UNIVERSITY OF CINCINNATI
Date: 22-Jan-2010
I, Amruta Desai , hereby submit this original work as part of the requirements for the degree of: Master of Science in Computer Engineering It is entitled: Design support for biomolecular systems
Student Signature: Amruta Desai
This work and its defense approved by: Committee Chair: Carla Purdy, C, PhD Carla Purdy, C, PhD
Wen-Ben Jone, PhD Wen-Ben Jone, PhD
George Purdy, PhD George Purdy, PhD
2/2/2010 389 Design Support for Biomolecular Systems
A thesis submitted to the Division of Graduate Research and Advanced Studies of The University of Cincinnati
In partial fulfillment of the Requirements for the degree of
Master of Science in the Department of Electrical and Computer Engineering of the College of Engineering
By Amruta Desai BE in Electrical Engineering, Rajiv Gandhi Technical University, 2005
January, 2010
Thesis Advisor and Committee Chair: Dr. Carla Purdy
Abstract
Systems biology is an emerging field which connects system level understanding to molecular level understanding. Biomolecular systems provide a comprehensive view of a biological phenomenon, in the form of a network of inter-related reactions or processes. The work described in this thesis focuses on developing the support for virtual experiments in systems biology. This will help biologists to make choices about which wet lab experiments are likely to be the most informative, thereby saving both time and material resources. Our goal is to support synthetic biology by providing tools which can be employed by biologists, engineers, and computational scientists. Our approach makes use of well-developed techniques from the field of VLSI design.
Modeling the biochemical reactions helps in studying and analyzing a biological pathway. This provides an affordable and convenient virtual experimental platform. There are several challenges as it is an emerging field.
Our lab introduced a new conversion tool to support mathematical modeling of the biological systems, called as Bio Model Development Language (BMDL). It uses the concept of weighted “gate”. The work in this thesis focuses on metabolic pathways. We extend BMDL to account for the presence of inhibitors, activators and enzymes of biological pathways, components similar to feedback loops in electrical circuits. As a use case we study the pyrimidine pathway.
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Acknowledgements
I am heartily thankful to my advisor and committee chair Dr. Carla Purdy for her excellent guidance throughout my thesis work. This would not be possible without her help, encouragement, and support from the initial to the final level.
I would also like to thank the committee members, Dr. George Purdy and Dr. Wen Ben
Jone, for taking the time and effort to review my research and serve on my thesis defense committee.
I would like to express my heartfelt gratitude to my parents for their love, encouragement and belief in me. I would like to thank my sister Ankita for her love, encouragement and belief in me. She was always there to help me through the difficult phases in my life and motivated me to complete my thesis.
I am thankful to my all cousins specially Krupa, Hitendra and Viraj for their faith and support throughout my Masters.
I would like to thank all my friends who have helped me in many ways and made my stay at Cincinnati wonderful. Thanks to University of Cincinnati for giving me an opportunity to study here.
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To my family
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Contents
1 Introduction 1
1.1 Motivation 2
1.2 Goals 3
1.2.1 Long term goals 3
1.2.2 Short term goals 3
1.3 Outline 4
2 Biological Pathways 5
2.1 Introduction 5
2.2 Introduction to biological pathways 5
2.2.1 Gene regulatory network 7
2.2.2 Cell signaling pathway 7
2.2.3 Metabolic pathway 8
2.3 Modeling and Control of Biological Pathways 8
2.3.1 Deterministic modeling 9
2.3.2 Stochastic modeling 9
2.3.3 Agent based modeling 9
2.4 Challenges in computational biomodeling 10
2.5 Box algorithm 10
2.6 Bio model development language (BMDL)[2] 14
2.7 Limitations of BMDL 15
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2.8 Chapter summary 16
3 Enhancement of BMDL Weighted Gates 17
3.1 Need for enhancement 17
3.1.1 Enzymes and their classifications 17
3.1.2 Activators 18
3.1.3 Inhibitors 18
3.2 BMDL expression to ODE model conversion 19
3.2.1 Gates added to BMDL 23
3.2.1.1 Two input /two output bi-directional reaction 23
3.2.1.2 Two input/ two output reaction with inhibitors and activator 24
3.2.1.3 Three input/ four output reaction with inhibitor and activator 26
3.2.1.4 Four input/ four output reaction with one inhibitor 27
3.3 Generalization of BMDL expressions 29
3.3.1 Bidirectional biochemical reactions 30
3.3.2 Unidirectional biochemical reactions 31
3.3.2.1 Simple biochemical reactions 31
3.3.2.2 Complex biochemical reactions 33
3.4 Classification of different BMDL functions 36
3.5 Chapter summary 37
4 Use Case: Pyrimidine Pathway 38
4.1 Introduction 38
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4.2 Nucleotides 38
4.3 Introduction to the Pyrimidine pathway 39
4.3.1 Biochemical reactions 42
4.3.2 BMDL model of Pyrimidine Pathway 43
4.3.3 ODE model of Pyrimidine pathway 48
4.4 Bio-control database and modifications for metabolic pathway 48
4.4.1 Bio-control database for Pyrimidine pathway 52
4.5 Simulation results of Carbomyl Phosphate (CPSase) 60
4.6 Application of the Box algorithm to Pyrimidine pathway 62
4.7 Chapter summary 62
5 Conclusions and Future Work 63
5.1 Introduction 63
5.2 Conclusions 63
5.3 Suggestions for future work 64
5.4 List of publications and conference proceedings 64
Bibliography 66
Appendix A 71
Appendix B 75
Appendix C 79
Appendix D 80
Appendix E 82
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Appendix F 82
Appendix G 87
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List of Figures
2.1 Biological pathways studied in our lab or included in database of [7] 7
2.2 Box algorithm with the integrated BMDL and bio-control database [2] 12
2.3 Bio-Model Development Language (BMDL) 15
3.1 Mechanism for a single substrate enzyme catalyzed reaction 17
3.2 Role of competitive inhibitor 18
3.3 Weighted gate symbol used in BMDL expression 20
3.4 Weighted gate representing two input /two output bi-directional reaction 23
3.5 Weighted gate representing two input /two output unidirectional reactions with inhibitors and activators 25
3.6 Weighted gate representing three inputs /four output unidirectional reaction with inhibitors and activators 26
3.7 Weighted gate representing four input /four output unidirectional reaction with inhibitors 28
3.8 Classification of biochemical reactions studied in our lab 29
3.9 Weighted gate representing n input /m output bi-directional reaction 30
3.10 Weighted gate representing n input /m output unidirectional simple reaction 32
3.11 Weighted gate representing n input /m output unidirectional complex reaction 34
4.1 Purine and Pyrimidine rings 39
4.2 Pyrimidine pathway 41
4.3 Effect of UMP on CPSase 60 4.4 Effect of activator 61
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List of Tables
3.1 Classification of BMDL gates 36
4.1 Bio-control database entry for the rate of transcription for the protein Cro of phage lambda 50
4.2 Bio-control database entry for Carbomyl phosphate synthase of pyrimidine pathway 51
4.3: Bio-control database entry for Carbomyl phosphate synthase of pyrimidine pathway 52
4.4: Bio-control database entry for AspartateCarbomyl transferase of pyrimidine pathway 53
4.5: Bio-control database entry for Dihydro orotate oxidase of pyrimidine pathway 54
4.6: Bio-control database for entry Orotate phosphoribosyl transferase of pyrimidine pathway 55
4.7: Bio-control database entry for Orodtidine- 5'- Phosphate Decarboxylaseas of pyrimidine
pathway 56
4.8: Bio-control database entry for Uridine diphosphate kinase of pyrimidine pathway 58
4.9: Bio-control database entry for Cytidine 5'- triphosphate synthetase of pyrimidine pathway 59
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Chapter 1
Introduction
In this chapter we provide an introduction to our research objectives. A detailed description of our thesis goals is also explained. An outline for all the chapters is also provided.
The work emphasizes developing support for virtual experiments in systems biology with the help of engineering techniques. Systems biology is an emerging opportunity to connect system level understanding to molecular level understanding. Broadly, systems level understanding can be classified into four different phases. The first phase is structural identification of the system. This lets us know the relationships between various components of the system. The second phase is the study of system dynamics. Various experiments, computational model development and theoretical analysis are required during this phase. The third phase is the control procedure. Here a proper methodology is identified to control the system externally. This helps in various applications such as drug development and environmental remediation. Finally, the fourth phase consists of construction of the modified biological system with desired features.[1]
Experimental studies of biological pathways are expensive and time consuming; hence we are trying to develop virtual support to study these biological networks, thereby saving both time and material resources. [2, 3] Previously our lab developed certain algorithms to support this approach. Here we are trying to contribute to this program by extending the work in [2].
1.1 Motivation
Systems biology is an emerging field which connects system level understanding to molecular level understanding. It improves the capability to understand natural phenomena
1 quantitatively. It also nurtures an engineering discipline, known as synthetic biology, for regulating complex cell behaviors in a predictable and reliable fashion [4, 5]. Broadly speaking it is the study of biological pathways through creating mathematical models and then simulating and analyzing them statistically. In order to support synthetic biology and the multidisciplinary area of bio/nano-circuit development, various concepts of mathematics, biology, chemistry and engineering are used. This is an opportunity for biologists, chemists, mathematicians, computer scientists and electrical and computer engineers to work together and add their contributions to this embryonic field.
The work done on biological pathways in our lab includes modeling and simulation. The
Box algorithm, a useful tool to study and characterize biological pathways has been developed
[2]. A new language to support our investigations, the Bio Model Development Language
(BMDL), has been developed and needs to be extended to include more templates for biochemical reactions. The work in [2] deals with gene regulation systems. To explore the vast area of systems biology it is necessary to study other types of biological pathways. Thus, here we focus on metabolic pathways. In particular, we extend BMDL to account for the presence of inhibitors, activators and enzymes.
The Pyrimidine pathway is a very common metabolic pathway which contains example of additional features which need to be studied. It has inhibitors and activators as well as enzymes, so it will be an excellent use case. It is also one of the complicated and common pathways found in almost all living cells. Thus, we have decided to consider the Pyrimidine pathway as our use case.
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1.2 Goals
1.2.1 Long term goals
Our overall objective is to develop a user-friendly simulation environment to virtually study bio/nano systems at the molecular level. The Box algorithm [2] is designed to perform experiments useful in studying systems biology virtually. The Box algorithm takes input in the form of a system of ordinary differential equations (ODEs). Many other simulation tools also rely on translation of biochemical reactions to ordinary differential equations. So we are trying to develop an automated tool which converts biochemical reactions to ordinary differential equations. Our approach is modeled on methods in the field of VLSI design. A crude manual translation procedure is a part of the Box algorithm but it is at a very primitive level. We are trying to extend and automate it since manual conversion can be error prone and time consuming. This efficient translation scheme is inspired by electrical circuits. Similar work focusing on the modification of simple pathways for use in bio/nano circuits has been done by
Weiss, H. El-Masri and C. Portier [4, 5, 6]. But our work aims to model more complex metabolic pathways.
All the above listed goals can be fulfilled by applying modeling and simulation techniques from VLSI design to biomolecular systems.
1.2.2 Goals for the work
Our main goal is to extend the Bio Modeling Development Language (BMDL) which is already introduced in [2]. We enhance our translation tool by introducing new BMDL templates which can be utilized to study metabolic pathways. Metabolic pathways are very complex in terms of modeling, as there are so many participants in a metabolic reaction, such as enzymes, activators and inhibitors. Activators and inhibitors of biological pathways are viewed as positive
3 and negative feedback paths in biological pathways in accordance with electrical engineering concepts. This calls for the enhancement of BMDL weighted gates with additional weights other than the K constants used in [2]. Also the presence of enzymes affects the modeling parameters and these effects need to be accounted for.
All these features can be tested on an appropriate metabolic pathway. The use case for our work is the Pyrimidine pathway. Hence our aim is to extract the ODE model for this pathway and develop a bio-control database for it.
1.3 Outline
The thesis is organized into five chapters. A brief description of these chapters is as follows:
In chapter 2, we briefly discuss biological pathways. The classification of biological pathways followed by previous and current work is discussed. A clear distinction between gene regulatory systems and metabolic pathways is provided, followed by a brief introduction to the
Box algorithm. Along with this, the Bio Modeling Development Language, BMDL, and its limitations are described briefly.
In chapter 3, we discuss the enhancement of BMDL weighted gates. A brief description of inhibitor and activators is given, emphasizing the necessity of the enhancement of BMDL. We also derive appropriate BMDL weighted gates.
