MSc Thesis

System level analysis of activator/repressor motifs to regulate the transcriptional process

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SYSTEM LEVEL ANALYSIS OF ACTIVATOR/REPRESSOR

MOTIFS TO REGULATE THE TRANSCRIPTIONAL PROCESS

Submitted in partial fulfillment for the award of degree of

Master of Science in Computational Biology

Work done by

SILPA BHASKARANReg. no : COB 090501

STATE INTERUNIVERSITY CENTRE FOR EXCELLENCE IN BIOINFORMATICS

UNIVERSITY OF KERALA

JULY 2011


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SYSTEM LEVEL ANALYSIS OF ACTIVATOR/REPRESSOR

MOTIFS TO REGULATE THE TRANSCRIPTIONAL PROCESS

Submitted in partial fulfillment for the award of degree of

Master of Science in Computational Biology

Work done by

SILPA BHASKARANReg. no : COB 090501

STATE INTERUNIVERSITY CENTRE FOR EXCELLENCE IN BIOINFORMATICS

UNIVERSITY OF KERALA

JULY 2011


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Dr Achuthsankar S Nair MTech(IIT, Bombay), MPhil (Cambridge), PhD (Kerala), MIEEEDirector

STATE INTER UNIVERSITY CENTRE OF EXCELLENCE

IN BIO-INFORMATICS, UNIVERSITY OF KERALA

Karyavattom North CampusThiruvananthapuram, Kerala, India 695581

Tel: (O) 0471 -2308759 (R) [email protected]

26/07/2011

CERTIFICATE

This is to certify that the project work entitled “System level analysis of

activator/ repressor motifs to regulate the transcriptional process” is the

bonafide record of work done by Ms. Silpa Bhaskaran (Reg. No: COB 090501),

in partial fulfillment of requirements for the award of Master’s Degree in

Computational Biology from the University of Kerala during the academic year

2009-2011.

Director


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DECLARATION

I hereby declare that the dissertation titled “System Level Analysis of

Activator/Repressor Motifs to Regulate the Transcriptional Process” submitted to

the University of Kerala in partial fulfillment of the requirement for the award of the

Degree of Master of Science in Computational Biology is an authentic record of work

carried out by me under the guidance of Prof. K.V. Venkatesh, Professor, Dept. of

Chemical Engineering, Indian Institute of Technology, Mumbai and that the dissertation

has not formed the basis for the award of any Degree/ Diploma/ Association/ Fellowship

or similar title to any candidate of any other University.

Place: Kariavattom Silpa Bhaskaran

Date: 26-07-2011


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ACKNOWLEDGMENT

By holding firmly, the saying, ‘Without GOD, I am a zero and with GOD, I am a

hero’, I thank GOD for all his kindness and blessings upon me, until this moment.

I believe firmly that it was due to His help, I was able to face all the difficulties

during the project work, both personal and academic, and was able to overcome

all of it successfully.

I am happy that I got a place here, in this page, to express my sincere gratitude

towards Prof. K.V. Venkatesh who permitted me to do this project at the

Biosystems Engineering lab in the Chemical Engineering Department of Indian

Institute of Technology, Mumbai, under his guidance. Beyond his simplicity and

supportive nature, it was his patience in answering even my questions that

served a lot for me. He cared well to make me settled with the new place and

environment.

It is beyond words to express my thanks to Dr. Achuthsankar S. Nair, Hon.

Director of the State Inter-University Centre for Excellence in Bioinformatics,

University of Kerala who is the person behind the opportunity I had to do the

work in such a prestigious institute. He pushed me for taking the steps for

attaining this opportunity. The motivation and encouragement throughout the

course work, from the head of our CBi family, was continued in the tenure of the

project work also. It was Achuth sir, who led my interest to the new field, systems

biology, by introducing me with its wonderful scope and nature.

I would also like to express my thanks and friendship towards my lab mates in

IIT especially, Smitha and Ajay, who were my good companions through out the

IIT life. Smitha helped me to get a starting in the initial stage of the work while I

was wondering on how to proceed with the suggestions from my guide in the

starting days. Ajay’s consoling words and support helped me a lot to alleviate my

difficulty in being a part of the new working environment. I am not able to

proceed without mentioning the names of my dear friends, Pournami and Nitya,

gifted by the three months IIT life.


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The support and assistance given by the lectures in the Centre for Bioinformatics

is also immense. I thank them, especially, Aswathy S. and Umesh P. for their

service from the distant and from near. I would like to mention the names of some

of the researchers and members of CBi, who provided their moral support not

only during the project work, but also throughout the course work. Vipin Thomas,

researcher, as usual, pushed, pulled and walked along with me through the

project tenure also, with his carefulness and affection, which gave me the

capability to overcome the troubles and difficulties. Amjesh R, the one who taught

us for the first two semesters, extended his friendship, critical comments and

suggestions, mostly silent encouragement and motivation, responsibility and

opened support, during the project phase also. Arun K.S, the course coordinator of

our first three semesters, cared and inspired me a lot with his loving and caring

words. I would also like to thank the seniormost member in our CBi, Joshua C.

M, the librarian, for his moral and emotional support throughout the master’s

program.

My next thanks go to my classmates, the beez, Msc-B-Batch with fourteen

members, who kept the friendship of two years, even when all are apart, through

the services offered by the e-world. Group discussions and chattings during the

term enabled us to understand the differences in the experiences and

environment we were then facing.

Last, but not the least, I would like to express my heartfelt gratitude and love

towards my family members. I would not try to belittle the support and strength

given by my parents and my brother for the successful completion of the project

work. As ever before, this time also, they encouraged and supported me, which

made me to learn something beyond the academics, from the new culture.


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ABSTRACT

Functioning of gene regulatory systems is supplemented greatly by the dynamic

behavior of the cell. Investigations into such dynamic behavior may provide a

better understanding of the biological control systems and make its analysis

rather undemanding. Systems biology, as a holistic approach for studying

biological systems contributed much to this area. It uses mathematical modeling

and simulation for analyzing such dynamic interactions between system

components and thereby explains the overall behavior of the system. The

approach can also be adopted for studying of biological control systems.

Transcription regulatory network is one such control system comprising of

repressor, activator and protein as the components. These components interact

with each other in various ways to yield a desired output. These different

interactions give rise to different structural motifs. Here, we develop a general

model for various feasible structures with combination of repressors and

activators to correlate with a desired output. The outputs range from transient to

graded response. The various motifs were analyzed with different objectives

correlated to existing natural motifs. The bistability of the existing motifs were

also analyzed using the models developed. The results of bistability analysis show

that the systems can have two stable states under the influence of positive

feedback loops and hybrid binding of both the transcription factors. The work can

be used for the analysis of the objectives behind the specific structural design of

the motifs.


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CONTENTS

1. FIELD OF COMPUTATIONAL BOLOGY-AN OUTLINE.................................1

1.1. Opening remarks............................................................................................2

1.2. Prologue..........................................................................................................2

1.3. Emergence and Advancement.......................................................................3

1.4. Bioinformatics and Computational Biology..................................................4

1.5. Relevance........................................................................................................5

1.6. Indian Scenario...............................................................................................7

1.7. Related Fields.................................................................................................8

1.7.1. Genomics................................................................................................8

1.7.2. Metabolomics.........................................................................................8

1.7.3. Proteomics..............................................................................................8

1.7.4. Cytomics.................................................................................................8

1.7.5. Epigenomics...........................................................................................9

1.7.6. Interactomics.........................................................................................9

1.7.7. Systems Biology.....................................................................................9

1.7.8. Synthetic Biology...................................................................................9

1.8. Closing remarks..............................................................................................9

2. MATHEMATICAL THEORIES + COMPUTATIONAL TECHNIQUES+

BIOLOGICAL PRINCIPLES = SYSTEMS BIOLOGY...................................9

2.1. Opening remarks..........................................................................................12

2.2. A System is....................................................................................................12

2.3. In Principle...................................................................................................13

2.4. Systems approach in Biology.......................................................................13

2.5. Let us open the door towards Systems Biology...........................................15

2.6. Importance of Perturbation Analysis..........................................................16

2.7. Significance of predictions............................................................................18


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2.8. Emergence.....................................................................................................18

2.9. What critics have to say...............................................................................19

2.10. Why is it still lively.....................................................................................20

2.11. Mathematical Modeling.............................................................................22

2.12. Matlab.........................................................................................................23

2.12.1. Overview of the Matlab Environment..............................................23

2.12.2. The Matlab system.............................................................................24

2.13. Network Motif.............................................................................................26

2.14. Relevance of Systems Biology in current work.........................................27

2.15. Closing remarks..........................................................................................28

3. WHAT OTHERS HAVE TO SAY.......................................................................29

3.1. Opening remarks..........................................................................................30

3.2. Systems Biology............................................................................................30

3.3. Gene Expression...........................................................................................31

3.4. Transcriptional Regulatory Network..........................................................33

3.5. Modeling in Systems Biology.......................................................................34

3.5.1. Mathematical Modeling......................................................................34

3.5.1.1. Kinetic Modeling.........................................................................35

3.5.1.2. Modeling using Ordinary Differential Equation.......................36

3.6. Network Motifs.............................................................................................36

3.7. Closing remarks............................................................................................38

4. HOW IT WAS ACHIEVED………………………….............................................39

4.1. Opening remarks..........................................................................................40

4.2. Biological background..................................................................................40

4.3. Gene expression and regulation..................................................................41

4.4. Motivation.....................................................................................................45

4.5. Kinetic Modeling...........................................................................................53


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4.6. Methodology..................................................................................................54

4.7. Modeling using ODE Solver.........................................................................58

4.8. Steady State analysis...................................................................................62

4.9. Verification of the model using Hill equation.............................................65

4.10. Dynamics analysis......................................................................................66

4.11. Bistability analysis.....................................................................................66

4.12. Closing remarks..........................................................................................69

5. ACHIEVING THE GOALS-RESULTS AND DISCUSSION.............................70

5.1. Opening remarks..........................................................................................71

5.2. Generic model...............................................................................................71

5.3. Steady state and dynamics analysis of existing motifs..............................76

5.3.1. Steady State analysis results..............................................................84

5.3.1.1. Verification using Hill equation.................................................86

5.3.2. Dynamics analysis...............................................................................88

5.4. Bistability analysis.......................................................................................90

5.5. Closing remarks............................................................................................93

6. CONCLUDING REMARKS................................................................................95

6.1. Opening remarks..........................................................................................96

6.2. A quick review..............................................................................................97

6.3. Hopefully.......................................................................................................98

7. THROUGH THE LENS......................................................................................98

7.1. Opening remarks........................................................................................100

7.2. Discussion...................................................................................................100

7.3. Future prospects........................................................................................101

8. REFERENCES..................................................................................................103

9. APPENDIX

9.1. Sample code


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9.2. Glossary of terms

LIST OF FIGURES

Fig.1.1: Computational Biology process..........................................................6

Fig.2.1: A system seen as an interconnection of subsystems with

inputs and outputs.............................................................. ...14

Fig.2.2: A schematic representation of the methodology of

Systems Biology.....................................................................17

Fig.2.3: Systems Biology concept....................................................................21

Fig.2.4: Process of Mathematical Modeling...................................................23

Fig.2.5: Basic types of motifs..........................................................................27

Fig.3.1: Gene expression.................................................................................31

Fig.3.2: Gene regulation..................................................................................32

Fig.3.3: Gene regulatory network...................................................................32

Fig.3.4: a) FFM b) SIM c) MIM.....................................................................37

Fig.4.1: Central Dogma of Molecular Biology................................................41

Fig.4.2: Gene expression regulation...............................................................42

Fig.4.3: Representation of a simple transcription factor network................44

Fig.4.4: Protein feedback in gene expression.................................................45

Fig.4.5: R on P and A on R..............................................................................46

Fig.4.6: R on R and R on A and R on P...........................................................47

Fig.4.7: A on A and Aon R and R on R and R on P........................................48

Fig.4.8: R on A and A on P..............................................................................48

Fig.4.9: A on R and A on A and A on P...........................................................49

Fig.4.10: R on R and R on A and A on A and A on P.......................................49


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Fg.4.11: A on R and A on P and R on P...........................................................50

Fig.4.12: A on A and R on R and A on P and R on P.......................................51

Fig.4.13: A on A and A on R and A on P and R onP........................................51

Fig.4.14: Open loop............................................................................................62

Fig.4.15: Motif 1.................................................................................................63

Fig.4.16: Motif 2.................................................................................................63

Fig.4.17: Motif 3.................................................................................................64

Fig.4.18: Motif 1 for bistability analysis..........................................................67



Fig.5.1: Activator concentration vs. time.......................................................72

Fig.5.2: Protein concentration vs. time..........................................................72

Fig.5.3: Repressor concentration vs. time......................................................73

Fig.5.4: Activator concentration in open loop................................................74

Fig.5.5: Protein concentration in open loop...................................................75

Fig.5.6: Repressor concentration in open loop...............................................75

Fig.5.7: Repressor concentration....................................................................77

Fig.5.8: Activator concentration.....................................................................78

Fig.5.9: Protein concentration.........................................................................79

Fig.5.10: Repressor concentration with low basal value for repressor...........79

Fig.5.11: Activator concentration with low basal value for repressor............80

Fig.5.12: Protein concentration with low basal value for repressor...............80

Fig.5.13: Repressor concentration with high basal value for repressor.........81

Fig.5.14: Activator concentration with high basal value for repressor..........81


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Fig.5.15: Protein concentration with high basal value for repressor.............82

Fig.5.16: Activator concentration.....................................................................82

Fig.5.17: Repressor concentration....................................................................83

Fig.5.18: Protein concentration.......................................................................83

Fig.5.19: Repressor basal values vs. steady state values for activator

and protein for motif 1...........................................................84





Fig.5.22: Basal value vs. time for motif 1.........................................................88



Fig.5.25: Repressor steady states for motif 1...................................................90

Fig.5.26: Protein steady states for motif 1.......................................................91






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LIST OF TABLES

Tab.4.1: Possible combinations of structural motifs.......................................53

Tab.4.2: ODE solvers in Matlab.................................................................58-59

Tab.4.3: Defintion of parameters used in calling ODE solvers......................59

Tab.4.4: Initial values......................................................................................60

Tab.4.5: Parameter values..........................................................................60-61


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1FIELD OF COMPUTATIONAL BIOLOGY – AN OUTLINE


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1.1. Opening remarks

Through this opening chapter of my dissertation work, I am wishing to give you

awareness on my field, Computational Biology. Here, you will get a general

introduction on the discipline, imbibed from what I had understood about the

discipline, throughout the two-year programme. I have also made an attempt to

trace the emergence of this field.

