modelLna, 66 f'Biomass Chlamy mixo','Biomass Chlamy hetero'g,0,'b'); 113 A.7. Appendix 7: Matlab Codes 67 modelLna = changeObjective(modelLna,'Biomass Chlamy auto'); 68 69 % Base growth. 70 solutionLna = optimizeCbModel(modelLna,'max','one'); 71 72 modelabs = abs(model.S); 73 fluxsum(1,:) = modelabs * solutionLna.x*0.5 ; 74 75 76 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 77 %%% light, aerobic, w/ acetate, biomass objective 78 modelLwac = model; 79 % The single PRISM reaction being used has 80 %to be commentedout below. 81 modelLwac = changeRxnBounds(modelLwac,f... 82 % 'PRISM solar litho',... 83 'PRISM solar exo',... 84 'PRISM incandescent 60W',... 85 'PRISM fluorescent cool 215W',... 86 'PRISM metal halide',... 87 'PRISM high pressure sodium',... 88 'PRISM growth room',... 89 'PRISM white LED',... 90 'PRISM red LED array 653nm',... 91 'PRISM red LED 674nm'... 92 'PRISM fluorescent warm 18W'... 93 'PRISM design growth',... 94 g,0,'b'); 95 modelLwac = changeRxnBounds(modelLwac, 96 f'EX o2(e)','EX ac(e)'g,10,'l'); 97 modelLwac = changeRxnBounds(modelLwac, 98 f'EX starch(h)'g,0,'b'); 99 modelLwac = changeRxnBounds(modelLwac, 114 A.7. Appendix 7: Matlab Codes 100 'STARCH300DEGRA', 101 starchDegAerLight/2,'u'); 102 modelLwac = changeRxnBounds(modelLwac, 103 'STARCH300DEGR2A',0,'u'); 104 modelLwac = changeRxnBounds(modelLwac,'STARCH300DEGRB', 105 starchDegAerLight/2,'u'); 106 modelLwac = changeRxnBounds(modelLwac, 107 'STARCH300DEGR2B',0,'u'); 108 modelLwac = changeRxnBounds(modelLwac,f'PCHLDR'g,0,'b'); 109 modelLwac = changeRxnBounds(modelLwac,f'PFKh'g,0,'b'); 110 modelLwac = changeRxnBounds(modelLwac, 111 f'G6PADHh','G6PBDHh'g,0,'b'); 112 modelLwac = changeRxnBounds(modelLwac,f'FBAh'g,0,'b'); 113 modelLwac = changeRxnBounds(modelLwac,f'H2Oth'g,0,'u'); 114 modelLwac = changeRxnBounds(modelLwac, 115 f'Biomass Chlamy auto','Biomass Chlamy hetero'g,0,'b'); 116 modelLwac = changeObjective(modelLwac,'Biomass Chlamy mixo'); 117 118 % Base growth 119 solutionLwac = optimizeCbModel(modelLwac,'max','one'); 120 121 fluxsum(2,:) = modelabs * solutionLwac.x*0.5 ; 122 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 123 %%% dark, aerobic, w/ acetate, biomass objective 124 modelDa = model; 125 modelDa = changeRxnBounds(modelDa,'EX photonVis(e)',0,'l'); 126 modelDa = changeRxnBounds(modelDa,f'EX o2(e)'g,10,'l'); 127 modelDa = changeRxnBounds(modelDa,'EX co2(e)',0,'l'); 128 modelDa = changeRxnBounds(modelDa, 129 'STARCH300DEGRA',0,'u'); 130 modelDa = changeRxnBounds(modelDa, 131 'STARCH300DEGR2A' 132 ,starchDegAerDark/2,'u'); 115 A.7. Appendix 7: Matlab Codes 133 modelDa = changeRxnBounds(modelDa, 134 'STARCH300DEGRB',0,'u'); 135 modelDa = changeRxnBounds(modelDa, 136 'STARCH300DEGR2B' 137 ,starchDegAerDark/2,'u'); 138 modelDa = changeRxnBounds(modelDa,f'GLPThi'g,0,'u'); 139 modelDa = changeRxnBounds(modelDa,f'ATPSh'g,0,'b'); 140 modelDa = changeRxnBounds(modelDa,f'GAPDH(nadp)hi'g,0,'b'); 141 modelDa = changeRxnBounds(modelDa,f'MDH(nadp)hi', 142 'MDHC(nadp)hr'g,0,'b'); % inactive in dark (Buchanan 1980) 143 modelDa = changeRxnBounds(modelDa,f'PPDKh'g,0,'b'); 144 modelDa = changeRxnBounds(modelDa,f'IDPh'g,0,'b'); 145 modelDa = changeRxnBounds(modelDa,f'PRUK'g,0,'b'); 146 modelDa = changeRxnBounds(modelDa,f'RBPCh','RBCh'g,0,'b'); 147 modelDa = changeRxnBounds(modelDa,f'SBP'g,0,'b'); 148 modelDa = changeRxnBounds(modelDa,f'H2Oth'g,0,'l'); 149 modelDa = changeRxnBounds(modelDa, 150 f'Biomass Chlamy auto','Biomass Chlamy mixo'g,0,'b'); 151 modelDa = changeObjective(modelDa,'Biomass Chlamy hetero'); 152 153 % Base growth 154 solutionDa = optimizeCbModel(modelDa,'max','one'); 155 fluxsum(3,:) = modelabs * solutionDa.x*0.5 ; Flux Sum Analysis for Cobratoolbox 1 %% Replace the optimizeCbModel in CobraToolbox with this code to 2 % obtain flux sum attenuation analysis. 3 if (nargin < 2) 4 osenseStr = 'max'; 116 A.7. Appendix 7: Matlab Codes 5 end 6 if (nargin < 3) 7 primalOnlyFlag = true; 8 end 9 if (nargin < 4) 10 minNormFlag = false; 11 end 12 if (nargin < 5) 13 verbFlag = false; 14 end 15 16 % LP solution tolerance 17 if exist('CBTLPTOL','var') 18 tol = CBTLPTOL; 19 else 20 tol = 1e6; 21 end 22 23 % Figure out objective sense 24 if (strcmp(osenseStr,'max')) 25 LPproblem.osense = 1; 26 else 27 LPproblem.osense = +1; 28 end 29 30 % All constraints are equalities 31 LPproblem.csense = []; 32 %LPproblem.csense = zeros(1707,1); 33 %LPproblem.csense(1707,1) = 'L'; 34 35 % Fill in the RHS vector if not provided 36 if (˜isfield(model,'b')) 37 LPproblem.b = zeros(length(model.mets),1); 117 A.7. Appendix 7: Matlab Codes 38 else 39 LPproblem.b = model.b; 40 end 41 % Rest of the LP problem 42 LPproblem.A = model.S; 43 LPproblem.c = model.c; 44 =; 45 LPproblem.ub = model.ub; 46 47 %% Solve initial LP 48 49 LPsolution = solveCobraLP(LPproblem,primalOnlyFlag); 50 time1 = 0; 51 52 %% Solve secondary LP to minimize jv j 53 54 if (LPsolution.stat ˜= 1) 55 if (verbFlag) 56 warning('Optimal solution was not found'); 57 end 58 59 FBAsolution.f = 0; 60 FBAsolution.x = []; 61 else 62 % Store results 63 FBAsolution.f = LPsolution.obj; 64 FBAsolution.x = LPsolution.full; 65 if (˜primalOnlyFlag) 66 FBAsolution.y = LPsolution.dual; 67 FBAsolution.w = LPsolution.rcost; 68 end 69 70 % Minimize the absolute value of fluxes to avoid 118 A.7. Appendix 7: Matlab Codes 71 % loopy solutions 72 if (minNormFlag) 73 if (strcmp(osenseStr,'max')) 74 FBAsolution.f = floor(FBAsolution.f/tol)*tol; 75 else 76 FBAsolution.f = ceil(FBAsolution.f/tol)*tol; 77 end 78 if (FBAsolution.f ˜= 0) 79 [nMets,nRxns] = size(model.S); 80 % Set up the optimization problem 81 % min sum(delta+ + delta) 82 % 1: S*v1 = 0 83 % 3: delta+ >= v1 84 % 4: delta >= v1 85 % 5: c'v1 >= f (optimal value of objective) 86 % 87 % delta+,delta >= 0 88 LPproblem2.A = [model.S sparse(nMets,2*nRxns); 89 speye(nRxns,nRxns) speye(nRxns,nRxns) 90 sparse(nRxns,nRxns); 91 speye(nRxns,nRxns) sparse(nRxns,nRxns) 92 speye(nRxns,nRxns); 93 model.c' sparse(1,2*nRxns)]; 94 LPproblem2.c = [zeros(nRxns,1);ones(2*nRxns,1)]; 95 = [;zeros(2*nRxns,1)]; 96 LPproblem2.ub = [model.ub;10000*ones(2*nRxns,1)]; 97 LPproblem2.b = [LPproblem.b;zeros(2*nRxns,1);FBAsolution.f]; 98 LPproblem2.csense(1:nMets) = 'E'; 99 LPproblem2.csense((nMets+1):(nMets+2*nRxns)) = 'G'; 100 LPproblem2.csense(nMets+2*nRxns+1) = 'G'; 101 LPproblem2.csense = columnVector(LPproblem2.csense); 102 LPproblem2.osense = 1; 103 % Resolve the problem 119 A.7. Appendix 7: Matlab Codes 104 time1 = LPsolution.time; 105 LPsolution = solveCobraLP(LPproblem2,primalOnlyFlag); 106 %[f,x,y,w,solStatus] = solveLPStm(A,b,c,lb,ub, 107 1,columnVector(csense)); 108 if (LPsolution.stat > 0) 109 FBAsolution.x = LPsolution.full(1:nRxns); 110 else 111 FBAsolution.x = []; 112 end 113 end 114 end 115 end 116 117 FBAsolution.stat = LPsolution.stat; 118 FBAsolution.solver = LPsolution.solver; 119 FBAsolution.time = LPsolution.time+time1; Draw gures for 