Chapter 4 is dedicated to our use case. Here, we are verifying our newly developed
BMDL weighted gates by extracting an ordinary differential equation (ODE) model for a complex metabolic pathway, the Pyrimidine pathway. The bio-control database is developed for a general Pyrimidine pathway.
In chapter 5, we conclude this research work and the scope of future work is discussed.
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Chapter 2
Biological Pathways
2.1 Introduction
Computational bio-modeling is an emerging field which helps in the study of biological pathways; it uses applied mathematics techniques and tools. Work in our lab is concentrated on the development of a virtual tool which supports wet lab experiments in systems biology. Since systems biology is a vast field with large variations, generalizations are difficult. In this work we are considering metabolic pathways, whereas previously we looked at simpler gene regulation pathways. The classification of biological pathways is discussed. This is followed by a brief introduction to biological mathematical modeling. We also summarize the work done in [2], which is the basis for our work. A clear distinction between gene regulatory systems and metabolic pathways is provided followed by a brief introduction to the Box algorithm developed in [2]. Along with this, the Bio Modeling Development Language, BMDL, and its limitations are also described briefly.
2.2 Introduction to biological pathways
Biological processes are represented as biological pathways, also called biological networks. These pathways are a useful abstraction of biological concepts and events. Biological pathways are a series of chemical reactions or interactions or transformations in genes, proteins and metabolites. Systems level understanding can be classified into four different phases, namely, structural identification of the system, study of systems dynamics, control procedure and construction of the modified biological system with desired features [1]. Thus, systems level
5 research is a vast field which utilizes various concepts of mathematics, biology, chemistry and engineering. This area provides an opportunity for biologists, chemists, mathematicians, computer scientists and electrical and computer engineers to work collectively and advance this developing field. To perform these studies of biological pathways, a new domain of knowledge is needed, one that borrows the approach of a computer engineer but utilizes the knowledge of a biologist [2].
Biological networks are classified according to their nature as gene regulation systems, metabolic pathways, signal transduction pathways, transcriptional regulatory networks, protein- protein interactions, etc. There may also be variations in pathways of the same types if they occur in different types of organisms. The work done in [2, 7] considers gene regulation systems and protein signaling pathways, while we are contributing to this emerging field by studying metabolic pathways. The biological pathways covered in our so far lab are phage lambda, bioluminicence in Vibrio fischeri, TNFα- Mediated NF- κβ and Wnt signaling pathway. [2,7,8,
9]. The various types of biological pathways studied in our lab so far are shown in Figure 2.1.
Phage lambda has also been studied extensively by Weiss [5, 6, 10, 11]. In addition, the TNFα-
Mediated NF- κβ has been studied in [12-14] and Vibrio fischeri in [15-19].
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Biological Pathways
Gene Regulatory Cell signaling Metabolic Pathways Networks pathway
Phage Vibrio Nucleotide Lambd Fischeri Metabolism a
Wnt Signaling TNFα-Mediated Pathway NF-κβ Pyrimidine
Figure 2.1 Biological pathways studied in our lab or included in database of [7]
2.2.1 Gene regulatory network
Genes, the basic units of heredity, are sequences of nucleic acid. They hold the information from an organism's cells and pass genetic traits to offspring. The process by which cells or viruses turns this information into gene products is included in gene regulatory networks.
Regulation of gene expression includes the processes that regulate protein coding genes [20].
This can increase the versatility and adaptability of an organism by allowing the cell to express protein when needed. Phage lambda and vibrio fischeri are two gene regulatory networks studied in our lab [2, 8].
2.2.2 Cell signaling pathway
A part of a complex system of communication among cells which governs basic cellular activities and coordinates cell actions is called cell signaling [21]. Cell signaling may be of
7 different types like unicellular, signaling between cells of a single organism, or multicellular where one cell interacts with cells of other organism. An error in such a signaling pathway may led to different diseases like cancer, autoimmunity, and diabetes [22]. TNFα- Mediated NF- κβ and Wnt signaling pathway are two cell signaling pathways studied in our lab. [2,7, 9]
2.2.3 Metabolic pathway
All the chemical reactions carried out by a cell are referred as metabolism. Thus a series of chemical reactions occurring within a cell is called as a metabolic pathway. Each metabolic pathway is comprised of a principal chemical which is modified by a set of chemical reactions.
These reactions are catalyzed by enzymes and require dietary minerals and vitamins along with several other cofactors in order to function properly [23]. Metabolic pathways are intricate because of the involvement of many chemicals. A cell may have many pathways and all these pathways are collectively, called a metabolic network. Pyrimidine, a metabolic pathway, is our use case. [24]
2.3 Modeling and control of biological pathways
The modeling and control of biological pathways is vital for increasing our understanding of various diseases, such as cancer, and our ability to develop bio-engineered drugs to combat diseases. Computational bio-modeling helps in studying and analyzing biological systems and thus, provides an affordable and convenient virtual experimental platform. A biological system consists of various biochemical reactions which describe the interactions between various components such as proteins, genes, enzymes, etc; of the biological network. An equivalent model of equations is obtained for corresponding biochemical reactions. These equations are
8 solved and analyzed either numerically or symbolically to see the behavior of the biological system either over time or at equilibrium. The type of modeling is chosen on the basis of the nature of the equations and their behavior. The most common types of mathematical models and their descriptions are as follows:
2.3.1 Deterministic modeling
A deterministic model is a mathematical model in which every set of variable states is uniquely determined by parameters in the model and by sets of previous states of these variables.
Deterministic models carry out the same rules for a given set of initial conditions. The mathematical models are based on a set of initial conditions. Ordinary differential equations
(ODE) and partial differential equations (PDE) are based on the deterministic approach [25].
2.3.2 Stochastic modeling
Stochastic models account for randomness of participating species. The changes in biological species do not occur at regular intervals of time [26]. Stochastic simulation includes the randomness of changes in molecular species, time interval and reaction rates while modeling any biological model. Petri nets are based on the stochastic approach.
A petri net is a type of mathematical modeling language suitable for only those systems which can be represented by a finite set of discrete states. This modeling does not allow the spatial properties of the entities to be taken into account [27]. Many biological models have also been based on the stochastic approach developed by Gillespie [26].
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2.3.3 Agent based Modeling
Agent based modeling (ABM) is a computational modeling technique which simulates interaction of agents, or objects with other agents, based on a set of rules [28]. ABM models the biological process using a bottom up approach unlike top down approach of deterministic and stochastic models [29]. Vallurupalli et al [30] have modeled the phage lambda system while
Mylavarapu [31] modeled vibrio fischeri using agent based modeling. Rajendran has developed a three dimensional agent based model of cell growth [32].
2.4 Challenges in Computational Bio modeling
Modeling of biological systems has certain challenges, including stochasticity and availability of data for simulation. Bio modeling involves tradeoffs between complexity, simplicity and accuracy. Simple pathways can be modeled using complex and accurate models while complex models need to be modeled in a simple way to better understand the system, but this compromises its accuracy. Stochasticity of biological system plays a vital role here.
Modeling of a biological system depends on the experimental values, available from biological labs, may have large variance because of environmental conditions. A wide variety of biological pathways is one of the challenges. Some laboratories spends several years on just one pathway in order to cover the effects of various factors like temperature, pressure and many more on biological pathways. Collecting experimental data in many cases is expensive, time consuming and requires that many other factors be taken into account.
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2.5 Box algorithm
The work done in [2] is the fundamental piece of our work. The box algorithm, a useful tool, has been developed in [2] to study and characterize biological pathways. This algorithm integrates the laboratory constraints and process behavior of a biological pathway into a heuristic model.
The algorithm can be applied for simulating and controlling any gene regulation pathway.
Using the Box algorithm, a user can input a biological pathway (Bio-Model), determine favorable approaches to control the inputted pathway analytically (Analytical Tools), incorporate information from a Bio-Control database, supplemented by specific information available through laboratory experiments (Bio-Control Database), determine appropriate priority rules and settings for the aim of the individual experiment, and then perform an optimization using simulated annealing or a genetic algorithm. The algorithm terminates if the results of the optimization are satisfactory, otherwise the whole process can be repeated. The Box algorithm has six different logical blocks as shown in Figure2.2. Their details are described below [2]:
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Bio- Model Development Weighted Gates Language (BMDL) (1)
Bio Model (ODE or Stochastic)
User Defined Analytical Tools Controls (RS-HDMR) (2)
Bio-rules and Priority Bio-control Database (3) settings (4)
(Simulated Annealing SA Optimization (5) or Genetic Algorithm GA)
Expected Output NO
Compare Block (6)
Modified rate Parameters and Control YES
Figure 2.2 Box algorithm with the integrated BMDL and bio-control database [2]
1. Bio-Model Development Language: The biochemical reactions are represented using weighted gates and each weighted gate has a particular ordinary differential equation
(ODE) template. Thus biochemical reactions are converted into ODEs using the weighted gate system.
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2. Analytical Tools: This block applies the RS-HDMR procedure [33] and estimates the effect of each rate constant on the output. It also calculates the effect of the pair correlation of the rate constants on the output [34]. On the basis of obtained results, the rate constants are sorted in terms of the sensitivity of the output to each of them, and then a priority number is assigned accordingly. The rate constant with highest priority number has a greater impact on the output.
3. Bio-Control Database: This block provides the control parameters for each reaction, on the basis of its reaction type. This database is developed by thorough data mining of publications and review of the articles from the PubMed database [34].
4. Bio-Rules: This is the most crucial block of this algorithm as it allows the biologists/researchers to set priorities and fitness levels, based on their experience and desired objectives. Bio-rules enable the user to convert simulation results into practical results. First of all a priority for controlling a biochemical reaction on the basis of laboratory constraints is derived. Then these priorities are merged with priorities obtained from the RS-HDMR procedure
(step 2), which results in a combination of both mathematical and laboratory constraints.
5. Optimization: This block applies simulated annealing or a genetic algorithm to optimize the chosen output concentrations. Here, the optimization block chooses a subset of rate constants having the highest priority levels. The subset may include two or more rate constants according to the user’s preference. Finally, optimization is carried out by both heuristic algorithms and the best output (closest to the desired output) is chosen.
6. Compare Block: The output from the optimization block is compared with the expected output to see if further iterations are needed. Finally, this block outputs the modified rate parameters and the experimental steps through which the reactions can be controlled.
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2.6 Bio Model Development Language (BMDL) [2]
Traditionally biological pathways are represented as either biochemical reactions or as a set of ordinary differential equations (ODEs). In [2] a new type of representation, BMDL weighted gates, was introduced. This new representation facilitates conversion between biochemical reactions and ordinary differential equations. These weighted gates are also useful representations for electrical and computer engineers who are working to implement bio-circuits
[35].
In order to perform a computational study of any biological network, an equivalent ODE model of biochemical reactions is preferred. Similarly an ODE model of equations can be used as input to the Box algorithm [2, 3]. BMDL acts a bridge between two universal forms of representation. This is shown schematically in Figure 2.3. Each biochemical reaction can be represented as a BMDL weighted gate with an equivalent BMDL expression. Further, these expressions are allied with the subsequent ODE template from the ODE templates library. Thus,
BMDL will convert a set of biochemical reactions to an ODE model of the biological system.
The BMDL weighted gates use notation similar to electrical circuits, but they represent biological pathways, not electrical circuits [2].
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Biochemical Reactions
BMDL Weighted gates or BMDL Expressions
Ordinary Differential Equations
Figure 2.3 Bio-Model Development Language (BMDL)
2.7 Limitations of BMDL
Systems biology is a vast field. This is an emerging field, so many tools are still at a novice level. The work done in our lab [2, 7] mainly emphasizes gene regulatory networks
(GRNs). A GRN consists of simple biochemical equations without interference of any other components except reactants and products. The BMDL templates developed in [2] are capable of extracting ODE models of phage lambda, Vibrio fischeri, the Wnt signaling pathway, TNFα-
Mediated NF- κβ and similar pathways. Here we extend this BMDL concept to metabolic networks. Metabolic networks are complex pathways with inhibitors, activators and enzymes.
There are seven BMDL templates developed in [2] and now we are adding four new BMDL
15 templates to this library. Even after adding these four new templates, still there is scope to extend this library.
Currently, BMDL does not support any GUI and the user needs to perform all calculations manually for a new system. An approach to automate this system is also suggested in our work.
