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Modelling of interphase chromosomes [Elektronische Ressource] : from genome function to spatial organization / put forward by Manfred Bohn

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DISSERTATIONsubmitted to theCombined Faculties for theNatural Sciences and for Mathematicsof the Ruperto-Carola University of HeidelbergGermanyfor the degree ofDoctor of Natural Sciencesput forward byDipl.-Phys. Manfred Bohnborn in: MarburgDate of oral examination: 21.04.2010Modelling of Interphase Chromosomes:FromGenome FunctiontoSpatial OrganizationReferees: Prof. Dr. Dieter W. HeermannProf. Dr. Christoph CremerAbstractGenome function in higher eukaryotes involves major changes in the spatial organizationofthechromatinfiber. Nevertheless, ourunderstandingofchromatinfoldingisremarkablylimited. Experimentalresultssuggestthatchromatinloopsnotonlyimpacttranscriptionalregulation but also act as a major epigenetic mechanism, playing a pivotal role in the ob-served compartmentalization of chromosomes. However, aunified descriptionof chromatinfolding comprising various experimental results is still lacking. After showing that the the-ory of compact polymers is inconsistent with experimental data, we develop a new modelfor chromatin based on probabilistic formation of loops. This Random-Loop-Model cor-rectly describes folding into a confined sub-space of the nucleus as well as the observedcell-to-cell variation, suggesting a close relation between expression-dependent compactionand local variations in the looping probabilities.

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DISSERTATION
submitted to the
Combined Faculties for the
Natural Sciences and for Mathematics
of the Ruperto-Carola University of Heidelberg
Germany
for the degree of
Doctor of Natural Sciences
put forward by
Dipl.-Phys. Manfred Bohn
born in: Marburg
Date of oral examination: 21.04.2010Modelling of Interphase Chromosomes:
From
Genome Function
to
Spatial Organization
Referees: Prof. Dr. Dieter W. Heermann
Prof. Dr. Christoph CremerAbstract
Genome function in higher eukaryotes involves major changes in the spatial organization
ofthechromatinfiber. Nevertheless, ourunderstandingofchromatinfoldingisremarkably
limited. Experimentalresultssuggestthatchromatinloopsnotonlyimpacttranscriptional
regulation but also act as a major epigenetic mechanism, playing a pivotal role in the ob-
served compartmentalization of chromosomes. However, aunified descriptionof chromatin
folding comprising various experimental results is still lacking. After showing that the the-
ory of compact polymers is inconsistent with experimental data, we develop a new model
for chromatin based on probabilistic formation of loops. This Random-Loop-Model cor-
rectly describes folding into a confined sub-space of the nucleus as well as the observed
cell-to-cell variation, suggesting a close relation between expression-dependent compaction
and local variations in the looping probabilities. We find that formation of loops is highly
beneficial for the nucleus to maintain order and to accomplish entropy-driven segregation
of chromosomes. A dynamic model is proposed, showing that the formation of loops can
be accomplished solely on the basis of diffusional motion without invoking active mech-
anisms. Such a dynamic model provides a unified explanatory framework of chromatin
folding, yielding testable predictions, which for the first time consistently explain many
experimental findings.
Zusammenfassung
DieSteuerungderGenexpressioninhöherenEukaryontenerfordertgrößereVeränderungen
in der räumlichen Anordnung der Chromatinfiber. Nichtsdestotrotz ist unser Wissen über
dieStrukturvonChromosomenäußerstbegrenzt. WieexperimentelleResultatezeigen,be-
influssen Chromatin-Schleifen nicht nur Genexpression, sondern wirken als epigenetischer
Mechanismus, welcher eine entscheidende Rolle bei der Bildung von Chromosomenterrito-
rien spielen. Trotz dieses Wissens gibt es noch kein einheitliches Modell der Chromatinfal-
tung unter Integration verschiedenster experimenteller Resultate. Wir zeigen, dass Chro-
mosome sich anders verhalten, als es die klassische Polymertheorie vorhersagt. Ausgehend
von der Annahme probabilistischer Schleifenbildung wird ein das neue Random-Loop-
Modell entwickelt. Diese Modell erklärt sowohl die Faltung von Chromosomen in einen be-
grenztenTeilraumdesZellkernsalsauchdiebeobachtetehoheVariabilitätzwischenZellen.