1.2. Prologue

If technology needs to be interesting, we have to be aware of the possibilities and

facilities it offers. If it needs to be exciting, then we have to be associated with it.

By hearing the term ‘Computational Biology’, one may become curious and

suspicious. I t happens so because of the two aspects or entities in that term,

computation and biology, which we kept apart because of the belief that there is

nothing for them to do in between. According to us, computer science is all around

an electronic device that consists of non-living entities such as chips, circuits etc

and uses voltage and power for their processing. Conversely, biology deals with

life and life processes. It is concerned with the study of structure, function,

evolution etc of living organisms. No wonder, computational biology became a

question mark for a non-professional.

But for a technology expert or for a scientist of today, there is no need for getting

amazed.

It can be said that there is not at all any single field in science advancing without

utilizing the benefits of computerization, otherwise, digitization. Even though,

one may doubt that whether it is an exaggeration, that biology, the science of life,

can also be studied using computational techniques. If you too felt so, it is

necessary that you must be more aware of this interesting field.

Computational biology, by definition, deals with the development of

computational techniques and applications inorder to gain an understanding on

biology at the cellular and molecular level.


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1.3. Emergence and Advancement

Scientists recognized that in order to understand life in its depth, it must start

from the base and they found that this base is in the molecular or cellular level.

Here cell is the stage where the DNA, RNA and Proteins are the actors. These

components are the factors behind all the cellular processes, inturn, the life

processes. Thus, the field of molecular biology began to grow up. With the

introduction of efficient technologies, the field progressed more and generated

more data.

Between 1950 and 1960, this field of biology advanced with many vital discoveries

like the structure of DNA, RNA, Protein formation etc. All these were turning

points for the biological studies. However, data retrieved from these discoveries

contain certain problems that required computational approach for its solution [1].

Fortunately, the field of computer science and information theory was also facing

a revolution at the same time. Computer science was also advancing, as it laid out

many of the basics of the field like the information theory.

Series of developments were seen, when these computational approaches began to

apply experimental data from biology. More and more insights were gained on the

secrets that restrained our biological knowledge. Computational biology was thus

sooner fixing its place as a highly advanced and technology based discipline. With

the application of computational algorithms, the field advanced by contributing

more into the studies of protein structures, evolutionary studies, upto the central

dogma.

The discipline laid its theoretical foundations in the 70s [1]. The specific problems

in the field of molecular biology were identified and it was attempted to solve

using the techniques of computational biology. Some of them are RNA structure

prediction methods, sequence alignment methods, various studies on molecular

evolution, phylogenetic studies, and so on. Thus, by the application of

computational techniques, more and more awareness was generated. Along with

it, enormous amount of data was produced. Inorder to store all those data, digital

libraries and databases became necessary. By 80s, this problem was also

answered by the introduction of many curated computer archives (e.g: GenBank,


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EMBL). Applications were generated to retrieve and analyze these records and to

use it for further studies. This field gained more and more with the advancement

of World Wide Web architecture. Online tools, databases, open source softwares,

all contributed and enabled this discipline to gain significance and recognition as

an independent discipline.

1.4. Bioinformatics and Computational Biology

It is not possible to consider both disciplines either as the same or as the opposite

sides of a single coin. Instead, they are like two songs with same rhythm, same

musical instruments and same singers, but with different raga. Bioinformatics

and computational biology, both work with same entities but even though, a small

difference makes them entirely different. The difference is in how they execute to

achieve the aim.

In very simple words, we can define that bioinformatics is the scientific discipline

that make use of computational tools and techniques for studying molecular

biology and computational biology involves the development of these

computational tools and techniques.

Yes, exactly like the difference between a driver and a vehicle manufacturer, or

like a music director and a singer. A computational biologist uses his

computational skills and develops softwares, tools, applications, databases and

algorithms for handling and analyzing biological data. A bioinformatician must

have the skills to run the computer softwares and tools only. But he/she is

expected to have the ability to biologically interpret and analyze the data

provided by the computer techniques. Both are required for each other.

According to one definition,

“Computational Biology involves the development and application of

data analytical and theoretical methods, mathematical modeling and

computational simulation techniques to the study of biological,

behavioral and social systems.”

This interdisciplinary field makes its extensive journey through the wonderful

fields of computer science, applied mathematics, statistics, biochemistry,


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chemistry, biophysics, molecular biology, genetics, ecology, evolution, anatomy,

neuroscience and visualization. There is no wonder if more and more new fields

joined in the voyage to climb up the tree of life, in future.

1.5. Relevance

Experimental biology is essential, however it has reached up in such a situation

that it cannot advance without the application of computational techniques in it.

This happened so because of the realization of the necessity of quantitative

information that can be provided by computational techniques only. Quantitative

study provides us with the information that is more basic. Quantitative

information is essential for unraveling the secrets of life, which is one of the

major aims of the biologists.

The computational approaches in the study of molecular biology had enabled the

scientific world to find solutions to the unanswered questions encircling the

biological sequences. Computational biology proceeds on strings - the string or

textual representation of sequences, which may be DNA, RNA or protein. There is

no need for inquiring too much into the chemical and biological aspects of DNA

and protein, while making computational biology a companion, in the attempt of

revealing biological facts.

Computational methods attempts to resolve problems regarding the statistics,

sequence similarity, motifs, profiles, protein folds etc. Here are some of the

various applications of computational biology i.e. where the computational

approaches are applied in molecular biological study.

reconstructing long strings of DNA from overlapping string fragments;

storing, retrieving, and comparing DNA strings;

tracing the evolutionary relationship between genes;

searching databases for related strings and substrings;

defining and exploring different notions of string relationships;

identification of nucleotide sequence of functional genes;


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looking for new or ill-defined patterns occurring frequently in DNA;

looking for structural patterns in DNA and protein;

predicting the secondary(two-dimensional) structure of RNA;

predicting the three-dimensional structure of proteins;

finding conserved, but faint, patterns in many DNA and protein

sequences; and more;

molecular modeling of biomolecules;

designing of drugs for medical treatment;

handling of the vast biological data obtained from high-throughput

technologies and microarray analysis;

Computational Biology

Functional genomics and

proteomics

Sequence analysis, statistical tools and

analysis, data mining

Protein structure, de novo design,

molecular modeling and

Metabolic engineering

and Bioprocess

control.

Pharmaco kinetc insilicomodeling, drug design

Systems Biology

Fig.1.1: Computational Biology processes [2]


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1.6. Indian Scenario

In India, the strength gained in the field of information technology, computing

and software technology have lead to a drift towards this new attempt of

integrating of biological data, development of useful software and databases in

biology, genome-wide structure and function analysis, neuronal simulations and

mathematical modeling. The launching of various bioinformatics and

computational research centers throughout the country, by the software and

pharmaceutical companies created surge for this field. The development of

various tools and softwares by these companies had contributed much to the

advancement of computational biology field in this country. The Bangalore based

company, Strand Life Sciences is one among them that contributed that made

many developments to the biological research, this way. Their Sphatika is a

crystal image classification tool for high throughput X-ray crystallography and it

classifies protein crystals into two broad categories, one comprising crystal hits

and harvestable crystals and the other comprising empty wells, clear drops and

precipitates. Also, they had developed Chitraka, an image analysis and

management tool for semi-automatic recognition and quantification of expressed

gene spots from microarray experiments. The State Inter-university Centre for

excellence in Bioinformatics of University of Kerala had also put their signature

in the field by their effort in developing Kera, an object oriented programming

language to create, dislay, combine and edit biological constructs and convert

them into sequence. The Indian based IT gaints, Infosys and TCS had estalished

computational life science wings as a part, which enabled to catch the attraction

of the career searchers.

As this is a new field, lot of research opportunities is there. And because of the

same reason, the outputs from the studies will be very relevant and of high

significance. May be, by noticing the rapid progress and scope of the approach in

blending the computational and mathematical principles in biology, the US

President Barack Obama warned his country youth to focus more on science,

mathematics and technology as the Indian and Chinese students are marching

ahead in these fields and will seize the areas in the near future.


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Even though, the blending of modern technology and computational

advancements with biological studies had grabbed the Indian as well as foreign

students with an interest to choose this field of computational biology as the

career.

1.7. Related Fields

The field of computational biology is supported and complemented by its various

novel omics sub-fields such as genomics, proteomics, metabolomics,

transcriptomics, cytomics, epigenomics, along with the systems biology, synthetic

biology areas. Let us look at what these fields do, in brief.

1.7.1. Genomics [3]

Genomics refers to the use of computational analysis to decipher biology from

genome sequences and related data, including DNA and RNA sequence as well as

other "post-genomic" data (i.e. experimental data obtained with technologies that

require the genome sequence, such as genomic DNA microarrays). It focuses on

using whole genomes (rather than individual genes) to understand the principles

of how the DNA of a species controls its biology at the molecular level and beyond.

1.7.2. Metabolomics [4]

Metabolomics is the scientific study of chemical processes involving metabolites.

Metabolites are the intermediates and products of metabolism and are often

defined as any molecule less than 1 kDa in size.

1.7.3. Proteomics [5]

Proteomics is the large-scale study of proteins, particularly their structures and

functions.

1.7.4. Cytomics [6]

Cytomics is the study of cell systems (cytomes) at a single cell level. It combines

all the bioinformatics knowledge to attempt to understand the molecular

architecture and functionality of the cell system. This is achieved by using

molecular and microscopic techniques that allow the various components of a cell

to be visualized as they interact in vivo.


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1.7.5. Epigenomics [7]

Epigenomics is the study of the effects of chromatin structure on the function of

the included genes.

1.7.6. Interactomics [8]

Interactomics is a discipline at the intersection of bioinformatics and biology that

deals with studying both the interactions and the consequences of those

interactions between and among proteins, and other molecules within a cell. The

network of all such interactions is called the interactome. Interactomics thus

aims to compare such networks of interactions (i.e., interactomes) between and

within species in order to find how the traits of such networks are either

preserved or varied. From a computational biology viewpoint, an interactome

network is a graph or a category representing the most important interactions

pertinent to the normal physiological functions of a cell or organism.

1.7.7. Systems Biology

The inter-disciplinary approach to studying biology, that studies biological

entities as a system, by perturbing them, monitoring the gene, protein and

informational pathway responses; integrating these data; and ultimately,

formulating mathematical models that describe the structures of the system and

its repsonse to individual perturbations.

1.7.8. Synthetic Biology

Very new attempt, that designs and builds new biological systems by adding or

modifying biological functions to existing organisms, or, creating novel organisms

with tailored properties.

1.8. Closing remarks

We have to make use of technological advancements in computer science,

information theory and World Wide Web in biological studies also. According to

Charles DeLisi, the bioinformatics and systems biologist trainer, within twenty

years biology will be the most computational of all sciences. Relying in the

optimistic words of DeLisi, we have to travel a long distance ahead. For that we


24

have to keep ourself updated with the recent progresses in both fields. Let us be a

part of the attempt to use electronic chips and transistors for tracing and making

the mystery of life and life processes obvious.


25

2MATHEMATICAL THEORIES + COMPUTATIONAL

TECHNIQUES + BIOLOGICAL PRINCIPLES = SYSTEMS

BIOLOGY


26

“The book of nature is written in the language of mathematics.”

- Galileo


This chapter of the dissertation work is an attempt to introduce you to the

interesting field of systems biology, the field to which the current work belongs.

Here you can find the information I have gained through reading the literature

and discussions, along with the concepts and conclusions resulting from my own

thoughts.

The basic concepts of systems theory, the principles of systems biology, its

emergence, relevance and challenges leading up to an idea on how all these

satisfy the current work are discussed here.

2.2. A System is...

The term ‘system’ might remind you of the picture of a set of components

interconnected with each other. Such a perspective can enable us to consider

every entity as a system. For example, an electrical circuit, a computer system, a

biological system, a classroom, family, an organism, a plant, a toy, all can be

called as a system, as there are some components within them that give it its own

life. We have to doubt if there exists something, which is not possible to be

included in this set of systems.

Consider the classroom as a system. The teacher, students, table, chair,

blackboard, books, room, all together constitute the classroom. All these

components have a role to play, which makes it the classroom. Therefore, we can

consider these roles as interactions that occur between the components of a

system. These interactions make the components a part of the system. All are

essential, no matter how small or large, for the existence of the classroom. All are

important as each contributes to the general behaviour of the classroom. It may

be apt, if the story of six blind men who went to see the elephant is mentioned

here. Each of them identified each organ of the elephant and regarded it as the

animal itself. Nevertheless, in practice, each of these organs together constitutes

the animal and gives it its own property.


27

2.3. In principle...

A system is an orderly arrangement of objects according to a scheme. The concept

of a system gives a bird’s eye view of the entity of interest. This is opposite to the

reductionist approach that focuses on the component parts and not the system as a

whole.

A system is something that exists and operates in time and space. It receives

inputs and produces a specific output for which the system is intended. The

components of a system always exchange certain signals between them during

their functioning. The final output behaviour of the system is generated by

integrating all such signals. These signals can be considered as the interactions

between the components. The system maintains its existence through such

interactions that ultimately lead to produce the output for which the system is

intended. A system may consist of subsystems that again can be composed of

small systems.

The function or the property of a system, contributed by its elements or

components is known as the emergent property. We can gain an idea on these

emergent properties only by studying the system as a whole and not by studying

the individual parts. This makes the system irreducible.