2.8 Chapter summary
In this chapter we introduced the concept of biological pathways along with the three main types of pathways which are studied in our lab. Here, we have shown the challenges in the field of computational bio-modeling. Further, we reviewed the Box algorithm developed in [2].
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Chapter 3
Enhancement of BMDL Weighted Gates
3.1 Need for enhancement
The BMDL templates developed in [2] covers gene regulatory systems. They don’t address the effect of enzymes as all the use cases were free of enzymatic actions. We are extending our work to metabolic pathways, which consist of enzyme chains, justifying the enhancement of BMDL weighted gates. Metabolic pathways can be analyzed by understanding and investigating the enzyme chains involved in the process [36].
3.1.1 Enzymes and their classifications
In biological systems, enzymes are the biocatalysts, which can change the rate of reaction. In enzymatic reactions, the molecules at the beginning of the process are called substrates, and the enzyme converts them into different molecules, called the products. [37]
Generally, enzymes are proteins which combine with substrates and form an intermediate enzyme-substrate complex leading to an enzyme-product complex and finally forming product and enzyme. This basic mechanism is shown in a Figure 3.1 below:
Figure 3.1 Mechanism for a single substrate enzyme catalyzed reaction
The enzyme binds a substrate (S) and produces a product (P)
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3.1.2 Activators
Molecules that bind to enzymes, thereby increasing their activity, are called activators.
Enzymes have an allosteric site, i.e., a site other than enzyme’s active site. Activators have the tendency to attach themselves to the allosteric site of enzymes, further increasing their affinity to the substrate [38]. Thus, enzyme activator enhances enzyme rate reaction.
3.1.3 Inhibitors
Enzyme inhibitors are molecules which can degrade enzymatic reaction. These molecules decrease the acitivity of enzymes. Inhibitors involve themselves in the enzymatic reaction in different ways thereby reducing the rate of formation of product. There are various mechanism like competitive inibition, noncompetitive inhibition and mixed inhibition [38]. Basically, inhibitors attach themselves either to the active site of enzymes, further reducing the possibility of formation of enzyme substrate complex or to the allosteric site, further reducing the affinity to attract the substrate. Thus, inhibitors act aa a negative rate of constant or negative feedback mechanism. [39]
Figure 3.2 Role of competitive inhibitor
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3.2 BMDL expression to ODE model conversion
Biochemical reactions can be represented as BMDL weighted gates and BMDL expressions will be converted to an ODE model of the biological system. This ODE model of equations is generally required for deterministic processes. The main reason to develop BMDL is because of it can be used as input to the Box algorithm to perform simulation, characterization and control of a biological pathway.
BMDL expressions are explicitly written in [2]. Certain conventions were used in [2] to denote the BMDL expression. A weighted buffer gate symbol is used for representing a reaction with one input in the forward direction, while an inverter symbol is used for the reverse direction. The rate constant of the reaction is given as the weight of the gate. An and gate symbol is used for multiple inputs in the forward direction while a nand gate symbol is used in the reverse direction. An Activator acts as a positive feedback and hence is represented by a buffer symbol while inhibitor has a negative feedback and is represented by an inverter symbol. All symbols are shown in Figure 3.3.
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A k A B 1 C B
(a) Weighted buffer gate symbol (b) Weighted and gate symbol (Forward direction) (Forward direction)
A C k2 C A D B
(c) Weighted inverter gate symbol (d) Weighted nand gate symbol (Reverse direction) (Reverse direction)
A A C BMDL gate C BMDL gate B B
k2 E k3 F
(e) Weighted buffer symbol for (f) Weighted inverter symbol for activator inhibitor
Figure 3.3 Weighted gate symbol used in BMDL expression
The choice of a BMDL weighted gate will be dependent on the nature of the chemical reaction. Altogether, there are about 30 gates which will need to be included in the final system.
There are seven BMDL functions developed in [2]. They are as follows:
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1 One input/one output bidirectional reaction can be represented by function
reversible_1in_1out_ and (‘C’, ‘A’, ‘Karray’)
2 Decay reaction can be represented by function decay (‘A’, ‘Karray’)
3 Two input/one output bidirectional reaction can be represented by function
reversible_2in_1out_ and (‘C’, ‘A’, ‘B’, ‘Karray’)
4 Two input/one output reaction can be represented by function 2in_1out_and (‘C’, ‘A’,
‘B’, ‘Karray’)
5 Four input/two output bi-directional reaction can be represented by function
reversible_4in_2out_and (‘E’, ‘F’, ‘B’, ‘C’, ‘D’, ‘Karray’)
6 One input/one output reaction can be represented by function 1in_1out_buf (‘B’, ‘A’,
‘Karray’ )
7 One input/two output reaction can be represented by function 1in_2out_and (‘C’, ‘B’,
‘A’, ‘Karray’ )
In each case the variable A, B, C, etc; are inputs, outputs, inhibitors or activators; ‘Karray’ is the array of kinetic rate constants. For example, a chemical reaction for expression 3 is given as,
푘1 (3.1) 퐴 + 퐵 퐶
푘2 (3.2) 퐶 퐴 + 퐵
The above chemical reaction is a bidirectional reaction with A and B as inputs and C as output. The kinetic constant of rate of reaction for the forward reaction is k1, with k2, for reverse reaction. Thus, this BMDL function can be represented by function reversible_2in_1out_ and
(‘C’, ‘A’, ‘B’, ‘Karray’). Other details for this function are given below:
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BMDL construct or expression:
Karray = [k1, k2];
function reversible_2in_2out and (‘D’, ‘C’, ‘B’, ‘A’, ‘K’array)
ODE Template
푑[퐴] (3.3) = −푘 퐴 퐵 + 푘 퐶 푑푡 1 2
푑[퐵] (3.4) = −푘 퐴 퐵 + 푘 퐶 푑푡 1 2
푑[퐶] (3.5) = 푘 퐴 퐵 − 푘 퐶 푑푡 1 2
The above mentioned BMDL functions [2] were basically derived in order to model two main pathways, i.e., phage lambda and vibio fischeri. Since both pathways are from gene regulatory systems and here in our work we are trying to model a metabolic pathway, these
BMDL functions were not sufficient to perform our task. Thus four new BMDL functions are developed to support more complex pathways, which exhibit feedback. These BMDL functions are introduced to include effects of inhibitors and activators. The development uses the concept of feedback systems. An inhibitor acts as a negative feedback path while an activator acts as a positive feedback path. This new set of BMDL gates, along with the seven developed in [2] allows us to investigate two complex pathways, de novo Pyrimidine biosynthesis [24] and Wnt signaling pathway [40, 41]. The new gates are described below.
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3.2.1 Gates added to BMDL
3.2.1.1 Two input /two output bi-directional reaction
A bidirectional biochemical reaction with two inputs and two outputs, similar to BMDL function developed in [2], but this function was not included in [2].
푘1 (3.6) 퐴 + 퐵 퐶 + 퐷
푘2 (3.7) 퐶 + 퐷 퐴 + 퐵
Weighted Gate:
A C k1 B D
k2
Figure 3.4 Weighted gate representing two input /two output bi-directional reaction
BMDL construct or expression:
Karray = [k1, k2];
function reversible_2in_2out and (‘D’, ‘C’, ‘B’, ‘A’, ‘K’array)
ODE Template
23
푑[퐴] (3.8) = −푘 퐴 퐵 + 푘 퐶 퐷 푑푡 1 2
푑[퐵] (3.9) = −푘 퐴 퐵 + 푘 퐶 퐷 푑푡 1 2
푑[퐶] (3.10) = 푘 퐴 퐵 − 푘 퐶 퐷 푑푡 1 2
푑[퐷] (3.11) = 푘 퐴 퐵 − 푘 퐶 퐷 푑푡 1 2
3.2.1.2 Two input/ two output reaction with inhibitors and activator
A unidirectional biochemical reaction involving enzyme, inhibitor and activator is represented in equation 3.12. Substrate A and B are input which react to produce C and D as products. E is an activator whose presence enhances rate of reaction while F and G are inhibitors which degrade rate of reaction. For an enzymatic reaction, value of k1 depends on the concentration of enzyme. Effect of activator E is included in modeling by using kinetic rate constant k2. Similarly F and G affect the reaction with inhibition constant k3 and k4.
푘1 (3.12) 퐴 + 퐵 퐶 + 퐷
E activates with activation constant k2 while F and G inhibits with inhibition constant k3 and k4
Weighted Gate:
24
k1 C A k1 B
k1 D
E k2
F k3
G k4
Figure 3.5 Weighted gate representing two input /two output unidirectional reactions with inhibitors and activators
BMDL construct or expression:
Karray = [k1, k2, k3, k4];
function 2in_2out_inh_act_buf (‘G’,‘F’,‘E’,‘D’,‘C’,‘B’,‘A’,‘K’array);
ODE Template
푑[퐴] (3.13) = −푘 퐴 퐵 − 푘 퐸 + 푘 퐹 + 푘 퐺 푑푡 1 2 3 4
푑[퐵] (3.14) = −푘 퐴 퐵 − 푘 퐸 + 푘 퐹 + 푘 퐺 푑푡 1 2 3 4
푑[퐶] (3.15) = 푘 퐴 퐵 + 푘 퐸 − 푘 퐹 − 푘 퐺 푑푡 1 2 3 4
푑[퐷] (3.16) = 푘 퐴 퐵 + 푘 퐸 − 푘 퐹 − 푘 퐺 푑푡 1 2 3 4
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3.2.1.3 Three input/ four output reaction with inhibitor and activator
A unidirectional biochemical reaction involving enzyme, inhibitor and activator is represented in equation 3.17. Substrates A, B and C are inputs which react to produce D, E, F and G as products. H, activator, enhances rate of reaction while I, inhibitor, degrades rate of reaction. For an enzymatic reaction, value of k1 depends on the concentration of enzyme. Effect of activator H is included in modeling by using kinetic rate constant k2. Similarly I affects the reaction with inhibition constant k3.
푘1 (3.17) 퐴 + 퐵 + 퐶 퐷 + 퐸 + 퐹 + 퐺
H activates with activation constant k2 while I inhibits with inhibition constant k3
Weighted Gate:
k1 D
k1 E
k1 F A k1 B C k1 G
k2 H
k3 I
Figure 3.6 Weighted gate representing three inputs /four output unidirectional reaction with inhibitors
and activators
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BMDL construct or expression:
Karray = [k1, k2, k3];
function 3in_4out_inh_act_buf (‘I’,‘H’,‘G’,‘F’,‘E’,‘D’,‘C’,‘B’,‘A’,‘K’array);
ODE Template
푑 퐴 (3.18) = −푘 퐴 퐵 퐶 − 푘 퐻 + 푘 퐼 푑푡 1 2 3
푑[퐵] (3.19) = −푘 퐴 퐵 [퐶] − 푘 퐻 + 푘 퐼 푑푡 1 2 3
푑[퐶] (3.20) = −푘 퐴 퐵 [퐶] − 푘 퐻 + 푘 퐼 푑푡 1 2 3
푑[퐷] (3.21) = 푘 퐴 퐵 퐶 + 푘 퐻 − 푘 퐼 푑푡 1 2 3
푑[퐸] (3.22) = 푘 퐴 퐵 퐶 + 푘 퐻 − 푘 퐼 푑푡 1 2 3
푑[퐹] (3.23) = 푘 퐴 퐵 퐶 + 푘 퐻 − 푘 퐼 푑푡 1 2 3
푑[퐺] (3.24) = 푘 퐴 퐵 퐶 + 푘 퐻 − 푘 퐼 푑푡 1 2 3
3.2.1.4 Four input/ four output reaction with one inhibitor
A unidirectional biochemical reaction involving enzyme, inhibitor and activator is represented in equation 3.25. Substrate A, B, C and D are inputs which react to produce E, F, G and H as products. I degrade the formation of product by inhibition constant k2. For an enzymatic reaction, value of k1 depends on the concentration of enzyme.
