DELAYED STOCHASTIC MODELLING OF PROKARYOTIC TRANSCRIPTION WITH ABORTIVE ...

86 Pages·2017·3.18 MB·English

DELAYEDSTOCHASTICMODELLINGOFPROKARYOTICTRANSCRIPTION
WITHABORTIVEINITIATION
SILKYSHARMA
BachelorofTechnology,UttarPradeshTechnicalUniversity,India,2013
AThesis
SubmittedtotheSchoolofGraduateStudies
oftheUniversityofLethbridge
inPartialFulfillmentofthe
RequirementsfortheDegree
MASTEROFSCIENCE
DepartmentofChemistryandBiochemistry
UniversityofLethbridge
LETHBRIDGE,ALBERTA,CANADA
(cid:13)c SilkySharma,2017
DELAYEDSTOCHASTICMODELLINGOFPROKARYOTICTRANSCRIPTION
WITHABORTIVEINITIATION
SILKYSHARMA
DateofDefense: January20,2017
Dr. MarcR.Roussel
Supervisor Professor Ph.D.
Dr. RobertLaird
CommitteeMember AssociateProfessor Ph.D.
Dr. StaceyWetmore
CommitteeMember Professor Ph.D.
Dr. DennisSalahub
Externalexaminer Professor Ph.D.
Dr. NehalThakor
ExaminationCommitteeChair AssistantProfessor Ph.D.
Dedication
Tomyparents,
Mr. andMrs. Sharma,
andmybelovedbrotherSahil,
whosehard-work,love,encouragementandprayersbydayandnightmakemeabletoget
suchsuccessandhonour.
Alongwithmysupervisor,Dr. MarcR.Roussel,
whoalwayspickedmeupontimeandhasbeenaconstantsourceofknowledgeand
inspirationforme.
iii
Abstract
A quantitative model for gene transcription should treat two main features: stochastic fluc-
tuations due to low copy numbers, and time delays resulting from the lengthy sequence of
reactions that form the transcription process. Bratsun et al. (PNAS, 102(41):14593-14598,
2005) proposed an algorithm by which we can include both of these features. I have stud-
iedadelaystochasticmodelforRNAtranscriptionincludingabortiveinitiation. Thisstudy
focused on the parametric dependence of the mean stationary RNA concentration and of
therisetime,i.e.thecharacteristictimetakentoachievethestationaryconcentrations. The
mean RNA concentration depends on initiation, elongation, polymerase arrest and RNA
degradation rates including delays associated with clearance of promoter and polymerase
arrest. Rise time depends on initiation, polymerase arrest, termination and RNA degrada-
tionrates. Ihavedevelopedananalytictheoryofrisetimebasedonthedelayedmass-action
formalismtovalidatethesimulationresults.
iv
Acknowledgments
This journey has been so special to me because of a few special people who helped me to
get through this adventure. My deep gratitude goes to my supervisor Dr. Marc R. Rous-
sel, thank you. He gave me this wonderful opportunity to pursue my Master’s under his
supervision. Thisthesiswouldnothavebeenpossiblewithouthisguidanceandsupport.
I also wish to thank my other committee members at the University of Lethbridge, Dr.
RobertLairdandDr. StaceyWetmore,fortheirsubstantialfeedbackandguidance.
Last but not the least, I would like to thank all the members of the Roussel lab for helping
meeverytimeIneededandmakingthisperiodunforgettable.
