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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 ...

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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    • System level analysis of activator/repressor motifs to regulate the transcriptional processSYSTEM LEVEL ANALYSIS OF ACTIVATOR/REPRESSORMOTIFS 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 BHASKARAN Reg. no : COB 090501STATE INTERUNIVERSITY CENTRE FOR EXCELLENCE IN BIOINFORMATICS UNIVERSITY OF KERALA JULY 2011 1
    • System level analysis of activator/repressor motifs to regulate the transcriptional process SYSTEM LEVEL ANALYSIS OF ACTIVATOR/REPRESSORMOTIFS 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 BHASKARAN Reg. no : COB 090501STATE INTERUNIVERSITY CENTRE FOR EXCELLENCE IN BIOINFORMATICS UNIVERSITY OF KERALA JULY 2011 2
    • System level analysis of activator/repressor motifs to regulate the transcriptional process STATE INTER UNIVERSITY CENTRE OF EXCELLENCE IN BIO-INFORMATICS, UNIVERSITY OF KERALA Karyavattom North CampusDr Achuthsankar S Nair Thiruvananthapuram, Kerala, India 695581MTech(IIT, Bombay), MPhil (Cambridge), PhD (Kerala), MIEEE Tel: (O) 0471 -2308759 (R) 0471-2542220Director sankar.achuth@gmail.com 26/07/2011 CERTIFICATEThis is to certify that the project work entitled “System level analysis ofactivator/ repressor motifs to regulate the transcriptional process” is thebonafide record of work done by Ms. Silpa Bhaskaran (Reg. No: COB 090501),in partial fulfillment of requirements for the award of Master’s Degree inComputational Biology from the University of Kerala during the academic year2009-2011. Director 3
    • System level analysis of activator/repressor motifs to regulate the transcriptional process DECLARATIONI hereby declare that the dissertation titled “System Level Analysis ofActivator/Repressor Motifs to Regulate the Transcriptional Process” submitted tothe University of Kerala in partial fulfillment of the requirement for the award of theDegree of Master of Science in Computational Biology is an authentic record of workcarried out by me under the guidance of Prof. K.V. Venkatesh, Professor, Dept. ofChemical Engineering, Indian Institute of Technology, Mumbai and that the dissertationhas not formed the basis for the award of any Degree/ Diploma/ Association/ Fellowshipor similar title to any candidate of any other University.Place: Kariavattom Silpa BhaskaranDate: 26-07-2011 4
    • System level analysis of activator/repressor motifs to regulate the transcriptional process ACKNOWLEDGMENTBy holding firmly, the saying, ‘Without GOD, I am a zero and with GOD, I am ahero’, 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 difficultiesduring the project work, both personal and academic, and was able to overcomeall of it successfully.I am happy that I got a place here, in this page, to express my sincere gratitudetowards Prof. K.V. Venkatesh who permitted me to do this project at theBiosystems Engineering lab in the Chemical Engineering Department of IndianInstitute of Technology, Mumbai, under his guidance. Beyond his simplicity andsupportive nature, it was his patience in answering even my questions thatserved a lot for me. He cared well to make me settled with the new place andenvironment.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 thework in such a prestigious institute. He pushed me for taking the steps forattaining this opportunity. The motivation and encouragement throughout thecourse work, from the head of our CBi family, was continued in the tenure of theproject work also. It was Achuth sir, who led my interest to the new field, systemsbiology, by introducing me with its wonderful scope and nature.I would also like to express my thanks and friendship towards my lab mates inIIT especially, Smitha and Ajay, who were my good companions through out theIIT life. Smitha helped me to get a starting in the initial stage of the work while Iwas wondering on how to proceed with the suggestions from my guide in thestarting days. Ajay’s consoling words and support helped me a lot to alleviate mydifficulty in being a part of the new working environment. I am not able toproceed without mentioning the names of my dear friends, Pournami and Nitya,gifted by the three months IIT life. 5
    • System level analysis of activator/repressor motifs to regulate the transcriptional processThe support and assistance given by the lectures in the Centre for Bioinformaticsis also immense. I thank them, especially, Aswathy S. and Umesh P. for theirservice from the distant and from near. I would like to mention the names of someof the researchers and members of CBi, who provided their moral support notonly during the project work, but also throughout the course work. Vipin Thomas,researcher, as usual, pushed, pulled and walked along with me through theproject tenure also, with his carefulness and affection, which gave me thecapability to overcome the troubles and difficulties. Amjesh R, the one who taughtus for the first two semesters, extended his friendship, critical comments andsuggestions, mostly silent encouragement and motivation, responsibility andopened support, during the project phase also. Arun K.S, the course coordinator ofour first three semesters, cared and inspired me a lot with his loving and caringwords. 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’sprogram.My next thanks go to my classmates, the beez, Msc-B-Batch with fourteenmembers, who kept the friendship of two years, even when all are apart, throughthe services offered by the e-world. Group discussions and chattings during theterm enabled us to understand the differences in the experiences andenvironment we were then facing.Last, but not the least, I would like to express my heartfelt gratitude and lovetowards my family members. I would not try to belittle the support and strengthgiven by my parents and my brother for the successful completion of the projectwork. As ever before, this time also, they encouraged and supported me, whichmade me to learn something beyond the academics, from the new culture. 6
    • System level analysis of activator/repressor motifs to regulate the transcriptional process ABSTRACTFunctioning of gene regulatory systems is supplemented greatly by the dynamicbehavior of the cell. Investigations into such dynamic behavior may provide abetter understanding of the biological control systems and make its analysisrather undemanding. Systems biology, as a holistic approach for studyingbiological systems contributed much to this area. It uses mathematical modelingand simulation for analyzing such dynamic interactions between systemcomponents and thereby explains the overall behavior of the system. Theapproach can also be adopted for studying of biological control systems.Transcription regulatory network is one such control system comprising ofrepressor, activator and protein as the components. These components interactwith each other in various ways to yield a desired output. These differentinteractions give rise to different structural motifs. Here, we develop a generalmodel for various feasible structures with combination of repressors andactivators to correlate with a desired output. The outputs range from transient tograded response. The various motifs were analyzed with different objectivescorrelated to existing natural motifs. The bistability of the existing motifs werealso analyzed using the models developed. The results of bistability analysis showthat the systems can have two stable states under the influence of positivefeedback loops and hybrid binding of both the transcription factors. The work canbe used for the analysis of the objectives behind the specific structural design ofthe motifs. 7
    • System level analysis of activator/repressor motifs to regulate the transcriptional process CONTENTS1. 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..............................................................................................92. 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 8
    • System level analysis of activator/repressor motifs to regulate the transcriptional process 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..........................................................................................283. 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............................................................................................384. 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 9
    • System level analysis of activator/repressor motifs to regulate the transcriptional process 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..........................................................................................695. 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............................................................................................936. CONCLUDING REMARKS................................................................................95 6.1. Opening remarks..........................................................................................96 6.2. A quick review..............................................................................................97 6.3. Hopefully.......................................................................................................987. THROUGH THE LENS......................................................................................98 7.1. Opening remarks........................................................................................100 7.2. Discussion...................................................................................................100 7.3. Future prospects........................................................................................1018. REFERENCES..................................................................................................1039. APPENDIX 9.1. Sample code 10
    • System level analysis of activator/repressor motifs to regulate the transcriptional process 9.2. Glossary of terms LIST OF FIGURESFig.1.1: Computational Biology process..........................................................6Fig.2.1: A system seen as an interconnection of subsystems with inputs and outputs.............................................................. ...14Fig.2.2: A schematic representation of the methodology of Systems Biology.....................................................................17Fig.2.3: Systems Biology concept....................................................................21Fig.2.4: Process of Mathematical Modeling...................................................23Fig.2.5: Basic types of motifs..........................................................................27Fig.3.1: Gene expression.................................................................................31Fig.3.2: Gene regulation..................................................................................32Fig.3.3: Gene regulatory network...................................................................32Fig.3.4: a) FFM b) SIM c) MIM.....................................................................37Fig.4.1: Central Dogma of Molecular Biology................................................41Fig.4.2: Gene expression regulation...............................................................42Fig.4.3: Representation of a simple transcription factor network................44Fig.4.4: Protein feedback in gene expression.................................................45Fig.4.5: R on P and A on R..............................................................................46Fig.4.6: R on R and R on A and R on P...........................................................47Fig.4.7: A on A and Aon R and R on R and R on P........................................48Fig.4.8: R on A and A on P..............................................................................48Fig.4.9: A on R and A on A and A on P...........................................................49Fig.4.10: R on R and R on A and A on A and A on P.......................................49 11
    • System level analysis of activator/repressor motifs to regulate the transcriptional processFg.4.11: A on R and A on P and R on P...........................................................50Fig.4.12: A on A and R on R and A on P and R on P.......................................51Fig.4.13: A on A and A on R and A on P and R onP........................................51Fig.4.14: Open loop............................................................................................62Fig.4.15: Motif 1.................................................................................................63Fig.4.16: Motif 2.................................................................................................63Fig.4.17: Motif 3.................................................................................................64Fig.4.18: Motif 1 for bistability analysis..........................................................67Fig.4.19: Motif 2 for bistability analysis..........................................................68Fig.4.20: Motif 3 for bistability analysis..........................................................68Fig.5.1: Activator concentration vs. time.......................................................72Fig.5.2: Protein concentration vs. time..........................................................72Fig.5.3: Repressor concentration vs. time......................................................73Fig.5.4: Activator concentration in open loop................................................74Fig.5.5: Protein concentration in open loop...................................................75Fig.5.6: Repressor concentration in open loop...............................................75Fig.5.7: Repressor concentration....................................................................77Fig.5.8: Activator concentration.....................................................................78Fig.5.9: Protein concentration.........................................................................79Fig.5.10: Repressor concentration with low basal value for repressor...........79Fig.5.11: Activator concentration with low basal value for repressor............80Fig.5.12: Protein concentration with low basal value for repressor...............80Fig.5.13: Repressor concentration with high basal value for repressor.........81Fig.5.14: Activator concentration with high basal value for repressor..........81 12
    • System level analysis of activator/repressor motifs to regulate the transcriptional processFig.5.15: Protein concentration with high basal value for repressor.............82Fig.5.16: Activator concentration.....................................................................82Fig.5.17: Repressor concentration....................................................................83Fig.5.18: Protein concentration.......................................................................83Fig.5.19: Repressor basal values vs. steady state values for activator and protein for motif 1...........................................................84Fig.5.20: Repressor basal values vs. steady state values for activator and protein for motif 2...........................................................85Fig.5.21: Repressor basal values vs. steady state values for activator and protein for motif 3...........................................................85Fig.5.22: Basal value vs. time for motif 1.........................................................88Fig.5.23: Basal value vs. time for motif 2.........................................................89Fig.5.24: Basal value vs. time for motif 3.........................................................89Fig.5.25: Repressor steady states for motif 1...................................................90Fig.5.26: Protein steady states for motif 1.......................................................91Fig.5.27: Repressor steady states for motif 2...................................................91Fig.5.28: Protein steady states for motif 2.......................................................92Fig.5.29: Protein steady states for motif 3.......................................................92Fig.5.30: Repressor steady states for motif 3...................................................93 13
    • System level analysis of activator/repressor motifs to regulate the transcriptional process LIST OF TABLESTab.4.1: Possible combinations of structural motifs.......................................53Tab.4.2: ODE solvers in Matlab.................................................................58-59Tab.4.3: Defintion of parameters used in calling ODE solvers......................59Tab.4.4: Initial values......................................................................................60Tab.4.5: Parameter values..........................................................................60-61 14
    • System level analysis of activator/repressor motifs to regulate the transcriptional process 1FIELD OF COMPUTATIONAL BIOLOGY – AN OUTLINE 15