푘1 (3.25) 퐴 + 퐵 + 퐶 + 퐷 퐸 + 퐹 + 퐺 + 퐻
I inhibits with inhibition constant k2
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Weighted Gate:
k1 E
k1 F
A B k1 C k1 G
D
k1 H
k2 I
Figure 3.7 Weighted gate representing four input /four output unidirectional reaction with inhibitors
BMDL construct or expression:
Karray = [k1, k2];
function 3in_4out_inh_act_buf (‘I’,‘H’,‘G’,‘F’,‘E’,‘D’,‘C’,‘B’,‘A’,‘K’array);
ODE Template
푑[퐴] (3.26) = −푘 퐴 퐵 퐶 퐷 + 푘 퐼 푑푡 1 2
푑[퐵] (3.27) = −푘 퐴 퐵 퐶 퐷 + 푘 퐼 푑푡 1 2
푑[퐶] (3.28) = −푘 퐴 퐵 퐶 퐷 + 푘 퐼 푑푡 1 2
푑[퐷] (3.29) = −푘 퐴 퐵 퐶 퐷 + 푘 퐼 푑푡 1 2
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푑[퐴] (3.30) = 푘 퐴 퐵 퐶 퐷 − 푘 퐼 푑푡 1 2
푑[퐵] (3.31) = 푘 퐴 퐵 퐶 퐷 − 푘 퐼 푑푡 1 2
푑[퐶] (3.32) = 푘 퐴 퐵 퐶 퐷 − 푘 퐼 푑푡 1 2
푑[퐷] (3.33) = 푘 퐴 퐵 퐶 퐷 − 푘 퐼 푑푡 1 2
3.3 Generalization of BMDL expressions
BMDL functions developed in [2] and in section 3.2, are generalized in this section. This generalization is based on the classification given in Figure 3.8 and explained below. This classification can be expanded further to accommodate more biochemical equations. Our work includes all the possible reactions for pathways studied in our lab. Since biological pathways are very large in number, generalization for all is not possible but this work may help to develop
BMDL gates for more complex pathways.
Biochemical Reactions
Bidirectional Unidirectional Reactions Reactions
Simple Complex Enzymatic Reactions Non- enzymatic Reactions (includes inhibitors and activators)
Figure 3.8 Classification of biochemical reactions studied in our lab
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3.3.1 Bidirectional biochemical reactions
A bidirectional biochemical reaction with n inputs and m outputs, similar to BMDL function developed in [2] and section 3.2.1.1. For any such biochemical reactions we will have n + m ODE. k1 and k2 are the kinetic rate constants for forward and reverse directions respectively.
푘1 (3.34) 퐴1 + 퐴2 + … … … … + 퐴푛 퐵1 + 퐵2 + … … … … + 퐵푚
푘2 (3.35) 퐵1 + 퐵2 + … … … … + 퐵푚 퐴1 + 퐴2 + … … … … + 퐴푛
Weighted Gate:
B1 A1 A2 k1 B2
An
Bm
k2
Figure 3.9 Weighted gate representing n input /m output bi-directional reaction
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BMDL construct or expression:
Karray = [k1, k2];
function reversible_nin_mout and (‘Bm’, ……, ‘B2’, ‘B1’, ‘An’, ……, ‘A2’, ‘A1’, ‘K’array)
ODE Template
푑[퐴1] (3.36) = −푘 퐴 퐴 … … 퐴 + 푘 퐵 퐵 … … 퐵 푑푡 1 1 2 푛 2 1 2 푚
푑[퐴2] (3.37) = −푘 퐴 퐴 … … 퐴 + 푘 퐵 퐵 … … 퐵 푑푡 1 1 2 푛 2 1 2 푚
푑[퐴푛 ] (3.38) = −푘 퐴 퐴 … … 퐴 + 푘 퐵 퐵 … … 퐵 푑푡 1 1 2 푛 2 1 2 푚
푑[퐵 ] (3.39) 1 = 푘 퐴 퐴 … … 퐴 − 푘 퐵 퐵 … … 퐵 푑푡 1 1 2 푛 2 1 2 푚
푑[퐵 ] (3.40) 2 = 푘 퐴 퐴 … … 퐴 − 푘 퐵 퐵 … … 퐵 푑푡 1 1 2 푛 2 1 2 푚
푑[퐵 ] (3.41) 푚 = 푘 퐴 퐴 … … 퐴 − 푘 퐵 퐵 … … 퐵 푑푡 1 1 2 푛 2 1 2 푚
3.3.2 Unidirectional biochemical reactions
A unidirectional biochemical reaction is a reaction which occurs in one direction.
Formation of reactants from products is not possible. These can be further classified as simple and complex reactions. Simple reactions are those reactions which do not have any enzyme action. Complex reactions contain basically enzymatic reactions which include the effects of activators and inhibitors.
3.3.2.1 Simple biochemical reactions
31
A simple biochemical reaction with n inputs and m outputs, similar to BMDL function developed in [2], the general BMDL expression is derived below. For any such biochemical reactions we will have n ODEs, In expression 3.42, k1 is the kinetic rate of constant. General
BMDL function is as follows:
푘1 (3.42) 퐴1 + 퐴2 + … … … … + 퐴푛 퐵1 + 퐵2 + … … … … + 퐵푚
Weighted Gate:
B1 A1 A2 k1 B2
An
Bm
Figure 3.10 Weighted gate representing n input /m output unidirectional simple reaction
BMDL construct or expression:
Karray = [k1];
Function_nin_mout and (‘Bm’, ……, ‘B2’, ‘B1’, ‘An’, ……, ‘A2’, ‘A1’, ‘K’array)
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ODE Template
푑[퐴 ] (3.43) 1 = −푘 퐵 퐵 … … 퐵 푑푡 1 1 2 푚
푑[퐴 ] (3.44) 2 = −푘 퐵 퐵 … … 퐵 푑푡 1 1 2 푚
푑[퐴 ] (3.45) 푛 = −푘 퐵 퐵 … … 퐵 푑푡 1 1 2 푚
푑[퐵1] (3.46) = 푘 퐴 퐴 … … 퐴 푑푡 1 1 2 푛
푑[퐵2] (3.47) = 푘 퐴 퐴 … … 퐴 푑푡 1 1 2 푛
푑[퐵푚 ] (3.48) = 푘 퐴 퐴 … … 퐴 푑푡 1 1 2 푛
3.3.2.2 Complex biochemical reactions
An enzymatic biochemical reaction with n inputs and m outputs, similar to BMDL function developed in section 3.2.1, with x activators and y inhibitors is as follows. For any such biochemical reactions we will have n ODE. For expression 3.49, k1 is kinetic rate constant, which depends on concentration of enzymes. X1,X2…..Xi are activators with corresponding kinetic constants of kx1, kx2 to kxi, while Y1, Y2…..Yj are inhibitors with corresponding inhibition constants of ky1, ky2 to kyj.
General BMDL function for a enzymatic biochemical equation is as follows:
푘1 (3.49) 퐴1 + 퐴2 + … … … … + 퐴푛 퐵1 + 퐵2 + … … … … + 퐵푚
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X1,X2…..Xi are activators with corresponding kinetic constant of kx1, kx2 to kxi, while Y1, Y2…..Yj are inhibitors with corresponding inhibition constant of ky1, ky2 to kyj.
Weighted Gate:
B1 A1 A2 k1 B2
An
Bm
kx1 X 1
kxi Xi
ky1 Y1
Yj kyj
Figure 3.11 Weighted gate representing n input /m output unidirectional complex reaction
BMDL construct or expression:
Karray = [k1, kx1, kx2...... kxi, ky1, ky2...... kyj];
function nin_mout_inh_act_buf (‘Bm’, ……, ‘B2’, ‘B1’, ‘An’, ……, ‘A2’, ‘A1’, ‘K’array)
34
ODE Template
푑[퐴 ] (3.50) 1 = −푘 퐵 퐵 … … 퐵 − 푘 − 푘 푋 … … 푘 푋 + 푘 푌 푑푡 1 1 2 푚 푥1 푥2 2 푥푖 푖 푦1 1
+ 푘푦2 푌2 … … 푘푦푖 푌푗
푑[퐴 ] (3.51) 2 = −푘 퐵 퐵 … … 퐵 − 푘 − 푘 푋 … … 푘 푋 + 푘 푌 푑푡 1 1 2 푚 푥1 푥2 2 푥푖 푖 푦1 1
+ 푘푦2 푌2 … … 푘푦푖 푌푗
푑[퐴 ] (3.52) 푛 = −푘 퐵 퐵 … … 퐵 − 푘 − 푘 푋 … … 푘 푋 + 푘 푌 푑푡 1 1 2 푚 푥1 푥2 2 푥푖 푖 푦1 1
+ 푘푦2 푌2 … … 푘푦푖 푌푗
푑[퐵 ] (3.53) 1 = 푘 퐴 퐴 … … 퐴 + 푘 푋 + 푘 푋 … … 푘 푋 − 푘 푌 푑푡 1 1 2 푛 푥1 1 푥2 2 푥푖 푖 푦1 1
+ 푘푦2 푌2 … … 푘푦푖 푌푗
푑[퐵 ] (3.54) 2 = 푘 퐴 퐴 … … 퐴 + 푘 푋 + 푘 푋 … … 푘 푋 − 푘 푌 푑푡 1 1 2 푛 푥1 1 푥2 2 푥푖 푖 푦1 1
− 푘푦2 푌2 … … 푘푦푖 푌푗
푑[퐵 ] (3.55) 푚 = 푘 퐴 퐴 … … 퐴 + 푘 푋 + 푘 푋 … … 푘 푋 − 푘 푌 푑푡 1 1 2 푛 푥1 1 푥2 2 푥푖 푖 푦1 1
− 푘푦2 푌2 … … 푘푦푖 푌푗
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3.4 Classification of different BMDL functions
Different BMDL gates developed in [2] and in section 3.2 are categorized according to their general BMDL expression.
Bidirectional Reaction
General BMDL Expression BMDL Expression
function reversible_nin_mout and (‘Bm’, 1 function reversible_1in_1out_and (‘C’, ‘A’,
……, ‘B2’, ‘B1’, ‘An’, ……, ‘A2’, ‘A1’, Karray);
‘K’array) 2 function reversible_2in_1out_and (‘C’, ‘A’,’B’,
Karray);
3 function reversible_4in_2out_and (‘E’, ‘F’,
‘A’,’B’, ‘C’, ‘D’, Karray);
4 function reversible_2in_2out and (‘D’, ‘C’, ‘B’,
‘A’, ‘K’array)
Unidirectional simple reaction
General BMDL Expression BMDL Expression
Function_nin_mout and (‘Bm’, ……, ‘B2’, 5 function 2in_1out_and (‘C’, ‘A’,’B’, Karray);
‘B1’, ‘An’, ……, ‘A2’, ‘A1’, ‘K’array) 6 function decay (‘A’, Karray);
7 function 1in_1out_buf (‘B’, ‘A’, Karray); 8 function 1in_2out_buf (‘C’, ‘B’, ‘A’, Karray);
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Unidirectional complex reaction
General BMDL Expression BMDL Expression
function nin_mout_inh_act_buf (‘Bm’, 9. function 2in_2out_inh_act_buf
……, ‘B2’, ‘B1’, ‘An’, ……, ‘A2’, ‘A1’, (‘G’,‘F’,‘E’,‘D’,‘C’,‘B’,‘A’,‘K’array);
‘K’array) 10. function 3in_4out_inh_act_buf
(‘I’,‘H’,‘G’,‘F’,‘E’,‘D’,‘C’,‘B’,‘A’,‘K’array);
11. function 3in_4out_inh_act_buf
(‘I’,‘H’,‘G’,‘F’,‘E’,‘D’,‘C’,‘B’,‘A’,‘K’array);
Table 3.1 Classification of BMDL gates
3.5 Chapter summary
In this chapter, we have focused on the Bio Modeling Development Language, BMDL, developed in [2] followed by the addition of new BMDL functions to include the effects of activators and inhibitors. BMDL has been improved to cover the effect of enzymatic reactions in order to cover metabolic pathways. Further, we enhanced the existing BMDL functions by generalizing them.
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Chapter 4
Use Case: Pyrimidine Pathway
4.1 Introduction
In this chapter we apply our newly developed BMDL weighted gates to study a use case, the Pyrimidine pathway. A brief introduction to nucleotides along with Purine and Pyrimidine ring structures is given. The synthesis of Pyrimidine is given, followed by the set of biochemical equations involved in the pathway. The extraction of the ODE model of the Pyrimidine pathway using BMDL weighted gates is given. New parameters are added to the bio control database mentioned in [2], in order to cover this metabolic pathway. Simulation results for the Pyrimidine pathway are also included in this chapter.