2.4. Systems approach in biology

Traditionally, biology had been studied with a reductionist approach. For

studying a biological system, scientists used to identify and study its component

parts in isolation. For example for studying the entire human system, they

studied each sub system in it like the nervous system, circulatory system or the

digestive system. According to this notion, the interaction or the signal exchange

does not have any role to play. They are not emphasizing on the saying that ‘the

whole is bigger than the sum of its parts’. However, the reductionist approach

provides us with the knowledge regarding the system; that gives us insights into

how and what the system is comprised of.

It is only recently that the systemic approach has been started to apply to

understand the complexity of life. Since that time, biology has become a branch of


28

science that can be studied with advanced computational applications and the

perplexing theories of the queen of science. Thus biology has been revolutionized

to give rise to a new field called ‘systems biology’ which is making rapid strides

now a days.

Fig.2.1: A system seen as an interconnection of subsystems with inputs and outputs [9]

The living cells are composed of a large number of subsystems, which involved in

various processes such as cell growth and maintenance, division, and death. The

studying of each of these subsystems will enable to understand the emergent

properties of the system. There is no need of raising questions on the application

of the systems theory in the cellular studies as we can view the significance of

components, their interactions, their interaction rules, the input-output signals in

the cellular studies.

Systems biology is a holistic approach. It analyses how the elements in a system

and their interactions give rise to emergent properties of that system. Rather

than revealing what constitutes the system (reductionist approach), systems

biology explains why they are so constituted (holistic approach). This field makes

use of various disciplines like mathematics, engineering, computer science for the

profound understanding of the biological facts that underlie life.


29

2.5. Let us open the door towards systems biology

As mentioned above, systems biology focuses on the interaction between the

components in a biological system and seems that these interactions make the

system behave as it does. This is the basis of the approach. This in-silico biology

combines the biological data collected through various experimental techniques

and through various bioinformatics tools into interactive models. Then these

models can be used for simulation and further analysis that help us to arrive at

inferences or predictions that light up the interior of the complex living systems.

Systems biology can be considered as a result of an attempt to blend engineering

science with biology that is contradictory to the traditional way of looking at

biological science. Due to its highly interdisciplinary nature and youthfulness, an

exact definition of the field has not been generated yet, even though various

attempts were made to define it.

According to Leroy Hood, the president of the Institute for Systems Biology, it is

‘the science of discovering, modeling, understanding and ultimately engineering at

the molecular level, the dynamic relationships between the biological molecules

that define living organisms.’

Some others says that,

Systems biology studies biological systems by systematically perturbing them

(biologically, genetically or chemically); monitoring the gene, protein, and

informational pathway responses; integrating these data; and ultimately,

formulating mathematical models that describe the structure of the system and its

response to individual perturbations. (Ideker et al, 2001)

Systems biology is a scientific discipline that endeavours to quantify all of the

molecular elements of a biological system to assess their interaction into graphical

network models that serve as predictive hypothesis to explain emergent behaviour

(Leroy Hood, 2005)

The models of biological systems derived through the approach of systems biology

can be used for further analysis and study. Perturbation analysis through


30

simulation techniques is an adopted method. A model gives more understanding

on the system under study.

2.6. Importance of perturbation analysis

The best and most effective way of studying a system is by observing its

behaviour when a perturbation is applied. Perturbation analysis enables us to

understand the actual behaviour of the system of interest. We can attain a vast

amount of information from interpreting the model and by analyzing the results

of the perturbation analysis.

As the system's behaviour depends upon its components, the perturbation

analysis verifies how the change in any one of the components affects the overall

functioning of the system. This information can be used in turn to identify the

component’s significance by understanding how the change in it affected other

components, which in turn brought about the change in the system’s basic

behaviour. This knowledge can be used for making efficient predictions of the

system at a given condition and at a given time. The significance of systems

biology lies in such predictions. This will be discussed later.

This perturbation analysis can thus show the system dynamics, as it reveals how

the system behaves in different conditions. The system structure and system

dynamics are considered as the two important aspects of a system in systems

biology.

A general schematic representation of the approach used in systems biology is

shown below.


31

Using computational tools

and mathematical methods

Fig.2.1: A schematic representation of the methodology of systems biology

Biological systems are considered to be robust and modular. Here this

‘robustness’ indicates the ability of a system to remain with its own

characteristics despite perturbations, unpredictable circumstances and its ability

to exhibit graceful degradation. Perturbation analysis will give information

regarding the robustness of the system. Modularity denotes the ability to

approach the systems as module. In a module, there will be a set of nodes that

have strong interactions in between and a common function. A module will have

defined input nodes and output nodes for regulating the interactions. As in an

engineering system, the module in a biological system will also have certain

features that make them to be easily embedded in any system. Modularity can be

considered as at the root of the success of gene functional assignment by

expression correlations.

DATA MODEL

PREDICTION

INFERENCE

SYSTEM

MetabolomicsProteomics

Genomics

Omics


32

2.7. Significance of predictions

It is said that the best and most effective way of studying a system is by

observing its behaviour when a perturbation is applied. The model will give

different results for different inputs. By analyzing these results, we can predict

the effect of changes to the system. A model can turn assumptions into

conclusions.

The concept is that a good system model will successfully predict the system

behavior under specific perturbations. These perturbations are genetic or

environmental, provided by experimental alterations given under specific time.

When a model achieves the ability for prediction, one can also generate the

desired output from the system. For that, first we have to experiment this on the

model we have, by changing the input parameters to generate the desired output

by making use of the predictions. Then by applying this on the real system, we

will be able to control the system. This makes us possible to make the system

behave according to our will.

In systems biology, for achieving this predictive nature, initially, the

computational model is compared with the actual systemic behavior under

experimental conditions. If this initial validation is succeeded, then the model can

be used for predictions, which is further tested under experimental alterations.

This will reduce the risk of in-vivo experiments.

2.8. Emergence

It is in the early 20th century that biological studies began to change due to the

understanding of systems constituted in it [10]. Before that, biology was sustained

by the reductionist and mechanistic approach. The end of that era was marked

with the publication of Williams in 1956. The work compiled the molecular,

physiological and anatomical individuality in animals by considering numerous

biochemical, hormonal and physiological parameters. The study indicated the

significance of a systemic view in biological study. With this, the mechanistic

approach almost ended. The insight that the biological systems follow a

hierarchical level of organization and that the communication and control within


33

the systems is carried out by the interaction of these different system levels led to

the use of system’s approach in studying biology. It was required for untangling

the components of the systems and for determining what lies beneath the cellular

processes.

Even though the definition of systems biology is in conflict, it seems that most of

the eminent scientists in the field have agreed that the emergence of this

appealing field is from molecular biology.

It is a fact that need not be disputed, that, the molecular level study of the

biological systems has contributed much to unravel the secrets of life. The high

throughput technologies used in experiments produce huge volume of biological

data. The human genome sequencing, microarray analysis and advances in mass

spectrometry, all contributed to the shelf of biological knowledge. When more

studies began to be conducted at the molecular level, in order to handle the

multiple molecules identified, it became necessary to understand more about the

interactions between them. This gave light to the role of the regulatory

mechanisms within these molecular systems. All such genomic knowledge could

be transformed into descriptive records using the systems biology techniques.

2.9. What critics have to say...

Even though we may find out resemblances between an electrical circuit and a

biological network, we cannot study or analyze a biological system comfortably in

studying electrical circuits or any other entities. The only reason is the complexity

and oscillative nature of the biological systems and we have still not achieved

proficiency in clearing its mysteries and understanding its causes and

complexities thoroughly. Therefore, it is doubted whether systems biology will

succeed in its goal of understanding the mechanisms of life.

Even though the offerings of systems biology are fascinating, crtitics have much

to demur about. In addition, there are many challenges that this young field has

to face.

Systems biology accepts the data derived from biological experiments, which are

stored in databases. This data has to be retrieved from a single cell. Molecular


34

biological methods and high-throughput technologies are required to study the

large number of genes and proteins in the genome, which will enable to

understand on the network of interactions. Technological advancements are not

yet capable of conducting numerous measurements in a single cell. Due to this

lack of sufficient technology, we are not able to retrieve the complete data and

thereby the databases remain incomplete. Therefore, the techniques, databases

and the datasets are not available as required. This may be the reason that

makes the skeptics of the field consider it as a premature baby.

The extent of the reliablity of the predictions and conclusions drawn from the

models is a matter of uncertainty. It is not sure whether they reveal the dynamics

in the behaviour of the cell accurately.

Sociological challenges also act as a barrier to the smooth rise of systems biology.

For the success of systems biology, knowledge integration is required. A biologist

with experimental skills and a computer scientist or a mathematician with coding

skills are equally important to this embryonic field. Inorder to achieve this, the

traditional mentality of keeping mathematics and biology at the two ends of the

spectrum of knowledge needs to be changed. Moreover, both must be interested in

or willing to learn the advancements and techniques used in the other field.

2.10. Why is it still lively?

Because, it approaches life science in a different way from what others have done

yet by promising explanations on the quantitative behaviour of the underlying

processes and systems. It is important, because if it can overcome the challenges

put forward by its critics, it can ultimately contribute a lot to our understanding

of human diseases and their treatment. Furthermore, it considers what internal

factors give a specific behaviour to a system by considering the interior

interactions.


35

Fig 2.2: System Biology concept [11]

Traditional biological approaches, upto molecular biology tried to answer only

how biological systems work. But this new approach, systems biology, is trying to

find out answers for why it works so or why it doesnt work so. It is at from this

point of view that systems biology had to consider all the interactions of the

components in a system that contribute to its working. Thus, systems biology

tries to find out the rationale behind a specific design for a system, with its

quantitative approach. This is crucial for our efforts to find out the secret of life.

As said earlier, systems biology receives the data contributed by the ‘omics’ fields

and the data retrieved using the bioinformatics tools. The quantity of this data is

very massive. Also, biological systems are treated as being fluctuative. In order to

track the fluctuations, we require a lot of parameters and variables as data sets.

The human brain cannot handle and analyze such huge quantity of diverse data

altogether. So obviously, they depended upon computers for this task, which in

turn brought mathematics into play. All these are adopted and integrated by

systems biology. Along with its oscillative nature, systems biology also explains

the robustness held by the biological systems. All these help us to widen and

deepen our biological knowledge.


36

2.11. Mathematical Modeling

As we told earlier, systems biology proceeds by applying mathematical modeling

using computational techniques. The mathematical modeling of bological systems

means creating an abstract representation of the system under study using

mathematics. The models can answer questions about ‘how much’ rather than

‘how’. That is, models of biological systems give quantitative descriptions of the

system for which the scientists are eagerly waiting for. The interactions are

modeled using the differential equations.

Mathematical model are approved as the ideal tools for studying gene networks

like the transcriptional regulatory network because they can identify the

components of the network and are able to analyze the interaction patterns

among them. Models developed using computational techniques and

mathematical methods can convey relevant information that will be beneficial to

future studies. Also, mathematical studies enables to conduct experiments as in

silico and thus avoid the time, effort and expense that in vivo or in vitro

experiments take.

According to Don Kulsari et.al, the role of mathematical models in systems

biology is multi-faceted. They point out four statements to justify this, which is

explained below.

While properly constructed mathematical models enable validation of

current knowledge by comparing model predictions with experimental

data, when discrepancies are found in these types of comparisons, our

knowledge of the underlying networks can be systematically expanded.

Mathematical models can suggest novel experiments for testing hypothesis

that are formulated from modeling experiences.

Mathematical models enable the study and analysis of systems properties

that are not accessible through in vitro experiments.

Mathematical models can be used for designing desirable products based

on existing biological networks.


37

2.12. Matlab

The present work is done using the ordinary differential equation solving method

provided by Matlab, which is called as the language of technical computing.

Matlab is a suitable platform for the modeling and simulation purposes. For the

same reason, it complements the mathematical modeling approaches of systems

biology. Lets us have a brief overview on the Matlab environment here. This

information is retrieved from the website www.mathworks.com, who patented

Matlab.

2.12.1 Overview of the MATLAB Environment [13]

The MATLAB (MATrix LABoratory) is a high-performance language for technical

computing integrates computation, visualization, and programming in an easy-to-

use environment where problems and solutions are expressed in familiar

mathematical notation. Typical uses include,

Math and computation

Algorithm development

Real-world data Model

Predictions/Explanations

MathematicalConclusions

Formulation

Test

Interpretation

Analysis

Fig. 2.3: Process of mathematical modeling [12]


38

Data acquisition

Modeling, simulation, and prototyping

Data analysis, exploration, and visualization

Scientific and engineering graphics

Application development, including graphical user interface building

MATLAB is an interactive system whose basic data element is an array that does

not require dimensioning. It allows you to solve many technical computing

problems, especially those with matrix and vector formulations, in a fraction of

the time it would take to write a program in a scalar noninteractive language

such as C or FORTRAN.

The name MATLAB stands for matrix laboratory. MATLAB was originally

written to provide easy access to matrix software developed by the LINPACK and

EISPACK projects. Today, MATLAB engines incorporate the LAPACK and BLAS

libraries, embedding the state of the art in software for matrix computation.

MATLAB has evolved over a period of years with input from many users. In

university environments, it is the standard instructional tool for introductory and

advanced courses in mathematics, engineering and science. In industry, MATLAB

is the tool of choice for high-productivity research, development and analysis.

MATLAB features a family of add-on application-specific solutions called

toolboxes. Very important to most users of MATLAB, toolboxes allow you to learn

and apply specialized technology. Toolboxes are comprehensive collections of

MATLAB functions (M-files) that extend the MATLAB environment to solve

particular classes of problems. We can add on toolboxes for signal processing,

control systems, neural networks, fuzzy logic, wavelets, simulation, and many

other areas.

2.12.2. The MATLAB System

The MATLAB system consists of these main parts:

Desktop Tools and Development Environment


39

This is the set of tools and facilities that help you use and become more

productive with MATLAB functions and files. Many of these tools are

graphical user interfaces. It includes the MATLAB desktop and

Command Window, a command history, an editor and debugger, a code

analyzer and other reports, and browsers for viewing help, the

workspace, files, and the search path.

Mathematical Function Library

This is a vast collection of computational algorithms ranging from

elementary functions, like sum, sine, cosine, and complex arithmetic,

to more sophisticated functions like matrix inverse, matrix

eigenvalues, Bessel functions, and fast Fourier transforms.

