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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
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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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) 0471-2542220sankar.achuth@gmail.com
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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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.
System level analysis of activator/repressor motifs to regulate the transcriptional process
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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.
System level analysis of activator/repressor motifs to regulate the transcriptional process
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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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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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.4.19: Motif 2 for bistability analysis..........................................................68
Fig.4.20: Motif 3 for bistability analysis..........................................................68
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.5.20: Repressor basal values vs. steady state values for activator
and protein for motif 2...........................................................85
Fig.5.21: Repressor basal values vs. steady state values for activator
and protein for motif 3...........................................................85
Fig.5.22: Basal value vs. time for motif 1.........................................................88
Fig.5.23: Basal value vs. time for motif 2.........................................................89
Fig.5.24: Basal value vs. time for motif 3.........................................................89
Fig.5.25: Repressor steady states for motif 1...................................................90
Fig.5.26: Protein steady states for motif 1.......................................................91
Fig.5.27: Repressor steady states for motif 2...................................................91
Fig.5.28: Protein steady states for motif 2.......................................................92
Fig.5.29: Protein steady states for motif 3.......................................................92
Fig.5.30: Repressor steady states for motif 3...................................................93
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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,
System level analysis of activator/repressor motifs to regulate the transcriptional process
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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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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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.
System level analysis of activator/repressor motifs to regulate the transcriptional process
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2MATHEMATICAL THEORIES + COMPUTATIONAL
TECHNIQUES + BIOLOGICAL PRINCIPLES = SYSTEMS
BIOLOGY
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“The book of nature is written in the language of mathematics.”
- Galileo
2.1. Opening remarks
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.
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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
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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.
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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
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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.
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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
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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
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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
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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.
System level analysis of activator/repressor motifs to regulate the transcriptional process
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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.
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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.
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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]
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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
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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
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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.
System level analysis of activator/repressor motifs to regulate the transcriptional process
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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
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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.
2.15. Closing remarks
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.
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3WHAT OTHERS HAVE TO SAY...
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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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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]
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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]
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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.
System level analysis of activator/repressor motifs to regulate the transcriptional process
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,
System level analysis of activator/repressor motifs to regulate the transcriptional process
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.
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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.
System level analysis of activator/repressor motifs to regulate the transcriptional process
53
4HOW IT WAS ACHIEVED
System level analysis of activator/repressor motifs to regulate the transcriptional process
54
4.1. Opening remarks
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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.
System level analysis of activator/repressor motifs to regulate the transcriptional process
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]
System level analysis of activator/repressor motifs to regulate the transcriptional process
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.
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
R binding site A binding siteR
A
P
R binding site A binding site
R binding site A binding site
Gene 1: produces the repressor
Gene 2: produces the activator
Gene 3: produces the protein
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
R binding site A binding siteR
A
P
R binding site A binding site
R binding site A binding site
Gene 1: produces the repressor
Gene 2: produces the activator
Gene 3: produces the protein
R binding site A binding siteR
A
P
R binding site A binding site
R binding site A binding site
Gene 1: produces the repressor
Gene 2: produces the activator
Gene 3: produces the protein
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
R binding site A binding siteR
A
P
R binding site A binding site
R binding site A binding site
Gene 1: produces the repressor
Gene 2: produces the activator
Gene 3: produces the protein
R binding site A binding siteR
A
P
R binding site A binding site
R binding site A binding site
Gene 1: produces the repressor
Gene 2: produces the activator
Gene 3: produces the protein
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
R binding site A binding siteR
A
P
R binding site A binding site
R binding site A binding site
Gene 1: produces the repressor
Gene 2: produces the activator
Gene 3: produces the protein
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
R binding site A binding siteR
A
P
R binding site A binding site
R binding site A binding site
Gene 1: produces the repressor
Gene 2: produces the activator
Gene 3: produces the protein
R binding site A binding siteR
A
P
R binding site A binding site
R binding site A binding site
Gene 1: produces the repressor
Gene 2: produces the activator
Gene 3: produces the protein
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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.