4.2 Nucleotides
Nucleotides are molecules consisting of a phosphate group, a five carbon sugar called pentose (either ribose or deoxyribose) and a one or two ring nitrogen containing base. Nucleotides form the basic constituent of DNA and RNA. All living cells are capable of synthesizing nucleotides. They can be synthesized in by different ways, both in vitro and in vivo
[42]. DNA and RNA are composed of nucleotides containing a phosphoribosyl component along with one of the aromatic bases adenine, guanine, cytosine, thymine and uracil. The bases adenine, guanine and cytosine are present in both DNA and RNA. Thymine is present in DNA and uracil in RNA. These bases are differentiated by their nitrogen containing, aromatic ring structures. These are either Pyrimidines or Purines. Single ring structures like cytosine, thymine and uracil are called Pyrimidine nucleosides while double ring structures like adenine and
38 guanine are called as Purine nucleosides. These ring structures are shown in Figure 4.1.
(Nucleoside refers to one molecule, nucleotide to a chain of molecules.)
The processing of nucleotide consists of numerous biochemical steps which add and remove atoms using numerous enzymes. De novo synthesis of Pyrimidine and Purine follows two different pathways. Pyrimidine is synthesized first from aspartate and carbamoyl-phosphate in the cytoplasm to the common precursor ring structure orotic acid (C00295), onto which a phosphorylated ribosyl unit is covalently linked [43]. Purine, however, is first synthesized from the sugar template onto which the ring synthesis occurs.
Adenine (Double ring structure) Guanine (Double ring structure)
Cytosine (Single ring Thymine (Single ring Uracil (Single ring structure) structure) structure)
Figure4.1 Purine and Pyrimidine rings
4.3 Introduction to the Pyrimidine pathway
The De novo biosynthetic pathway of E. coli encompasses a series of nine reactions that lead to the production of UTP and CTP. De novo Pyrimidine synthesis of E.coli begins with
39 condensation of glutamine with bicarbonate and ends in the formation of UMP, UTP, CTP, dCTP and dTTP [24] Aspartate transcarbammoylase (ATCase, EC2.1.3.2) and carbamoyl phosphate synthetase (CPSase, EC 6.3.5.5) are controlling the metabolic flux through the pathway [46]. Here we will focus on the Pyrimidine pathway, which is shown in figure 4.2 and explained in section 4.2.1.
Pyrimidine metabolism is an important pathway for drugs development. Uridine monophosphate synthase (UMP) is one of the vital enzymes involved in Pyrimidine metabolism,
Deficiency of uridine monophosphate synthase is a hereditary disorder. This enzyme catalyzes orotate phosphoribosyl transferase and orotidine-5′-monophosphate decarboxylase reactions.
This deficiency accumulates orotic acid, which causes clinical manifestations of megaloblastic anemia, orotic crystalluria and nephropathy, cardiac malformations, strabismus, and recurrent infections [44]. Modulating the pyrimidine metabolism pharmacologically has therapeutic uses, especially with regard to rheumatoid arthritis and psoriatic arthritis.
Pyrimidine is a biological pathway which depends a lot on environmental conditions and hereditary conditions. We are focusing on de novo synthesis of Pyrimidine which is an in vivo experimentation method. This pathway can vary from organism to organism, so modeling needs a lot of experimental data on the pathway of a particular organism. This adds a limitation for our study of metabolic pathways.
40
ADP + P1 + Glu HCO CTP 3 + 2- ATP + Gln 9 Glutamine 2ATP + H2O
EC 6.3.5.5 1 UTP ADP 8 ATP
Carbamyl Phosphate
EC 2.1.3.2 Asp UDP ADP 2 P 7 1 ATP
Carbamoyl Aspartate UMP 3 CO2 EC 3.5.2.3 EC 2.4.2.10
6 H2O + EC 4.1.1.23 NADH.H EC 1.3.3.1
5 PRPP 4 OMP PP1 Orotate Dihyrdoorotate NAD+
Figure 4.2 Pyrimidine pathway Color schem, dotted red arrows inhibitors, circled black numbers are reaction numbers corresponding to section 4.2.1,
41
4.3.1Biochemical reactions
Pyrimidine pathway is a metabolic pathway which may vary from organism to organism.
Here we are considering a general case, reactions may vary with a particular organism. Reactions involved in the Pyrimidine pathway, corresponding to Figure 4.2, are as follows:
Reaction 1: Carbamoyl Phosphate Synthetase
푘1 − (4.1) 퐺푙푛 + 2퐴푇푃 + 퐻퐶푂3 + 퐻2푂 퐶푃 + 2퐴퐷푃 + 퐺푙푢 + 푃1
Reaction 2: Aspartate Carbomyl Transferase
푘2 (4.2) 퐶푃 + 퐴푠푝 퐶퐴 + 푃1
Reaction 3: Dihydroorotase
푘3 (4.3) 퐶퐴 퐷퐻푂 + 퐻2푂
Reaction 4: Dihydro orotate oxidase
푘4 (4.4) 퐷퐻푂 + 푁퐴퐷+ 푂푟표
Reaction 5: Orotate phosphoribosyltransferase
푘5 (4.5) 푂푟표 + 푃푅푃푃 푂푀푃 + 푃푃1
Reaction 6: Orodtidine- 5'- Phosphate Decarboxylaseas
푘6 (4.6) 푂푀푃 푈푀푃 + 퐶푂2
Reaction 7: Uridylate kinase
푘7 (4.7) 푈푀푃 + 퐴푇푃 푈퐷푃 + 퐴퐷푃
Reaction 8: Uridine diphosphate kinase
푘8 (4.8) 푈퐷푃 + 퐴푇푃 푈푇푃 + 퐴퐷푃
Reaction 9: Cytidine 5'- triphosphate Synthetase
푘9 (4.9) 푈푇푃 + 퐴푇푃 + 퐺푙푛 퐶푇푃 + 퐴퐷푃 + 푃1 + 퐺푙푢
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4.3.2 BMDL model of Pyrimidine pathway
BMDL acts as a viaduct between biochemical reactions and the ordinary differential equation (ODE) model. Our new gates specifically account for the effect of activators and inhibitors. BMDL model is useful for extracting the ODE model of the Pyrimidine pathway. In chapter 3, BMDL templates are developed. Those are general models and thus include rate of change of each and every component of reaction. Here we will focus on main reactants. Further, for unidirectional reactions we generated ODE models for products only. But here the case is different, as the Pyrimidine pathway includes a chain of reactions and we are supposed to include rate of change of both reactant and product. The ODE equations derived from the templates for each biological weighted gate model are shown below. The augmented set of BMDL gates allows us to model the entire Pyrimidine network, as shown below.
Reaction 1: Carbamoyl Phosphate Synthetase (CPSase)
푘1 − (4.10) 퐺푙푛 + 2퐴푇푃 + 퐻퐶푂3 + 퐻2푂 퐶푃 + 2퐴퐷푃 + 퐺푙푢 + 푃1
BMDL Function: Apply function 4in_4out_inh_act_buf ( ) from section
3.2.1.4
ODE Template:
푑[퐶푃] (4.11) = 푘 퐺푙푛 − 푘 푈푀푃 푑푡 1 푖푢푚푝
43
Reaction 2: Aspartate Carbomyl Transferase (ACTase)
푘2 퐶푃 + 퐴푠푝 퐶퐴 + 푃1
(4.12)
BMDL Function: Apply function 2in_2out_inh_act_buf ( ) from section
3.2.1.2
ODE Template:
푑[퐶푃] (4.13) = −푘 퐶푃 퐴푠푝 푑푡 2
푑[퐶퐴] = 푘 퐶푃 [퐴푠푝] − 푘 푈푇푃 − 푘 퐶푇푃 푑푡 2 푖푢푡푝 푖푐푡푝 (4.14)
Reaction 3: Dihydroorotase (DHOase)
푘3 퐶퐴 퐷퐻푂 + 퐻 푂 (4.15) 2 BMDL Function: Apply function 1in_2out_buf ( ) from section 3.2.1[2]
ODE Template:
푑 퐶퐴 (4.16) = −푘 퐶퐴 푑푡 3
푑[퐷퐻푂] = 푘 퐶퐴 (4.17) 푑푡 3
44
Reaction 4: Dihydro orotate oxidase (DHOdeHase)
푘4 퐷퐻푂 + 푁퐴퐷+ 푂푟표 (4.17)
BMDL Function: Apply function 2in_1out_and ( ) from section 3.2.1[2]
ODE Template:
푑[퐷퐻푂] (4.18) = −푘 퐶퐴 푑푡 4
푑[푂푟표] = 푘 퐷퐻푂 (4.19) 푑푡 4
Reaction 5: Orotate phosphoribosyltransferase (OPRTase)
푘5 (4.20) 푂푟표 + 푃푅푃푃 푂푀푃 + 푃푃 1
BMDL Function: Apply function 2in_2out_inh_act_buf ( ) from section
3.2.1.2. Here inhibitors and activators are absent so ODE consists of only reactants and products.
ODE Template:
푑[푂푟표] (4.21) = −푘5 푂푟표 푃푅푃푃 푑푡
푑[푂푀푃] = 푘 푂푟표 푃푅푃푃 푑푡 5 (4.22)
45
Reaction 6: Orodtidine- 5'- Phosphate Decarboxylaseas (ODCase)
푘6 푂푀푃 푈푀푃 + 퐶푂 (4.23) 2
BMDL Function: Apply function 1in_2out_buf ( ) from section 3.2.1[2]
ODE Template:
푑 푂푀푃 (4.24) = −푘 푂푀푃 푑푡 6
푑[푈푀푃] = 푘 푂푀푃 (4.25) 푑푡 6
Reaction 7: Uridylate kinase (UMP kinase)
푘7 푈푀푃 + 퐴푇푃 푈퐷푃 + 퐴퐷푃 (4.26)
BMDL Function: Apply function 2in_2out_inh_act_buf ( ) from section
3.2.1.2. Here inhibitors and activators are absent so ODE consists of only reactants and products.
ODE Template:
푑 푈푀푃 (4.27) = − 푘 푈푀푃 푑푡 7
푑[푈퐷푃] = 푘 푈푀푃 퐴푇푃 (4.28) 푑푡 7
46
Reaction 8: Uridine diphosphate kinase (NDKinase)
푘8 푈퐷푃 + 퐴푇푃 푈푇푃 + 퐴퐷푃 (4.29)
BMDL Function: Apply function 2in_2out_inh_act_buf ( ) from section
3.2.1.2. Here inhibitors and activators are absent so ODE consists of only reactants and products.
ODE Template:
푑 푈퐷푃 (4.30) = − 푘 푈퐷푃 푑푡 8
푑[푈푇푃] = 푘 푈퐷푃 퐴푇푃 (4.31) 푑푡 8
Reaction 9: Cytidine 5'- triphosphate Synthetase (CTP Synthase)
푘9 푈푇푃 + 퐴푇푃 + 퐺푙푛 퐶푇푃 + 퐴퐷푃 + 푃 + 퐺푙푢 (4.32) 1
BMDL Function: Apply function 3in_4out_inh_act_buf ( ) from section
3.2.1.2. Here inhibitors and activators are absent so ODE consists of only reactants and products.
ODE Template:
푑 푈푇푃 (4.33) = − 푘 푈푇푃 푑푡 9
푑[퐶푇푃] = 푘 푈푇푃 (4.34) 푑푡 9
47
4.3.3 ODE model of Pyrimidine pathway
After extracting all ordinary differential equations, the final ODE model for the
Pyrimidine pathway is summarized below. It consists of nine differential equations.
푑[퐶푃] (4.36) = 푘 퐺푙푛 − 푘 퐶푃 퐴푠푝 − 푘 푈푀푃 푑푡 1 2 푖푢푚푝
푑[퐶퐴] (4.37) = 푘 퐶푃 [퐴푠푝] − 푘 퐶퐴 − 푘 푈푇푃 − 푘 퐶푇푃 푑푡 2 3 푖푢푡푝 푖푐푡푝
푑[퐷퐻푂] (4.38) = 푘 퐶퐴 − 푘 [퐷퐻푂] 푑푡 3 4
푑[푂푟표] (4.39) = 푘 퐷퐻푂 −푘 푂푟표 푃푅푃푃 푑푡 4 5
푑[푂푀푃] (4.40) = 푘 푂푟표 푃푅푃푃 − 푘 푂푀푃 푑푡 5 6
푑[푈푀푃] (4.41) = 푘 푂푀푃 − 푘 푈푀푃 푑푡 6 7
푑[푈퐷푃] (4.42) = 푘 푈푀푃 퐴푇푃 − 푘 푈퐷푃 푑푡 7 8
푑[푈푇푃] (4.43) = 푘 푈퐷푃 퐴푇푃 − 푘 푈푇푃 푑푡 8 9
푑[퐶푇푃] (4.44) = 푘 푈푇푃 푑푡 9
4.4 Bio-Control database and modifications for metabolic pathway
The bio-control database includes the effects of various parameters like pressure, temperature, chemicals, ribosomal binding sites and proteins. In [2] these parameters are used as experimental controls which are derived from the literature. These parameters are mainly used
48 for determining the controllability of a reaction in order to apply the Box algorithm. The database entry [2] covers all parameters affecting the gene regulatory system.