The Language

This is a high-level matrix/array language with control flow

statements, functions, data structures, input/output, and object-

oriented programming features. It allows both "programming in the

small" to rapidly create quick and dirty throw-away programs, and

"programming in the large" to create large and complex application

programs.

Graphics

MATLAB has extensive facilities for displaying vectors and matrices as

graphs, as well as annotating and printing these graphs. It includes

high-level functions for two-dimensional and three-dimensional data

visualization, image processing, animation and presentation graphics.

It also includes low-level functions that allow you to fully customize the

appearance of graphics as well as to build complete graphical user

interfaces on your MATLAB applications.

External Interfaces

This is a library that allows you to write C and Fortran programs that

interact with MATLAB. It includes facilities for calling routines from


40

MATLAB (dynamic linking), for calling MATLAB as a computational

engine, and for reading and writing MAT-files.

2.13. Network Motif

The reason for the idea behind applying engineering principles in the study of

biological systems is the presence of certain features, which are found common in

both the engineering systems and the biological systems. Modularity and

robustness, we discussed earlier are main among them. A third principle, the use

of recurring circuit elements, also plays a significant role. Engineers make use of

various basic elements in the circuitry in which they are working, that may

repeats thousands of times in the same circuitry. Like wise, biology also shows

the presence of key wiring patterns that appears again and again throughout a

network. Such repeating biological patterns are named as motifs (network

motifs). Network motifs define the few basic patterns that recur in a network and,

in principle, can provide specific experimental guidelines to determine whether

they exist in a given system.

Network motifs are the small recurring patterns found in the gene networks.

They are considered as the fundamental unit of a network. Each of these motifs

represents a circuit of interaction and it is upon this motif that the network is

built. Each network motif can carry out specific information-processing functions.

Mathematical modeling is used to analyze these motifs.

Studies showed that the network motifs have been conserved among different

organisms. That means the same network motifs have been found in various

organisms ranging from bacteria to human. This proves the role of network motifs

as the basic building blocks in a biological network. Different network motifs are

interlinked in specific ways to form the global structure of each network. Thus,

the motifs represent the network to which it belongs in a compact way. In the

current study, we work on motifs found in the transcriptional regulatory network

found in organisms. For example, let us have a look on the three common motifs

found in the transcritional regulatory network.


41

Fig.2.4: Basic types of motifs [14]

2.14. Relevance of systems biology in current work

Systems biology obviously requires model organisms. Practically researchers use

simple systems such as yeast. By scaling up the models of such simple systems we

can learn complex systems like the human system, by means of comparative

genomics which has become one of the most powerful tools in systems biology.

Since the basic strategy may be simliar, this will be effective upto a certain

extent. Nevertheless, in certain cases this may not be true. However there will be

some universal principles which is applicable for all.

Due to the nature of systems biology, it satisfies the aesthetic quality of

simplicity. This requires the identification of those universal principles. These

universal principles, otherwise the general laws, are supposed to lay the

foundation for all species without any specific interest. The concept of universal

principle gave systems biology a bottom-up approach. This led to the modelling of

a) Feed Forward Motif b) Single Input Motif

c) Multiple Input Motif


42

small units within the complex biological sytems with a belief that they follow the

same rules independent of their substrate. These small units, probably, act as the

control elements in a system. Therefore, scientists consider 'control elements' for

modeling that is conserved in both the simple and complex systems. Control

elements are small elements such as binding sites for transcription factors in

transcription network. We can model the biological control systems by integrating

the models of many such control elements.

In systems biology, the systems are viewed as networks with the components as

the nodes and the interactions as the edges. In such a view point, the small,

fundamental, control units are called as motifs, which are identified in different

places within a network. Thus, in short, the awareness of the design of these

motifs acts as a critical factor in the progress of the discipline.

In the following pages, you can find that the current work endeavors to fabricate

a generic model for the network motifs in the transcription regulatory network.


Through this chapter an attempt to give an introductory idea into the field of

systems biology is made. The various aspects of systems biology such as aim,

scope, approach, emergence, challenges etc. are described. Specific explanation on

mathematical modeling, matlab, and network motifs are given as it will be

relevant for explaning the current work.


43

3WHAT OTHERS HAVE TO SAY...


44

3.1. Opening Remarks

In this chapter, a detailed review on the literature in the field has done. Hope this

chapter will give you awareness on the basic principles that undelie and support

the current work, which are derived from literature related to the field. Besides,

you will get an idea about recent advances in the field.

3.2. Systems biology

Systems Biology as a holistic approach, studies the system as a whole not as

parts. It held that a system receives some input signals and contain control

elements, which process these inputs to produce the desired output signals.

Systems approach in biological studies gave significance to the small control

elements that are preserved among organisms. Based on these small control

units, the whole system is studied and analyzed.

Systems biology relies on the universal principle that lays the foundation of all

species. The concept of universal principle gave systems biology a bottom-up

approach. This led to the modelling of small units within the complex biological

sytems with a belief that they follow the same rules independent of their

substrate (Breitling, 2010). These small units, probably, act as the control

elements in a system. Therefore, scientists consider 'control elements' for

modeling that is conserved in both the simple and complex systems.

Adam Arkin, the director of the Physical Biosciences Division of the U.S.

Department of Energy (DOE)'s Lawrence Berkeley National Laboratory and a

leading computational biologist says that System biology aims to understand how

individual elements of the cell generate behaviors that allow survival in

changeable environments, and collective cellular organization into structured

communities. According to him, cellular networks would ultimately, assemble

into larger population networks to form large-scale ecologies and thinking

machines, such as humans.

Arkin says that as the complete genomes of more organisms are sequenced, and

measurement and genetic manipulation technologies are improved, scientists will

be able to compare systems across a broader expanse of phylogenetic trees. This


45

will inturn enhance our understanding of mechanistic features that are necessary

for function and evolution.

"The increasing integration of experimental and computational technologies will

thus corroborate, deepen and diversify the theories that the earliest systems

biologists used logic to infer," Arkin says. "This will thereby inch us ever closer to

answering the, what is Life question."

3.3. Gene Expression

Gene expression is the synthesis of proteins using the information contained in

genes. The information in DNA is first used to make mRNA through the

transcription process and this mRNA is then used to synthesize protein through

the translation process. Not all proteins are required in all time for the normal

functioning of the biological system. Also, the synthesis is not required in equal

amount all the time. How much protein is produced in a specific time from a

specific gene determines the level of gene expression at that time. This level of

gene expression determines the level of the functioning of the gene. Genes must

be correspondingly turned on or off for the required level of gene expression.

Fig.3.1: Gene expression [15]


46

Gene expression is a complex process, which is regulated at multiple

levels. Apart from the regulation of transcription and translation, the gene

expression is controlled at various stages, during RNA processing and transport

(in eukaryotes), RNA translation, and the posttranslational modification of

proteins.

Fig.3.2: Gene expression regulation [16]

The gene expression regulation is carried out by the regulatory proteins within

the cell. There may be one regulatory protein which controls the production of

another regulatory protein that may in turn control the production of another set

of regulatory proteins and so on. Such numerous chains of interactions constitute

to form a gene regulatory network (GRN). Representing such interactions

between biological molecules as a network provides us with a conceptual

framework that allows us to identify the general principles that govern the

complex biological systems [1].

Fig. 3.3: Gene Regulatory Network [17]


47

3.4. Transcriptional Regulatory Network

Even though gene expression is regulated at various stages, the predominant site

of gene expression regulation is considered as the control of transcription [18]. Also

transcriptional regulation constitutes perhaps the most experimentally tractable

of these regulatory mechanisms, as mRNA abundance and DNA binding are

easier to measure than, for example, protein abundance and activity [19]. The

proteins that regulate the gene expression are called transcription factors (TFs).

TFs are DNA binding proteins that bind to specific regions named as the cis-

regulatory elements, in the promoter regions of certain genes [20]. This binding

influences the gene expression either positively or negatively depending upon

whether it is an activator or a repressor. An activator activates the protein

production while a repressor retards it. Transcription factors are only one of the

means by which our cells express different combinations of genes, allowing for

differentiation into the various types of cells, tissues and organs that make up our

bodies. Their function is to respond to the various biological signals and

accordingly change the transcription rate of genes, thereby allowing the cells to

produce the necessary amount of proteins at the appropriate time [21].

Transcriptional regulation at the protein level is achieved by the transcription

factors binding to different promoter regions of genes under different

environmental conditions [22]. Since there will be multiple binding sites in a

regulatory region where multiple TFs can bound, transcriptional regulation may

involve combinatorial interactions between several TFs. (Kulasiri D, et.al, 2008).

i.e., several transcription factors may bind to the same gene in different

combinations resulting in different rates of transcription (Roy, Lane, & Werner-

Washburne). So, if two TFs can bind to a gene, there are four possible

combinations of the transcription factors, which may be present on the promoter

region of the gene. These various possible combinations will result in a complex;

combinatorial and non-linear control on transcription.

According to Uri Alon, the transcription regulation networks describe the

interactions between transcription factor proteins and the genes that they

regulate.


48

Transcriptional networks are the most studied biological network (Alon, U.

,2007). This makes it to be the subject matter of current work too.

3.5. Modeling in Systems Biology

Why we should model the biological systems? [23]

For,

Testing whether the model is accurate, in the sense that it reflects – or can

be made to reflect – known experimental facts

Analyzing the model to understand which parts of the system contribute

most to some desired properties of interest

Hypothesis generation and testing, allow one to rapidly analyze the effects

of manipulating experimental conditions in the model without having to

perform complex and costly experiments (or to restrict the number that

are performed)

Testing what changes in the model would improve the consistency of its

behavior with experimental observations.

We may use such models to seek evidence that existing hypotheses are wrong,

that tells that the model is inadequate or that hidden variables need to be

invoked or that existing data are inadequate, or that new theories are needed. In

kinetic modeling this is often the case with ‘inverse problems’ in which one is

seeking to find a (‘forward’) model that best explains a time series of experimental

data (see below).

3.5.1. Mathematical Modeling

Mathematical models are considered as the ideal tools for studying gene

regulatory networks and it can deal with the underlying complexity of these

networks. Mathematical modeling provides sophisticated frameworks for

investigating the components of the networks and analyzing the rules governing

their interactions (Kulasiri, Nguyen, Samarasinghe, & Xie, 2008). Normally, it is

difficult to gain perceptions on the functioning of these networks as it presents

different behavior on different time scales corresponding to various processes,


49

along with its structural complexity. Mathematical models can answer this issue

up to an extent. Such models and their simulation can enable us to conduct in-

silico experiments upon the given models so that we can make benefit by reducing

the effort, expense, time and risk taken for the traditional in-vivo experiments.

According to Kulasiri and his team, mathematical modeling plays a multi-faceted

role in the biological studies through systems biology. The first role they had

pointed out is that the properly constructed mathematical models can be used for

the validation of the current knowledge by comparing the model predictions with

the experimental data. Even if discrepancies are found out during such

comparisons, it will only enable us to expand our knowledge systematically.

Secondly, mathematical modeling can suggest novel experiments for testing

hypotheses that are formulated from the modeling experiences. Third, they

enable to study and analysis the system properties, which are not revealed by the

in-vitro experiments. The final role they considered is that, they can produce

desirable new designs based on the existing biological networks.

3.5.1.1. Kinetic Modeling

Deterministic modeling is an approach for mathematical modeling that considers

Boolean logic and differential equations for modeling. The peculiarity of the

deterministic models is that they don’t take uncertainties into consideration.

Instead, it is based on the principle of causality that believes on the unique

relationship between causes and their resulting effects (Kulasiri, Nguyen,

Samarasinghe, & Xie, 2008). The popular deterministic approach to modeling a

gene regulatory network is the differential equation approach, which proceeds by

modeling the interactions of the elements in the GRN as a series of coupled

chemical reactions represented by the ordinary differential equations (ODE).

These chemical reactions are then subjected to deterministic kinetic modeling,

which describes the dynamic behavior of the concentrations of reactive

components. The rate of a reaction representing the concentration change per

unit time is written as a function of the concentration of reactants and products

in those chemical reactions.


50

The series of interactions among the components in a biological network will

ultimately give rise to the biological processes. The kinetic models can model

these processes.

There are various rate laws corresponding to the various reaction mechanisms.

One of such is the hill function proposed by A.V. Hill. In a GRN, the hill function

describes the co-operativity of the transcription factors with its binding region

within the promoter region.

3.5.1.2. Modeling using Ordinary Differential Equation (ODE approach)

It had been already mentioned that the deterministic modeling approach depends

upon the ordinary differential equations for modeling. It considers that the rate of

change of a product obtained, when the interactions are denoted as chemical

equations, is dependent upon its degradation as well as synthesis (Roy, Lane, &

Werner-Washburne).

3.6. Network Motifs

In the second chapter of my dissertation work, I have mentioned about the

network motifs. Network motifs are considered as the fundamental unit of a

transcriptional network. They act as the control elements with recurring

regulation patterns [24]. Alon presented his paper regarding network motifs with

the basic idea that these network motifs carry out specific information- processing

functions. He says that these motifs have been analyzed using the mathematical

models and tested using the living cell experiments so as to gain a vivid idea on

the dynamicity of the network functioning.

When biological interactions are represented as networks, its analysis can be

carried out at two levels: one, in the local level and the other in the global level.

At the local level, analysis can be carried out at network motifs [14]. Network motif

presents itself as a small pattern of interconnections that recur at many different

part of the network.

The three types of motifs depicted in the paper, as most commonly occuring, are

the FFM (Feed Forward Motif), SIM (Single Input Motif), and the Multiple Input


51

Motif (MIM). The below given diagram will show the difference between the

three.

In Feed-forward motif, a top-level transcription factor regulates both the

intermediate-level TF and the target genes, and the intermediate-level TF

regulates the target gene. In Single input motif, a single TF regulates the

expression of several target genes simultaneously. In Multiple Input Motif,

multiple TFs simultaneously regulate the expression of multiple target genes.

Figure 3: a) FFM b) SIM c) MIM

All types of motifs in the network combine to form the global structure of the

network. Network motifs portray the network in a compact way. They seem to be

the most robust. What make them very special is that they use the least number

of components of the large set of circuits that leads to the network to function so.