    • System level analysis of activator/repressor motifs to regulate the transcriptional process1.1. Opening remarksThrough this opening chapter of my dissertation work, I am wishing to give youawareness on my field, Computational Biology. Here, you will get a generalintroduction on the discipline, imbibed from what I had understood about thediscipline, throughout the two-year programme. I have also made an attempt totrace the emergence of this field.1.2. PrologueIf technology needs to be interesting, we have to be aware of the possibilities andfacilities 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 andsuspicious. 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 isnothing for them to do in between. According to us, computer science is all aroundan electronic device that consists of non-living entities such as chips, circuits etcand uses voltage and power for their processing. Conversely, biology deals withlife and life processes. It is concerned with the study of structure, function,evolution etc of living organisms. No wonder, computational biology became aquestion mark for a non-professional.But for a technology expert or for a scientist of today, there is no need for gettingamazed.It can be said that there is not at all any single field in science advancing withoututilizing 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 isnecessary that you must be more aware of this interesting field.Computational biology, by definition, deals with the development ofcomputational techniques and applications inorder to gain an understanding onbiology at the cellular and molecular level. 16
    • System level analysis of activator/repressor motifs to regulate the transcriptional process1.3. Emergence and AdvancementScientists recognized that in order to understand life in its depth, it must startfrom 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. Thesecomponents are the factors behind all the cellular processes, inturn, the lifeprocesses. Thus, the field of molecular biology began to grow up. With theintroduction of efficient technologies, the field progressed more and generatedmore data.Between 1950 and 1960, this field of biology advanced with many vital discoverieslike the structure of DNA, RNA, Protein formation etc. All these were turningpoints for the biological studies. However, data retrieved from these discoveriescontain certain problems that required computational approach for its solution [1].Fortunately, the field of computer science and information theory was also facinga revolution at the same time. Computer science was also advancing, as it laid outmany of the basics of the field like the information theory.Series of developments were seen, when these computational approaches began toapply experimental data from biology. More and more insights were gained on thesecrets that restrained our biological knowledge. Computational biology was thussooner fixing its place as a highly advanced and technology based discipline. Withthe application of computational algorithms, the field advanced by contributingmore into the studies of protein structures, evolutionary studies, upto the centraldogma.The discipline laid its theoretical foundations in the 70s [1]. The specific problemsin the field of molecular biology were identified and it was attempted to solveusing the techniques of computational biology. Some of them are RNA structureprediction methods, sequence alignment methods, various studies on molecularevolution, phylogenetic studies, and so on. Thus, by the application ofcomputational techniques, more and more awareness was generated. Along withit, enormous amount of data was produced. Inorder to store all those data, digitallibraries and databases became necessary. By 80s, this problem was alsoanswered by the introduction of many curated computer archives (e.g: GenBank, 17
    • System level analysis of activator/repressor motifs to regulate the transcriptional processEMBL). Applications were generated to retrieve and analyze these records and touse it for further studies. This field gained more and more with the advancementof World Wide Web architecture. Online tools, databases, open source softwares,all contributed and enabled this discipline to gain significance and recognition asan independent discipline.1.4. Bioinformatics and Computational BiologyIt is not possible to consider both disciplines either as the same or as the oppositesides of a single coin. Instead, they are like two songs with same rhythm, samemusical instruments and same singers, but with different raga. Bioinformaticsand computational biology, both work with same entities but even though, a smalldifference makes them entirely different. The difference is in how they execute toachieve the aim.In very simple words, we can define that bioinformatics is the scientific disciplinethat make use of computational tools and techniques for studying molecularbiology and computational biology involves the development of thesecomputational tools and techniques.Yes, exactly like the difference between a driver and a vehicle manufacturer, orlike a music director and a singer. A computational biologist uses hiscomputational skills and develops softwares, tools, applications, databases andalgorithms for handling and analyzing biological data. A bioinformatician musthave the skills to run the computer softwares and tools only. But he/she isexpected to have the ability to biologically interpret and analyze the dataprovided 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 wonderfulfields of computer science, applied mathematics, statistics, biochemistry, 18
    • System level analysis of activator/repressor motifs to regulate the transcriptional processchemistry, biophysics, molecular biology, genetics, ecology, evolution, anatomy,neuroscience and visualization. There is no wonder if more and more new fieldsjoined in the voyage to climb up the tree of life, in future.1.5. RelevanceExperimental biology is essential, however it has reached up in such a situationthat it cannot advance without the application of computational techniques in it.This happened so because of the realization of the necessity of quantitativeinformation that can be provided by computational techniques only. Quantitativestudy provides us with the information that is more basic. Quantitativeinformation is essential for unraveling the secrets of life, which is one of themajor aims of the biologists.The computational approaches in the study of molecular biology had enabled thescientific world to find solutions to the unanswered questions encircling thebiological sequences. Computational biology proceeds on strings - the string ortextual representation of sequences, which may be DNA, RNA or protein. There isno need for inquiring too much into the chemical and biological aspects of DNAand protein, while making computational biology a companion, in the attempt ofrevealing biological facts.Computational methods attempts to resolve problems regarding the statistics,sequence similarity, motifs, profiles, protein folds etc. Here are some of thevarious applications of computational biology i.e. where the computationalapproaches 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; 19
    • System level analysis of activator/repressor motifs to regulate the transcriptional process 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; Sequence analysis, statistical tools and analysis, data mining Functional genomics and Protein proteomics structure, de novo design, molecular modeling and Computational Biology Metabolic engineering and Systems Bioprocess Biology control. Pharmaco kinetc insilico modeling, drug design Fig.1.1: Computational Biology processes [2] 20
    • System level analysis of activator/repressor motifs to regulate the transcriptional process1.6. Indian ScenarioIn India, the strength gained in the field of information technology, computingand software technology have lead to a drift towards this new attempt ofintegrating of biological data, development of useful software and databases inbiology, genome-wide structure and function analysis, neuronal simulations andmathematical modeling. The launching of various bioinformatics andcomputational research centers throughout the country, by the software andpharmaceutical companies created surge for this field. The development ofvarious tools and softwares by these companies had contributed much to theadvancement of computational biology field in this country. The Bangalore basedcompany, Strand Life Sciences is one among them that contributed that mademany developments to the biological research, this way. Their Sphatika is acrystal image classification tool for high throughput X-ray crystallography and itclassifies protein crystals into two broad categories, one comprising crystal hitsand harvestable crystals and the other comprising empty wells, clear drops andprecipitates. Also, they had developed Chitraka, an image analysis andmanagement tool for semi-automatic recognition and quantification of expressedgene spots from microarray experiments. The State Inter-university Centre forexcellence in Bioinformatics of University of Kerala had also put their signaturein the field by their effort in developing Kera, an object oriented programminglanguage to create, dislay, combine and edit biological constructs and convertthem into sequence. The Indian based IT gaints, Infosys and TCS had estalishedcomputational life science wings as a part, which enabled to catch the attractionof the career searchers.As this is a new field, lot of research opportunities is there. And because of thesame reason, the outputs from the studies will be very relevant and of highsignificance. May be, by noticing the rapid progress and scope of the approach inblending the computational and mathematical principles in biology, the USPresident Barack Obama warned his country youth to focus more on science,mathematics and technology as the Indian and Chinese students are marchingahead in these fields and will seize the areas in the near future. 21
    • System level analysis of activator/repressor motifs to regulate the transcriptional processEven though, the blending of modern technology and computationaladvancements with biological studies had grabbed the Indian as well as foreignstudents with an interest to choose this field of computational biology as thecareer.1.7. Related FieldsThe field of computational biology is supported and complemented by its variousnovel omics sub-fields such as genomics, proteomics, metabolomics,transcriptomics, cytomics, epigenomics, along with the systems biology, syntheticbiology 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 fromgenome sequences and related data, including DNA and RNA sequence as well asother "post-genomic" data (i.e. experimental data obtained with technologies thatrequire the genome sequence, such as genomic DNA microarrays). It focuses onusing whole genomes (rather than individual genes) to understand the principlesof 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 oftendefined 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 andfunctions.1.7.4. Cytomics [6]Cytomics is the study of cell systems (cytomes) at a single cell level. It combinesall the bioinformatics knowledge to attempt to understand the moleculararchitecture and functionality of the cell system. This is achieved by usingmolecular and microscopic techniques that allow the various components of a cellto be visualized as they interact in vivo. 22
    • System level analysis of activator/repressor motifs to regulate the transcriptional process1.7.5. Epigenomics [7]Epigenomics is the study of the effects of chromatin structure on the function ofthe included genes.1.7.6. Interactomics [8]Interactomics is a discipline at the intersection of bioinformatics and biology thatdeals with studying both the interactions and the consequences of thoseinteractions between and among proteins, and other molecules within a cell. Thenetwork of all such interactions is called the interactome. Interactomics thusaims to compare such networks of interactions (i.e., interactomes) between andwithin species in order to find how the traits of such networks are eitherpreserved or varied. From a computational biology viewpoint, an interactomenetwork is a graph or a category representing the most important interactionspertinent to the normal physiological functions of a cell or organism.1.7.7. Systems BiologyThe inter-disciplinary approach to studying biology, that studies biologicalentities as a system, by perturbing them, monitoring the gene, protein andinformational pathway responses; integrating these data; and ultimately,formulating mathematical models that describe the structures of the system andits repsonse to individual perturbations.1.7.8. Synthetic BiologyVery new attempt, that designs and builds new biological systems by adding ormodifying biological functions to existing organisms, or, creating novel organismswith tailored properties.1.8. Closing remarksWe have to make use of technological advancements in computer science,information theory and World Wide Web in biological studies also. According toCharles DeLisi, the bioinformatics and systems biologist trainer, within twentyyears biology will be the most computational of all sciences. Relying in theoptimistic words of DeLisi, we have to travel a long distance ahead. For that we 23
    • System level analysis of activator/repressor motifs to regulate the transcriptional processhave to keep ourself updated with the recent progresses in both fields. Let us be apart of the attempt to use electronic chips and transistors for tracing and makingthe mystery of life and life processes obvious. 24
    • System level analysis of activator/repressor motifs to regulate the transcriptional process 2 MATHEMATICAL THEORIES + COMPUTATIONALTECHNIQUES + BIOLOGICAL PRINCIPLES = SYSTEMS BIOLOGY 25
    • System level analysis of activator/repressor motifs to regulate the transcriptional process “The book of nature is written in the language of mathematics.” - Galileo2.1. Opening remarksThis chapter of the dissertation work is an attempt to introduce you to theinteresting field of systems biology, the field to which the current work belongs.Here you can find the information I have gained through reading the literatureand discussions, along with the concepts and conclusions resulting from my ownthoughts.The basic concepts of systems theory, the principles of systems biology, itsemergence, relevance and challenges leading up to an idea on how all thesesatisfy the current work are discussed here.2.2. A System is...The term ‘system’ might remind you of the picture of a set of componentsinterconnected with each other. Such a perspective can enable us to considerevery entity as a system. For example, an electrical circuit, a computer system, abiological system, a classroom, family, an organism, a plant, a toy, all can becalled as a system, as there are some components within them that give it its ownlife. We have to doubt if there exists something, which is not possible to beincluded 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 thesecomponents have a role to play, which makes it the classroom. Therefore, we canconsider these roles as interactions that occur between the components of asystem. These interactions make the components a part of the system. All areessential, no matter how small or large, for the existence of the classroom. All areimportant as each contributes to the general behaviour of the classroom. It maybe apt, if the story of six blind men who went to see the elephant is mentionedhere. Each of them identified each organ of the elephant and regarded it as theanimal itself. Nevertheless, in practice, each of these organs together constitutesthe animal and gives it its own property. 26
    • System level analysis of activator/repressor motifs to regulate the transcriptional process2.3. In principle...A system is an orderly arrangement of objects according to a scheme. The conceptof a system gives a bird’s eye view of the entity of interest. This is opposite to thereductionist approach that focuses on the component parts and not the system as awhole.A system is something that exists and operates in time and space. It receivesinputs and produces a specific output for which the system is intended. Thecomponents of a system always exchange certain signals between them duringtheir functioning. The final output behaviour of the system is generated byintegrating all such signals. These signals can be considered as the interactionsbetween the components. The system maintains its existence through suchinteractions that ultimately lead to produce the output for which the system isintended. A system may consist of subsystems that again can be composed ofsmall systems.The function or the property of a system, contributed by its elements orcomponents is known as the emergent property. We can gain an idea on theseemergent properties only by studying the system as a whole and not by studyingthe individual parts. This makes the system irreducible.2.4. Systems approach in biologyTraditionally, biology had been studied with a reductionist approach. Forstudying a biological system, scientists used to identify and study its componentparts in isolation. For example for studying the entire human system, theystudied each sub system in it like the nervous system, circulatory system or thedigestive system. According to this notion, the interaction or the signal exchangedoes not have any role to play. They are not emphasizing on the saying that ‘thewhole is bigger than the sum of its parts’. However, the reductionist approachprovides us with the knowledge regarding the system; that gives us insights intohow and what the system is comprised of.It is only recently that the systemic approach has been started to apply tounderstand the complexity of life. Since that time, biology has become a branch of 27