Die Ergebnisse zeigen eine mögliche Verbindung zwischen expressionsabhängiger Kompak-
tifizierung und der lokalen Schleifenwahrscheinlichkeit. Wir finden, dass Schleifenbildung
ein treibende Kraft im Zellkern ist um sowohl Ordnung als auch Chromosomensegrega-
tion aufrechtzuhalten. Ein dynamisches Modell wird präsentiert, in dem Loops sich ohne
aktive Mechanismen lediglich aufgrund von Diffusion bilden und welches eine expression-
sabhängige Chromatinstruktur postuliert. Es erklärt eine große Anzahl experimenteller
Resultate mittels eines einheitlichen Modells und liefert überprüfbare Vorhersagen für
weitere Experimente.Publications related to this thesis
Large parts of this thesis have already been published or are currently submitted. The
following list contains the journal references, or the journal to which the paper has been
submitted. Papers in preparation are also listed. (Information as of January 29th, 2010)
Bohn,M.,Heermann,D.W.&vanDriel,R. Randomloopmodelforlongpolymers.
Physical Review E (2007), 76, 051805
DOI: 10.1103/PhysRevE.76.051805 preprint: arXiv:0705.1470v3 [cond-mat.soft]
1 1 Langerak, J. M. , Bohn, M. , de Leeuw, W., Giromus, O., Manders, E. M. M.,
Verschure, P. J., Indemans, M. H. G., Gierman, H. J., Heermann, D. W., van Driel,
R. & Goetze, S. Spatially confined folding of chromatin in the interphase nucleus.
Proc. Natl. Acad. Sci. U.S.A. (2009), 106, 3812-3817
DOI: 10.1073/pnas.0809501106
Bohn, M. & Heermann, D. W. Conformational properties of compact polymers.
Journal of Chemical Physics (2009), 130, 174901+
DOI: 10.1063/1.3126651 preprint: arXiv:0905.0798v1 [cond-mat.soft]
Bohn, M. & Heermann, D.W. Topological interactions between ring polymers:
Implications for chromatin loops. Journal of Chemical Physics (2010), 132 (4),
044904
DOI: 10.1063/1.3302812 preprint: arXiv:1001.4246 [cond-mat.soft]
Bohn, M. &Heermann, D.W. Diffusion-drivenloopingprovidesaconsistentframe-
work for chromatin organization. PLoS Comp. Biol. (submitted, under review)
Bohn, M., Heermann, D. W., Lourenço, O. & Cordeiro, C. E. On the influence of
topological catenation and bonding constraints on ring polymers. Macromolecules
(submitted, under review)
1 1 Bohn, M. , Diesinger, P. et al. Localization microscopy reveals expression-depen-
dent parameters of chromatin nanostructure. Biophys. J. (submitted)
Heermann, D. W., Bohn, M., Diesinger, P. The Relation between the Gene Net-
work and the Physical Structure of Chromosomes. Proceedings of the 4th Interna-
tional Conference on High Performance Scientific Computing: Modeling, Simulation
and Optimization of Complex Processes. (submitted, under review) (2010)
Bohn, M. & Heermann, D.W. Repulsive Forces between Chromosomes. (in prepa-
ration)
Tolhuis B., Kerkhoven R., Pagie L., Bohn M., Teunissen H., Nieuwland M., Simo-
nis M., de Laat W., Heermann D.W., v. Lohuizen M.& v. Steensel B. Interactions
among Polycomb Domains are Guided by Chromosome Architecture. Cell (submit-
ted)
1
Shared first authorship due to equal contributionContents
1 Scope and Intentions 15
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.2 Intention of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.3 The structure of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2 The organization of life – Biological Background 21
2.1 The Cell – Building block of life . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 Chromatin – The carrier of information . . . . . . . . . . . . . . . . . . . . 22
2.2.1 From DNA to the 10 nm chromatin fiber . . . . . . . . . . . . . . . 23
2.2.2 The 30 nm chromatin fiber . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.3 Higher-order folding in interphase and metaphase . . . . . . . . . . . 25
2.3 The connection between genome folding and function . . . . . . . . . . . . . 25
2.3.1 Non-random alignment of active and inactive regions along the 1D
genome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.2 The histone code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.3.3 3D organization of sub-chromosomal regions dependents on tran-
scriptional activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.3.4 Folding of chromosomes into sub-nuclear domains . . . . . . . . . . . 26
2.3.5 The formation of chromosome territories . . . . . . . . . . . . . . . . 28
2.4 Chromatin loops as a mediator of the folding-function relationship . . . . . 29
2.4.1 Gene regulation and long-range control . . . . . . . . . . . . . . . . 29