Bio- control database in our work includes the database for the enzyme. Our work is to extend the idea of analyzing biological pathways, emphasizing a complex metabolic pathway. A metabolic pathway depends on the participation of enzymes as they are main components. Here we are adding additional slots to the database entry so that it can summarize major parameters involved in metabolic pathways. Table 4.1 shows a bio-control database entry developed for a gene regulatory pathway in [2] while table 4.2 shows one developed for a metabolic pathway.
Bio-control database for Pyrimidine pathway is mainly referred from the Enzymes handbook [46], which has a collection of all enzymatic reactions.
49
Table 4.1 Bio-control database entry for the rate of transcription for the protein Cro of Phage lambda[2]
50
[46]
Table 4.2: Bio-control database entry for Carbomyl phosphate synthase of Pyrimidine pathway
51
4.4.1 Bio-Control database for Pyrimidine pathway
The bio control database for the Pyrimidine pathway is as follows. These entries are included in [7].
Reaction 1 Carbomyl phosphate synthase
[46]
Table 4.3: Bio-control database entry for Carbomyl phosphate synthase of Pyrimidine pathway
52
Reaction 2 Aspartate Carbomyl Transferase
[46]
Table 4.4: Bio-control database entry for AspartateCarbomyl transferase of Pyrimidine pathway
53
Reaction 3 Carbamoyl Phosphate Synthetase 푘3 퐶퐴 퐷퐻푂 + 퐻2푂
Unavailability of sufficient published literature.
Reaction 4 Dihydro orotate oxidase
[46]
Table 4.5: Bio-control database entry for (Dihydro orotate oxidase) reaction 4 of Pyrimidine pathway
54
Reaction 5 Orotate phosphoribosyltransferase
[46]
Table 4.6: Bio-control database for entry Orotate phosphoribosyl transferase of Pyrimidine pathway
55
Reaction 6 Orodtidine- 5'- Phosphate Decarboxylaseas
[46]
Table 4.7: Bio-control database entry for Orodtidine- 5'- Phosphate Decarboxylaseas of Pyrimidine pathway
56
Reaction 7 Carbamoyl Phosphate Synthetase
푘7 푈푀푃 + 퐴푇푃 푈퐷푃 + 퐴퐷푃
Unavailability of sufficient published literature.
57
Reaction 8 Uridine diphosphate kinase
[46] Table 4.8: Bio-control database entry for Uridine diphosphate kinase of Pyrimidine pathway
58
Reaction 9 Cytidine 5'- triphosphate Synthetase
[46]
Table 4.9: Bio-control database entry for Cytidine 5'- triphosphate synthetase of Pyrimidine pathway
59
4.5 Simulation results of Carbomyl Phosphate Synthase (CPSase)
Pyrimidine pathway is modeled in MATLAB using the BMDL expressions developed in section 4.2. We are showing the effect of Uridine Monophosphate, UMP, on Carbomyl
Phosphate Synthase (CPSase). UMP acts as an inhibitor for CPSase. We modeled the pyrimidine pathway including the effect of inhibitors and activators to simulate it to obtain the results matching the laboratory result.
CPSase is an enzymatic reaction which has two main products Carbomyl phosphate and glutamine, here we are focusing on the concentration of Carbomyl Phosphate in absence or presence of UMP. This is shown as in Figure 4.3.
Effect of UMP on CPSase 700
600
500
400 CP in absence of UMP 300 CP in presence of UMP
CP conc (µM) conc CP 200
100
0
0 6
12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 Time (sec)
Figure 4.3 Effect of UMP on CPSase
60
This simulation result is validated with the experimental results obtained in [45]. In [45], the effect of inhibitor, UMP, is studied on the concentration of CPSase with respect to formation of glutamine. Glutamine is a byproduct formed during CPSase and is further not consumed in the
Pyriminde pathway. Thus, validation for CPSase verifies our model developed for Pyrimidine pathway.
In order to verify our modeling for activator, a pseudo experiment is performed on
Carbomyl phosphate synthase and its simulation result is shown in Figure 4.4. These experiments behavior shows that if an activator is added to Pyrimidine synthesis then it increases concentration of CP.
700 Effect of Activator
600
500
400 CP in 300 absence of activator
CP conc (µM) conc CP CP in 200 presence of activator 100
0 0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 Time (sec) Figure 4.4 Effect of Activator on CPSase
61
4.6 Application of the Box algorithm to Pyrimidine pathway
The Box algorithm, a useful tool, has been developed in [2] to study and characterize biological pathways. This algorithm integrates the laboratory constraints and process behavior of a biological pathway into a mathematical model. The algorithm can be applied for simulating and controlling any gene regulation pathway. There are certain limitations while applying this pathway to metabolic pathway.
Pyrimidine pathway is a metabolic pathway including all enzymatic reactions. The bio control database for this pathway is developed in section 4.3. These bio control entries are not sufficient to calculate bio- rules priority in order to optimize the pathway using the Box algorithm. The unavailability of enough biocontrols to control kinetic constant for all reactions of the pathway is a major challenge in applying the Box algorithm on our use case. But the framework we have developed here can support virtual experiments which can aid the biologists in choosing laboratory experiments to fill in the gaps in our knowledge.
4.7 Chapter summary
In this chapter, we focused on our use case, the Pyrimidine pathway, a metabolic pathway. This complex pathway is modeled using BMDL templates developed in [2] and in section 3.3. A bio control database was created for this pathway [46]. Matlab simulations are performed for this Carbomyl Phosphate syntahse, focusing on the modeling of an inhibitor, matching the results obtained in [24]. A virtual experiment modeling the effect of an activator is also carried out.
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Chapter 5
Conclusions and Future Work
5.1 Introduction
In this chapter we present a summary of our work and the conclusions we have derived followed by suggestions for future work.
5.2 Conclusions
In our work, we have extended the work done by Rajesh Krishnan in [2]. We extended his work to complex metabolic, pathways. We have developed the new BMDL templates capable of modeling a complex biochemical reaction. Biochemical reactions with activators and inhibitors can be modeled using the new BMDL templates. These BMDL templates are generalized, making BMDL capable of modeling a wide range of biological pathways. We discuss the extended bio-control database, which includes more complex biological processes and metabolic pathways. This bio control database for the Pyrimidine pathways was explained originally in [7].
The Pyrimidine pathway is modeled using BMDL templates developed so far. CPSase of the pyrimidine pathway is modeled using MATLAB and validated against the experimental results obtained by Robin et al [44]. Due to the unavailability of bio controls for all reactions involved in the Pyrimidine pathway, we were not able to optimize results using the Box algorithm.
A wide range of biological pathways can be modeled using the generalized BMDL gates.
63
5.3 Suggestions for future work
We provide some areas that have a scope for improvement and expansion:
1. Limitation of availability of all kinetic constants involved in the Pyrimidine pathway can be
overcome by assuming different values of K constants and simulating all reactions in order
to study the controllability of all reactions. On the basis of this controllability, we can apply
the Box algorithm to optimize this pathway. Thus, it becomes a challenge for the biologist
to obtainvalues for highly controllable data by referring to our simulation results.
2. The BMDL weighted gate model extracts the ODE model of the process manually by
referring to BMDL templates. Automation to extract the ODE model from the biological
model will be a great help to the biologist, and preferably would exclude a graphical
standard user interface (GUI) for the BMDL model so that the user can represent the
reactions using graphical weighted gates rather than writing a program.
5.4 List of Publications and Conference Proceedings
The following publications use material from this thesis:
S. Mailavaram, A. Desai and C. Purdy, Intelligent tools for the study of biological
pathways, Proc. Midwest Artificial Intelligence and Cognitive Science Conference
(MAICS08), Cincinnati, OH, 2008;
A. Desai, S.Mailavaram and C. Purdy, Enabling virtual experiments for the study of
Biological Pathways, 3rd Electrical and Computer Science Engineering Graduate Student
Association Poster Symposium (ECECS GSA), Cincinnati, OH, 2008;
64
A. Desai and C. Purdy, Simulation environment for the study of enzymatic pathways, Third
Ohio Graduate Student Symposium on Computer and Information Science & Engineering
(OGSS-CISE '08) Kent, OH;
A. Desai and C. Purdy, BMDL weighted gates for the modeling of the Pyrimidine pathway,
Ohio Collaborative Conference on Bioinformatics (OCCBIO 08), Toledo, OH, 2008.
65
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Appendix A
References for Reaction1:
[A1] T. Aoki and H. Oya, “Kinetic properties of carbamoyl-phosphate synthetase II (glutamine-hydrolyzing) in the parasitic protozoan Crithidia fasciculata and separation of the enzyme from aspartate carbamoyltransferase.” Comparative biochemistry and physiology. B, Comparative biochemistry, vol. 87, no. 1, pp. 143–50, 1987.
[A2] T. Aoki and H. Oya, “Inactivation of Crithidia fasciculata carbamoyl phosphate synthetase II by the antitumor drug acivicin.” Molecular and biochemical parasitology, vol. 23, no. 2, pp. 173–81, 1987.
[A3] T. Meek, W. Karsten, and C. DeBrosse, “Carbamoyl-phosphate synthetase II of the mammalian CAD protein: kinetic mechanism and elucidation of reaction intermediates by positional isotope exchange,” Biochemistry, vol. 26, no. 9, pp. 2584–2593, 1987.
[A4] P. Anderson, “Carbamoyl-phosphate synthetase: an example of effects on enzyme properties of shifting an equilibrium between active monomer and active oligomer,” Biochemistry, vol. 25, no. 19, pp. 5576–5582, 1986.
[A5] A. Wandinger-Ness, S. Ness, and R. Weiss, “Simultaneous purification of three mitochondrial enzymes. Acetylglutamate kinase, acetylglutamyl-phosphate reductase and carbamoyl-phosphate synthetase from Neurospora crassa,” Journal of Biological Chemistry, vol. 261, no. 11, pp. 4820–4827, 1986.
[A6] D. Kaseman and A. Meister, “Carbamyl phosphate synthetase (glutamine-utilizing) from Escherichia coli.” Methods in Enzymology, vol. 113, pp. 305–326, 1985.
[A7] S. Lyons and R. Christopherson, “Regulation of hamster carbamoylphosphate synthase II by 5-phospho-alpha-D-ribosyl 1-diphosphate and uridine 5’-triphosphate.” European Journal of Biochemistry, vol. 147,no. 3, pp. 587–592, 1985.
71
[A8] V. L. Abdelal A.T., Bussey L, “Carbamoylphosphate synthetase from pseudomonas aeruginosa. Subunit composition, kinetic analysis and regulation.” European Journal of Biochemistry, vol. 129, pp. 697–702, 1983
[A9] D. P. S. Patrick F. Coleman and G. R. Stark, “Purification of a multifunction protein bearing carbamyl-phosphate synthase, aspartate transcarbamylase, and dihydroorotase enzyme activities from mutant hamster cells.” Methods in Enzymology, vol. 51, pp. 121– 34, 1978.
[A10] T. Kensler, L. Reck, and D. Cooney, “Therapeutic effects of acivicin and N- (Phosphonacetyl)-L-aspartic acid in a biochemically designed trial against a N- (Phosphonacetyl)-L-aspartic acid-resistant variant of the Lewis Lung Carcinoma,” Cancer Research, vol. 41, no. 3, p. 905, 1981.
[A11] M. Mori and M. Tatibana, “A multienzyme complex of carbamoylphosphate synthase (glutamine): aspartate carbamoyltransferase: dihydoorotase (rat ascites hepatoma cells and rat liver).” Methods in Enzymology, vol. 51, pp. 111–20, 1978.
[A12] J. Ingraham and A. Abdelal, “Carbamoyl-phosphate synthetase (glutamine): Salmonella.” Methods in Enzymology, vol. 51, pp. 29–35, 1978.
[A13] P. Trotta, M. Burt, L. Pinkus, L. Estis, R. Haschemeyer, and A. Meister, “Glutamine- dependent carbamyl-phosphate synthetase (Escherichia coli); preparation of subunits.” Methods in Enzymology, vol. 51, pp. 21–9, 1978.