    • System level analysis of activator/repressor motifs to regulate the transcriptional processscience that can be studied with advanced computational applications and theperplexing theories of the queen of science. Thus biology has been revolutionizedto give rise to a new field called ‘systems biology’ which is making rapid stridesnow 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 invarious processes such as cell growth and maintenance, division, and death. Thestudying of each of these subsystems will enable to understand the emergentproperties of the system. There is no need of raising questions on the applicationof the systems theory in the cellular studies as we can view the significance ofcomponents, their interactions, their interaction rules, the input-output signals inthe cellular studies.Systems biology is a holistic approach. It analyses how the elements in a systemand their interactions give rise to emergent properties of that system. Ratherthan revealing what constitutes the system (reductionist approach), systemsbiology explains why they are so constituted (holistic approach). This field makesuse of various disciplines like mathematics, engineering, computer science for theprofound understanding of the biological facts that underlie life. 28
    • System level analysis of activator/repressor motifs to regulate the transcriptional process2.5. Let us open the door towards systems biologyAs mentioned above, systems biology focuses on the interaction between thecomponents in a biological system and seems that these interactions make thesystem behave as it does. This is the basis of the approach. This in-silico biologycombines the biological data collected through various experimental techniquesand through various bioinformatics tools into interactive models. Then thesemodels can be used for simulation and further analysis that help us to arrive atinferences 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 engineeringscience with biology that is contradictory to the traditional way of looking atbiological science. Due to its highly interdisciplinary nature and youthfulness, anexact definition of the field has not been generated yet, even though variousattempts 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 atthe molecular level, the dynamic relationships between the biological moleculesthat define living organisms.’Some others says that,Systems biology studies biological systems by systematically perturbing them(biologically, genetically or chemically); monitoring the gene, protein, andinformational pathway responses; integrating these data; and ultimately,formulating mathematical models that describe the structure of the system and itsresponse to individual perturbations. (Ideker et al, 2001)Systems biology is a scientific discipline that endeavours to quantify all of themolecular elements of a biological system to assess their interaction into graphicalnetwork models that serve as predictive hypothesis to explain emergent behaviour(Leroy Hood, 2005)The models of biological systems derived through the approach of systems biologycan be used for further analysis and study. Perturbation analysis through 29
    • System level analysis of activator/repressor motifs to regulate the transcriptional processsimulation techniques is an adopted method. A model gives more understandingon the system under study.2.6. Importance of perturbation analysisThe best and most effective way of studying a system is by observing itsbehaviour when a perturbation is applied. Perturbation analysis enables us tounderstand the actual behaviour of the system of interest. We can attain a vastamount of information from interpreting the model and by analyzing the resultsof the perturbation analysis.As the systems behaviour depends upon its components, the perturbationanalysis verifies how the change in any one of the components affects the overallfunctioning of the system. This information can be used in turn to identify thecomponent’s significance by understanding how the change in it affected othercomponents, which in turn brought about the change in the system’s basicbehaviour. This knowledge can be used for making efficient predictions of thesystem at a given condition and at a given time. The significance of systemsbiology lies in such predictions. This will be discussed later.This perturbation analysis can thus show the system dynamics, as it reveals howthe system behaves in different conditions. The system structure and systemdynamics are considered as the two important aspects of a system in systemsbiology.A general schematic representation of the approach used in systems biology isshown below. 30
    • System level analysis of activator/repressor motifs to regulate the transcriptional process Metabolomics PREDICTION Proteomics Omics SYSTEM INFERENCE Genomics DATA Using computational tools MODEL and mathematical methods Fig.2.1: A schematic representation of the methodology of systems biologyBiological systems are considered to be robust and modular. Here this‘robustness’ indicates the ability of a system to remain with its owncharacteristics despite perturbations, unpredictable circumstances and its abilityto exhibit graceful degradation. Perturbation analysis will give informationregarding the robustness of the system. Modularity denotes the ability toapproach the systems as module. In a module, there will be a set of nodes thathave strong interactions in between and a common function. A module will havedefined input nodes and output nodes for regulating the interactions. As in anengineering system, the module in a biological system will also have certainfeatures that make them to be easily embedded in any system. Modularity can beconsidered as at the root of the success of gene functional assignment byexpression correlations. 31
    • System level analysis of activator/repressor motifs to regulate the transcriptional process2.7. Significance of predictionsIt is said that the best and most effective way of studying a system is byobserving its behaviour when a perturbation is applied. The model will givedifferent results for different inputs. By analyzing these results, we can predictthe effect of changes to the system. A model can turn assumptions intoconclusions.The concept is that a good system model will successfully predict the systembehavior under specific perturbations. These perturbations are genetic orenvironmental, provided by experimental alterations given under specific time.When a model achieves the ability for prediction, one can also generate thedesired output from the system. For that, first we have to experiment this on themodel we have, by changing the input parameters to generate the desired outputby making use of the predictions. Then by applying this on the real system, wewill be able to control the system. This makes us possible to make the systembehave according to our will.In systems biology, for achieving this predictive nature, initially, thecomputational model is compared with the actual systemic behavior underexperimental conditions. If this initial validation is succeeded, then the model canbe used for predictions, which is further tested under experimental alterations.This will reduce the risk of in-vivo experiments.2.8. EmergenceIt is in the early 20th century that biological studies began to change due to theunderstanding of systems constituted in it [10]. Before that, biology was sustainedby the reductionist and mechanistic approach. The end of that era was markedwith the publication of Williams in 1956. The work compiled the molecular,physiological and anatomical individuality in animals by considering numerousbiochemical, hormonal and physiological parameters. The study indicated thesignificance of a systemic view in biological study. With this, the mechanisticapproach almost ended. The insight that the biological systems follow ahierarchical level of organization and that the communication and control within 32
    • System level analysis of activator/repressor motifs to regulate the transcriptional processthe systems is carried out by the interaction of these different system levels led tothe use of system’s approach in studying biology. It was required for untanglingthe components of the systems and for determining what lies beneath the cellularprocesses.Even though the definition of systems biology is in conflict, it seems that most ofthe eminent scientists in the field have agreed that the emergence of thisappealing field is from molecular biology.It is a fact that need not be disputed, that, the molecular level study of thebiological systems has contributed much to unravel the secrets of life. The highthroughput technologies used in experiments produce huge volume of biologicaldata. The human genome sequencing, microarray analysis and advances in massspectrometry, all contributed to the shelf of biological knowledge. When morestudies began to be conducted at the molecular level, in order to handle themultiple molecules identified, it became necessary to understand more about theinteractions between them. This gave light to the role of the regulatorymechanisms within these molecular systems. All such genomic knowledge couldbe 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 abiological network, we cannot study or analyze a biological system comfortably instudying electrical circuits or any other entities. The only reason is the complexityand oscillative nature of the biological systems and we have still not achievedproficiency in clearing its mysteries and understanding its causes andcomplexities thoroughly. Therefore, it is doubted whether systems biology willsucceed in its goal of understanding the mechanisms of life.Even though the offerings of systems biology are fascinating, crtitics have muchto demur about. In addition, there are many challenges that this young field hasto face.Systems biology accepts the data derived from biological experiments, which arestored in databases. This data has to be retrieved from a single cell. Molecular 33
    • System level analysis of activator/repressor motifs to regulate the transcriptional processbiological methods and high-throughput technologies are required to study thelarge number of genes and proteins in the genome, which will enable tounderstand on the network of interactions. Technological advancements are notyet capable of conducting numerous measurements in a single cell. Due to thislack of sufficient technology, we are not able to retrieve the complete data andthereby the databases remain incomplete. Therefore, the techniques, databasesand the datasets are not available as required. This may be the reason thatmakes the skeptics of the field consider it as a premature baby.The extent of the reliablity of the predictions and conclusions drawn from themodels is a matter of uncertainty. It is not sure whether they reveal the dynamicsin 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 biologistwith experimental skills and a computer scientist or a mathematician with codingskills are equally important to this embryonic field. Inorder to achieve this, thetraditional mentality of keeping mathematics and biology at the two ends of thespectrum of knowledge needs to be changed. Moreover, both must be interested inor 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 doneyet by promising explanations on the quantitative behaviour of the underlyingprocesses and systems. It is important, because if it can overcome the challengesput forward by its critics, it can ultimately contribute a lot to our understandingof human diseases and their treatment. Furthermore, it considers what internalfactors give a specific behaviour to a system by considering the interiorinteractions. 34
    • System level analysis of activator/repressor motifs to regulate the transcriptional process Fig 2.2: System Biology concept [11]Traditional biological approaches, upto molecular biology tried to answer onlyhow biological systems work. But this new approach, systems biology, is trying tofind out answers for why it works so or why it doesnt work so. It is at from thispoint of view that systems biology had to consider all the interactions of thecomponents in a system that contribute to its working. Thus, systems biologytries to find out the rationale behind a specific design for a system, with itsquantitative 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’ fieldsand the data retrieved using the bioinformatics tools. The quantity of this data isvery massive. Also, biological systems are treated as being fluctuative. In order totrack 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 dataaltogether. So obviously, they depended upon computers for this task, which inturn brought mathematics into play. All these are adopted and integrated bysystems biology. Along with its oscillative nature, systems biology also explainsthe robustness held by the biological systems. All these help us to widen anddeepen our biological knowledge. 35
    • System level analysis of activator/repressor motifs to regulate the transcriptional process2.11. Mathematical ModelingAs we told earlier, systems biology proceeds by applying mathematical modelingusing computational techniques. The mathematical modeling of bological systemsmeans creating an abstract representation of the system under study usingmathematics. The models can answer questions about ‘how much’ rather than‘how’. That is, models of biological systems give quantitative descriptions of thesystem for which the scientists are eagerly waiting for. The interactions aremodeled using the differential equations.Mathematical model are approved as the ideal tools for studying gene networkslike the transcriptional regulatory network because they can identify thecomponents of the network and are able to analyze the interaction patternsamong them. Models developed using computational techniques andmathematical methods can convey relevant information that will be beneficial tofuture studies. Also, mathematical studies enables to conduct experiments as insilico and thus avoid the time, effort and expense that in vivo or in vitroexperiments take.According to Don Kulsari et.al, the role of mathematical models in systemsbiology is multi-faceted. They point out four statements to justify this, which isexplained 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. 36
    • System level analysis of activator/repressor motifs to regulate the transcriptional process Real-world data Model Formulation Test Analysis Predictions/ Interpretation Mathematical Explanations Conclusions Fig. 2.3: Process of mathematical modeling [12]2.12. MatlabThe present work is done using the ordinary differential equation solving methodprovided by Matlab, which is called as the language of technical computing.Matlab is a suitable platform for the modeling and simulation purposes. For thesame reason, it complements the mathematical modeling approaches of systemsbiology. Lets us have a brief overview on the Matlab environment here. Thisinformation is retrieved from the website www.mathworks.com, who patentedMatlab.2.12.1 Overview of the MATLAB Environment [13]The MATLAB (MATrix LABoratory) is a high-performance language for technicalcomputing integrates computation, visualization, and programming in an easy-to-use environment where problems and solutions are expressed in familiarmathematical notation. Typical uses include,  Math and computation  Algorithm development 37
