Chromatin Phase DiagramThis PhD thesis addressed and succeeded in answering a fundamental question concerning genome folding at the 30nm scale by proving that a higher-order DNA folding pattern beyond the nucleosome, i.e. chromatin, actually exists. A model for chromatin was developed that allows to study very long fibers (in the range of Mega base pairs). Furthermore, linker histone depletion as well as nucleosome depletion have been included for the first time in a chromatin model. This allowed to study the chromatin phase diagram and the corresponding structures are discussed against the background of compaction and DNA accessibility and other important chromatin features. The basic model parameter distributions come from experimental data [186,187]. Together with the histone depletion effects they show that every chromatin conformation consists of a distribution of different structures. This explains why regular 30nm fibers are so hard to find experimentally.

Histone_DepletionThe results show that histone depletion massively affects the properties of chromatin. Nucleosome depletion can either lead to a collapse or to swelling of chromatin and the predicted regime of optimal DNA condensation coincides with experimental data [186] which proves that histone depletion is used as a regulatory tool for DNA extension. Moreover, the model is in good agreement with many experimentally determined chromatin properties. A comparison of the developed model with 5C experimental data [72] proves that histone depletion is an important chromatin feature because only fibers with depletion allow the important physical contacts on a small length scale. Random chromatin collisions are theoretically studied to improve 3C-based experimental technologies by allowing to distinguish more accurately between specific and random DNA contacts.

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Comparison with Electron Micrographs

The following figures show a comparison of simulated chromatin fibers with electrom micrographs (adapted from Olins, D.E. and Ada L. Olins. 2003. Chromatin history: our view from the bridge. Nat Rev Mol Cell Biol 4: 809-14.).

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ParameterverteilungWe present a Monte Carlo model for genome folding at the 30nm scale with focus on linker histone and nucleosome depletion effects. We find that parameter distributions from experimental data do not  lead to one specific chromatin fiber structure but instead to a  distribution of structures in the chromatin phase diagram.

Depletion of linker histones and nucleosomes affects massively the flexibility and the extension of chromatin fibers. Increasing the amount of nucleosome skips (i.e. nucleosome depletion) can either lead to a collapse or to swelling of chromatin fibers. These opposing effects are discussed and we show that depletion effects may even contribute to chromatin compaction. Furthermore, we find that predictions from experimental data for the average nucleosome skip rate lie exactly in the regime of maximum chromatin compaction.

Finally we determine the pair distribution function of chromatin. This function reflects the structure of the fiber and its Fourier transform can be measured experimentally. Our calculations show that even in the case of fibers with depletion effects the main dominant peaks (characterizing the structure and the length scales) can still be identified.

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View into the cell nucleus: This figure shows an illustration of 1 Mbp of chromatin with histone and nucleosome depletion.

Nucleoporin_with_hydrophobic_clustersIn this work we address the question whether hydrophobic parts of FG-rich nucleoporins can be the reason for their ability to form a hydro-gel. We focus on the N-terminal fsFG-domain of the essential yeast nucleoporin Nsp1p [18] as a nucleoporin model system and on the question whether a phase transition between a sol and a gel phase exists. It comprises 18 regular FSFG-repeats and 16 less regular  FG-repeats. This domain is modeled and equilibrated ensembles of peptide networks were generated by a Metropolis Monte-Carlo algorithm which then were analyzed by percolation theoretical methods.