The modelling of these small units within the complex biological systems is based

on the belief that they follow the same rules independent of their substrate

(Breitling, 2010). These small units, probably, act as the control elements in a

system. That make the scientists to consider these 'control elements' for modeling

that is conserved in both the simple and complex systems. Control elements are

small elements such as binding sites for transcription factors in transcription

network. We can model the biological control systems by integrating the models of

many such control elements.

The current work discusses how the various interactions between the repressor,

activator and protein led to the various design of the motifs in the transcriptional


52

regulatory network and attempting to build a general model for all the possible

motif designs.

3.7. Closing Remarks

In this chapter of my dissertation work, a literature review on the works related

to the current work is done. Hope this chapter gave you an idea on how the

previous works in the field supports the current work.


53

4HOW IT WAS ACHIEVED


54


Here, we shall define the current work and discuss the methodologies adopted in

attaining the objectives.

In the current work we are looking at the local network structure, the motif. A

network motif can be considered as the building block of a network structure.

Here we consider the motifs in transcription regulatory network constituted by

the three components, activator, repressor and the protein. The transcription

factors- activator and repressor, regulate the production of the protein. Our aim is

to create a generic model for all the possible interactions between these three

components.

This chapter reports the approach for modeling along with the necessary

background details.

4.2. Biological Background

The fundamental fact that underlies the studies in molecular biology is none

other than the Central Dogma of Molecular Biology. According to this central

dogma, the information flow within the cell is unidirectional i.e, from DNA to

protein through the intermediate mRNA. The single stranded mRNA is formed

from the double stranded DNA through a process known as transcription. The

sequence of nucleotides in the DNA is transcribed into its corresponding mRNA,

which will be an exact copy of one of the two strands in DNA. The information in

this mRNA is used to synthesize the corresponding protein. Proteins are made up

of amino acids that are twenty in number (even though, debates are going on

among the scientists regarding the count). The process of producing protein from

RNA is known as translation.

If explained more precisely, the gene regions of the DNA are transcribed into the

mRNA (messenger RNA) which is one kind of RNA, which in turn travels to

protein production sites and is translated into corresponding sequence of amino

acids that constitute the protein. Thus, protein became the final product of a

gene. The given figure will give you the idea on the principle of central dogma of


55

molecular biology (fig.4.1). The DNA, RNA and the protein are the key players in

the cellular and thereby biological processes.

Different cells in our body produce different proteins. In each minute, every cell in

the body synthesizes a variety of proteins. Each of these proteins is essential for

the various physiological properties and biological activities in our body like skin

color, shape of the hair, activating specific cellular processes etc.

Fig.4.1: Central Dogma of Molecular Biology

Thus, DNA contains the complete genetic information that defines the

physiological and functional properties of the organism.

4.3. Gene expression and regulation

The process by which a protein is produced from its corresponding gene through

transcription and translation is known as gene expression. If a protein is

produced from a gene, then that gene can be said to be expressed or turned on.

The real problem is that, not all proteins are required at all time and also, every

time the requirement will not be in equal quantities. This brings the necessity for

regulating the gene expression and this regulation occur at various stages during

gene expression. Not only the synthesis of proteins but its degradation should

also be regulated.


56

The regulation occurs at several stages like regulation during transcription,

translation, RNA processing, posttranslational modification e.t.c. Among these,

most studies are conducted on transcriptional regulation, as it is the major site

for the control of gene expression. In the current work also, we focuses on

transcriptional regulation.

The gene in the DNA contains a regulatory region called promoter preceding the

protein-coding region. The transcription process is initiated by the action of an

enzyme called RNA polymerase (RNAp), by binding to the promoter region. The

efficiency in this binding determines the transcription rate, the number of

mRNAs produced per unit time. This efficiency in binding in turn is determined

by the activity of the transcription factors.

Transcription factors are specialized proteins that can regulate the transcription

process. They bind to specific sites in the promoters of the regulated genes and

can affect the rate of RNAp binding. Through this binding, they can change

(either by increasing or by decreasing) the probability per unit time by which the

RNAp binds to the promoter region and thereby affect the production of mRNA

molecules which ultimately determines the protein production. The transcription

factors can regulate a set of specific genes in this manner, which can in

DNAGene Y

Promoter

RNA Polymerase

Gene Y

mRNA

Transcription

YProtein

(a)

(b)

Fig 4.2: Gene transcription regulation [24]


57

turn create variations in the protein production i.e. at the level of gene expression

itself. The transcription factors can regulate a set of specific genes in this manner,

which can create variations in the gene product i.e. in the gene expression itself.

Transcription factors are known as trans-regulatory elements and the regulatory

sites where they bind are called cis-regulatory elements. It was the genetic and

biochemical experiments of 1960's that revealed the presence of regulatory

sequences in the proximity of genes and the existence of proteins that are able to

bind to those elements and control the activity of genes by either activation or

repression of transcription [25]. These regulatory proteins are themselves encoded

by genes.

The interaction among the proteins through the enzymatic action or through

binding, either directly or indirectly, is achieved through this regulation of gene

expression.

The transcription factors are of two types - activator and repressor. If the

transcription factor enhances the binding of RNAp to the promoter and thereby

increases the gene expression rate, then it is known as activator. If the gene

expression rate is decreased by the transcription factor by inhibiting the binding

of RNAp to the promoter, then it is called repressor. When an activator is bound,

the binding site is known as enhancer and when a repressor is bound, it is known

as silencer. The activator has a positive effect on the gene upon which it binds due

to the enhancement of protein production while the repressor has a negative

effect due to the inhibition of protein production.


58

Fig. 4.3: Representation of a simple transcription factor network [25]

The interesting fact that resides in the regulatory process is that this set of

transcription factors themselves are encoded by another set of genes in the DNA

sequence, which is regulated by another set of transcription factor proteins which

in turn may be regulated by yet another set of transcription factors and so on.

The figure (fig.4.2) shall explain this. The interactions that contain such feedback

loops are critical to the cell’s function [26]. The below figure (fig. 4.3) illustrates the

influence of the protein feedback loops in gene expression. In the figure, Bgene1 is

the regulatory site for the gene that produces the protein A. It is to this Bgene1, the

regulatory proteins will attach. Similarly, Bgene2 acts as the regulatory site for

gene B, B1gene3, and B2gene3 for the gene C. The figure shows that the proteins

produced by the genes A and B act as the regulatory proteins for the production of

gene C. The protein C produced by the gene C consecutively regulates the

production of protein A by binding to the gene A. Similar kind of various

combinations of interactions are possible which contribute to the non-linear

behavior of the cell and the cellular processes. All such interactions that arise

from the chain of regulatory factors together form the transcriptional regulatory

network (TRN).

Transcription factor bindingsite

Coding DNA

Transcription factor


59

Fig.4.4: Protein feedback in gene expression

4.4. Motivation

As we said above, the transcription factors itself can be proteins produced by yet

another set of genes whose production is regulated by the transcriptional factors

produced by another set of genes.

As we consider activator, repressor and protein as the components of a TRN, the

process of transcription can be viewed here as the result of the interaction

between them. Each of these components interacts with each other in various

ways. For example, an activator component can activates it own production where

at the same time activating the production of a repressor or the final gene

product, the protein. Like wise, 16 different interactions are possible for each of

these components.

The interesting fact is that each of these different interactions can give rise to

different structural motifs for the TRN. Considering, a single component, 16

structural motifs can be produced. Thus, 16*3 different structural motifs are

possible for all the three components. (A basic idea on the network motifs was

given in the second chapter).

For example, let us take the component repressor.

Bgene1

Gene A

Bgene2

Gene BInput

B1gene3 B2gene3

Gene C

Protein C

Protein A

Protein B

feedback


60

Consider the following figure.

Now, we are considering the motifs in which the protein production is influenced

by the repressor alone. So, allowing R to act on P, we are drawing out all the

other possible interactions that can take part among these three components. One

of them is given in the above figure. In the figure, the activator produced is

binding to the Gene 1 that produces the repressor (i.e. A on R and R on P).

Therefore, the repressor production is activated and since this repressor binds to

the protein and the protein production will get inhibited.

In the above figure and in the coming figures that represent the network motifs,

the edges or the connections given represent the interactions.

Two other examples for the motif in which the repressor acts on protein are given

below;

R binding site A binding siteR

A

P

R binding site A binding site


Gene 1: produces the repressor

Gene 2: produces the activator

Gene 3: produces the protein

Fig 4.5: R on P and A on R


61

In this motif, autoregulation occur as repressor controls itself. Along with it, the

repressor represses the activator production also. In the motif given below

(Fig.4.7), which has a more complicated design, autoregulation is done by both

repressor and the activator. Besides, the activator activates repressor production

also. Like this, sixteen structural motifs can be generated by allowing only R to

bind to the gene that produces the protein.

Fig. 4.6: R on R and R on A and R on P


A

P







62

Like this, consider other three examples (Fig.4.5, Fig.4.6, and Fig.4.7) of

structural motifs in which the protein production is influenced by the activator

alone.

Fig 4.7: A on A and A on R and R on R and R on P

Fig. 4.8: R on A and A on P


A

P







A

P







63

In this motif (fig.4.5), the repressor inhibits the production of the activator that

binds to the protein-producing gene. In the motif given below (Fig.4.8), activator

is binding to itself and to the repressor while activating protein production.

Fig. 4.9: A on R and A on A and A on P

Fig. 4.10: R on R and R on A and A on A and A on P


A

P







A

P







64

In the last figure (Fig.4.10), the motif defines the binding of R on A and

autoregulations of R and A along with activator activating the production of

protein.

Till now, we have discussed some of the motifs formed by either A or R alone

binding to the gene that produces protein. Now we are going to see the examples

of motifs formed by the binding of both A and R on protein producing protein.

Here, we can see structural motifs that involve interactions, which make the

structural design of the motifs more complicated.

The first example for AR on P given below (fig.4.8) shows that the along with the

binding of A and R on P, A is binding to R also.

In the next example (fig.4.9), the interactions other than AR on P are A on R and

A on A. In the third example (fig.4.10), both the activator and repressor are

binding to the gene that produces the protein. Autoregulation is also shown by

Fig .4.11: A on R and A on P and R on P


A

P







65

the activator activating itself and the repressor represses its own production. Let

us see how these motifs’ structures are.

Fig. 4.13: A on A and A on R and A on P and R on P

Fig. 4.12: A on A and R on R and A on P and R on P


A

P







A

P







66

Like R on P, it is also possible for each of these A on P and AR on P to have

sixteen various structural motifs by varying the interactions among the

components. Thus the total number of different structural motifs formed from all

the posible interactions among the three components, activator, repressor and

protein are 16*3 i.e. 48 different structural motifs. As these motifs act as the

building blocks of the biological networks, they are also known as the network

motifs.

Let us draw out all the 48 possible structural motifs in the following table.

Sl.

no

Repressor alone

binding to protein

Activator alone

binding to protein

Both Repressor and

Activator binding to

protein

1 R-P and R-R A-P and R-R RA-P and R-R

2 R-P and A-R A-P and A-R RA-P and A-R

3 R-P and R-A A-P and R-A RA-P and R-A

4 R-P and A-A A-P and A-A RA-P and A-A

5 R-P and R-R and R-A A-P and R-R and R-A RA-P and R-R and R-A

6 R-P and R-R and A-A A-P and R-R and A-A RA-P and R-R and A-A

7 R-P and A-R and R-A A-P and A-R and R-A RA-P and A-R and R-A

8 R-P and A-A and A-R A-P and A-A and A-R RA-P and A-A and A-R

9 R-P and R-R and R-A

and A-A

A-P and R-R and R-A

and A-A

RA-P and R-R and R-A and A-A

10 R-P and R-R and R-A

and A-A

A-P and R-R and R-A

and A-A

RA-P and R-R and R-A and A-A

11 R-P and R-R and A-A

and R-A

A-P and R-R and A-A

and R-A

RA-P and R-R and A-A and R-A


67

12 R-P and R-R and A-A

and A-R

A-P and R-R and A-A

and A-R

RA-P and R-R and A-A and A-R

13 R-P and A-R and R-A

and A-A

A-P and A-R and R-A

and A-A

RA-P and A-R and R-A and A-A

14 R-P and A-R and R-A

and R-R

A-P and A-R and R-A

and R-R

RA-P and A-R and R-A and R-R

15 R-P and A-A and A-R

and R-R

A-P and A-A and A-R

and R-R

RA-P and A-A and A-R and R-R

16 R-P and A-A and A-R

and R-A

A-P and A-A and A-R

and R-A

RA-P and A-A and A-R and R-A

Tab.4.1: Possible combination of structural motifs

It is these structural motifs, otherwise, these interactions that decide how the

control mechanism should works up. So creating a generic model will be

advantageous. This work aims to create the general model for all these forty-eight

motifs, which can be made specific by adjusting the parameter values. A general

introduction on mathematical modeling was given in the chapter 2. Here, we

adopted one approach in mathematical modeling called kinetic modeling.

Before going to the modeling process, let us understand about the kinetic

modeling approach.

4.5. Kinetic Modeling

In the current work for modeling the structural motifs produced by the

interactions between repressor, activator and the protein, we adopted the

differential equation modeling method included in the deterministic approach of

mathematical modeling. Differential equation modeling can give more

descriptions of the network dynamics that other approaches failed to explain.

This approach belongs to the macroscopic scale of modeling biochemical systems.

In this scale the system is supposed to homogenous. The behavior of every


68

particle is assumed to be the average behavior of its kind. So, the system can be

represented by the concentrations of the particles, which in turn can be

represented, and modeled using the differential equations. Thus, differential

equations explain the network dynamics by explicitly modelling the concentration

changes of molecules over time.

In differential equation approach, the interactions are represented as series of

coupled chemical reactions, with the state of the system represented by the

concentration of the molecules. In Ordinary Differential Equation (ODE)

approach, differential equations are generated corresponding to those coupled

chemical reactions, thereby characterizes the gene regulatory networks.