    • System level analysis of activator/repressor motifs to regulate the transcriptional process  Data acquisition  Modeling, simulation, and prototyping  Data analysis, exploration, and visualization  Scientific and engineering graphics  Application development, including graphical user interface buildingMATLAB is an interactive system whose basic data element is an array that doesnot require dimensioning. It allows you to solve many technical computingproblems, especially those with matrix and vector formulations, in a fraction ofthe time it would take to write a program in a scalar noninteractive languagesuch as C or FORTRAN.The name MATLAB stands for matrix laboratory. MATLAB was originallywritten to provide easy access to matrix software developed by the LINPACK andEISPACK projects. Today, MATLAB engines incorporate the LAPACK and BLASlibraries, embedding the state of the art in software for matrix computation.MATLAB has evolved over a period of years with input from many users. Inuniversity environments, it is the standard instructional tool for introductory andadvanced courses in mathematics, engineering and science. In industry, MATLABis the tool of choice for high-productivity research, development and analysis.MATLAB features a family of add-on application-specific solutions calledtoolboxes. Very important to most users of MATLAB, toolboxes allow you to learnand apply specialized technology. Toolboxes are comprehensive collections ofMATLAB functions (M-files) that extend the MATLAB environment to solveparticular classes of problems. We can add on toolboxes for signal processing,control systems, neural networks, fuzzy logic, wavelets, simulation, and manyother areas.2.12.2. The MATLAB SystemThe MATLAB system consists of these main parts:  Desktop Tools and Development Environment 38
    • System level analysis of activator/repressor motifs to regulate the transcriptional process 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 39
    • System level analysis of activator/repressor motifs to regulate the transcriptional process MATLAB (dynamic linking), for calling MATLAB as a computational engine, and for reading and writing MAT-files.2.13. Network MotifThe reason for the idea behind applying engineering principles in the study ofbiological systems is the presence of certain features, which are found common inboth the engineering systems and the biological systems. Modularity androbustness, we discussed earlier are main among them. A third principle, the useof recurring circuit elements, also plays a significant role. Engineers make use ofvarious basic elements in the circuitry in which they are working, that mayrepeats thousands of times in the same circuitry. Like wise, biology also showsthe presence of key wiring patterns that appears again and again throughout anetwork. Such repeating biological patterns are named as motifs (networkmotifs). Network motifs define the few basic patterns that recur in a network and,in principle, can provide specific experimental guidelines to determine whetherthey 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 motifsrepresents a circuit of interaction and it is upon this motif that the network isbuilt. 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 differentorganisms. That means the same network motifs have been found in variousorganisms ranging from bacteria to human. This proves the role of network motifsas the basic building blocks in a biological network. Different network motifs areinterlinked 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 thecurrent study, we work on motifs found in the transcriptional regulatory networkfound in organisms. For example, let us have a look on the three common motifsfound in the transcritional regulatory network. 40
    • System level analysis of activator/repressor motifs to regulate the transcriptional process a) Feed Forward Motif b) Single Input Motif c) Multiple Input Motif Fig.2.4: Basic types of motifs [14]2.14. Relevance of systems biology in current workSystems biology obviously requires model organisms. Practically researchers usesimple systems such as yeast. By scaling up the models of such simple systems wecan learn complex systems like the human system, by means of comparativegenomics 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 certainextent. Nevertheless, in certain cases this may not be true. However there will besome universal principles which is applicable for all.Due to the nature of systems biology, it satisfies the aesthetic quality ofsimplicity. This requires the identification of those universal principles. Theseuniversal principles, otherwise the general laws, are supposed to lay thefoundation for all species without any specific interest. The concept of universalprinciple gave systems biology a bottom-up approach. This led to the modelling of 41
    • System level analysis of activator/repressor motifs to regulate the transcriptional processsmall units within the complex biological sytems with a belief that they follow thesame rules independent of their substrate. These small units, probably, act as thecontrol elements in a system. Therefore, scientists consider control elements formodeling that is conserved in both the simple and complex systems. Controlelements are small elements such as binding sites for transcription factors intranscription network. We can model the biological control systems by integratingthe models of many such control elements.In systems biology, the systems are viewed as networks with the components asthe 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 differentplaces within a network. Thus, in short, the awareness of the design of thesemotifs acts as a critical factor in the progress of the discipline.In the following pages, you can find that the current work endeavors to fabricatea generic model for the network motifs in the transcription regulatory network.2.15. Closing remarksThrough this chapter an attempt to give an introductory idea into the field ofsystems biology is made. The various aspects of systems biology such as aim,scope, approach, emergence, challenges etc. are described. Specific explanation onmathematical modeling, matlab, and network motifs are given as it will berelevant for explaning the current work. 42
    • System level analysis of activator/repressor motifs to regulate the transcriptional process 3 WHAT OTHERS HAVE TO SAY... 43
    • System level analysis of activator/repressor motifs to regulate the transcriptional process3.1. Opening RemarksIn this chapter, a detailed review on the literature in the field has done. Hope thischapter will give you awareness on the basic principles that undelie and supportthe 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 biologySystems Biology as a holistic approach, studies the system as a whole not asparts. It held that a system receives some input signals and contain controlelements, which process these inputs to produce the desired output signals.Systems approach in biological studies gave significance to the small controlelements that are preserved among organisms. Based on these small controlunits, the whole system is studied and analyzed.Systems biology relies on the universal principle that lays the foundation of allspecies. The concept of universal principle gave systems biology a bottom-upapproach. This led to the modelling of small units within the complex biologicalsytems with a belief that they follow the same rules independent of theirsubstrate (Breitling, 2010). These small units, probably, act as the controlelements in a system. Therefore, scientists consider control elements formodeling 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 aleading computational biologist says that System biology aims to understand howindividual elements of the cell generate behaviors that allow survival inchangeable environments, and collective cellular organization into structuredcommunities. According to him, cellular networks would ultimately, assembleinto larger population networks to form large-scale ecologies and thinkingmachines, such as humans.Arkin says that as the complete genomes of more organisms are sequenced, andmeasurement and genetic manipulation technologies are improved, scientists willbe able to compare systems across a broader expanse of phylogenetic trees. This 44
    • System level analysis of activator/repressor motifs to regulate the transcriptional processwill inturn enhance our understanding of mechanistic features that are necessaryfor function and evolution."The increasing integration of experimental and computational technologies willthus corroborate, deepen and diversify the theories that the earliest systemsbiologists used logic to infer," Arkin says. "This will thereby inch us ever closer toanswering the, what is Life question."3.3. Gene ExpressionGene expression is the synthesis of proteins using the information contained ingenes. The information in DNA is first used to make mRNA through thetranscription process and this mRNA is then used to synthesize protein throughthe translation process. Not all proteins are required in all time for the normalfunctioning of the biological system. Also, the synthesis is not required in equalamount all the time. How much protein is produced in a specific time from aspecific gene determines the level of gene expression at that time. This level ofgene expression determines the level of the functioning of the gene. Genes mustbe correspondingly turned on or off for the required level of gene expression. ] Fig.3.1: Gene expression [15 45
    • System level analysis of activator/repressor motifs to regulate the transcriptional processGene expression is a complex process, which is regulated at multiplelevels. Apart from the regulation of transcription and translation, the geneexpression is controlled at various stages, during RNA processing and transport(in eukaryotes), RNA translation, and the posttranslational modification ofproteins. Fig.3.2: Gene expression regulation [16]The gene expression regulation is carried out by the regulatory proteins withinthe cell. There may be one regulatory protein which controls the production ofanother regulatory protein that may in turn control the production of another setof regulatory proteins and so on. Such numerous chains of interactions constituteto form a gene regulatory network (GRN). Representing such interactionsbetween biological molecules as a network provides us with a conceptualframework that allows us to identify the general principles that govern thecomplex biological systems [1]. Fig. 3.3: Gene Regulatory Network [17] 46
    • System level analysis of activator/repressor motifs to regulate the transcriptional process3.4. Transcriptional Regulatory NetworkEven though gene expression is regulated at various stages, the predominant siteof gene expression regulation is considered as the control of transcription [18]. Alsotranscriptional regulation constitutes perhaps the most experimentally tractableof these regulatory mechanisms, as mRNA abundance and DNA binding areeasier to measure than, for example, protein abundance and activity [19]. Theproteins 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 bindinginfluences the gene expression either positively or negatively depending uponwhether it is an activator or a repressor. An activator activates the proteinproduction while a repressor retards it. Transcription factors are only one of themeans by which our cells express different combinations of genes, allowing fordifferentiation into the various types of cells, tissues and organs that make up ourbodies. Their function is to respond to the various biological signals andaccordingly change the transcription rate of genes, thereby allowing the cells toproduce the necessary amount of proteins at the appropriate time [21].Transcriptional regulation at the protein level is achieved by the transcriptionfactors binding to different promoter regions of genes under differentenvironmental conditions [22]. Since there will be multiple binding sites in aregulatory region where multiple TFs can bound, transcriptional regulation mayinvolve combinatorial interactions between several TFs. (Kulasiri D, et.al, 2008).i.e., several transcription factors may bind to the same gene in differentcombinations resulting in different rates of transcription (Roy, Lane, & Werner-Washburne). So, if two TFs can bind to a gene, there are four possiblecombinations of the transcription factors, which may be present on the promoterregion 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 theinteractions between transcription factor proteins and the genes that theyregulate. 47
    • System level analysis of activator/repressor motifs to regulate the transcriptional processTranscriptional 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 BiologyWhy 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 beinvoked or that existing data are inadequate, or that new theories are needed. Inkinetic modeling this is often the case with ‘inverse problems’ in which one isseeking to find a (‘forward’) model that best explains a time series of experimentaldata (see below).3.5.1. Mathematical ModelingMathematical models are considered as the ideal tools for studying generegulatory networks and it can deal with the underlying complexity of thesenetworks. Mathematical modeling provides sophisticated frameworks forinvestigating the components of the networks and analyzing the rules governingtheir interactions (Kulasiri, Nguyen, Samarasinghe, & Xie, 2008). Normally, it isdifficult to gain perceptions on the functioning of these networks as it presentsdifferent behavior on different time scales corresponding to various processes, 48
    • System level analysis of activator/repressor motifs to regulate the transcriptional processalong with its structural complexity. Mathematical models can answer this issueup 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 reducingthe effort, expense, time and risk taken for the traditional in-vivo experiments.According to Kulasiri and his team, mathematical modeling plays a multi-facetedrole in the biological studies through systems biology. The first role they hadpointed out is that the properly constructed mathematical models can be used forthe validation of the current knowledge by comparing the model predictions withthe experimental data. Even if discrepancies are found out during suchcomparisons, it will only enable us to expand our knowledge systematically.Secondly, mathematical modeling can suggest novel experiments for testinghypotheses that are formulated from the modeling experiences. Third, theyenable to study and analysis the system properties, which are not revealed by thein-vitro experiments. The final role they considered is that, they can producedesirable new designs based on the existing biological networks.3.5.1.1. Kinetic ModelingDeterministic modeling is an approach for mathematical modeling that considersBoolean logic and differential equations for modeling. The peculiarity of thedeterministic models is that they don’t take uncertainties into consideration.Instead, it is based on the principle of causality that believes on the uniquerelationship between causes and their resulting effects (Kulasiri, Nguyen,Samarasinghe, & Xie, 2008). The popular deterministic approach to modeling agene regulatory network is the differential equation approach, which proceeds bymodeling the interactions of the elements in the GRN as a series of coupledchemical 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 reactivecomponents. The rate of a reaction representing the concentration change perunit time is written as a function of the concentration of reactants and productsin those chemical reactions. 49
    • System level analysis of activator/repressor motifs to regulate the transcriptional processThe series of interactions among the components in a biological network willultimately give rise to the biological processes. The kinetic models can modelthese 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 functiondescribes the co-operativity of the transcription factors with its binding regionwithin the promoter region.3.5.1.2. Modeling using Ordinary Differential Equation (ODE approach)It had been already mentioned that the deterministic modeling approach dependsupon the ordinary differential equations for modeling. It considers that the rate ofchange of a product obtained, when the interactions are denoted as chemicalequations, is dependent upon its degradation as well as synthesis (Roy, Lane, &Werner-Washburne).3.6. Network MotifsIn the second chapter of my dissertation work, I have mentioned about thenetwork motifs. Network motifs are considered as the fundamental unit of atranscriptional network. They act as the control elements with recurringregulation patterns [24]. Alon presented his paper regarding network motifs withthe basic idea that these network motifs carry out specific information- processingfunctions. He says that these motifs have been analyzed using the mathematicalmodels and tested using the living cell experiments so as to gain a vivid idea onthe dynamicity of the network functioning.When biological interactions are represented as networks, its analysis can becarried 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 motifpresents itself as a small pattern of interconnections that recur at many differentpart of the network.The three types of motifs depicted in the paper, as most commonly occuring, arethe FFM (Feed Forward Motif), SIM (Single Input Motif), and the Multiple Input 50
