WRAP Theses Du Lac 2017
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SIS
UN
MENS T A T A G I MOLEM
IVERSITAS WARWICEN
Modelling and Simulation of Heterogeneous Growth Dynamics in Bacterial Populations using a Novel Multiphasic Growth Method
by
Melchior du Lac
Thesis
Submitted to the University of Warwick for the degree of
Doctor of Philosophy
School of Engineering
September 2017
Contents
List of Figures
iv
Acknowledgments
vii
Declarations
viii
Abstract
ix
Chapter 1 Introduction
1
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Biological Background . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 The Central Dogma of the Cell Division Cycle . . . . . . . . 3
1.2.2 Population Heterogeneity and Biological Noise . . . . . . . . 14
1.3 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.3.1 Cooper-Helmstetter Model . . . . . . . . . . . . . . . . . . . 16
1.3.2 Individual Based Simulation . . . . . . . . . . . . . . . . . . . 20
1.3.3 Genetic Optimisation . . . . . . . . . . . . . . . . . . . . . . 22
1.4 Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Chapter 2 Materials and Methods
24
2.1 Media and Bacterial Strains . . . . . . . . . . . . . . . . . . . . . . . 24
2.1.1 Chromosomal DNA Quantification . . . . . . . . . . . . . . . 25
2.2 Computational Methods and Packages . . . . . . . . . . . . . . . . . 26
2.2.1 Normalising Fluorescence to Genomic Content . . . . . . . . 26
2.2.2 Computational Packages . . . . . . . . . . . . . . . . . . . . . 28
Chapter 3 Model Development
29
3.1 Growth Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.1.1 Single Cell Growth Dynamics . . . . . . . . . . . . . . . . . . 30
3.1.2 Balanced Growth . . . . . . . . . . . . . . . . . . . . . . . . . 33
i
3.1.3 Modelling Population Growth . . . . . . . . . . . . . . . . . . 34 3.1.4 Non-Balanced Growth . . . . . . . . . . . . . . . . . . . . . . 41 3.2 Chromosome Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.2.1 Critical Mass and the Eclipse Period . . . . . . . . . . . . . . 46 3.2.2 Replication . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.3 Cell Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.3.1 Sizer model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.3.2 Timer model . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.3.3 Adder model . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.4 CH Model: Linking Chromosome and Division Dynamics . . . . . . 59 3.4.1 Mixed Timer and Sizer Model . . . . . . . . . . . . . . . . . . 59 3.5 Conclusion: The Model . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.5.1 Flow Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.5.2 Inclusion of Stochastic Effects . . . . . . . . . . . . . . . . . . 64
Chapter 4 Model Examination and Optimisation to recA1 Mutants 67 4.1 HMG Examination Experiments . . . . . . . . . . . . . . . . . . . . 67 4.1.1 Wild Type Cells . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.1.2 Nutritional Shift-up Experiment . . . . . . . . . . . . . . . . 72 4.2 Optimisation to recA1 Mutants . . . . . . . . . . . . . . . . . . . . . 81 4.2.1 The Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.2.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.2.3 Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.3 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . 98
Chapter 5 Predicting Cell Cycle and SGC Properties Throughout
Disparate Growth Regimes
100
5.1 Determining Chromosomal Gene Copy Number . . . . . . . . . . . . 100
5.1.1 Predicting Gene Copy Number . . . . . . . . . . . . . . . . . 102
5.1.2 Calculating Gene Copy Number . . . . . . . . . . . . . . . . 104
5.1.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.2 HMG ODE Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.2.1 Partition Extrinsic Noise . . . . . . . . . . . . . . . . . . . . 107
5.2.2 Transient Chromosomal Gene Copy Number . . . . . . . . . 112
5.3 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . 118
ii
Chapter 6 Summary, Conclusions and Further Work
119
6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.2 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.3 Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
iii
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