The macroscopic level of deterministic kinetic modeling describes the dynamic

behavior of the concentrations of the reacting components. When the chemical

reactions are represented by differential equations, the rate of the reaction is

determined by the concentration change of the reactants and products. The

concentration change of a reactant or product, say protein, is dependent on its

synthesis and degradation or can be calculated as the difference between them.

The problem with the differential equation modeling is that the approach depends

upon numeric parameters, which are difficult to find out experimentally. The

stability of the modeled systems is also a matter of concern. The question is

whether the system’s behaviour depends on the parameter values and initial

value concentrations or whether it behaves in a similar manner to different

conditions. The probability that an unstable system represents a biological model

exactly is less. And, a stable system will not require all the parameters that we

considered as essential.

4.6. Methodology

Here we have to find out the reactants and products involved and formed during

the interactions. So we are representing these interactions as chemical reactions

for deriving differential equations.


69

Here eq. (1) specifies that a repressor protein (R) can bind to the DNA that

contain the gene for repressor protein denoted by Dr to form the complex DrR,

which can inturn bound by the activator protein to form DrRA complex. Eq. (2)

specifies that the same DNA for repressor can be bound by an activator which

inturn can be bounded by a repressor to form the DrRA complex.

The eq. (3) says that the repressor is bound to the DNA for activator protein (Da)

to form DaR which in turn is bound by the activator protein to form the complex

DaRA. Similarly, eq. (4) represents the binding of an activator to the DNA that

produces the activator protein to produce that DaA complex. A repressor is bound

to this DaA to form the DaRA complex.

Next is the protein interaction. Here, Dp denotes the DNA that produces the

protein, the final product of DNA. A repressor when bound to the Dp will produce

DpR complex and an activator can bind to this complex to produce the DpRA

complex. This is represented by eq. (5). Eq. (6) represents that to the DNA for

protein, an activator complex can be bound to produce DpA which inturn can be

bound by the repressor to produce DpRA complex.

Repressor:

DrR + A DrRADr + R

Dr + A DrA + R DrRA

Activator:

Da + R Da + A DaRA

Da + A DaA + R DaRA

Protein:

Dp + R DpR + A DpRA

Dp + A DpA + R DpRA

Kr1fKr1b

Ka2fKa2b

Ka1fKa1b

Kr2bKr2f

Kr1fKr1b

Ka1fKa1b

Ka2ffKa2b

Kr2fKr2b

Kr1fKr1b

Ka1fKa1b

Ka2fKa2b

Kr2fKr2b

eqn. (1)

eqn. (2)

eqn. (3)

eqn. (4)

eqn. (5)

eqn. (6)


70

The double-sided arrow shows the forward and backward reaction. The forward

reaction shows the synthesis process while the backward reaction shows the

dissociation process. Kr1f denotes the rate constant at which the repressor binds

in the forward reaction while Kr1b denotes that in the backward reaction. Ka1f and

Ka1b denote the binding of the activator in the forward reaction and backward

reaction respectively.

Now we are going to model all these reactants and products as a system of

ordinary differential equations (ODE) that describe their kinetics as a function of

time. The differential equations will show the rate of change of each of these

reactants and products. The rate of change of a specific component is written as

the difference between its synthesis and degradation.

Here, kr1f and ka2f are negative as free Dr is losing there due to the binding of R

and A repectively to it. kr1b and ka2b are positive as both the values show the

degradation rate of DrR and DrA respectively, which gives free Dr. Other

differential equations can be drawn out in the same manner.

These all are the differential equations for the interactions associated with

Dr.Here, km is the synthesis rate of mRNA for R, k is the synthesis rate for R and

eqn. (7)

eqn. (8)

eqn. (9)

eqn. (10)

eqn. (11)

eqn. (12)


71

kd is the dissociation rate. Kmr0 is the basal rate at which the repressor is

produced. Kmr0 denotes the small amount of repressor produced even though

there is no interaction.

Like this, six differential equations can be drawn out for each of the remaining

components, activator and protein.

Activator:

Protein:

eqn. (13)

eqn. (14)

eqn. (15)

eqn. (16)

eqn. (17)

eqn. (18)

eqn. (19)

eqn. (20)

eqn. (21)

eqn. (22)

eqn. (23)

eqn. (24)


72

Thus eighteen equations were derived with six for each component. Modeling

these eighteen equations will generate a super structure, which can be considered

as a generic model.

4.7. Modeling using ODE solver

All the eighteen equations were modeled in Matlab using the ODE solver ode15s.

ODE solvers are advanced solvers provided by Matlab inorder to solve the initial

value problems for ordinary differential equations. The solvers available in

Matlab are ode45, ode23, ode113, ode15s, ode23s, ode23t or ode23tb. They differ

in the type of the problem in which they are applied, order of accuracy, situation

and the algorithm. A brief explanation of the solvers are given in the below

table[27].

Solver Problem

type

Order of

accuracy

When to use

Ode45 Nonstiff Medium Most of the time. This should be

the first solver you try.

Oder23 Nonstiff Low For problems with crude error

tolerances or for solving

moderately stiff problems.

Ode113 Nonstiff Low to high For problems with stringent error

tolerances or for solving

computationally intensive

problems.

Ode15s Stiff Low to medium If ode45 is slow because the

problem is stiff.

Ode23s Stiff Low If using crude error tolerances to

solve stiff systems and the mass

matrix is constant.

Ode23t Moderately Low For moderately stiff problems if


73

Since ode45 is slow due to the stiffness of the problem, we used ode15s. ode15s is

a variable order solver based on the numerical differentiation formulas (NDFs).

Optionally, it uses the backward differentiation formulas (BDFs, also known as

Gear's method) that are usually less efficient. ode15s is a multistep solver.

The Matlab ODE solvers are accessed by calling a function of the form

[x,t] = odesolver (@name, timespan, xo, Options, P1, P2, P3)

stiff you need a solution without

numerical damping.

Ode23tb Stiff Low If using crude error tolerances to

solve stiff systems.

Tab.4.2: ODE solvers in Matlab

@name a handle to a function which returns a vector of rates of

change

timespan a row vector of times at which the solution is needed OR

a vector of the form [start, end]

xo A vector of initial values

Options (if omitted or set to

[], the default settings are

used)

A data structure which allows the user to set various

options associated with the ode solver

P1,P2,P3... These are additional arguments which will be passed to

@name

Tab.4.3: Definition of parameters used in calling ode solver [28]


74

The initial value set we used throughout is as follows:

Parameter Initial Value

Dr 4

DrR 0

DrA 0

DrRA 0

mRNAR 0

R 0

Da 4

DaR 0

DaA 0

DaRA 0

mRNAA 0

A 20

Dp 4

DpR 0

DpA 0

DpRA 0

mRNAP 0

P 0

Tab.4.4: Inital values

The parameter values are summarized in the following table.

Parameter Value

Kr1f 50 m-1

Kr1b 50 *3 nM


75

Kr2f 50 m-1

Kr2b 50*0.003*10-6

Ka1f 40 m-1

Ka1b 40*0.009*10-6

Ka2f 40 m-1

Ka2b 40*0.009*10-6

Kd 0.01 m-1

Km 15 m-1

K 90 m-1

Tab.4.5: Parameter values used

Thus, the generic model was produced. The code is executed with the help of two

files. i.e, the entire model is described in two files. The first file named

‘generalplot1’ is the main program through which the initial values are passed

and the ODE solver is called. The second file, ‘generalplot2’ contains the

differential equations, which are executed using the values passed from

‘generalplot1’ and the values are collected in the first file. The initial values and

the ODE solver calling statement are as below.

initial=[4 0 0 0 0 0 4 0 0 0 0 20 4 0 0 0 0 0];

[t,x]=ode15s (@generalplot2, [t0,tf],initial);

where, to and tf and initial and final values of time which are inputed as 0 and

7000 respectively.

The plots obtained are given in the next chapter. This model can be used for

analysing the existing structures by changing the parameter values. We have to

achieve this by giving zero or its specific value to the rate constant if there is no

such interaction or if such an interaction is present in the motif respectively.

As an initial attempt, it was done for an open loop. An open loop is a control

system with a preprogrammed set of instructions to an effector that has no

feedback or error-detection process. As a result, the prescribed system will not be


76

able to do any compensation through adjustments. It has been suggested that

open loop systems control certain movements, which are executed without any

alterations due to sensory feedback. There will not be any interactions between

the components in an open loop. In our case, R, A and P will be free in the open

loop. So, all the parameters will be zero. The figure is given below.

Now, we can apply the model to all those forty-eight various motifs mentioned

earlier.

4.8. Steady State Analysis

In a general sense, a system is said to be stable when it possess minimal energy.

We can say that a stable system is in a steady state. A system is said to be in a

steady state if there is no change in its stable state, even if external or internal

perturbances are applied. Here, steady state is the state in which the production

and degradation rates of the product remain balanced.

Here, three specific structural motifs were given for conducting the steady state

and dynamics analysis. This can be considered as a means of validating the

generic model we created. The motifs are as given below.


A

P





Fig.4.14: Open loop



77

Fig.4.16: motif 2

Fig.4.15: motif 1


A

P







A

P







78

The selected motifs are existing ones. They were identified in the microorganism

Saccharomyces cerevisiae. They were found in the glucose-repression systems in

the GAL genes in S. cerevisiae, which is mediated by the Mig1p, which is a

homologue of Wilms’ tumour protein and is a global repressor protein dedicated to

glucose repression [29]. We have to first model the three structural motifs and then

perform its steady state and dynamics analysis.

Since no factor is binding to the Dr, in all the three motifs, kr1f = kr1b = ka1f =

ka1b = ka2f = ka2b = kr2f = kr2b = zero. For obtaining a general model, kmr0 s

given as 0.15 m-1. Kmr0 is the basal rate for repressor. Even if there is no

interaction, small amount of repressor is produced. Basal rate is the rate at which

this small quantity of repressor is produced.

For steady state analysis, the kmr0 values are varied from very low value to high.

Here in these three motifs, repressor directs the production of the protein directly

or indirectly. So when a low value is given for kmr0, the protein production will

be high. As the value is increased, the repressor concentration increases and both

activator and protein concentration decreases and finally shut off. The kmr0

Fig. 4.17: motif 3


A

P







79

value is varied from 0.00000001 to 50000000. For each of these values, the steady

state values of the three components, repressor (Rss), activator (Ass) and protein

(Pss) are collected. All these steady state values are plotted aganist kmr0 to obtain

the plots kmr0 vs Rss, kmr0 vs Ass and kmr0 vs Pss.

Next, the model is verified with the Hill equation.

4.9. Verification of the model using Hill equation

In a chemical system, the reaction rate at a time will be a unique function of the

concentrations of all its reactants and products. There are different rate laws

correspoding to the different types of the reaction mechanisms. Hill equation is

one among them. Hill equation explains the degree of cooperativity in the binding

among molecules. The Hill equation is used here to verify our model.

Hill equation was proposed by Archibald Hill in 1910 to describe the binding of

oxygen to haemoglobin. He used it to analyze the binding equilibrium as ligand-

receptor interaction. The binding of the transcription factors to the promoter

region of a DNA can also be treated as a ligand-receptor interaction. We have

already seen that the transcription factors influence the transcription rate

through its binding to the promoter. That is why an evaluation on the binding

rate is essential and Hill function is used for performing this.

The Pss values are normalized by dividing each of the P steady state value with

the maximum steady state value to make the scale as 0 - 1. This Pss/Pmax is then

plotted aganist Rss.

The Hill equation is,

,

This implies,

orIf,

eqn. (25)

eqn. (26)

eqn. (27)


80

For each of the motif, the R value at y = 0.1 and y = 0.9 are found out and is

applied in the equation to find out the value of n. Then the R-value at y = 0.5 is

found and is applied in the eqn. (26) and k value is calculated with the n value

obtained from eqn. (25). The K value was equal to the R-value and hence, the

model be regarded as satisfying the Hill equation.

4.10. Dynamics Analysis

For analyzing the dynamics of the system, the kinetic constant, kmr0 is kept at a

small value initially. The y-axis was normalized in the range of 0-1 as before. The

steady state value for each variable are collected and is then given as the initial

condition with high kmr0 value. This will give the switching off process of the

protein. The time value in the x-axis will give the time taken to achieve the

switching off process. Then using the same initial values, use a different range of

kmr0 values. After that a low kmr0 value was given. Then again it is plotted with

a different range of kmr0 values.

The time taken to attain 90% of the steady state by each of the three motifs was

found out and is plotted against its corresponding kmr0 value. This will give the

dynamics of the structures, which can be utilized for further analysis.

4.11. Bistability Analysis

Some biological systems are said to be bistable. Bistability is the ability of the

system to transit from one stable state to the other in repsonse of a specific input

signal. i.e, they will have two stable states. One main example of the bistable

systems is the lac operon in the bacteria Escherichia coli, a group of genes, which

are repressed in the presence of glucose but transcribed in the absence of glucose

and presence of lactose.

The general model we created was applied in the analysis of the bistability of the

structural motifs rather than the steady state and dynamics analysis. Bistability

analysis checks whether the system has two stable states. The analysis was done

as follows;

Initially the stable states of all the parameters of the motif were obtained by

giving very low value for the kinetic constant of repressor.Then these stable state


81

values were given as the initial condition and the value of the kinetic constant

was varied from low value (0.00000001) to high value (50000000). The stable

state value of the repressor and protein at each value of the repressor basal value

was noted. We can plot the steady state values with basal values (kmr0) in the x-

axis and the obtained steady state values in the y-axis.

As the next stage, the stable state values of all the parameters were obtained by

putting the kinetic constant of repressor at a high value. These stable states were

then given as the initial condition and then the plots for different basal values of

repressor were obtained from high to low. Again, we made a steady state plot

with kmr0 in x-axis and steady state values in the y-axis.

If both the plots give same variation, then there is only one steady state for that

particular motif. If it is different, then the motif has multiple steady states, and

so it can be regarded as possessing the bistability property.

The three network motifs selected for the bistability analysis are as the following.

These motifs are selected as they are commonly seen in genetic regulatory

networks.