    • System level analysis of activator/repressor motifs to regulate the transcriptional processMotif (MIM). The below given diagram will show the difference between thethree.In Feed-forward motif, a top-level transcription factor regulates both theintermediate-level TF and the target genes, and the intermediate-level TFregulates the target gene. In Single input motif, a single TF regulates theexpression 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) MIMAll types of motifs in the network combine to form the global structure of thenetwork. Network motifs portray the network in a compact way. They seem to bethe most robust. What make them very special is that they use the least numberof 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 basedon the belief that they follow the same rules independent of their substrate(Breitling, 2010). These small units, probably, act as the control elements in asystem. That make the scientists to consider these control elements for modelingthat is conserved in both the simple and complex systems. Control elements aresmall elements such as binding sites for transcription factors in transcriptionnetwork. We can model the biological control systems by integrating the models ofmany 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 51
    • System level analysis of activator/repressor motifs to regulate the transcriptional processregulatory network and attempting to build a general model for all the possiblemotif designs.3.7. Closing RemarksIn this chapter of my dissertation work, a literature review on the works relatedto the current work is done. Hope this chapter gave you an idea on how theprevious works in the field supports the current work. 52
    • System level analysis of activator/repressor motifs to regulate the transcriptional process 4 HOW IT WAS ACHIEVED 53
    • System level analysis of activator/repressor motifs to regulate the transcriptional process4.1. Opening remarksHere, we shall define the current work and discuss the methodologies adopted inattaining the objectives.In the current work we are looking at the local network structure, the motif. Anetwork motif can be considered as the building block of a network structure.Here we consider the motifs in transcription regulatory network constituted bythe three components, activator, repressor and the protein. The transcriptionfactors- activator and repressor, regulate the production of the protein. Our aim isto create a generic model for all the possible interactions between these threecomponents.This chapter reports the approach for modeling along with the necessarybackground details.4.2. Biological BackgroundThe fundamental fact that underlies the studies in molecular biology is noneother than the Central Dogma of Molecular Biology. According to this centraldogma, the information flow within the cell is unidirectional i.e, from DNA toprotein through the intermediate mRNA. The single stranded mRNA is formedfrom the double stranded DNA through a process known as transcription. Thesequence 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 inthis mRNA is used to synthesize the corresponding protein. Proteins are made upof amino acids that are twenty in number (even though, debates are going onamong the scientists regarding the count). The process of producing protein fromRNA is known as translation.If explained more precisely, the gene regions of the DNA are transcribed into themRNA (messenger RNA) which is one kind of RNA, which in turn travels toprotein production sites and is translated into corresponding sequence of aminoacids that constitute the protein. Thus, protein became the final product of agene. The given figure will give you the idea on the principle of central dogma of 54
    • System level analysis of activator/repressor motifs to regulate the transcriptional processmolecular biology (fig.4.1). The DNA, RNA and the protein are the key players inthe cellular and thereby biological processes.Different cells in our body produce different proteins. In each minute, every cell inthe body synthesizes a variety of proteins. Each of these proteins is essential forthe various physiological properties and biological activities in our body like skincolor, shape of the hair, activating specific cellular processes etc. Fig.4.1: Central Dogma of Molecular BiologyThus, DNA contains the complete genetic information that defines thephysiological and functional properties of the organism.4.3. Gene expression and regulationThe process by which a protein is produced from its corresponding gene throughtranscription and translation is known as gene expression. If a protein isproduced 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, everytime the requirement will not be in equal quantities. This brings the necessity forregulating the gene expression and this regulation occur at various stages duringgene expression. Not only the synthesis of proteins but its degradation shouldalso be regulated. 55
    • System level analysis of activator/repressor motifs to regulate the transcriptional processThe 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 sitefor the control of gene expression. In the current work also, we focuses ontranscriptional regulation.The gene in the DNA contains a regulatory region called promoter preceding theprotein-coding region. The transcription process is initiated by the action of anenzyme called RNA polymerase (RNAp), by binding to the promoter region. Theefficiency in this binding determines the transcription rate, the number ofmRNAs produced per unit time. This efficiency in binding in turn is determinedby the activity of the transcription factors. Promoter DNA Gene Y (a) Protein Y RNA Polymerase mRNA Transcription Gene Y (b) Fig 4.2: Gene transcription regulation [24]Transcription factors are specialized proteins that can regulate the transcriptionprocess. They bind to specific sites in the promoters of the regulated genes andcan 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 theRNAp binds to the promoter region and thereby affect the production of mRNAmolecules which ultimately determines the protein production. The transcriptionfactors can regulate a set of specific genes in this manner, which can in 56
    • System level analysis of activator/repressor motifs to regulate the transcriptional processturn create variations in the protein production i.e. at the level of gene expressionitself. 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 regulatorysites where they bind are called cis-regulatory elements. It was the genetic andbiochemical experiments of 1960s that revealed the presence of regulatorysequences in the proximity of genes and the existence of proteins that are able tobind to those elements and control the activity of genes by either activation orrepression of transcription [25]. These regulatory proteins are themselves encodedby genes.The interaction among the proteins through the enzymatic action or throughbinding, either directly or indirectly, is achieved through this regulation of geneexpression.The transcription factors are of two types - activator and repressor. If thetranscription factor enhances the binding of RNAp to the promoter and therebyincreases the gene expression rate, then it is known as activator. If the geneexpression rate is decreased by the transcription factor by inhibiting the bindingof 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 knownas silencer. The activator has a positive effect on the gene upon which it binds dueto the enhancement of protein production while the repressor has a negativeeffect due to the inhibition of protein production. 57
    • System level analysis of activator/repressor motifs to regulate the transcriptional process Coding DNA Transcription factor binding site Transcription factor Fig. 4.3: Representation of a simple transcription factor network [25]The interesting fact that resides in the regulatory process is that this set oftranscription factors themselves are encoded by another set of genes in the DNAsequence, which is regulated by another set of transcription factor proteins whichin 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 feedbackloops are critical to the cell’s function [26]. The below figure (fig. 4.3) illustrates theinfluence of the protein feedback loops in gene expression. In the figure, Bgene1 isthe regulatory site for the gene that produces the protein A. It is to this Bgene1, theregulatory proteins will attach. Similarly, Bgene2 acts as the regulatory site forgene B, B1gene3, and B2gene3 for the gene C. The figure shows that the proteinsproduced by the genes A and B act as the regulatory proteins for the production ofgene C. The protein C produced by the gene C consecutively regulates theproduction of protein A by binding to the gene A. Similar kind of variouscombinations of interactions are possible which contribute to the non-linearbehavior of the cell and the cellular processes. All such interactions that arisefrom the chain of regulatory factors together form the transcriptional regulatorynetwork (TRN). 58
    • System level analysis of activator/repressor motifs to regulate the transcriptional process feedback Protein C Gene A Protein A Bgene1 Gene B Input Protein B Gene C Bgene2 B1gene3 B2gene3 Fig.4.4: Protein feedback in gene expression4.4. MotivationAs we said above, the transcription factors itself can be proteins produced by yetanother set of genes whose production is regulated by the transcriptional factorsproduced by another set of genes.As we consider activator, repressor and protein as the components of a TRN, theprocess of transcription can be viewed here as the result of the interactionbetween them. Each of these components interacts with each other in variousways. For example, an activator component can activates it own production whereat the same time activating the production of a repressor or the final geneproduct, the protein. Like wise, 16 different interactions are possible for each ofthese components.The interesting fact is that each of these different interactions can give rise todifferent structural motifs for the TRN. Considering, a single component, 16structural motifs can be produced. Thus, 16*3 different structural motifs arepossible for all the three components. (A basic idea on the network motifs wasgiven in the second chapter).For example, let us take the component repressor. 59
    • System level analysis of activator/repressor motifs to regulate the transcriptional processConsider the following figure. R R binding site A binding site Gene 1: produces the repressor A R binding site A binding site Gene 2: produces the activator P R binding site A binding site Gene 3: produces the protein Fig 4.5: R on P and A on RNow, we are considering the motifs in which the protein production is influencedby the repressor alone. So, allowing R to act on P, we are drawing out all theother possible interactions that can take part among these three components. Oneof them is given in the above figure. In the figure, the activator produced isbinding 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 tothe 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 givenbelow; 60
    • System level analysis of activator/repressor motifs to regulate the transcriptional process R R binding site A binding site Gene 1: produces the repressor A R binding site A binding site Gene 2: produces the activator P R binding site A binding site Gene 3: produces the protein Fig. 4.6: R on R and R on A and R on PIn this motif, autoregulation occur as repressor controls itself. Along with it, therepressor represses the activator production also. In the motif given below(Fig.4.7), which has a more complicated design, autoregulation is done by bothrepressor and the activator. Besides, the activator activates repressor productionalso. Like this, sixteen structural motifs can be generated by allowing only R tobind to the gene that produces the protein. 61
    • System level analysis of activator/repressor motifs to regulate the transcriptional process R R binding site A binding site Gene 1: produces the repressor A R binding site A binding site Gene 2: produces the activator P R binding site A binding site Gene 3: produces the protein Fig 4.7: A on A and A on R and R on R and R on PLike this, consider other three examples (Fig.4.5, Fig.4.6, and Fig.4.7) ofstructural motifs in which the protein production is influenced by the activatoralone. R R binding site A binding site Gene 1: produces the repressor A R binding site A binding site Gene 2: produces the activator P R binding site A binding site Gene 3: produces the protein Fig. 4.8: R on A and A on P 62
    • System level analysis of activator/repressor motifs to regulate the transcriptional processIn this motif (fig.4.5), the repressor inhibits the production of the activator thatbinds to the protein-producing gene. In the motif given below (Fig.4.8), activatoris binding to itself and to the repressor while activating protein production. R R binding site A binding site Gene 1: produces the repressor A R binding site A binding site Gene 2: produces the activator P R binding site A binding site Gene 3: produces the protein Fig. 4.9: A on R and A on A and A on P RR binding site A binding site Gene 1: produces the repressor AR binding site A binding site Gene 2: produces the activator PR binding site A binding site Gene 3: produces the protein Fig. 4.10: R on R and R on A and A on A and A on P 63
    • System level analysis of activator/repressor motifs to regulate the transcriptional processIn the last figure (Fig.4.10), the motif defines the binding of R on A andautoregulations of R and A along with activator activating the production ofprotein.Till now, we have discussed some of the motifs formed by either A or R alonebinding to the gene that produces protein. Now we are going to see the examplesof 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 thestructural design of the motifs more complicated.The first example for AR on P given below (fig.4.8) shows that the along with thebinding of A and R on P, A is binding to R also. R R binding site A binding site Gene 1: produces the repressor A R binding site A binding site Gene 2: produces the activator P R binding site A binding site Gene 3: produces the protein Fig .4.11: A on R and A on P and R on PIn the next example (fig.4.9), the interactions other than AR on P are A on R andA on A. In the third example (fig.4.10), both the activator and repressor arebinding to the gene that produces the protein. Autoregulation is also shown by 64
    • System level analysis of activator/repressor motifs to regulate the transcriptional processthe activator activating itself and the repressor represses its own production. Letus see how these motifs’ structures are. R R binding site A binding site Gene 1: produces the repressor A R binding site A binding site Gene 2: produces the activator P R binding site A binding site Gene 3: produces the protein Fig. 4.12: A on A and R on R and A on P and R on P R R binding site A binding site Gene 1: produces the repressor A R binding site A binding site Gene 2: produces the activator P R binding site A binding site Gene 3: produces the protein Fig. 4.13: A on A and A on R and A on P and R on P 65
    • System level analysis of activator/repressor motifs to regulate the transcriptional processLike R on P, it is also possible for each of these A on P and AR on P to havesixteen various structural motifs by varying the interactions among thecomponents. Thus the total number of different structural motifs formed from allthe posible interactions among the three components, activator, repressor andprotein are 16*3 i.e. 48 different structural motifs. As these motifs act as thebuilding blocks of the biological networks, they are also known as the networkmotifs.Let us draw out all the 48 possible structural motifs in the following table. Sl. Repressor alone Activator alone Both Repressor and no binding to protein binding to protein 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 A-P and R-R and R-A RA-P and R-R and R-A and A-A and A-A and A-A 10 R-P and R-R and R-A A-P and R-R and R-A RA-P and R-R and R-A and A-A and A-A and A-A 11 R-P and R-R and A-A A-P and R-R and A-A RA-P and R-R and A-A and R-A and R-A and R-A 66
    • System level analysis of activator/repressor motifs to regulate the transcriptional process 12 R-P and R-R and A-A A-P and R-R and A-A RA-P and R-R and A-A and A-R and A-R and A-R 13 R-P and A-R and R-A A-P and A-R and R-A RA-P and A-R and R-A and A-A and A-A and A-A 14 R-P and A-R and R-A A-P and A-R and R-A RA-P and A-R and R-A and R-R and R-R and R-R 15 R-P and A-A and A-R A-P and A-A and A-R RA-P and A-A and A-R and R-R and R-R and R-R 16 R-P and A-A and A-R A-P and A-A and A-R RA-P and A-A and A-R and R-A and R-A and R-A Tab.4.1: Possible combination of structural motifsIt is these structural motifs, otherwise, these interactions that decide how thecontrol mechanism should works up. So creating a generic model will beadvantageous. This work aims to create the general model for all these forty-eightmotifs, which can be made specific by adjusting the parameter values. A generalintroduction on mathematical modeling was given in the chapter 2. Here, weadopted one approach in mathematical modeling called kinetic modeling.Before going to the modeling process, let us understand about the kineticmodeling approach.4.5. Kinetic ModelingIn the current work for modeling the structural motifs produced by theinteractions between repressor, activator and the protein, we adopted thedifferential equation modeling method included in the deterministic approach ofmathematical modeling. Differential equation modeling can give moredescriptions 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 67