[A14] H. Ishida, M. Mori, and M. Tatibana, “Effects of dimethyl sulfoxide and glycerol on catalytic and regulatory properties of glutamine-dependent carbamoyl phosphate synthase from rat liver and dual effects of uridine triphosphate.” Archives of biochemistry and biophysics, vol. 182, no. 1, pp. 258–65, 1977.
[A15] S. Powers, O. Griffith, and A. Meister, “Inhibition of carbamyl phosphate synthetase by P1, P5-di (adenosine 5’)-entaphosphate: evidence for two ATP binding sites,” Journal of Biological Chemistry, vol. 252, no. 10, pp. 3558–3560, 1977.
72
[A16] M. Mori and M. Tatibana, “Glutamine-dependent carbamoyl phosphate synthetase: polyamines inhibit the activity and modify the activating effect of 5-phosphoribosyl 1- pyrophosphate.” Biochemical and biophysical research communications, vol. 67, no. 1, pp. 287–293, 1975.
[A17] P. Trotta, L. Pinkus, R. Haschemeyer, and A. Meister, “Reversible dissociation of the monomer of Glutamine-dependent Carbamyl Phosphate Synthetase into Catalytically Active Heavy and Light Subunits,” Journal of Biological Chemistry, vol. 249, no. 2, pp. 492–499, 1974.
[A18] P. Trotta, L. Estis, A. Meister, and R. Haschemeyer, “Self-Association and allosteric properties of glutamine-dependent Carbamyl Phosphate Synthetase Reversible dissociation to monomeric species,” Journal of Biological Chemistry, vol. 249, no. 2, pp. 482– 489, 1974.
[A19] P. Anderson, J. Carlson, G. Rosenthal, and A. Meister, “Effect of potassium cyanate on the catalytic activities of carbamyl phosphate synthetase.” Biochemical and biophysical research communications,, vol. 55, no. 1, pp. 246–252, 1973.
[A20] M. Yip and W. Knox, “Glutamine-dependent Carbamyl Phosphate Synthetase properties and distribution in normal and neoplastic rat tissues,” Journal of Biological Chemistry, vol. 245, no. 9, pp. 2199–2204, 1970.
[A21] S. Kalman, P. Duffield, and T. Brzozowski, “Purification and properties of a bacterial Carbamyl Phosphate Synthetase,” Journal of Biological Chemistry, vol. 241, no. 8, pp. 1871–1877, 1966.
[A22] P. Anderson and A. Meister, “Evidence for an Activated Form of Carbon dioxide in the reaction catalyzed by Escherichia coli Carbamyl Phosphate Synthetase,” Biochemistry, vol. 4, no. 12, pp. 2803–2809,1965.
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[A23] M. Rodriguez, T. Good, M. Wales, J. Hua, and J. Wild, “Modeling allosteric regulation of de novo pyrimidine biosynthesis in Escherichia coli,” Journal of Theoretical Biology, vol. 234, no. 3, pp. 299–310, 2005.
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Appendix B
References for Reaction 2:
[B1] M. Shepherdson and A. Pardee, “Production and Crystallization of Aspartate Transcarbamylase,” Journal of Biological Chemistry, vol. 235, no. 11, pp. 3233–3237, 1960.
[B2] J. Lowenstein and P. Cohen, “Studies on the biosynthesis of Carbamylaspaparatic acid,” Journal of Biological Chemistry, vol. 220, no. 1, pp. 57–70, 1956.
[B3] E. Kantrowitz and W. Lipscomb, “Escherichia coli aspartate transcarbamoylase: the molecular basis for a concerted allosteric transition.” Trends in biochemical sciences, vol. 15, no. 2, pp. 53–59, 1990.
[B4] P. England and G. Herve, “Synergistic inhibition of Escherichia coli aspartate transcarbamylase by CTP and UTP: binding studies using continuous-flow dialysis,” Biochemistry, vol. 31, no. 40, pp. 9725–9732, 1992.
[B5] J. Mort and W. Chan, “Subunit interactions in aspartate transcarbamylase. Characterization of a complex between the catalytic and the regulatory subunits,” Journal of Biological Chemistry, vol. 250, no. 2, pp. 653–660, 1975.
[B6] Y. Zhang and E. Kantrowitz, “The synergistic inhibition of Escherichia coli aspartate carbamoyltransferase by UTP in the presence of CTP is due to the binding of UTP to the low affinity CTP sites,” Journal of Biological Chemistry, vol. 266, no. 33, pp. 22154– 22158, 1991.
[B7] J. Rao and A. Wlodawer, “Is the pseudo-dyad in retroviral proteinase monomers structural or evolutionary?” FEBS Lett, vol. 260, no. 2, pp. 201–205, 1990.
[B8] S. Nowlan and E. Kantrowitz, “Superproduction and rapid purification of Escherichia coli aspartate transcarbamylase and its catalytic subunit under extreme derepression of
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the pyrimidine pathway,” Journal of Biological Chemistry, vol. 260, no. 27, pp. 14 712– 14 716, 1985.
[B9] E. Swyryd, S. Seaver, and G. Stark, “N-(Phosphonacetyl)-l-Aspartate, a Potent Transition State Analog Inhibitor of Aspartate Transcarbamylase, Blocks Proliferation of Mammalian Cells in Culture,” Journal of Biological Chemistry, vol. 249, no. 21, pp. 6945–6950, 1974.
[B10] C. Enns and W. Chan, “Chemical stabilization of conformational states of aspartate transcarbamoylase.” Methods in Enzymology, vol. 135, pp. 569– 577, 1987.
[B11] G. Jagannatha Rao, H. Savithri, S. Seethalakshmi, and N. Appaji Rao, “Plant aspartate transcarbamylase: An affinity chromatographic method for the purification of the enzyme from germinated seedlings,” Analytical Biochemistry, vol. 95, no. 2, pp. 401–405, 1979.
[B12] J. Brabson and R. Switzer, “Purification and properties of Bacillus subtilis aspartate transcarbamylase,” Journal of Biological Chemistry, vol. 250, no. 22, pp. 8664–8669, 1975.
[B13] R. Yon, “Versatility of mixed-function adsorbents in biospecific protein desorption: Accidental affinity and an improved purification of aspartate transcarbamoylase from wheat germ,” Analytical Biochemistry, vol. 113, no. 2, pp. 219–228, 1981.
[B14] J. Grayson, R. Yon, and P. Butterworth, “Wheat-germ aspartate transcarbamoylase. Purification and cold-lability.” Biochemical Journal, vol. 183, no. 2, p. 239, 1979.
[B15] D. Grayson and D. Evans, “The isolation and characterization of the aspartate transcarbamylase domain of the multifunctional protein, CAD,” Journal of Biological Chemistry, vol. 258, no. 7, pp. 4123–4129, 1983.
[B16] G. Jacobson and G. Stark, “Aspartate transcarbamylase of Escherichia coli. Mechanisms of inhibition and activation by dicarboxylic acids and other anions,” Journal of Biological Chemistry, vol. 250, no. 17, pp. 6852–6860, 1975.
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[B17] M. Mathieu, “Partial characterisation of aspartate transcarbamylase from the mantle of the mussel Mytilus edulis.” Comparative biochemistry and physiology. B, vol. 82, no. 4, pp. 667–674, 1985.
[B18] J. Brabson, M. Maurizi, and R. Switzer, “Aspartate transcarbamylase from Bacillus subtilis.” Methods in Enzymology, vol. 113, pp. 627–35, 1985.
[B19] T. Chang, L. Prescott, and M. Jones, “Aspartate carbamyltransferase (Streptococcus faecalis).” Methods in Enzymology, vol. 51, pp. 41–50, 1978.
[B20] L. Adair and M. Jones, “Aspartate carbamyltransferase (Pseudomonas fluorescens).” Methods in Enzymology, vol. 51, pp. 51–58, 1978.
[B21] T. Chang and M. Jones, “Aspartate transcarbamylase from Streptococcus faecalis. Purification, properties, and nature of an allosteric activator site,” Biochemistry, vol. 13, no. 4, pp. 629–638, 1974.
[B22] T. Chang and M. Jones, “Aspartate transcarbamylase from Streptococcus faecalis. Steadystate kinetic analysis,” Biochemistry, vol. 13, no. 4, pp. 638–645, 1974.
[B23] B. Ong and J. Jackson, “Aspartate transcarbamoylase from Phaseolus aureus. pPartial purification and properties,” Biochemical Journal, vol. 129, no. 3, pp. 571, 1972.
[B24] L. Adair and M. Jones, “Purification and characteristics of Aspartate Transcarbamylase from Pseudomonas fluorescens,” Journal of Biological Chemistry, vol. 247, no. 8, pp. 2308–2315, 1972.
[B25] R. Masood and T. Venkitasubramanian, “Purification and properties of aspartate transcarbamylase from Mycobacterium smegmatis.” Biochimica et biophysica acta, vol. 953, no. 1, pp. 106–113, 1988.
[B26] M. Mori and M. Tatibana, “A multienzyme complex of carbamoylphosphate synthase (glutamine): aspartate carbamoyltransferase: dihydoorotase (rat ascites hepatoma cells and rat liver).” Methods in Enzymology, vol. 51, pp. 111–120, 1978.
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[B27] S. D. Coleman, P.F. and G. Stark, “Purification of a multifunction protein bearing carbamyl-phosphate synthase, aspartate transcarbamylase, and dihydroorotase enzyme activities from mutant hamster cells.” Methods in Enzymology, vol. 51, pp. 121–134, 1978.
[B28] M. Rodriguez, T. Good, M. Wales, J. Hua, and J. Wild, “Modeling allosteric regulation of de novo pyrimidine biosynthesis in Escherichia coli,” Journal of Theoretical Biology, vol. 234, no. 3, pp. 299–310, 2005.
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Appendix C
References for Reaction 4:
[C1] W. Taylor, M. Taylor, and D. Eames, “Two Functionally Different Dihydroorotic Dehydrogenases in Bacteria,” Journal of Bacteriology, vol. 91, no. 6, pp. 2251, 1966.
[C2] W. Taylor, C. Taylor, and M. Taylor, “Biosynthetic Dihydroorotate Dehydrogenase from Lactobacillus bulgaricus: Partial Characterization of the Enzyme,” Journal of Bacteriology, vol. 119, no. 1, pp. 98, 1974.
[C3] R. Pascal Jr, N. Le Trang, A. Cerami, and C. Walsh, “Purification and properties of dihydroorotate oxidase from Crithidia fasciculata and Trypanosoma brucei,” Biochemistry, vol. 22, no. 1, pp. 171–178, 1983.
[C4] M. Taylor, W. Taylor, D. Eames, and C. Taylor, “Biosynthetic dihydroorotate dehydrogenase from Lactobacillus bulgaricus,” Journal of Bacteriology, vol. 105, no. 10, pp. 1, 1971.
[C5] R. Pascal Jr and C. Walsh, “Mechanistic studies with deuterated dihydroorotates on the dihydroorotate oxidase from Crithidia fasciculata,” Biochemistry, vol. 23, no. 12, pp. 2745–2752, 1984.
[C6] M. Rodriguez, T. Good, M. Wales, J. Hua, and J. Wild, “Modeling allosteric regulation of de novo pyrimidine biosynthesis in Escherichia coli,” Journal of Theoretical Biology, vol. 234, no. 3, pp. 299–310, 2005.
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Appendix D
References for Reaction 5:
[D1] M. Jones, P. Kavipurapu, and T. Traut, “Orotate phosphoribosyltransferase: orotidylate decarboxylase (Ehrlich ascites cell).” Methods in Enzymology, vol. 51, pp. 155–167, 1978.
[D2] R. McClard, M. Black, L. Livingstone, and M. Jones, “Isolation and initial characterization of the single polypeptide that synthesizes uridine 5’-monophosphate from orotate in Ehrlich ascites carcinoma. Purification by tandem affinity chromatography of uridine-5’-monophosphate synthase,” Biochemistry, vol. 19, no. 20, pp. 4699–4706, 1980.
[D3] M. Bhatia and C. Grubmeyer, “The role of divalent magnesium in activating the reaction catalyzed by orotate phosphoribosyltransferase.” Archives of biochemistry and biophysics, vol. 303, no. 2, pp. 321–325, 1993.
[D4] A. Yoshimoto, T. Amaya, K. Kobayashi, and K. Tomita, “Orotatephosphoribosyltransferase (yeast).” Methods in Enzymology, vol. 51, pp. 69–74, 1978.