v
Contents
Contents vi
ListofTables viii
ListofFigures ix
1 Introduction 1
1.1 Transcription . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Stagesoftranscription . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 StallingofRNApolymerase . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 ReasonsforRNApolymerasestalling . . . . . . . . . . . . . . . . 5
1.3 RNAdegradation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Stochasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4.1 Stochasticsimulation . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4.2 Pipemodelfortranscription . . . . . . . . . . . . . . . . . . . . . 8
1.4.3 Delaystochasticsimulationmethod . . . . . . . . . . . . . . . . . 9
1.5 Planofthethesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 Modeldescription 13
2.1 Detailedtranscriptionmodel . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 SimpleRNAexpressionmodel . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.1 Initiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.2 Elongation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.3 Termination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.4 RNAdegradation . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.5 ParameterEstimates . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Modeloftranscriptionwithabortiveinitiation . . . . . . . . . . . . . . . . 21
2.3.1 Parameterestimates . . . . . . . . . . . . . . . . . . . . . . . . . 23
3 Stochasticsimulation 25
3.1 SimpleRNAexpressionmodel . . . . . . . . . . . . . . . . . . . . . . . . 26
3.1.1 AnalysisofthesimpleRNAexpressionmodel . . . . . . . . . . . 26
3.1.2 DependenceofRNAlevelsandrisetimeonkineticparameters . . . 27
3.2 Delaystochasticsimulationmodelwitharrest . . . . . . . . . . . . . . . . 38
3.2.1 Analysisofdelaystochasticsimulationmodelwitharrest . . . . . . 38
3.2.2 DependenceofRNAlevelsandrisetimeonkineticparameters . . . 41
3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
vi
CONTENTS
4 Mathematicalanalysis 48
4.1 AnalytictheoryofmeanstationaryRNAnumber . . . . . . . . . . . . . . 49
4.2 Analytictheoryofrisetime . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.2.1 Atsmallvaluesofk . . . . . . . . . . . . . . . . . . . . . . . . . 54
8
4.2.2 Atsmallvaluesofk . . . . . . . . . . . . . . . . . . . . . . . . . 59
6
5 Conclusions 62
5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.3 Futureperspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
Bibliography 66
Appendices 71
A 71
vii
List of Tables
2.1 Defaultkineticparametersusedinthemodel . . . . . . . . . . . . . . . . . 20
2.2 Initialconditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 Defaultkineticparametersusedinmodelwithabortiveinitiation . . . . . . 24
3.1 Tablesshowingthevaluesofk andk usedtogeneratefigure3.17 . . . 40
2 arrest
3.2 Table showing the value of arrest probability corresponding to the value of
k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
arrest
viii
List of Figures
1.1 SchematicdiagramshowingthefatesoftranscribingRNApolymerasedur-
ingatranscriptionprocess . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Pipemodelofthetranscriptionprocess . . . . . . . . . . . . . . . . . . . . 9
1.3 AlgorithmforthedelaystochasticsimulationalgorithmasgivenbyRoussel
andZhu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4 SchematicdiagramofRNApolymerasearrestinthemodel . . . . . . . . . 11
2.1 Initiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Elongation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Termination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4 Schematic diagram of RNA polymerase arrest in the model showing the
definitionsofτ andτ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2 as
3.1 Curves showing the number of RNA molecules produced with respect to
timeinasinglesimulationofthesimpleRNAexpressionmodel . . . . . . 27
3.2 R versuslog k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
ss 10 x
3.3 Risetimeversuslog k . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
10 x
3.4 R versuslog k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
ss 10 2
3.5 Risetimeversuslog k . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
10 2
3.6 R versuslog k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
ss 10 6
3.7 Risetimeversuslog k . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
10 6
3.8 R versuslog k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
ss 10 7
3.9 Risetimeversuslog k . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
10 7
3.10 R versuslog k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
ss 10 8
3.11 Risetimeversuslog k . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
10 8
3.12 R versuslog τ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
ss 10 1
3.13 Risetimeversuslog τ . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
10 1
3.14 R versuslog τ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
ss 10 2
3.15 Risetimeversuslog τ . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
10 2
3.16 Curves showing the number of RNA molecules produced with respect to
time by simulating the simple RNA expression model and by simulating
thedelaystochasticsimulationmodelwithabortiveinitiation . . . . . . . . 39
3.17 Curves showing the number of RNA molecules produced with respect to
time by simulating the simple RNA model, the model with abortive initia-
tion,andthesimpleRNAmodelwithk increasedto100s−1 andthemodel
2
withabortiveinitiationandk increasedto100s−1 . . . . . . . . . . . . . 40
2
3.18 R versuslog k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
ss 10 arrest
3.19 Risetimeversuslog k . . . . . . . . . . . . . . . . . . . . . . . . . . 43
10 arrest
ix
LISTOFFIGURES
3.20 Risetimeversuslog k atseveralvaluesofk . . . . . . . . . . . . . . 45
10 arrest 6
3.21 R versuslog τ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
ss 10 3
3.22 Risetimeversuslog τ . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
10 3
4.1 AnalyticalcurveandsimulationresultsforR versuslog k . . . . . . . . 54
ss 10 x
4.2 AnalyticalcurveandsimulationresultsforR versuslog k . . . . . . . . 55
ss 10 2
4.3 AnalyticalcurveandsimulationresultsforR versuslog k . . . . . . . . 55
ss 10 8
4.4 AnalyticalcurveandsimulationresultsforR versuslog τ . . . . . . . . 56
ss 10 3
4.5 AnalyticalcurveandsimulationresultsforR versuslog k . . . . . . 56
ss 10 arrest
4.6 Analyticalcurveandsimulationresultsfortherisetimeversuslog k . . . 58
10 8
4.7 Analyticalcurveandsimulationresultsfortherisetimeversuslog k . . . 60
10 6
x