    • System level analysis of activator/repressor motifs to regulate the transcriptional processparticle is assumed to be the average behavior of its kind. So, the system can berepresented by the concentrations of the particles, which in turn can berepresented, and modeled using the differential equations. Thus, differentialequations explain the network dynamics by explicitly modelling the concentrationchanges of molecules over time.In differential equation approach, the interactions are represented as series ofcoupled chemical reactions, with the state of the system represented by theconcentration of the molecules. In Ordinary Differential Equation (ODE)approach, differential equations are generated corresponding to those coupledchemical reactions, thereby characterizes the gene regulatory networks.The macroscopic level of deterministic kinetic modeling describes the dynamicbehavior of the concentrations of the reacting components. When the chemicalreactions are represented by differential equations, the rate of the reaction isdetermined by the concentration change of the reactants and products. Theconcentration change of a reactant or product, say protein, is dependent on itssynthesis and degradation or can be calculated as the difference between them.The problem with the differential equation modeling is that the approach dependsupon numeric parameters, which are difficult to find out experimentally. Thestability of the modeled systems is also a matter of concern. The question iswhether the system’s behaviour depends on the parameter values and initialvalue concentrations or whether it behaves in a similar manner to differentconditions. The probability that an unstable system represents a biological modelexactly is less. And, a stable system will not require all the parameters that weconsidered as essential.4.6. MethodologyHere we have to find out the reactants and products involved and formed duringthe interactions. So we are representing these interactions as chemical reactionsfor deriving differential equations. 68
    • System level analysis of activator/repressor motifs to regulate the transcriptional processRepressor: Kr1f Ka1f Dr + R DrR + A DrRA eqn. (1) Kr1b Ka1b Ka2f Kr2f Dr + A DrA + R DrRA eqn. (2) Ka2b Kr2bActivator: Kr1f Ka1f Da + R Da + A DaRA eqn. (3) Kr1b Ka1b Ka2f Kr2f eqn. (4) Da + A DaA + R DaRA Ka2b f Kr2bProtein: Kr1f Ka1f Dp + R DpR + A DpRA eqn. (5) Kr1b Ka1b Ka2f Kr2f eqn. (6) Dp + A Ka2b DpA + R Kr2b DpRAHere eq. (1) specifies that a repressor protein (R) can bind to the DNA thatcontain 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 whichinturn 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 complexDaRA. Similarly, eq. (4) represents the binding of an activator to the DNA thatproduces the activator protein to produce that DaA complex. A repressor is boundto this DaA to form the DaRA complex.Next is the protein interaction. Here, Dp denotes the DNA that produces theprotein, the final product of DNA. A repressor when bound to the Dp will produceDpR complex and an activator can bind to this complex to produce the DpRAcomplex. This is represented by eq. (5). Eq. (6) represents that to the DNA forprotein, an activator complex can be bound to produce DpA which inturn can bebound by the repressor to produce DpRA complex. 69
    • System level analysis of activator/repressor motifs to regulate the transcriptional processThe double-sided arrow shows the forward and backward reaction. The forwardreaction shows the synthesis process while the backward reaction shows thedissociation process. Kr1f denotes the rate constant at which the repressor bindsin the forward reaction while Kr1b denotes that in the backward reaction. Ka1f andKa1b denote the binding of the activator in the forward reaction and backwardreaction respectively.Now we are going to model all these reactants and products as a system ofordinary differential equations (ODE) that describe their kinetics as a function oftime. The differential equations will show the rate of change of each of thesereactants and products. The rate of change of a specific component is written asthe difference between its synthesis and degradation. eqn. (7)Here, kr1f and ka2f are negative as free Dr is losing there due to the binding of Rand A repectively to it. kr1b and ka2b are positive as both the values show thedegradation rate of DrR and DrA respectively, which gives free Dr. Otherdifferential equations can be drawn out in the same manner. eqn. (8) eqn. (9) eqn. (10) eqn. (11) eqn. (12)These all are the differential equations for the interactions associated withDr.Here, km is the synthesis rate of mRNA for R, k is the synthesis rate for R and 70
    • System level analysis of activator/repressor motifs to regulate the transcriptional processkd is the dissociation rate. Kmr0 is the basal rate at which the repressor isproduced. Kmr0 denotes the small amount of repressor produced even thoughthere is no interaction.Like this, six differential equations can be drawn out for each of the remainingcomponents, activator and protein.Activator: eqn. (13) eqn. (14) eqn. (15) eqn. (16) eqn. (17) eqn. (18)Protein: eqn. (19) eqn. (20) eqn. (21) eqn. (22) eqn. (23) eqn. (24) 71
    • System level analysis of activator/repressor motifs to regulate the transcriptional processThus eighteen equations were derived with six for each component. Modelingthese eighteen equations will generate a super structure, which can be consideredas a generic model.4.7. Modeling using ODE solverAll the eighteen equations were modeled in Matlab using the ODE solver ode15s.ODE solvers are advanced solvers provided by Matlab inorder to solve the initialvalue problems for ordinary differential equations. The solvers available inMatlab are ode45, ode23, ode113, ode15s, ode23s, ode23t or ode23tb. They differin the type of the problem in which they are applied, order of accuracy, situationand the algorithm. A brief explanation of the solvers are given in the belowtable[27]. Solver Problem Order of When to use type accuracy 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 72
    • System level analysis of activator/repressor motifs to regulate the transcriptional process 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 MatlabSince ode45 is slow due to the stiffness of the problem, we used ode15s. ode15s isa variable order solver based on the numerical differentiation formulas (NDFs).Optionally, it uses the backward differentiation formulas (BDFs, also known asGears 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) @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 A data structure which allows the user to set various [], the default settings are options associated with the ode solver used) 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] 73
    • System level analysis of activator/repressor motifs to regulate the transcriptional processThe 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 valuesThe parameter values are summarized in the following table. Parameter Value Kr1f 50 m-1 Kr1b 50 *3 nM 74
    • System level analysis of activator/repressor motifs to regulate the transcriptional process 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 usedThus, the generic model was produced. The code is executed with the help of twofiles. 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 passedand the ODE solver is called. The second file, ‘generalplot2’ contains thedifferential equations, which are executed using the values passed from‘generalplot1’ and the values are collected in the first file. The initial values andthe 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 and7000 respectively.The plots obtained are given in the next chapter. This model can be used foranalysing the existing structures by changing the parameter values. We have toachieve this by giving zero or its specific value to the rate constant if there is nosuch 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 controlsystem with a preprogrammed set of instructions to an effector that has nofeedback or error-detection process. As a result, the prescribed system will not be 75
    • System level analysis of activator/repressor motifs to regulate the transcriptional processable to do any compensation through adjustments. It has been suggested thatopen loop systems control certain movements, which are executed without anyalterations due to sensory feedback. There will not be any interactions betweenthe components in an open loop. In our case, R, A and P will be free in the openloop. So, all the parameters will be zero. The figure is given below. R R binding site A binding site Gene 1: produces the repressor A R binding site A binding site Gene 2: produces the activator P R binding site A binding site Gene 3: produces the protein Fig.4.14: Open loopNow, we can apply the model to all those forty-eight various motifs mentionedearlier.4.8. Steady State AnalysisIn 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 asteady state if there is no change in its stable state, even if external or internalperturbances are applied. Here, steady state is the state in which the productionand degradation rates of the product remain balanced.Here, three specific structural motifs were given for conducting the steady stateand dynamics analysis. This can be considered as a means of validating thegeneric model we created. The motifs are as given below. 76
    • System level analysis of activator/repressor motifs to regulate the transcriptional process RR binding site A binding site Gene 1: produces the repressor AR binding site A binding site Gene 2: produces the activator PR binding site A binding site Gene 3: produces the protein Fig.4.15: motif 1 RR binding site A binding site Gene 1: produces the repressor AR binding site A binding site Gene 2: produces the activator PR binding site A binding site Gene 3: produces the protein Fig.4.16: motif 2 77
    • System level analysis of activator/repressor motifs to regulate the transcriptional process R R binding site A binding site Gene 1: produces the repressor A R binding site A binding site Gene 2: produces the activator P R binding site A binding site Gene 3: produces the protein Fig. 4.17: motif 3The selected motifs are existing ones. They were identified in the microorganismSaccharomyces cerevisiae. They were found in the glucose-repression systems inthe GAL genes in S. cerevisiae, which is mediated by the Mig1p, which is ahomologue of Wilms’ tumour protein and is a global repressor protein dedicated toglucose repression [29]. We have to first model the three structural motifs and thenperform 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 sgiven as 0.15 m-1. Kmr0 is the basal rate for repressor. Even if there is nointeraction, small amount of repressor is produced. Basal rate is the rate at whichthis 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 directlyor indirectly. So when a low value is given for kmr0, the protein production willbe high. As the value is increased, the repressor concentration increases and bothactivator and protein concentration decreases and finally shut off. The kmr0 78
    • System level analysis of activator/repressor motifs to regulate the transcriptional processvalue is varied from 0.00000001 to 50000000. For each of these values, the steadystate values of the three components, repressor (Rss), activator (Ass) and protein(Pss) are collected. All these steady state values are plotted aganist kmr0 to obtainthe 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 equationIn a chemical system, the reaction rate at a time will be a unique function of theconcentrations of all its reactants and products. There are different rate lawscorrespoding to the different types of the reaction mechanisms. Hill equation isone among them. Hill equation explains the degree of cooperativity in the bindingamong molecules. The Hill equation is used here to verify our model.Hill equation was proposed by Archibald Hill in 1910 to describe the binding ofoxygen to haemoglobin. He used it to analyze the binding equilibrium as ligand-receptor interaction. The binding of the transcription factors to the promoterregion of a DNA can also be treated as a ligand-receptor interaction. We havealready seen that the transcription factors influence the transcription ratethrough its binding to the promoter. That is why an evaluation on the bindingrate is essential and Hill function is used for performing this.The Pss values are normalized by dividing each of the P steady state value withthe maximum steady state value to make the scale as 0 - 1. This Pss/Pmax is thenplotted aganist Rss.The Hill equation is, eqn. (25) or eqn. (26) , If,This implies, eqn. (27) 79
    • System level analysis of activator/repressor motifs to regulate the transcriptional processFor each of the motif, the R value at y = 0.1 and y = 0.9 are found out and isapplied in the equation to find out the value of n. Then the R-value at y = 0.5 isfound and is applied in the eqn. (26) and k value is calculated with the n valueobtained from eqn. (25). The K value was equal to the R-value and hence, themodel be regarded as satisfying the Hill equation.4.10. Dynamics AnalysisFor analyzing the dynamics of the system, the kinetic constant, kmr0 is kept at asmall value initially. The y-axis was normalized in the range of 0-1 as before. Thesteady state value for each variable are collected and is then given as the initialcondition with high kmr0 value. This will give the switching off process of theprotein. The time value in the x-axis will give the time taken to achieve theswitching off process. Then using the same initial values, use a different range ofkmr0 values. After that a low kmr0 value was given. Then again it is plotted witha different range of kmr0 values.The time taken to attain 90% of the steady state by each of the three motifs wasfound out and is plotted against its corresponding kmr0 value. This will give thedynamics of the structures, which can be utilized for further analysis.4.11. Bistability AnalysisSome biological systems are said to be bistable. Bistability is the ability of thesystem to transit from one stable state to the other in repsonse of a specific inputsignal. i.e, they will have two stable states. One main example of the bistablesystems is the lac operon in the bacteria Escherichia coli, a group of genes, whichare repressed in the presence of glucose but transcribed in the absence of glucoseand presence of lactose.The general model we created was applied in the analysis of the bistability of thestructural motifs rather than the steady state and dynamics analysis. Bistabilityanalysis checks whether the system has two stable states. The analysis was doneas follows;Initially the stable states of all the parameters of the motif were obtained bygiving very low value for the kinetic constant of repressor.Then these stable state 80
    • System level analysis of activator/repressor motifs to regulate the transcriptional processvalues were given as the initial condition and the value of the kinetic constantwas varied from low value (0.00000001) to high value (50000000). The stablestate value of the repressor and protein at each value of the repressor basal valuewas 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 byputting the kinetic constant of repressor at a high value. These stable states werethen given as the initial condition and then the plots for different basal values ofrepressor were obtained from high to low. Again, we made a steady state plotwith 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 thatparticular motif. If it is different, then the motif has multiple steady states, andso 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 regulatorynetworks. R R binding site A binding site Gene 1: produces the repressor A R binding site A binding site Gene 2: produces the activator P R binding site A binding site Gene 3: produces the protein Fig. 4.18: Motif 1 for bistability analysis 81
    • System level analysis of activator/repressor motifs to regulate the transcriptional process RR binding site A binding site Gene 1: produces the repressor AR binding site A binding site Gene 2: produces the activator PR binding site A binding site Gene 3: produces the protein Fig 4.19: Motif 2 for bistability analysis RR binding site A binding site Gene 1: produces the repressor AR binding site A binding site Gene 2: produces the activator PR binding site A binding site Gene 3: produces the protein Fig.4.20: Motif 3 for bistability analysisBistability is regarded as a minimal requirement for a network to possessmemory, where the state of the network stores information about its past [32].Jeff 82