[D5] J. Victor, A. Leo-Mensah, and D. Sloan, “Divalent metal ion activationof the yeast orotate phosphoribosyl transferase catalyzed reaction,” Biochemistry, vol. 18, no. 16, pp. 3597–3604, 1979.
[D6] P. Reyes and R. Sandouist, “Purification of orotate phosphoribosyltransferase and orotidylate decarboxylase by affinity chromatography on Sepharose dye derivatives,” Analytical Biochemistry, vol. 88, no. 2, pp. 522–531, 1978.
[D7] J. Victor, L. Greenberg, and D. Sloan, “Studies of the kinetic mechanism of orotate phosphoribosyltransferase from yeast,” Journal of Biological Chemistry, vol. 254, no. 8, pp. 2647–2655, 1979.
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[D8] Y. Ito, N. Seno, and I. Matsumoto, “Immobilization of Protein Ligands on New Formyl- Spacer-Carriers for the Preparation of Stable and High Capacity Affinity Adsorbents,” Journal of Biochemistry, vol. 97, no. 6, pp. 1689, 1985.
[D9] G. Dodin, “A rapid purification by affinity chromatography of orotate phosphoribosyltransferase from Escherichia coli K-12.” FEBS Lett, vol. 134, no. 1, pp. 20–24, 1981.
[D10] P. Rathod and P. Reyes, “Orotidylate-metabolizing enzymes of the human malarial parasite, Plasmodium falciparum, differ from host cell enzymes,” Journal of Biological Chemistry, vol. 258, no. 5, pp. 2852–2855, 1983.
[D11] E. Floyd and M. Jones, “Isolation and characterization of the orotidine 5’-monophosphate decarboxylase domain of the multifunctional protein uridine 5’-monophosphate synthase,” Journal of Biological Chemistry, vol. 260, no. 16, pp. 9443–9451, 1985.
[D12] M. Bhatia, A. Vinitsky, and C. Gr ubmeyer, “Kinetic mechanism of orotate phosphoribosyltransferase from Salmonella typhimurium,” Biochemistry, vol. 29, no. 46, pp. 10 480–10 487, 1990.
[D13] G. Scapin, J. Sacchettini, A. Dessen, M. Bhatia, and C. Grubmeyer, “Primary structure and crystallization of orotate phosphoribosyltransferase from Salmonella typhimurium.” Journal of molecular biology, vol. 230, no. 4, pp. 1304–1308, 1993.
[D14] H. Ashihara, “Orotage Phoshoribosyl transferase and Orotidine-5- monophosphate Decarboxylase of Black Gram (Phaseolus mungo) Seedlings.” Z. Pflanzenphysiol, vol. 87, pp. 225–241, 1978.
[D15] M. Kapoor and E. Waygood, “Orotidine-5-Phosphate Pyrophosphorylase of Wheat Embryos.” Journal of Biochemistry, vol. 43, pp. 143–151, 1965.
[D16] M. Rodriguez, T. Good, M. Wales, J. Hua, and J. Wild, “Modeling allosteric regulation of de novo pyrimidine biosynthesis in Escherichia coli,” Journal of Theoretical Biology, vol. 234, no. 3, pp. 299–310, 2005.
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Appendix E
References for Reaction6 :
[E1] M. Murray and C. Ross, “Molecular weight estimations of some pyrimidine-metabolizing enzymes from pea cotyledons by gel filtration,” Phytochemistry, vol. 10, pp. 2645–2648, 1971.
[E2] J. Fyfe, R. Miller, and T. Krenitsky, “Kinetic Properties and Inhibition of Orotidine 5’- Phosphate Decarboxylase Effects of some allopurinol metabolites on the enzyme,” Journal of Biological Chemistry, vol. 248, no. 11, pp. 3801–3809, 1973.
[E3] W. Shoaf and M. Jones, “Uridylic acid synthesis in Ehrlich ascites carcinoma. Properties, subcellular distribution, and nature of enzyme complexes of the six biosynthetic enzymes,” Biochemistry, vol. 12, no. 21, pp. 4039–4051, 1973.
[E4] G. Brown, R. Fox, and W. O’Sullivan, “Interconversion of different molecular weight forms of human erythrocyte orotidylate decarboxylase,” Journal of Biological Chemistry, vol. 250, no. 18, pp. 7352–7358, 1975.
[E5] A. Yoshimoto, K. Umezu, K. Kobayashi, and K. Tomita, “Orotidylate decarboxylase (yeast).” Methods in Enzymology, vol. 51, pp. 74–79, 1978.
[E6] S. Pragobpol, A. Gero, C. Lee, and W. O’Sullivan, “Orotate phosphoribosyltransferase and orotidylate decarboxylase from Crithidia luciliae: subcellular location of the enzymes and a study of substrate channeling.” Archives of Biochemistry and Biophysics, vol. 230, no. 1, pp. 285–293, 1984.
[E7] R. Brody and F. Westheimer, “The purification of orotidine-5’-phosphate decarboxylase from yeast by affinity chromatography,” Journal of Biological Chemistry, vol. 254, no. 10, pp. 4238–4244, 1979.
[E8] H. Levine, R. Brody, and F. Westheimer, “Inhibition of orotidine- 5’-phosphate decarboxylase by 1-(5’-phospho-. beta.-D-ribofuranosyl) barbituric acid, 6-azauridine 5’-
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phosphate, and uridine 5’-phosphate,” Biochemistry, vol. 19, no. 22, pp. 4993–4999, 1980.
[E9] M. Rodriguez, T. Good, M. Wales, J. Hua, and J. Wild, “Modeling allosteric regulation of de novo pyrimidine biosynthesis in Escherichia coli,” Journal of Theoretical Biology, vol. 234, no. 3, pp. 299–310, 2005.
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Appendix F
References for Reaction 8:
[F1] I. Lascu, M. Duc, and A. Cristea, “Rapid large-scale purification of pig heart nucleoside diphosphate kinase by affinity chromatography on Cibacron Blue 3G-A Sepharose,” Analytical Biochemistry, vol. 113, no. 2, pp. 207–211, 1981.
[F2] E. Presecan, A. Vonica, and I. Lascu, “Nucleoside diphosphate kinase from human erythrocytes: purification, molecular mass and subunit structure.” FEBS Letters, vol. 250, no. 2, pp. 629–32, 1989.
[F3] M. G. Colomb, A. Cheruy, and P. V. Vignais, “Nucleoside diphosphokinase from beef heart cytosol. i. physical and kinetic properties,” Biochemistry, vol. 11, no. 18, pp. 3370– 3378, 1972.
[F4] H. Nakamura and Y. Sugino, “Metabolism of Deoxyribonucleotides III. Purification and some properties of Nucleoside diphosphokinase of calf thymus,” Journal of Biological Chemistry, vol. 241, no. 21, pp. 4917–4922, 1966.
[F5] N. Kimura and N. Shimada, “Membrane-associated nucleoside diphosphate kinase from rat liver. Purification, characterization, and comparison with cytosolic enzyme,” Journal of Biological Chemistry, vol. 263, no. 10, pp. 4647–4653, 1988.
[F6] G. Buczynski and R. Potter, “Nucleoside diphosphate kinase from Xenopus oocytes; partial purification and characterization.” Biochimica et biophysica acta, vol. 1041, no. 3, pp. 296–304, 1990.
[F7] T. Nomura, T. Fukui, and A. Ichikawa, “Purification and characterization of nucleoside diphosphate kinase from spinach leaves.” Biochimica et biophysica acta, vol. 1077, no. 1, pp. 47–55, 1991.
[F8] S. Moisyadi, S. Dharmasiri, H. Harrington, and T. Lukas, “Characterization of a low molecular mass autophosphorylating protein in cultured sugarcane cells and its
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identification as a nucleoside diphosphate kinase.” Plant Physiology, vol. 104, no. 4, pp. 1401, 1994.
[F9] D. Sommer and P. Song, “A plant nucleoside diphosphate kinase homologous to the human Nm23 gene product: purification and characterization.” Biochimica et biophysica acta, vol. 1222, no. 3, pp. 464–470, 1994.
[F10] C. Dumas, G. Lebras, V. Wallet, M. Lacombe, M. Veron, and J. Janin, “Crystallization and preliminary X-ray diffraction studies of nucleoside diphosphate kinase from Dictyostelium discoideum.” Journal of Molecular Biology, vol. 217, no. 2, pp. 239–240, 1991.
[F11] A. Jong and J. Ma, “Saccharomyces cerevisiae nucleoside-diphosphate kinase: purification, characterization, and substrate specificity.” Archives of biochemistry and biophysics, vol. 291, no. 2, pp. 241–246, 1991.
[F12] R. Ratliff, R. Weaver, H. Lardy, and S. Kuby, “Nucleoside Triphosphate- Nucleoside Diphosphate Transphosphorylase (Nucleoside Diphosphokinase) I. Isolation of the crystalline enzyme from Brewer’s yeast.” Journal of Biological Chemistry, vol. 239, no. 1, pp. 301–309, 1964.
[F13] J. Ingraham and C. Ginther, “Nucleoside diphosphokinase from Salmonella typhimurium.” Methods in Enzymology, vol. 51, pp. 371–375, 1978.
[F14] T. SAEKI, M. HORI, and H. UMEZAWA, “Kinetic Studies on the Inhibition of Nucleoside Diphosphate Kinase by Desdanine,” Journal of Biochemistry, vol. 76, no. 3, pp. 623, 1974.
[F15] P. HUITOREL, C. SIMON, and D. PANTALONI, “Nucleoside diphosphate kinase from brain: purification and effect on microtubule assembly in vitro,” European journal of biochemistry(Print), vol. 144, no. 2, pp. 233–241, 1984
[F16] R. E. Parks and R.P. Agarwal, “Nucleoside diphosphokinases,” In The Enzymes, vol. 8 (ed. P. Boyer), pp. 307-33, 1973.
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[F17] M. Rodriguez, T. Good, M. Wales, J. Hua, and J. Wild, “Modeling allosteric regulation of de novo pyrimidine biosynthesis in Escherichia coli,” Journal of Theoretical Biology, vol. 234, no. 3, pp. 299–310, 2005.
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Appendix G
References for Reaction 9:
[G1] H. Kizaki, F. Ohsaka, and T. Sakurada, “Synthesis of N4-substituted CTP by mammalian CTP synthetase.” Biochemical and biophysical research communications, vol. 145, no. 1, pp. 569–574, 1987.
[G2] M. Weng and H. Zalkin, “Structural role for a conserved region in the CTP synthetase glutamine amide transfer domain.” Journal of Bacteriology, vol. 169, no. 7, pp. 3023, 1987.
[G3] H. Zalkin, “CTP synthetase.” Methods in Enzymology, vol. 113, pp. 282–287, 1985.
[G4] H. Kizaki, F. Ohsaka, and T. Sakurada, “CTP synthetase from Ehrlich ascites tumor cells. Subunit stoichiometry and regulation of activity.” Biochimica et biophysica acta, vol. 829, no. 1, pp. 34–43, 1985.
[G5] P. Anderson, “CTP synthetase from Escherichia coli: an improved purification procedure and characterization of hysteretic and enzyme concentration effects on kinetic properties,” Biochemistry, vol. 22, no. 13, pp. 3285–3292, 1983.
[G6] H. Kizaki, T. Sakurada, and G. Weber, “Purification and properties of CTP synthetase from Ehrlich ascites tumor cells.” Biochimica et biophysica acta, vol. 662, no. 1, pp. 48– 54, 1981.
[G7] H. Weinfeld, C. Savage Jr, and R. McPartland, “CTP synthetase of bovine calf liver.” Methods in Enzymology, vol. 51, pp. 84–90, 1978.
[G8] C. Long and D. Koshland Jr, “Cytidine triphosphate synthetase.” Methods in Enzymology, vol. 51, pp. 79–83, 1978.
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[G9] R. McPartland and H. Weinfeld, “Cytidine 5’-triphosphate synthetase of calf liver. Size, polymerization, and reaction stoichiometry,” Journal of Biological Chemistry, vol. 251, no. 14, pp. 4372–4378, 1976.
[G10] D. Koshland Jr and A. Levitzki, “CTP synthetase and related enzymes,” The Enzymes, vol. 10, pp. 539–559, 1974.
[G11] M. Rodriguez, T. Good, M. Wales, J. Hua, and J. Wild, “Modeling allosteric regulation of de novo pyrimidine biosynthesis in Escherichia coli,” Journal of Theoretical Biology, vol. 234, no. 3, pp. 299–310, 2005.
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