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Table of contents
Introduction
1.1 Gene expression
1.1.1 Central Dogma: fifty years of molecular biology
1.1.2 Gene expression: main biological mechanisms
1.1.3 Translation
1.2 Stochasticity: experiments
1.3 Intrinsic and extrinsic noise
1.4 Stochasticity: models
1.4.1 Limits of classic models
2 MPPP description of gene expression
2.1 Biology and mathematical assumptions
2.1.1 Biological context
2.1.2 Mathematical model of gene expression: three-stage model
2.1.3 Limits of classic models: the exponential assumption
2.2 MPPP Description of Gene Expression
2.3 General results
2.3.1 Gene state
2.3.2 Messengers
2.3.3 Proteins
2.4 Results: explicit formulas and numerical analysis
2.A Appendix: classic models
2.A.1 The Rigney’s model
2.A.2 Paulsson’s model survey
2.A.3 Swain’s model
3 Realistic model of gene expression
3.1 Four-Stage Model
3.1.1 Model and general results
3.1.2 Realistic assumptions
3.1.3 Explicit formulas under realistic assumptions
3.2 Qualitative and quantitative analysis
3.2.1 Biological data and model parameters
3.2.2 Estimation of fluctuations: deterministic elongation
3.2.3 Four-Stage Model: a counter-intuitive result
3.2.4 Proteolysis vs. dilution
3.2.5 Impact of different steps on protein fluctuations
3.A Reference parameters
4 Multi-protein model
4.1 Stochastic model
4.2 Asymptotic Behavior
4.3 Analysis of fixed point equation
4.3.1 The underloaded case
4.3.2 The Case of Overloaded mRNAs
A Mathematical tools
A.0.3 Marked Poisson Point Processes
B Biology
B.1 Biological Mechanisms
B.1.1 Gene activation
B.1.2 Transcription
B.1.3 Translation
B.1.4 mRNA degradation
B.1.5 Protein degradation
B.2 Biological glossary
B.2.1 16S ribosomal RNA
B.2.2 -galactosidase
B.2.3 DNA
B.2.4 Gene
B.2.5 Inducer
B.2.6 Operon
B.2.7 Promoter
B.2.8 Ribosomal Binding Site (RBS)
B.2.9 Ribosome
B.2.10 RNA
B.2.11 Messenger RNA (mRNA)
B.2.12 Ribosomal RNA (rRNA)
B.2.13 Transfer RNA (tRNA)
B.2.14 Shine-Dalgarno sequence