2.4.2 Long-range control mediated by chromatin loops . . . . . . . . . . . 30
2.4.3 Three-dimensionalstructureofloops: Transcriptionfactories,CTCF
and the nuclear matrix . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.4.4 Implications for a model of chromatin . . . . . . . . . . . . . . . . . 32
3 Polymer models of chromatin 33
3.1 Statistical Physics of Polymers . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1.1 The freely jointed chain model . . . . . . . . . . . . . . . . . . . . . 34
3.1.2 The Gaussian Chain model . . . . . . . . . . . . . . . . . . . . . . . 35
3.1.3 Effects of excluded volume – the self-avoiding walk . . . . . . . . . . 37
3.1.4 of the solvent – transition to the globular state . . . . . . . . 38
3.1.5 Intermingling in polymeric solutions . . . . . . . . . . . . . . . . . . 38
3.1.6 A question of scale – Coarse graining and bending rigidity . . . . . . 39
3.2 Models of chromatin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2.1 Random walk in a confined space . . . . . . . . . . . . . . . . . . . . 41
3.2.2 The Random Walk / Giant - Loop model . . . . . . . . . . . . . . . 42
3.2.3 The Multi-Loop-Subcompartment model . . . . . . . . . . . . . . . . 43
910 CONTENTS
3.2.4 Other models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4 The conformational properties of compact polymers 45
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2 Is chromatin organized as a random walk or self-avoiding walk? . . . . . . . 48
4.2.1 Scaling of the mean square displacement . . . . . . . . . . . . . . . . 48
4.2.2 Distance distributions . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2.3 Moment ratios of the distribution . . . . . . . . . . . . . . . . . . . . 50
4.3 Monte Carlo simulations of compact polymers . . . . . . . . . . . . . . . . . 53
4.3.1 The Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.3.2 Ergodicity and unbiased sampling . . . . . . . . . . . . . . . . . . . 54
4.3.3 Autocorrelation times . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.4 Conformational properties of compact polymers . . . . . . . . . . . . . . . . 57
4.4.1 End-to-end distance statistics . . . . . . . . . . . . . . . . . . . . . . 57
4.4.2 Intrachain . . . . . . . . . . . . . . . . . . . . . . 60
4.4.3 End-point statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.4.4 Correlations of intrachain segments . . . . . . . . . . . . . . . . . . . 62
4.4.5 Screening of excluded volume in compact polymers . . . . . . . . . . 64
4.4.6 The gyration tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.5 Is chromatin organized as a compact polymer? . . . . . . . . . . . . . . . . 66
4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5 The Random Loop Model 71
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.2 Basic model assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.3 The homogeneous Random Loop Model in the annealed and quenched average 75
5.3.1 The Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.3.2 Quenched or annealed ensemble? . . . . . . . . . . . . . . . . . . . . 75
5.3.3 The quenched average . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.3.4 Results and comparison to experiments . . . . . . . . . . . . . . . . 78
5.3.5 The annealed ensemble . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.3.6 Limiting cases without disorder . . . . . . . . . . . . . . . . . . . . . 83
5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6 Molecular Dynamics simulations of the Random Loop Model 87
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6.2 The Simulational Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.2.1 Molecular Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.2.2 Setting up the potentials . . . . . . . . . . . . . . . . . . . . . . . . 90
6.2.3 Details on the implementation . . . . . . . . . . . . . . . . . . . . . 92
6.2.4 Equilibration of the system . . . . . . . . . . . . . . . . . . . . . . . 93
6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.4 Simulations of the annealed ensemble . . . . . . . . . . . . . . . . . . . . . . 97
6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
7 A unified view of short and large scale folding 99
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.2 First evidence for different local looping probabilities . . . . . . . . . . . . . 101
7.3 Integration of short and long length scale data by the RL model . . . . . . 103

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