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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