    • System level analysis of activator/repressor motifs to regulate the transcriptional processHasty et.al said so beacuse a bistable system remains in its stable state even ifthe stimulus is shifted from one state to another.4.12. Closing remarksHere, in this main chapter of my dessertation work, I have explained the way Iproceeded to attain the aim and objectives of my work. The methodologies andapproaches I adopted through out my work are given detailed here withjustifcations. The results obtained by the application of the procedure andmethods discussed here, are given in the next chapter. You are welcome to readand interpret the next chapter, results and discussion. 83
    • System level analysis of activator/repressor motifs to regulate the transcriptional process 5ACHIEVING THE GOALS- RESULTS AND DISCUSSION 84
    • System level analysis of activator/repressor motifs to regulate the transcriptional process5.1. Opening RemarksLife is a dynamic process. Any attempt to capture the secrets behind it is acomplex process. Representation of biological networks had enabled the scientiststo reveal information regarding those life processes. Applying mathematicalmodeling in the molecular biological studies helps to extend our understanding onthe biological systems.The current work to develop a generic model for all the structural motifsconstituted by the activator, repressor and the protein, also followed the path ofmathematical modeling. In this chapter, the various results obtained are givenalong with its explanations. The current work used Matlab for the modelingpurpose.The current work not only achieved its aim of creating the generic model, but alsoapplied this model in three existing motifs for its steady state, dynamics andbistability analysis.5.2. Generic modelThe generic model was developed without changing any parameter values. Eachparameter holds its own specific value. The parameter values were given in theprevious chapter. In order to create the model of a single motif, we requireeighteen 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. 85
    • System level analysis of activator/repressor motifs to regulate the transcriptional process [A] 12000 10000 8000Concentration of A 6000 4000 2000 0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Time, t Fig.5.1: Activator concentration vs. time [P] 12000 10000 8000Concentration of P 6000 4000 2000 0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Time, t Fig.5.2: Protein concentration vs. time 86
    • System level analysis of activator/repressor motifs to regulate the transcriptional process [R] 12000 10000 8000 Concentration of R 6000 4000 2000 0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Time, t Fig.5.3: Repressor concentration vs. timeThese plots (Fig.5.1, Fig.5.2, and Fig.5.3) can be considered as the standardmodels of the components. However, by varying the parameters, in accordancewith the interaction between the transcriptional regulatory network components(activator, repressor, and protein) in each motif, we will be able to analyze themand reach on conclusions.First, we selected an open loop for applying our model. As mentioned earlier, anopen loop represents a motif that does not have any interconnections among thecomponents. Even though no impulse signal is received that is expected to acquirethrough the interaction, small amount of proteins will be produced. In our model,we represent the production rate of that quantity of proteins or transcriptionfactors (activator and repressor) using kinetic constant that is denoted by kmp0,kma0, and kmr0 respectively, which are called as basal values. 87
    • System level analysis of activator/repressor motifs to regulate the transcriptional processFor 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 theproduction rate of other components. [A]in an open loop 55 50 45 Concentration of A 40 35 30 25 20 15 0 2 4 6 8 10 12 14 16 18 20 Time, t Fig.5.4: Activator concentration in open loop 88
    • System level analysis of activator/repressor motifs to regulate the transcriptional process [P] in an open loop 60 50 40Concentration of P 30 20 10 0 0 2 4 6 8 10 12 14 16 18 20 Time, t Fig.5.5: Protein concentration in open loop [R]in an open loop 60 50 40 Concentration of R 30 20 10 0 0 2 4 6 8 10 12 14 16 18 20 Time, t Fig.5.6: Repressor concentration in open loop 89
    • System level analysis of activator/repressor motifs to regulate the transcriptional process5.3. Steady state and dynamics analysis of existing motifsAs told earlier, our model can be used for studying biological networks. Wedeveloped the general model with an intention to make such studies usingnetwork motifs easier. Motifs, the basic building blocks of a network will enableus to understand the structural design of that particular network. In the currentwork, we have developed a general model and applied it in three existing motifsfor the steady state and dynamics analysis. They were selected as a means ofvalidating 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 proteinand is a global repressor protein dedicated for glucose repression. We have to firstmodel the three structural motifs and then perform its steady state and dynamicsanalysis. Applying our general model to these existing motifs will help us tovalidate our model. The structural design of the model was given in the previouschapter.These three motifs were selected, as they exist in nature.Given below are the models of the protein, activator and repressor for each of themotifs. 90
    • System level analysis of activator/repressor motifs to regulate the transcriptional processMOTIF 1: -16 Repressor x 10 3 2.5 2 Concentration of R 1.5 1 0.5 0 -0.5 0 1000 2000 3000 4000 5000 6000 7000 Time Fig.5.7: Repressor concentrationIn the first motif, the repressor is binding to the promoter region of the gene thatproduces the activator and the activator in turn binds to the promoter region ofthe 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 isindependent. In such a case, the repressor production depends upon the basalvalue given. Since that basal value is zero, the repressor production is finallyshutting down to zero. Since the concentration of the repressor binding to theactivator gene is less, the activator production is not at all inhibited. In that caseit is based upon the basal rate given for activator, which is 1.5. The activatorconcentration is 5400 nM. As this activator binds to the promoter region of thegene that produces the protein, the protein production is being activated. Thebasal rate will be zero for protein as protein production is activated by theactivator. The production of protein will be high in this case. 91
    • System level analysis of activator/repressor motifs to regulate the transcriptional process Activator 6000 5000 4000Concentration of A 3000 2000 1000 0 0 1000 2000 3000 4000 5000 6000 7000 Time Fig.5.8: Activator concentration 4 x 10 Protein 6 5 4 Concentration of P 3 2 1 0 0 1000 2000 3000 4000 5000 6000 7000 Time Fig.5.9: Protein concentration 92
    • System level analysis of activator/repressor motifs to regulate the transcriptional processThe two remaining motif models also behaved in the similar manner when sameinput were given. In the second motif, the only interaction is the binding of theactivator and the repressor to the protein. In motif 2, we have attempted twoways, 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 whichin turn decreases the protein production which will eventually shuts down.MOTIF 2:With low basal value: -16 Repressor x 10 16 14 12 10 Concentration of R 8 6 4 2 0 -2 0 1000 2000 3000 4000 5000 6000 7000 Time Fig.5.10: Repressor concentration with low basal value for repressor 93
    • System level analysis of activator/repressor motifs to regulate the transcriptional process 5 Activator x 10 6 5 4Concentration of A 3 2 1 0 0 1000 2000 3000 4000 5000 6000 7000 Time Fig.5.11: Activator concentration with low basal value for repressor 6 x 10 Protein 6 5 4Concentration of P 3 2 1 0 0 1000 2000 3000 4000 5000 6000 7000 Time Fig.5.12: Protein concentration with low basal value for repressor. 94
    • System level analysis of activator/repressor motifs to regulate the transcriptional processWith high basal value for repressor: 12 x 10 Repressor 2 1.8 1.6 1.4 Concentration of R 1.2 1 0.8 0.6 0.4 0.2 0 0 1000 2000 3000 4000 5000 6000 7000 Time Fig.5.13: Activator concentration with high basal value for repressor Activator 600 500 400 Concentration of A 300 200 100 0 0 1000 2000 3000 4000 5000 6000 7000 Time Fig.5.14: Activator concentration with high basal value for repressor 95
    • System level analysis of activator/repressor motifs to regulate the transcriptional process -3 x 10 Protein 6 5 4 Concentration of P 3 2 1 0 0 1000 2000 3000 4000 5000 6000 7000 Time Fig.5.15: Protein concentration with high basal value for repressorMOTIF 3: 4 Activator x 10 6 5 4 Concentration of A 3 2 1 0 0 1000 2000 3000 4000 5000 6000 7000 Time Fig.5.16: Activator concentration 96
    • System level analysis of activator/repressor motifs to regulate the transcriptional process -14 Repressor x 10 3 2.5 2Concentration of R 1.5 1 0.5 0 -0.5 0 1000 2000 3000 4000 5000 6000 7000 Time Fig.5.17: Repressor concentration 6 Protein x 10 6 5 4 Concentration of P 3 2 1 0 0 1000 2000 3000 4000 5000 6000 7000 Time Fig.5.18.Protein concentration 97
    • System level analysis of activator/repressor motifs to regulate the transcriptional processIn the network motif 3, in addition to the binding of the repressor and activator toprotein, the repressor is also binding to activator. When the basal value of therepressor is kept very low, it resulted in the shutting down of repressorproduction and the increasing of protein production.5.3.1. Steady state analysis resultsThe steady state analysis conducts a study on the steady state concentration ofthe components. For different basal values of the repressor, the components tookdifferent concentrations and different time limit for reaching the steady state.The steady state analysis graphs given below plots the steady state values of theactivator and protein aganist the corresponding basal values. The plot shows thatas the kmr0 values increases the concentration taken to attain a steady state isalso being increasedMOTIF1: 7 x 10 6 Activator Protein 5 4 steadystate values 3 2 1 0 -10 -5 0 5 10 10 10 10 Kmr0 Fig.5.19: Repressor basal value vs steady state values of activator and protein for motif 1 98
    • System level analysis of activator/repressor motifs to regulate the transcriptional processMOTIF 2: 7 x 10 6 Activator Protein 5 4 steadystate values 3 2 1 0 -6 -4 -2 0 2 4 10 10 10 10 10 10 Kmr0Fig.5.20: Repressor basal value vs steady state values of activator and protein for motif 2MOTIF 3: 8 x 10 2 Activator 1.8 Protein 1.6 1.4 steadystate values 1.2 1 0.8 0.6 0.4 0.2 0 -10 -5 0 5 10 10 10 10 Kmr0Fig.5.21: Repressor basal value vs steady state values of activator and protein for motif 3 99
    • System level analysis of activator/repressor motifs to regulate the transcriptional process5.3.1.1. Verification using Hill equationHill function is a rate law that describes the binding activity of the transcriptionfactors to the gene in the DNA. Here we are checking whether our model obeysthe Hill equation. Since the value of the Hill coefficient, k obtained is equal to theconcentration of the repressor value, we can say that the model satisfies the Hillequation.The Hill equation is, , where ‘n’ is known as the Hill coefficient. eqn. 28Or, eqn. 29This implies, eqn. 30Motif 1:At y = 0.9, R = 102.5131 = 325.9117At y = 0.1, R= 104.4442 = 27810At y = 0.5, R = 103.47562 = 2989.6Put these values in eqn. (29): 100
    • System level analysis of activator/repressor motifs to regulate the transcriptional process 0.5k + 1494.8 = kMotif 2:At y = 0.1, R = 104.4509 = 28242At y = 0.9, R= 102.5106 = 324.0410At y = 0.5, R = 103.476 = 2992.3Put these values in eqn. (29): 0.5k + 1496.2 = kMotif 3:At y = 0.1, R = 107.37271 = 23589000At y = 0.9, R= 105.29059 = 195250At y = 0.5, R = 106.22 = 1659600 101
    • System level analysis of activator/repressor motifs to regulate the transcriptional processPut these values in eqn. (29): 0.5k + 829800 = k5.3.2. Dynamics analysisThe dynamics analysis is done by plotting the time taken to attain 90% of thesteady state by each protein component in each of the motif against itscorresponding kmr0 values. This will give the dynamics of the protein. structure 1-protein dynamics 100 90 80 70 time 60 50 40 30 20 -10 -5 0 5 10 10 10 10 10 10 kmr0 Fig.5.22: Basal value vs time for motif1 102
    • System level analysis of activator/repressor motifs to regulate the transcriptional process structure 2-protein dynamics 60 55 50 45 time 40 35 30 25 -10 -5 0 5 10 10 10 10 10 10 kmr0 Fig.5.23: Basal value vs time for motif 2 structure 3-protein dynamics 110 100 90 80 70time 60 50 40 30 20 -10 -5 0 5 10 10 10 10 10 10 kmr0 Fig.5.24: Basal value vs time for motif 3 103
    • System level analysis of activator/repressor motifs to regulate the transcriptional process5.4. Bistability AnalysisBistability analysis checks whether the system under study can be stable in twodistinct states. Three motifs given in the previous chapter were used forbistability analysis.The results are shown as below;In the first motif (Fig.5.25, Fig.5.26), the repressor component is not showing anybistability. But the protein is exhibiting bistability. In the second structuralmotif, both the repressor and protein components are showing bistable property.In the third motif given, the protein is exhibiting bistability, but not therepressor.Motif 1: Structure1:steady state Vs kmr0 1 0.9 Repressor at initial low k value 0.8 Repressor at high k value 0.7 steady state values 0.6 0.5 0.4 0.3 0.2 0.1 0 -6 -4 -2 0 2 4 6 10 10 10 10 10 10 10 kmr0 Fig.5.25: Repressor steady states for motif 1 104
    • System level analysis of activator/repressor motifs to regulate the transcriptional process Structre1:steady state Vs kmr0 1 Protein at initial low k value 0.9 Protein at high k value 0.8 0.7 steady state values 0.6 0.5 0.4 0.3 0.2 0.1 0 -6 -4 -2 0 2 4 6 10 10 10 10 10 10 10 kmr0 Fig.5.26: Protein steady states for motif 1Motif 2: Structure2:steady state Vs kmr0 1 0.95 Repressor at initial low k value 0.9 Repressor at initial high k value 0.85 steady state values 0.8 0.75 0.7 0.65 0.6 0.55 0.5 -6 -4 -2 0 2 4 6 10 10 10 10 10 10 10 kmr0 Fig.5.27: Repressor steady states for motif 2 105
    • System level analysis of activator/repressor motifs to regulate the transcriptional process Structure2:steady state Vs kmr0 1 0.9 Protein at high k value 0.8 Protein at initial low k value 0.7 steady state values 0.6 0.5 0.4 0.3 0.2 0.1 0 -6 -4 -2 0 2 4 6 10 10 10 10 10 10 10 kmr0 Fig.5.28: Protein steady states for motif 2Motif 3: Structure3:steady state Vs kmr0 1.0005 Protein at initial low k value Protein at initial high value 1 0.9995 0.999 steady state values 0.9985 0.998 0.9975 0.997 0.9965 0.996 -6 -4 -2 0 2 4 6 10 10 10 10 10 10 10 kmr0 Fig.5.29: Protein steady states for motif 3 106
    • System level analysis of activator/repressor motifs to regulate the transcriptional process Structure3:steady state Vs kmr0 1 0.9 Repressor at initial low k value 0.8 Repressor at initial high k value 0.7 steady state values 0.6 0.5 0.4 0.3 0.2 0.1 0 -6 -4 -2 0 2 4 6 10 10 10 10 10 10 10 kmr0 Fig.5.30: Repressor steady states for motif 3The common feature of a bistable system is the existence of the strong positivefeedback loops. This is considered as one of the main reasons for its bistability. Inour 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 thesecond structure, there is a hybrid control on the protein production. Here boththe negative and positive regulation can be the reasons for the bistabilityexhibited by the motif. In the third structure, P is showing bistability, as there isa positive regulation upon it. But R is not showing any bistability due to thenegative feedback.5.5. Closing remarksIn this chapter the result and analysis of the work is given. The plots given by thegeneric model is given along with the results of steady state and dynamics 107
    • System level analysis of activator/repressor motifs to regulate the transcriptional processanalysis, and the bistability analysis. The analysis of these results will help us todevelop understanding on the specific design of the given structure. 108
    • System level analysis of activator/repressor motifs to regulate the transcriptional process 6 CONCLUDING REMARKS 109