Fig. 4.18: Motif 1 for bistability analysis


A

P







82

Bistability is regarded as a minimal requirement for a network to possess

memory, where the state of the network stores information about its past [32].Jeff

Fig.4.20: Motif 3 for bistability analysis

Fig 4.19: Motif 2 for bistability analysis


A

P







A

P







83

Hasty et.al said so beacuse a bistable system remains in its stable state even if

the stimulus is shifted from one state to another.


Here, in this main chapter of my dessertation work, I have explained the way I

proceeded to attain the aim and objectives of my work. The methodologies and

approaches I adopted through out my work are given detailed here with

justifcations. The results obtained by the application of the procedure and

methods discussed here, are given in the next chapter. You are welcome to read

and interpret the next chapter, results and discussion.


84

5ACHIEVING THE GOALS- RESULTS AND DISCUSSION


85


Life is a dynamic process. Any attempt to capture the secrets behind it is a

complex process. Representation of biological networks had enabled the scientists

to reveal information regarding those life processes. Applying mathematical

modeling in the molecular biological studies helps to extend our understanding on

the biological systems.

The current work to develop a generic model for all the structural motifs

constituted by the activator, repressor and the protein, also followed the path of

mathematical modeling. In this chapter, the various results obtained are given

along with its explanations. The current work used Matlab for the modeling

purpose.

The current work not only achieved its aim of creating the generic model, but also

applied this model in three existing motifs for its steady state, dynamics and

bistability analysis.

5.2. Generic model

The generic model was developed without changing any parameter values. Each

parameter holds its own specific value. The parameter values were given in the

previous chapter. In order to create the model of a single motif, we require

eighteen differential equations which were explained in the previous chapter.

The plots of the general model for the interactions between the three components

(repressor, activator and the protein) are given below. These models (Fig.5.1,

Fig.5.2, and Fig.5.3) did not represent any specific network motif.

The models given below are similar since all the variable values are given alike.


86

0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000

2000

4000

6000

8000

10000

12000

Time, t

Con

cent

ratio

n of

A

[A]

Fig.5.1: Activator concentration vs. time

0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000

2000

4000

6000

8000

10000

12000

Time, t

Con

cent

ratio

n of

P

[P]

Fig.5.2: Protein concentration vs. time


87

0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000

2000

4000

6000

8000

10000

12000

Time, t

Con

cent

ratio

n of

R

[R]

Fig.5.3: Repressor concentration vs. time

These plots (Fig.5.1, Fig.5.2, and Fig.5.3) can be considered as the standard

models of the components. However, by varying the parameters, in accordance

with the interaction between the transcriptional regulatory network components

(activator, repressor, and protein) in each motif, we will be able to analyze them

and reach on conclusions.

First, we selected an open loop for applying our model. As mentioned earlier, an

open loop represents a motif that does not have any interconnections among the

components. Even though no impulse signal is received that is expected to acquire

through the interaction, small amount of proteins will be produced. In our model,

we represent the production rate of that quantity of proteins or transcription

factors (activator and repressor) using kinetic constant that is denoted by kmp0,

kma0, and kmr0 respectively, which are called as basal values.


88

For an open loop, we put the basal value as 0.15 for all the three components.

Varying the parameter values of any one of the component will not affect the

production rate of other components.

0 2 4 6 8 10 12 14 16 18 2015

20

25

30

35

40

45

50

55

Time, t

Con

cent

ratio

n of

A[A]in an open loop

Fig.5.4: Activator concentration in open loop


89

0 2 4 6 8 10 12 14 16 18 200

10

20

30

40

50

60

Time, t

Conc

entra

tion

of P

[P] in an open loop

Fig.5.5: Protein concentration in open loop

0 2 4 6 8 10 12 14 16 18 200

10

20

30

40

50

60

Time, t

Con

cent

ratio

n of

R

[R]in an open loop

Fig.5.6: Repressor concentration in open loop


90

5.3. Steady state and dynamics analysis of existing motifs

As told earlier, our model can be used for studying biological networks. We

developed the general model with an intention to make such studies using

network motifs easier. Motifs, the basic building blocks of a network will enable

us to understand the structural design of that particular network. In the current

work, we have developed a general model and applied it in three existing motifs

for the steady state and dynamics analysis. They were selected as a means of

validating the model.

The three models were identified in the microorganism Saccharomyces cerevisiae.

They were found in the glucose-repression systems in the GAL genes in S.

cerevisiae, which is mediated by the Mig1p, a homologue of Wilms’ tumour protein

and is a global repressor protein dedicated for glucose repression. We have to first

model the three structural motifs and then perform its steady state and dynamics

analysis. Applying our general model to these existing motifs will help us to

validate our model. The structural design of the model was given in the previous

chapter.

These three motifs were selected, as they exist in nature.

Given below are the models of the protein, activator and repressor for each of the

motifs.


91

MOTIF 1:

0 1000 2000 3000 4000 5000 6000 7000-0.5

0

0.5

1

1.5

2

2.5

3x 10

-16

Time

Con

cent

ratio

n of

R

Repressor

Fig.5.7: Repressor concentration

In the first motif, the repressor is binding to the promoter region of the gene that

produces the activator and the activator in turn binds to the promoter region of

the gene that produces the protein.

For the model given here, the basal value for the repressor was given as zero.

Since no other regulatory proteins are attaching to it, the repressor is

independent. In such a case, the repressor production depends upon the basal

value given. Since that basal value is zero, the repressor production is finally

shutting down to zero. Since the concentration of the repressor binding to the

activator gene is less, the activator production is not at all inhibited. In that case

it is based upon the basal rate given for activator, which is 1.5. The activator

concentration is 5400 nM. As this activator binds to the promoter region of the

gene that produces the protein, the protein production is being activated. The

basal rate will be zero for protein as protein production is activated by the

activator. The production of protein will be high in this case.


92

0 1000 2000 3000 4000 5000 6000 70000

1000

2000

3000

4000

5000

6000

Time

Con

cent

ratio

n of

A

Activator

Fig.5.8: Activator concentration

0 1000 2000 3000 4000 5000 6000 70000

1

2

3

4

5

6x 10

4

Time

Conc

entra

tion

of P

Protein

Fig.5.9: Protein concentration


93

The two remaining motif models also behaved in the similar manner when same

input were given. In the second motif, the only interaction is the binding of the

activator and the repressor to the protein. In motif 2, we have attempted two

ways, one with keeping kmr0 value low (0) and other with kmr0 value very high

(500000 m-1). When it was kept high, the repressor production is increased which

in turn decreases the protein production which will eventually shuts down.

MOTIF 2:

With low basal value:

0 1000 2000 3000 4000 5000 6000 7000-2

0

2

4

6

8

10

12

14

16x 10

-16

Time

Con

cent

ratio

n of

R

Repressor

Fig.5.10: Repressor concentration with low basal value for repressor


94

0 1000 2000 3000 4000 5000 6000 70000

1

2

3

4

5

6x 10

5

Time

Con

cent

ratio

n of

A

Activator

Fig.5.11: Activator concentration with low basal value for repressor

0 1000 2000 3000 4000 5000 6000 70000

1

2

3

4

5

6x 10

6

Time

Con

cent

ratio

n of

P

Protein

Fig.5.12: Protein concentration with low basal value for repressor.


95

With high basal value for repressor:

0 1000 2000 3000 4000 5000 6000 70000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2x 10

12

Time

Conc

entra

tion

of R

Repressor

Fig.5.13: Activator concentration with high basal value for repressor

0 1000 2000 3000 4000 5000 6000 70000

100

200

300

400

500

600

Time

Conc

entra

tion

of A

Activator

Fig.5.14: Activator concentration with high basal value for repressor


96

0 1000 2000 3000 4000 5000 6000 70000

1

2

3

4

5

6x 10

-3

Time

Con

cent

ratio

n of

P

Protein

Fig.5.15: Protein concentration with high basal value for repressor

MOTIF 3:

0 1000 2000 3000 4000 5000 6000 70000

1

2

3

4

5

6x 10

4

Time

Con

cent

ratio

n of

A

Activator

Fig.5.16: Activator concentration


97

0 1000 2000 3000 4000 5000 6000 7000-0.5

0

0.5

1

1.5

2

2.5

3x 10

-14

Time

Con

cent

ratio

n of

R

Repressor

Fig.5.17: Repressor concentration

0 1000 2000 3000 4000 5000 6000 70000

1

2

3

4

5

6x 10

6

Time

Con

cent

ratio

n of

P

Protein

Fig.5.18.Protein concentration


98

In the network motif 3, in addition to the binding of the repressor and activator to

protein, the repressor is also binding to activator. When the basal value of the

repressor is kept very low, it resulted in the shutting down of repressor

production and the increasing of protein production.

5.3.1. Steady state analysis results

The steady state analysis conducts a study on the steady state concentration of

the components. For different basal values of the repressor, the components took

different concentrations and different time limit for reaching the steady state.

The steady state analysis graphs given below plots the steady state values of the

activator and protein aganist the corresponding basal values. The plot shows that

as the kmr0 values increases the concentration taken to attain a steady state is

also being increased

MOTIF1:

10-10

10-5

100

105

0

1

2

3

4

5

6x 10

7

Kmr0

stea

dyst

ate

valu

es

Activator

Protein

Fig.5.19: Repressor basal value vs steady state values of activator and protein for motif 1


99

MOTIF 2:

10-6

10-4

10-2

100

102

104

0

1

2

3

4

5

6x 10

7

Kmr0

stea

dyst

ate

valu

es

Activator

Protein


MOTIF 3:

10-10

10-5

100

105

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2x 10

8

Kmr0

stea

dyst

ate

valu

es

Activator

Protein



100

5.3.1.1. Verification using Hill equation

Hill function is a rate law that describes the binding activity of the transcription

factors to the gene in the DNA. Here we are checking whether our model obeys

the Hill equation. Since the value of the Hill coefficient, k obtained is equal to the

concentration of the repressor value, we can say that the model satisfies the Hill

equation.

The Hill equation is,

, where ‘n’ is known as the Hill coefficient.

Or,

This implies,

Motif 1:

At y = 0.9, R = 102.5131 = 325.9117

At y = 0.1, R= 104.4442 = 27810

At y = 0.5, R = 103.47562 = 2989.6

Put these values in eqn. (29):

eqn. 28

eqn. 29

eqn. 30


101

0.5k + 1494.8 = k

Motif 2:

At y = 0.1, R = 104.4509 = 28242

At y = 0.9, R= 102.5106 = 324.0410

At y = 0.5, R = 103.476 = 2992.3


0.5k + 1496.2 = k

Motif 3:

At y = 0.1, R = 107.37271 = 23589000

At y = 0.9, R= 105.29059 = 195250

At y = 0.5, R = 106.22 = 1659600


102


0.5k + 829800 = k

5.3.2. Dynamics analysis

The dynamics analysis is done by plotting the time taken to attain 90% of the

steady state by each protein component in each of the motif against its

corresponding kmr0 values. This will give the dynamics of the protein.

10-10

10-5

100

105

1010

20

30

40

50

60

70

80

90

100

kmr0

time

structure 1-protein dynamics

Fig.5.22: Basal value vs time for motif1


103

10-10

10-5

100

105

1010

25

30

35

40

45

50

55

60

kmr0

time


Fig.5.23: Basal value vs time for motif 2

10-10

10-5

100

105

1010

20

30

40

50

60

70

80

90

100

110

kmr0

time


Fig.5.24: Basal value vs time for motif 3


104

5.4. Bistability Analysis

Bistability analysis checks whether the system under study can be stable in two

distinct states. Three motifs given in the previous chapter were used for


The results are shown as below;

In the first motif (Fig.5.25, Fig.5.26), the repressor component is not showing any

bistability. But the protein is exhibiting bistability. In the second structural

motif, both the repressor and protein components are showing bistable property.

In the third motif given, the protein is exhibiting bistability, but not the

repressor.

Motif 1:

10-6

10-4

10-2

100

102

104

106

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

kmr0

stea

dy s

tate

val

ues

Structure1:steady state Vs kmr0

Repressor at initial low k value

Repressor at high k value

Fig.5.25: Repressor steady states for motif 1


105

10-6

10-4

10-2

100

102

104

106

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

kmr0

stea

dy s

tate

val

ues

Structre1:steady state Vs kmr0

Protein at initial low k value

Protein at high k value

Fig.5.26: Protein steady states for motif 1

Motif 2:

10-6

10-4

10-2

100

102

104

106

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

kmr0

stea

dy s

tate

val

ues



Repressor at initial high k value



106

10-6

10-4

10-2

100

102

104

106

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

kmr0

stea

dy s

tate

val

ues


Protein at high k value



Motif 3:

10-6

10-4

10-2

100

102

104

106

0.996

0.9965

0.997

0.9975

0.998

0.9985

0.999

0.9995

1

1.0005

kmr0

stea

dy s

tate

val

ues



Protein at initial high value



107

10-6

10-4

10-2

100

102

104

106

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

kmr0

stea

dy s

tate

val

ues



Repressor at initial high k value


The common feature of a bistable system is the existence of the strong positive

feedback loops. This is considered as one of the main reasons for its bistability. In

our first motif structure, a strong positive feedback is given by the activator,

which binds to itself. The system showed bistability due to this reason. In the

second structure, there is a hybrid control on the protein production. Here both

the negative and positive regulation can be the reasons for the bistability

exhibited by the motif. In the third structure, P is showing bistability, as there is

a positive regulation upon it. But R is not showing any bistability due to the

negative feedback.


In this chapter the result and analysis of the work is given. The plots given by the

generic model is given along with the results of steady state and dynamics


108

analysis, and the bistability analysis. The analysis of these results will help us to

develop understanding on the specific design of the given structure.


109

6CONCLUDING REMARKS


110


This was an attempt to familiarize with the effort of the queen of sciences in

revealing the mysteries of life. There is no need of wondering about this intrusion

in the current scientific era. Now a days, biological studies cannot proceed

without the help of computers that play with numbers and calculations which in

turn underscores the significant role played by mathematics in such studies. The

recent understanding that most of the biological processes follow mathematical

principles has been upheld by the scientific world. No wonder that Systems

Biology, that merges the mathematical principles and computational approaches

in the biological studies for throwing light into the mysteries of life, has rapidly

grown up. The scientific world is now eagerly waiting for the results coming out

from the systems biology laboratories.

