Topological Interactions in Ring Polymers (eBook)

After his undergraduate studies in Padova (Italy) Davide Michieletto moved to the UK in 2011 where he attended the Doctoral Training Centre in Complexity Science at the University of Warwick until 2015. During this time he worked on a number of projects, the main one with Prof. Matthew Turner leading to his PhD in Physics and Complexity Science for a study of Topological Interactions in Ring Polymers.  In September 2015 he  became a Post-Doctoral Research Associate at the University of Edinburgh, working with Prof. Davide Marenduzzo on biophysical models for DNA and chromatin organisation in the cell nucleus.

Publications related to this thesis:(1) D. Michieletto, D. Marenduzzo, E. Orlandini, G.P. Alexander, M.S. Turner, Threading Dynamics of Ring Polymers in a Gel, ACS Macro Lett., 3, 255–259 (2014)(2) D. Michieletto, D. Marenduzzo, E. Orlandini, G.P. Alexander, M.S. Turner, Dynamics of Self-Threading Polymers in a Gel, Soft Matter, 10, 5936–5944 (2014)(3) D. Michieletto, E. Orlandini, M.S. Turner, Rings in Random Environments: Sensing Disorder Through Topology, Soft Matter, 11, 1100–1106 (2015)(4) D. Michieletto, D. Marenduzzo, E. Orlandini, Is the Kinetoplast DNA a Percolating Network of Linked Rings at its Critical Point?., Phys. Biol., 12, 036001 (2015)(5) D. Michieletto, D. Marenduzzo, E. Orlandini, Topological Patterns in Two-dimensional Gel Electrophoresis of DNA Knots, Proc. Natl. Acad. Sci. USA, 112 (40), E5471–E5477 (2015)(6) D. Michieletto and M.S. Turner, A Topologically Driven Glass in Ring Polymers, Proc. Natl. Acad. Sci. USA, doi:10.1073/pnas.1520665113 (2016) 6
Supervisor’s Foreword 7
Abstract 10
Acknowledgments 11
Contents 12
1 Introduction 14
References 22
2 Predicting the Behaviour of Rings in Solution 24
2.1 Statics 25
2.1.1 The Size of a Crumpled Coil 25
2.1.2 Contact Exponents for the Crumpled Globule 30
2.1.3 The Structure Factor 32
2.2 Dynamics 33
2.2.1 Diffusion Coefficient and Relaxation Time 33
2.2.2 How Rings Relax Stress 36
2.2.3 Inter-Coil Correlations Probed by Dynamic Scattering 37
References 39
3 Molecular Dynamics Models 41
3.1 Molecular Dynamics Scheme 42
3.1.1 Non-bonded Potentials 42
3.1.2 Bonded Potentials 43
3.1.3 Brownian Dynamics 45
3.2 Modelling 48
3.2.1 Modelling (Knotted) Ring Polymers 48
3.2.2 Modelling a Physical Gel 53
References 55
4 Threading Rings 58
4.1 Threading of Rings in a Gel 59
4.1.1 Detecting Threadings Between Rings 61
4.1.2 Extensive Threading Leads to Extensive Correlations 64
4.1.3 The Emergence of a Spanning Network of Inter-Threaded Chains 69
4.2 Threading of Rings in Dense Solutions 71
4.2.1 Overlapping Crumpled Globules 72
4.2.2 The Slow Exchange Dynamics of Rings 75
4.2.3 Inducing a Topological Glass by Randomly Pinning Rings 77
4.3 Conclusions 85
References 87
5 A Bio-Physical Model for the Kinetoplast DNA 90
5.1 Modelling the Network Replication 93
5.2 The Stable Point Is a Marginally Linked Network 96
5.3 Redundancy in the Genetic Material Allows for Faster Replication Times 99
5.4 Conclusions 102
References 103
6 The Role of Topology in DNA Gel Electrophoresis 106
6.1 Gel Electrophoresis of DNA Rings and Strands 109
6.1.1 Linear Polymers Are Insensitive to Microscopic Disorder 110
6.1.2 Getting More from Pushing Less 112
6.1.3 Topology Can Sense Disorder 114
6.2 Gel Electrophoresis of DNA Knots 116
6.2.1 Non-monotonic Speed of DNA Knots in Gel 117
6.2.2 Entanglement with Dangling Ends 120
6.2.3 An Equivalent Random Walk Description 124
6.3 Conclusions 127
References 129
7 Conclusions 132
Appendix AIdentifying Knots 134
References 135