    • System level analysis of activator/repressor motifs to regulate the transcriptional process6.1. Opening remarksThis was an attempt to familiarize with the effort of the queen of sciences inrevealing the mysteries of life. There is no need of wondering about this intrusionin the current scientific era. Now a days, biological studies cannot proceedwithout the help of computers that play with numbers and calculations which inturn underscores the significant role played by mathematics in such studies. Therecent understanding that most of the biological processes follow mathematicalprinciples has been upheld by the scientific world. No wonder that SystemsBiology, that merges the mathematical principles and computational approachesin the biological studies for throwing light into the mysteries of life, has rapidlygrown up. The scientific world is now eagerly waiting for the results coming outfrom the systems biology laboratories.It is through mathematical modeling that Systems Biology approaches biologicalproblems. The significance of the mathematical models relies in the fact that theycan give quantitative information of the biological systems under consideration. Itis an effective tool to capture the nature of the biological systems those behavedifferently in different environments, conditions, time etc. This is possiblebecause the models created using mathematical techniques, offered by systemsbiology can be used to simulate the biological process in silico. They can alsobehave differently according to the difference in the input we give.The fundamental principle of systems biology is to view the particular entity ofinterest as a system, not as component by component. Systems biology believesthat the behavior of the system is a sum up of all the interactions between itscomponents and not by any single component itself. This gave rise to theemergence of the concept of biological networks. A biological network isconstituted by nodes and edges that represent the components and interactionsrespectively. Systems biology approaches attempts to model these networks or thesubnetworks 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 ourwork, we used transcriptional regulatory network which is a dominant biological 110
    • System level analysis of activator/repressor motifs to regulate the transcriptional processregulatory network, as our system of interest. This network was chosen, as it isthe most studied one. The work intended to create a general model all the motifsconstituted by the activator, repressor and protein components in atranscriptional regulatory network.6.2. A quick reviewWe have already read about how the transcription factors regulate the geneexpression through directing the protein production. Transcription occurswith the help of the transcription factors- activator (activates protein production)and repressor (inhibits protein production) - through their binding to thepromoter region of the specific gene. The transcription factors bound to the genethat produces the protein, which is expected to perform a specific physiologicalfunction, forms a network motif. This is the system that we are considering in thepresent work. Of course, a system must have components and here the activator,repressor and the protein perform that role. The binding of the transcriptionfactors to the gene can be regarded as the interaction among them as it deliverssome signals to the gene to regulate protein production. The transcription factorsbind 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 indifferent rate of transcription or different network motifs that differ in theirstructural design, ultimately resulting in different rate of protein production.This difference in the binding will depend on the internal or external stimulusinduced by the environment. Our aim in this work is to identify all the possiblecombinations formed between the activator, repressor and protein i.e. all thepossible structural motifs that can be formed which will affect the proteinproduction 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 thetranscriptional regulatory network, it will make further studies easier. When thisgeneral model is applied in a specific motif, there will be change in its parametervalues according to the interactions in that specific motif. The general modelcreated takes into account every possible interaction, and so each parameter hasits own specific values. When we are using this model to study a specific motif, we 111
    • System level analysis of activator/repressor motifs to regulate the transcriptional processhave to look at whichever interactions are present and keep the correspondingparameters values as it is. The rest will have to be changed to zero. This willgenerate the model of that specific motif.If such a model of a particular biological system is available in front of us, theadvantage is that we can derive more information about that particular system..As a validation process, we have applied our model in three existing motifs andconducted their steady state and dynamics analysis and in three other for thebistability analysis.6.3. Hopefully...Now mathematics and computers had offered their aid to human intellect in itsattempt to reveal the secrets of life. The practice of doing experiments in theliving organisms has several ethical, social and economic issues. All thoseproblems can be resolved to a certain extent by the entry of computers andmathematics into the field. The increasing demand for the field of systems biologyshows that it had passed its childhood. But yet to be emerged with manypossibilities and advancements. 112
    • System level analysis of activator/repressor motifs to regulate the transcriptional process 7 THROUGH THE LENS... 113
    • System level analysis of activator/repressor motifs to regulate the transcriptional process7.1. Opening RemarksHere, in this final chapter of the three months effort, I am making a crtitical viewupon the work. Even though, the work presents what expected from it, it failed tohandle some issues. In this chapter, such failures of the current work, along withthe discussions on whatever advancements can make it better, and also whereverthis can be applied etc are made.7.2. DiscussionWe have seen that gene expression is the production of protein from a genethrough the process of transcription and translation. But, this gene expressionalone cannot explain everything about protein production. Protein productiondepends on various other intra cellular and intercellular processes. Cells requireexternal 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 takeplace, specific signals are required which will be the output generated from someother processes. Like this, there is a chain of numerous processes and sub-processes behind the selection of one specific transcription factor to bind to thepromoter region. This shows that it is not from the transcription factor bindingthat the transcriptional regulation initiates. Considering all these together willmake the task much complicated and demands more time and effort. Here wehave considered the transcriptional regulation starting from the binding of thetranscription 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, posttranscriptional regulation, post translational regulation, RNA transportregulation also contribute to the gene expression regulation.For any modeling work of biological systems, the major issue is the parameterestimation. Many times, the parameters were fixed by the trial and error method,even though it adopted the literature data. 114
    • System level analysis of activator/repressor motifs to regulate the transcriptional processThe truth behind any kind of modeling is that the model will describe only someproperties of the real system. Also there is a possibility that the revealedproperties may not be much relevant for the purpose of study. Some otherproperties that may be relevant may remain unrevealed.Also, the purpose of modeling is to provide a simple, abstract representation ofthe system under study. Biological systems are already notorious for theircomplexity. So we must take utmost care to make the model as simple as possibleat the same time maintaining the complex properties of the system as it is, whichis a tricky task.The engineering works follow the principles of robustness and modularity. Thesame principles have been identified in the biological systems also. This is one ofthe reasons for applying engineering methodologies in studying biologicalsystems. But many examples showed that natures designs are much differentand diverse from those used in engineering. This creates a question on thereliability of the mathematical models of biological systems generated by applyingthe engineering principles.7.3. Future prospectsThe work can be used for analyzing the objectives behind a specific structuraldesign of a particular network motif. Each structure- in cellular level, tissue levelor organ level- will have a purpose for existence. Here, by considering the modelsof structural motifs, we had lighted a path towards such studies. We can analyzethe model to find out how these structures helps in generating a phenotypicalresponse. But for that, we have to relate it to an organism. This will help to findout whether a specific feature in its structural design is essential for the survivalof the organism. The work can inturn be applied in the generation of syntheticnetworks also. If we understand the phenotypical benefit behind each specificdesign, then we can apply it to generate a system with the preferred phenotypicalbenefit.As each coin has two sides, the present work also has its own benefits andfailures. Considering this as only a template, in future I hope, we can add to its 115
    • System level analysis of activator/repressor motifs to regulate the transcriptional processpositives and correct the defects to make it a perfect one. Thereby I envision tomake humble contributions in the journey of mathematical modeling and systemsbiology in revealing the secrets of life. 116
    • System level analysis of activator/repressor motifs to regulate the transcriptional process 8 REFERENCES 117
    • System level analysis of activator/repressor motifs to regulate the transcriptional process1. Ouzounis, C. A., & Valencia, A. (2003). Early bioinformatics: the birth of a discipline—a personal view. Bioinformatics , 2176-2190.2. http://www.ircc.iitb.ac.in/webnew/R&DSpectrum/computational-biology.html3. http://en.wikipedia.org/wiki/Computational_genomics4. http://en.wikipedia.org/wiki/Metabolomics5. http://en.wikipedia.org/wiki/Proteomics6. http://en.wikipedia.org/wiki/Cytomics7. http://en.wikipedia.org/wiki/Epigenomics8. http://en.wikipedia.org/wiki/Interactomics9. Sontag, E. D. (2005). Molecular Systems Biology and Control. European Journal of Control ,1-40.10. Trewavas, A. (2006). A Brief History of Systems Biology. The Plant Cell , 18, 2420–2430.11. http://www.sysbio.de/info/background/WhatIs.shtml12. http://i-love-math.blogspot.com/2011/06/mathematical-modelling.htm;13. http://www.mathworks.com/help/techdoc/learn_matlab/f0-14059.html14. Babu, M. (2008). Evolutionary and temporal dynamics of transcriptional regulatory networks. Biowire 2007 (pp. 162-171). Springer.15. http://www.news-medical.net/health/What-is-Gene-Expression.aspx16. http://wwwsop.inria.fr/comore/arcgdyn/28fev/arc03-intro.pdf17. http://en.wikipedia.org/wiki/File:Gene_Regulatory_Network_2.jpg18. Kulasiri, D., Nguyen, L. K., Samarasinghe, S., & Xie, Z. (2008). A review of systems biology perspective on genetic regulatory networks with examples. Current Bioinformatics , 3, 197-225. 118
    • System level analysis of activator/repressor motifs to regulate the transcriptional process19. Herrgard, M. J., Covert, M. W., & Palsson, B. Ø. (2004). Reconstruction of microbial transcriptional regulatory networks. Current Opinion in Biotechnology , 15, 70-77.20. Babu, M. M., Luscombe, N. M., Aravind, L., Gerstein, M., & Teichmann, S. A. (2004). Structure and evolution of transcriptional regulatory networks. Current Opinion in Structural Biology , 14 (3), 283-291 .21. Alon, U. (2007). Network motifs: theory and experimental approaches. Nature , 8, 450-461.22. S.Roy, T.Lane, M.Werner--‐Washburne (2007).A Simulation Framework For Modeling Combinatorial Control in Transcription Regulatory Networks, UNM Computer Science Technical Report, TR-CS-2007-0623. Kell, D.B. and Knowles, J.D. (2006). The role of modeling in systems biology. In System Modeling in Cellular Biology: From Concepts to Nuts and Bolts, pp. 3–18, MIT Press24. Alon, U. (2007). Introduction to Systems Biology: Design Principles to Biological Circuits. Chapman and Hall/CRC.25. Brazma, T. S. (2007). Current approaches to gene regulatory network modelling. BMC Bioinformactics , 8 (6).26. Prill, R. J., Iglesias, P. A., & Levchenko, A. (2005). Dynamic Properties of Network Motifs Contribute to Biological Network Organization. PLoS Biology , 3 (11), 1881-1892.27. Shampine, L. F., & Reichelt, M. W. (1997). SIAM journal on scientific computing: a publication of the Society for Industrial and Applied Mathematics , 18 (1), 1-8.28. http://laser.cheng.cam.ac.uk/wiki/images/e/e5/NumMeth_Handout_7.pdf29. Verma, M., Bhat, P. J., & Venkatesh, K. V. (2005). Steady-state analysis of glucose repression reveals hierarchical expression of proteins under Mig1p control in Saccharomyces cerevisiae. Biochemical Journal , 843–849. 119
    • System level analysis of activator/repressor motifs to regulate the transcriptional process30. Adam P. Arkin and David V. Schaffer. (2011) Network News: Innovations in 21st Century Systems Biology. Cell, Volume 144, Issue 6, 844-84931. Hasty, J., McMillen, D., & Collins, J. (2002). Engineered gene circuits. Nature , 224-230.32. Barabasi, A.L., Oltvai, Z.N. (2004) Network biology: understanding the cell’s functional organization. Nature Revew Genetics. 5(2), 101-113.33. S., K. (2004). A proposal for using the ensemble approach to understanding genetic regulatory networks. Journal of Theoretical Biology , 581-580.34. Nair, A. S. (2007). Computational Biology & Bioinformatics: A Gentle Overview. Communications of the Computer Society of India , 30, 7-12.35. Hippel, P. H. (2004). Completing the View of Transcriptional Regulation. Science , 305, 350-352.36. de-Leon, S. B.-T., & Davidson, E. H. (2009). Modeling the dynamics of transcriptional gene regulatory networks for animal development. Developmental Biology , 317-328.37. Shampine, L. F. and M. W. Reichelt, 1997, The MATLAB ODE Suite, SIAM Journal on Scientific Computing, Vol. 18, 1997, pp 1-22.38. Beers, K. J. (2007). Numerical Methods for Chemical Engineering: Applications in MATLAB. New York: Cambridge University Press.39. http://www.systemsbiology.org/Intro_to_Systems_Biology40. http://blog-msb.embo.org/blog/2007/07/what_is_systems_biology_3.html41. Breitling, R. (2010). What is systems biology? Frontiers in Physiology , 1, 1-9.42. Shen-Orr, S. S., Milo, R., Mangan, S., & Alon, U. (2002). Network Motifs in the transcriptional regulation network of Escherichia coli. Nature Genetics , 31, 64-68.43. Srinivasan, N. (2006). Computational Biology and Bioinformatics: A tinge of Indian spice. Bioinformation , 1 (3), 105-109.44. http://www.bicpu.edu.in/seminar/05/pdf/st.pdf 120
    • System level analysis of activator/repressor motifs to regulate the transcriptional process45. The Times of India (June 14, 2011). Buckle up, Indians and Chinese are coming: Obama to Americans.46. http://sites.google.com/site/umeshsynbio/the-team.47. Alon, U. (2003). Biological Networks: The tinkerer as an engineer. Science , 301, 1866-1867. 121
    • System level analysis of activator/repressor motifs to regulate the transcriptional process 9 APPENDIX 122
    • System level analysis of activator/repressor motifs to regulate the transcriptional process9.1. Sample CodeThe code for producing the general model that represents all the possiblecombination of interactions between the activator, repressor and protein is givenbelow. The main program, generalplot passes the initial values to the subprogramand calls the ode solver, ode15s, receives the output values and displays the plotscorrespondingly.clear allclct0=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); 123
    • System level analysis of activator/repressor motifs to regulate the transcriptional processMa=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); 124
    • System level analysis of activator/repressor motifs to regulate the transcriptional processylabel(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) 125
    • System level analysis of activator/repressor motifs to regulate the transcriptional processxlabel(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) 126
    • System level analysis of activator/repressor motifs to regulate the transcriptional processxlabel(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) 127
    • System level analysis of activator/repressor motifs to regulate the transcriptional process 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 thedifferential equations. The code for this function is as below.function deriv = generalplot2(t,x) 128
    • System level analysis of activator/repressor motifs to regulate the transcriptional process 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 129
    • System level analysis of activator/repressor motifs to regulate the transcriptional process 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 130
    • System level analysis of activator/repressor motifs to regulate the transcriptional process9.2. Glossary of TermsDNA : Deoxyribonucleic AcidMatlab : Matrix LaboratorymRNA : Messenger RNAODE : Ordinary Differential EquationRNA : Ribonucleic AcidRNAp : RNA polymeraseTRN : Transcriptional Regulatory NetworkTF : Transcription Factor 131