It is through mathematical modeling that Systems Biology approaches biological

problems. The significance of the mathematical models relies in the fact that they

can give quantitative information of the biological systems under consideration. It

is an effective tool to capture the nature of the biological systems those behave

differently in different environments, conditions, time etc. This is possible

because the models created using mathematical techniques, offered by systems

biology can be used to simulate the biological process in silico. They can also

behave differently according to the difference in the input we give.

The fundamental principle of systems biology is to view the particular entity of

interest as a system, not as component by component. Systems biology believes

that the behavior of the system is a sum up of all the interactions between its

components and not by any single component itself. This gave rise to the

emergence of the concept of biological networks. A biological network is

constituted by nodes and edges that represent the components and interactions

respectively. Systems biology approaches attempts to model these networks or the

subnetworks or the subunits within such networks.

The building blocks of these biological networks are known as network motifs.

They are small patterns that appear frequently in the networks. Here, in our

work, we used transcriptional regulatory network which is a dominant biological


111

regulatory network, as our system of interest. This network was chosen, as it is

the most studied one. The work intended to create a general model all the motifs

constituted by the activator, repressor and protein components in a

transcriptional regulatory network.

6.2. A quick review

We have already read about how the transcription factors regulate the gene

expression through directing the protein production. Transcription occurs

with the help of the transcription factors- activator (activates protein production)

and repressor (inhibits protein production) - through their binding to the

promoter region of the specific gene. The transcription factors bound to the gene

that produces the protein, which is expected to perform a specific physiological

function, forms a network motif. This is the system that we are considering in the

present work. Of course, a system must have components and here the activator,

repressor and the protein perform that role. The binding of the transcription

factors to the gene can be regarded as the interaction among them as it delivers

some signals to the gene to regulate protein production. The transcription factors

bind to the gene in different ways or combinations according to the requirements.

Two transcription factors can bind to the same gene in different ways resulting in

different rate of transcription or different network motifs that differ in their

structural design, ultimately resulting in different rate of protein production.

This difference in the binding will depend on the internal or external stimulus

induced by the environment. Our aim in this work is to identify all the possible

combinations formed between the activator, repressor and protein i.e. all the

possible structural motifs that can be formed which will affect the protein

production and to develop a general model that can represent all those motifs.

If we can derive a general model that can represent the different motifs in the

transcriptional regulatory network, it will make further studies easier. When this

general model is applied in a specific motif, there will be change in its parameter

values according to the interactions in that specific motif. The general model

created takes into account every possible interaction, and so each parameter has

its own specific values. When we are using this model to study a specific motif, we


112

have to look at whichever interactions are present and keep the corresponding

parameters values as it is. The rest will have to be changed to zero. This will

generate the model of that specific motif.

If such a model of a particular biological system is available in front of us, the

advantage is that we can derive more information about that particular system..

As a validation process, we have applied our model in three existing motifs and

conducted their steady state and dynamics analysis and in three other for the


6.3. Hopefully...

Now mathematics and computers had offered their aid to human intellect in its

attempt to reveal the secrets of life. The practice of doing experiments in the

living organisms has several ethical, social and economic issues. All those

problems can be resolved to a certain extent by the entry of computers and

mathematics into the field. The increasing demand for the field of systems biology

shows that it had passed its childhood. But yet to be emerged with many

possibilities and advancements.


113

7THROUGH THE LENS...


114


Here, in this final chapter of the three months effort, I am making a crtitical view

upon the work. Even though, the work presents what expected from it, it failed to

handle some issues. In this chapter, such failures of the current work, along with

the discussions on whatever advancements can make it better, and also wherever

this can be applied etc are made.

7.2. Discussion

We have seen that gene expression is the production of protein from a gene

through the process of transcription and translation. But, this gene expression

alone cannot explain everything about protein production. Protein production

depends on various other intra cellular and intercellular processes. Cells require

external or internal stimulus or signals for activation and initiating life processes.

For the binding of transcription factor to the promoter region of the DNA to take

place, specific signals are required which will be the output generated from some

other processes. Like this, there is a chain of numerous processes and sub-

processes behind the selection of one specific transcription factor to bind to the

promoter region. This shows that it is not from the transcription factor binding

that the transcriptional regulation initiates. Considering all these together will

make the task much complicated and demands more time and effort. Here we

have considered the transcriptional regulation starting from the binding of the

transcription factors only.

The gene expression is regulated at various stages during the protein production.

But here we have considered the gene regulation at transcriptional level only.

Along with transcriptional regulation, translational regulation, post

transcriptional regulation, post translational regulation, RNA transport

regulation also contribute to the gene expression regulation.

For any modeling work of biological systems, the major issue is the parameter

estimation. Many times, the parameters were fixed by the trial and error method,

even though it adopted the literature data.


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The truth behind any kind of modeling is that the model will describe only some

properties of the real system. Also there is a possibility that the revealed

properties may not be much relevant for the purpose of study. Some other

properties that may be relevant may remain unrevealed.

Also, the purpose of modeling is to provide a simple, abstract representation of

the system under study. Biological systems are already notorious for their

complexity. So we must take utmost care to make the model as simple as possible

at the same time maintaining the complex properties of the system as it is, which

is a tricky task.

The engineering works follow the principles of robustness and modularity. The

same principles have been identified in the biological systems also. This is one of

the reasons for applying engineering methodologies in studying biological

systems. But many examples showed that nature's designs are much different

and diverse from those used in engineering. This creates a question on the

reliability of the mathematical models of biological systems generated by applying

the engineering principles.

7.3. Future prospects

The work can be used for analyzing the objectives behind a specific structural

design of a particular network motif. Each structure- in cellular level, tissue level

or organ level- will have a purpose for existence. Here, by considering the models

of structural motifs, we had lighted a path towards such studies. We can analyze

the model to find out how these structures helps in generating a phenotypical

response. But for that, we have to relate it to an organism. This will help to find

out whether a specific feature in its structural design is essential for the survival

of the organism. The work can inturn be applied in the generation of synthetic

networks also. If we understand the phenotypical benefit behind each specific

design, then we can apply it to generate a system with the preferred phenotypical

benefit.

As each coin has two sides, the present work also has its own benefits and

failures. Considering this as only a template, in future I hope, we can add to its


116

positives and correct the defects to make it a perfect one. Thereby I envision to

make humble contributions in the journey of mathematical modeling and systems

biology in revealing the secrets of life.


117

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9APPENDIX


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9.1. Sample Code

The code for producing the general model that represents all the possible

combination of interactions between the activator, repressor and protein is given

below. The main program, generalplot passes the initial values to the subprogram

and calls the ode solver, ode15s, receives the output values and displays the plots

correspondingly.

clear all

clc

t0=0;

tf=5000;

initial=[4 0 0 0 0 0 4 0 0 0 0 20 4 0 0 0 0 0];

[t,x]=ode15s(@generalplot2,[t0,tf],initial);

Dr=x(:,1);

DrR=x(:,2);

DrA=x(:,3);

DrRA=x(:,4);

Mr=x(:,5);

R=x(:,6);

Da=x(:,7);

DaR=x(:,8);

DaA=x(:,9);

DaRA=x(:,10);


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Ma=x(:,11);

A=x(:,12);

Dp=x(:,13);

DpR=x(:,14);

DpA=x(:,15);

DpRA=x(:,16);

Mp=x(:,17);

P=x(:,18);

figure(1);

plot(t,R,'m','linewidth',1.5)

xlabel('Time, t');

ylabel('Concentration of R');

title('[R]');

figure(2);

plot(t,Dr,'y','linewidth',1.5)

xlabel('Time, t');

ylabel('Concentration of DrA');

title('[Dr]');

figure(3);

plot(t,DrR,'r','linewidth',1.5)

xlabel('Time, t');


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ylabel('Concentration of DrR');

title('[DrR]');

figure(4);

plot(t,DrA,'g','linewidth',1.5)

xlabel('Time, t');

ylabel('Concentration of DrA');

title('[DrA]');

figure(5);

plot(t,DrRA,'b','linewidth',1.5)

xlabel('Time, t');

ylabel('Concentration of DrRA');

title('[DrRA]');

figure(6);

plot(t,Mr,'c','linewidth',1.5)

xlabel('Time, t');

ylabel('Concentration of mRNA of R');

title('[mRNAr]');

figure(7);

plot(t,A,'b','linewidth',1.5)


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xlabel('Time, t');

ylabel('Concentration of A');

title('[A]');

figure(8);

plot(t,Da,'m','linewidth',1.5)

xlabel('Time, t');

ylabel('Concentration of Da');

title('[Da]]');

figure(9);

plot(t,DaR,'m','linewidth',1.5)

xlabel('Time, t');

ylabel('Concentration of DaR');

title('[DaR]');

figure(10);

plot(t,DaA,'y','linewidth',1.5)

xlabel('Time, t');

ylabel('Concentration of DaA');

title('[DaA]');

figure(11);

plot(t,DaRA,'k','linewidth',1.5)


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xlabel('Time, t');

ylabel('Concentration of DaRA');

title('[DaRA]');

figure(12);

plot(t,Ma,'m','linewidth',1.5)

xlabel('Time, t');

ylabel('Concentration of mRNA of A');

title('[mRNAa]');

figure(13);

plot(t,P,'r','linewidth',1.5)

xlabel('Time, t');

ylabel('Concentration of P');

title('[P]');

figure(14);

plot(t,Dp,'m','linewidth',1.5)

xlabel('Time, t');

ylabel('Concentration of P');

title('[Dp]');

figure(15);

plot(t,DpR,'r','linewidth',1.5)


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xlabel('Time, t');

ylabel('Concentration of DpR');

title('[DpR]');

figure(16);

plot(t,DpA,'g','linewidth',1.5)

xlabel('Time, t');

ylabel('Concentration of DpA');

title('[DpA]');

figure(17);

plot(t,DpRA,'c','linewidth',1.5)

xlabel('Time, t');

ylabel('Concentration of DpRA');

title('[DpRA]');

figure(18);

plot(t,Mp,'m','linewidth',1.5)

xlabel('Time, t');

ylabel('Concentration of mRNA of P');

title('[mRNAp]');

The subprogram, generalplot2 receives the initial values and solves the

differential equations. The code for this function is as below.

function deriv = generalplot2(t,x)


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deriv=zeros(18,1);

deriv(1)=-(50*x(1)*x(6))+(50*0.003*x(2))-(40*x(1)*x(12))+(40*0.009*x(3));

% d[Dr]/dt

deriv(2)=(50*x(6)*x(1))-(50*0.003*x(2))-(40*x(2)*x(12))+(40*0.009*x(4));

% d[DrR]/dt

deriv(3)=(40*x(1)*x(12))-(40*0.009*x(3))-(50*x(6)*x(3))+(50*0.003*x(4));

% d[DrA]/dt

deriv(4)=(40*x(2)*x(12))-(40*0.009*x(4))+(50*x(3)*x(6))-(50*0.003*x(4));

% d[DrRA]/dt

deriv(5)=(15*x(3))-(0.01*x(5)) ; % d[Mr]/dt

deriv(6)=(90*x(5))-(0.01*x(6))-(50*x(6)*x(1))+(50*0.003*x(2))-

(50*x(3)*x(6))+(50*0.003*x(4))-(50*x(7)*x(6))+(50*0.003*x(8))-

(50*x(9)*x(6))+(50*0.003*x(10))-(50*x(13)*x(6))+(50*0.003*x(14))-

(50*x(15)*x(6))+(50*0.003*x(16)); % d[R]/dt

deriv(7)=(-50*x(7)*x(6))+(50*0.003*x(8))-(40*x(7)*x(12))+(40*0.009*x(9));

% d[Da]/dt

deriv(8)=(50*x(6)*x(7))-(50*0.003*x(8))-(40*x(8)*x(12))+(40*0.009*x(10));

% d[DaR]/dt

deriv(9)=(40*x(7)*x(12))-(40*0.009*x(9))-(50*x(9)*x(6))+(50*0.003*x(10));

% d[DaA]/dt

deriv(10)=(40*x(8)*x(12))-(40*0.009*x(10))+(50*x(9)*x(6))-(50*0.003*x(10));

% d[DaRA]/dt

deriv(11)=(15*x(9))-(0.01*x(11)); % d[Ma]/dt

deriv(12)=(90*x(11))-(0.01*x(12))-(40*x(8)*x(12))+(40*0.009*x(10))-

(40*x(7)*x(12))+(40*0.009*x(9))-(40*x(2)*x(12))+(40*0.009*x(4))-

(40*x(1)*x(12))+(40*0.009*x(3))-(40*x(14)*x(12))+(40*0.009*x(16))-

(40*x(13)*x(12))+(40*0.009*x(15)); % d[A]/dt


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deriv(13)=(-50*x(13)*x(6))+(50*0.003*x(14))

(40*x(13)*x(12))+(40*0.009*x(15)); % d[Dp]/dt

deriv(14)=(50*x(13)*x(6))-(50*0.003*x(14))-

(40*x(14)*x(12))+(40*0.009*x(16)); % d[DpR]/dt

deriv(15)=(40*x(13)*x(12))-(40*0.009*x(15))-

(50*x(15)*x(6))+(50*0.003*x(16)); % d[DpA]/dt

deriv(16)=(40*x(12)*x(14))-(40*0.009*x(16))+(50*x(15)*x(6))-

(50*0.003*x(16)); % d[DpRA]/dt

deriv(17)=(15*x(15))-(0.01*x(17)); % d[Mp]/dt

deriv(18)=(90*x(17))-(0.01*x(18)); % d[P]/dt


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9.2. Glossary of Terms

DNA : Deoxyribonucleic Acid

Matlab : Matrix Laboratory

mRNA : Messenger RNA

ODE : Ordinary Differential Equation

RNA : Ribonucleic Acid

RNAp : RNA polymerase

TRN : Transcriptional Regulatory Network

TF : Transcription Factor

MSc Thesis

Documents

informational

crude error

ordinary differential

ordinary differential

system level

microorganism

wilms tumour

ar binding