We take into account the excluded-volume of the protein backbone and all side chains which are at least medium-sized (starting with Glu / E) as well as the hydrophobic clusters of the amino acid sequence. There is a competition between two kinds of entropic forces in the system: The excluded volume interactions and the hydrophobic parts of the nucleoporin strands. Therefore, it is not a priori clear whether the system percolates at a biologically realistic density. Nevertheless, we find a sol-gel phase transition in the system at a critical density of 42 mg / mL

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E2A-modelWe present a model improving the two-angle model for interphase chromatin (E2A model). This model takes into account the cylindrical shape of the histone octamers, the H1 histones in front of boundaries_E2Athe nucleosomes, and the distance d between the in and outgoing DNA strands orthogonal to the axis of the corresponding nucleosome cylinder. Factoring these chromatin features in, one gets essential changes in the chromatin phase diagram: Not only the shape of the excluded-volume borderline changes but also the orthogonal distance d has a dramatic influence on the forbidden area. Furthermore, we examined the influence of H1 defects on the properties of the chromatin fiber.

Thus, we present two possible strategies for chromatin compaction: The use of very dense states in the H1_defectphase diagram in the gaps in the excluded-volume, borderline, or missing H1 histones can lead to very compact fibers. The chromatin fiber might use both of these mechanisms to compact itself at least locally. Line densities computed within the model coincident with the experimental values.

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phase_diagramWe have studied the phase diagram for chromatin within the framework of the two-angle model. Only a rough estimation of the forbidden surface of the phase diagram for chromatin was given in a previous work of Schiessel. We revealed the fine structure of this excluded-volume borderline numerically and analytically. Furthermore, we investigated the Coulomb repulsion of the DNA linkers to compare it with the previous results.excluded_volume_borderline

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Illustration of the mACN of a polymer chain with a loopWe develop new methods for the structural analysis of polymer systems (especially of DNA). So far we investigated the effects of excluded volume interactions on the mean average crossing number (mACN) [ref] and the knot statistics [ref] of polymers. The mACN is roughly speaking a measure for the entanglement of polymer chains.
At the moment we are about to publish a paper which shows the connection between the mACN and the scattering function as well as the loop number of polymer chains.

We study the influence of excluded volume interactions on the behaviour of the mean average crossing number (mACN) for random off-lattice walks. We investigated Gaussian and equilateral off-lattice random walks with and without ellipsoidal excluded volume up to chain lengths of N = 1500 and equilateral random walks on a cubic lattice up to N = 20000. We find that the excluded volume interactions have a strong influence on the behaviour of the local crossing number 〈 a(l1,l2) 〉 at very short distances but only a weak one at large distances. This behaviour is the basis of the proof in [ Y. Diao et al., Math. Gen. 36, 11561 (2003); Y. Diao and C. Ernst, Physical and Numerical Models in Knot Theory Including Applications to the Life Sciences] for the dependence of the mean average crossing number on the chain length N. We show that the data is compatible with an N ln(N)-bahaviour for the mACN, even in the case with excluded volume.

We investigated the effects of excluded volume interactions on the average crossing number (ACN) and found a power law for the number of knot-monomers with an exponent $0.39 \pm0.13$ in agreement with previous simulations. For the average size of a knot we also obtain a power law behaviour. We further present data on the average number of knots given a certain chain length and confirm a power law behaviour for the number of knot-monomers. Furthermore we study the average crossing number for random and self-avoiding walks as well as for a model polymer with and without geometric constraints. The data confirms the aN log N + bN law in the case of without excluded volume and determines the constants $a$ and $b$ for various cases. For chains with excluded volume the data for chains up to N=1500 is consistent with a N log N + bN rather than the proposed N^{4/3} law. Nevertheless our fits show that the N^{4/3} ACN of a polymer chain with a looplaw is a suitable approximation.

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nucleosome_line_densityIn this diploma thesis the influence of excluded volume interactions on the mean average crossing number of polymer chains was numerically and analytically investigated. It turned out that this influence is very strong and that the mean average crossing number of real polymers is much smaller than the theoretical predictions for ideal polymer chains in [22; 23; 26]. Furthermore the forbidden surfaces of the  chromatin phase diagram due to excluded volume restrictions were numerically revealed and very good analytical approximations could be found for it. The behavior of the nucleosome density, the accessibility and the energy of a single chromatin repeat unit at the determined excluded volume borderline was investigated.

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