ux sum attenuation to categorize metabolites 1 %%This is to draw figures for each metabolite with the flux sum attenuation 2 %%data to categorize them. 3 for i = 1 : 22; 4 xaxis(i) = 0.05*i; 5 end 6 7 for j = 1:1; 8 for i = 1: 100; 9 if MECR(i,2*j)> 0.5; 10 %if average(fsaatt(1,i,:)) > 0.02; 11 figure(i); 120 A.7. Appendix 7: Matlab Codes 12 fq(1:22) = fsaatt(j,i,1:22); 13 plot(xaxis(1:22),fq(1:22)); 14 m = num2str([j i]); 15 print(m,'djpeg') 16 close(i); 17 %end 18 end; 19 end; 20 end; Flux sum attenuation 1 %%%%% 2 % Manipulate fluxsum by attenuation 3 4 %%set model, and set the first FBA growth conditions. 5 %% set constraints. 6 % %%% light, aerobic, no acetate, biomass objective 7 % The single PRISM reaction being used has to be commentedout below. 8 modelLna = changeRxnBounds(modelLna,f... 9 % 'PRISM solar litho',... 10 'PRISM solar exo',... 11 'PRISM incandescent 60W',... 12 'PRISM fluorescent warm 18W',... 13 'PRISM fluorescent cool 215W',... 14 'PRISM metal halide',... 15 'PRISM high pressure sodium',... 16 'PRISM growth room',... 17 'PRISM white LED',... 18 'PRISM red LED array 653nm',... 121 A.7. Appendix 7: Matlab Codes 19 'PRISM red LED 674nm',... 20 'PRISM design growth',... 21 g,0,'b'); 22 modelLna = changeRxnBounds(modelLna,f'EX o2(e)'g,10,'l'); 23 modelLna = changeRxnBounds(modelLna,f'EX ac(e)'g,0,'l'); 24 modelLna = changeRxnBounds(modelLna,f'EX starch(h)'g,0,'b'); 25 modelLna = changeRxnBounds(modelLna, 26 'STARCH300DEGRA',starchDegAerLight/2,'u'); 27 modelLna = changeRxnBounds(modelLna, 28 'STARCH300DEGR2A',0,'u'); 29 modelLna = changeRxnBounds(modelLna, 30 'STARCH300DEGRB',starchDegAerLight/2,'u'); 31 modelLna = changeRxnBounds(modelLna,'STARCH300DEGR2B',0,'u'); 32 modelLna = changeRxnBounds(modelLna,f'PCHLDR'g,0,'b'); 33 modelLna = changeRxnBounds(modelLna,f'PFKh'g,0,'b'); 34 modelLna = changeRxnBounds(modelLna,f'G6PADHh','G6PBDHh'g,0,'b'); 35 modelLna = changeRxnBounds(modelLna,f'FBAh'g,0,'b'); 36 modelLna = changeRxnBounds(modelLna,f'H2Oth'g,0,'u'); 37 modelLna = changeRxnBounds(modelLna, 38 f'Biomass Chlamy mixo','Biomass Chlamy hetero'g,0,'b'); 39 modelLna = changeObjective(modelLna,'Biomass Chlamy auto'); 40 41 %% Base growth. 42 solutionLna = optimizeCbModel(modelLna,'max','one'); 43 44 %% add a flux sum constraints to implement flux sum attenuation 45 % analysis 46 for i = 1 : 1706; %sizem; 47 if MECR(i,2)> 0.5; 48 modelLnax = modelLna; 49 modelLnax.S(1707,:) = abs(modelLnax.S(i,:)); 50 for att = 1 : 20; 51 modelLnax.b(1707) = att/20*fluxsum(1,i)*2; 122 A.7. Appendix 7: Matlab Codes 52 %because we times 0.5 when get the flux sum. 53 solutionLnax = optimizeCbModel(modelLnax,'max','one'); 54 fsaatt(1,i,att) = solutionLnax.f 55 %xaxis(i) = att/20; 56 % end 57 58 end 59 end 123


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