System level analysis of activator/repressor motifs to regulate the transcriptional process
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)
System level analysis of activator/repressor motifs to regulate the transcriptional process
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)
System level analysis of activator/repressor motifs to regulate the transcriptional process
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)
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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]
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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.
R binding site A binding siteR
A
P
R binding site A binding site
R binding site A binding site
Gene 1: produces the repressor
Gene 2: produces the activator
Fig.4.14: Open loop
Gene 3: produces the protein
System level analysis of activator/repressor motifs to regulate the transcriptional process
77
Fig.4.16: motif 2
Fig.4.15: motif 1
R binding site A binding siteR
A
P
R binding site A binding site
R binding site A binding site
Gene 1: produces the repressor
Gene 2: produces the activator
Gene 3: produces the protein
R binding site A binding siteR
A
P
R binding site A binding site
R binding site A binding site
Gene 1: produces the repressor
Gene 2: produces the activator
Gene 3: produces the protein
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
R binding site A binding siteR
A
P
R binding site A binding site
R binding site A binding site
Gene 1: produces the repressor
Gene 2: produces the activator
Gene 3: produces the protein
System level analysis of activator/repressor motifs to regulate the transcriptional process
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)
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
R binding site A binding siteR
A
P
R binding site A binding site
R binding site A binding site
Gene 1: produces the repressor
Gene 2: produces the activator
Gene 3: produces the protein
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
R binding site A binding siteR
A
P
R binding site A binding site
R binding site A binding site
Gene 1: produces the repressor
Gene 2: produces the activator
Gene 3: produces the protein
R binding site A binding siteR
A
P
R binding site A binding site
R binding site A binding site
Gene 1: produces the repressor
Gene 2: produces the activator
Gene 3: produces the protein
System level analysis of activator/repressor motifs to regulate the transcriptional process
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.
4.12. Closing remarks
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.
System level analysis of activator/repressor motifs to regulate the transcriptional process
84
5ACHIEVING THE GOALS- RESULTS AND DISCUSSION
System level analysis of activator/repressor motifs to regulate the transcriptional process
85
5.1. Opening Remarks
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.
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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.
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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.
System level analysis of activator/repressor motifs to regulate the transcriptional process
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.
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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.
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
Fig.5.20: Repressor basal value vs steady state values of activator and protein for motif 2
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
Fig.5.21: Repressor basal value vs steady state values of activator and protein for motif 3
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
Put these values in eqn. (29):
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
102
Put these values in eqn. (29):
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
103
10-10
10-5
100
105
1010
25
30
35
40
45
50
55
60
kmr0
time
structure 2-protein dynamics
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
structure 3-protein dynamics
Fig.5.24: Basal value vs time for motif 3
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
bistability analysis.
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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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
Structure2:steady state Vs kmr0
Repressor at initial low k value
Repressor at initial high k value
Fig.5.27: Repressor steady states for motif 2
System level analysis of activator/repressor motifs to regulate the transcriptional process
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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
Structure2:steady state Vs kmr0
Protein at high k value
Protein at initial low k value
Fig.5.28: Protein steady states for motif 2
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
Structure3:steady state Vs kmr0
Protein at initial low k value
Protein at initial high value
Fig.5.29: Protein steady states for motif 3
System level analysis of activator/repressor motifs to regulate the transcriptional process
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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
Structure3:steady state Vs kmr0
Repressor at initial low k value
Repressor at initial high k value
Fig.5.30: Repressor steady states for motif 3
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.
5.5. Closing remarks
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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.
System level analysis of activator/repressor motifs to regulate the transcriptional process
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6CONCLUDING REMARKS
System level analysis of activator/repressor motifs to regulate the transcriptional process
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6.1. Opening remarks
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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
bistability analysis.
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.
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7THROUGH THE LENS...
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7.1. Opening Remarks
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.
System level analysis of activator/repressor motifs to regulate the transcriptional process
115
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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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.
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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);
System level analysis of activator/repressor motifs to regulate the transcriptional process
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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)
System level analysis of activator/repressor motifs to regulate the transcriptional process
126
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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127
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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128
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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129
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
130
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
System level analysis of activator/repressor motifs to regulate the transcriptional process
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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