Large DNA molecules are folded in cells of organisms on several hierarchical layers. The smallest scale folding-mechanism is the formation of nucleosomes. The nucleosomal structure however...Show moreLarge DNA molecules are folded in cells of organisms on several hierarchical layers. The smallest scale folding-mechanism is the formation of nucleosomes. The nucleosomal structure however sterically hinders the transcription of the underlying DNA sequence. The sequential passing of mismatches in the initial structure of the nucleosome allows the nucleosome to re-position along the DNA, hereby uncovering regions of the DNA. This twist defect driven mobility of nucleosomes has been observed in crystal structures and all-atom simulations. We re-produce the simulation on mobile twist defects in nucleosomes in the already existing Monte-Carlo based rigid base pair model. This allows us to effectively explore sequence-space for a torsionally frustrated nucleosome. We find estimations of the mobility of nucleosomes under the driving force of over- and undertwisted defects. On top of that we attempt to mutate the sequence in order to find a sequence on which a twist defect is preferred over the defect-free conformation of the nucleosome.Show less
Many eukaryotic organisms exhibit patterns in their DNA code that facilitate the wrapping of DNA into nucleosomes. At the same time, nucleosomes have been found to affect both interspecies DNA...Show moreMany eukaryotic organisms exhibit patterns in their DNA code that facilitate the wrapping of DNA into nucleosomes. At the same time, nucleosomes have been found to affect both interspecies DNA sequence divergence and mutational patterns in many cancer types. In my thesis I will propose a simple model capable of qualitatively reproducing all these features in a simulation. The model consists of treating the DNA code as a dynamical variable, with each specific sequence representing a state of the system. The energy required to wrap this sequence into one or more nucleosomes is the energy associated with such a state. The behaviour of the DNA sequence can then be deduced using the laws of statistical mechanics. The model turned out capable of qualitatively reproducing experimental facts.Show less
The most common DNA-protein complexes in cells are nucleosomes, which engages around 80% of the DNA. In nucleosomes DNA molecules are wrapped around a complex of eight histone proteins. The...Show moreThe most common DNA-protein complexes in cells are nucleosomes, which engages around 80% of the DNA. In nucleosomes DNA molecules are wrapped around a complex of eight histone proteins. The positioning of nucleosomes along the DNA is not simply random, instead it follows a certain nucleosome positioning code where nucleosomes prefer certain base pair sequences of the DNA. This is influenced by the mechanics and geometry of the DNA which depend on the underlying sequence. Another interesting object of study is to investigate a nucleosome under tension, where one pulls on the two ends of the wrapped DNA with equal force in opposite directions causing the DNA to unwrap. In this thesis we study the analytical model of a nucleosome presented in [ZES17], where the nucleosome is represented as an ideal superhelix. This model serves to explain the nucleosome positioning code and allows to reproduce the qualitative phenomena of this code. Furthermore we extend this model to an analytical model of a nucleosome under force, where the DNA arms that are unwrapped are represented by Euler elastica. Using this new model we repeat the analysis performed for the fully wrapped nucleosome. Finally, in [ZS19] it has been shown that one can use shortest path analysis to find the lowest and highest energy sequences of a DNA molecule wrapped in a nucleosome. Combining this method with the analytical models, we perform the shortest path analysis for the fully and partially unwrapped nucleosome, making use of the analytically obtained energy values that are necessary to do this.Show less
This study uses the rigid base pair model (rbp) and Markov Chain Monte Carlo (MCMCs) to simulate the unwrapping of nucleosome core particles (NCPs). The model is sequence dependent and is used to...Show moreThis study uses the rigid base pair model (rbp) and Markov Chain Monte Carlo (MCMCs) to simulate the unwrapping of nucleosome core particles (NCPs). The model is sequence dependent and is used to research the bias in left or right unwrapping and the effect of weakening the nucleosome bindings for several DNA sequences (Widom-601, sea urchin 5S gene and 601-derivatives). We are able to focus on intermediate stages in unwrapping, while these may not always be visible in experiments. We validate the model by comparing model outcomes to experimental results and we propose a (simple) method to find interesting sequences for future experiments.Show less
The DNA in eukaryotic organisms is largely stored in a compact wrap around histone proteins to form nucleosomes. The mechanics of the DNA play a major role in the biological processes for which the...Show moreThe DNA in eukaryotic organisms is largely stored in a compact wrap around histone proteins to form nucleosomes. The mechanics of the DNA play a major role in the biological processes for which the DNA is used. In this thesis we will computationally show that we can study the mechanics of the DNA with a simplified computational model. By parametrically constraining the DNA around a superhelical curve we can calculate the mechanical energy of the DNA by only the sequence of the DNA and the positions along the curve. We will demonstrate how, with Monte Carlo methods we can effectively estimate the sequence and position statistics of nucleosomal DNA.Show less
The nucleosome core particle is at the lowest level of DNA compaction, a mechanism that enables the DNA to fit inside the cell nucleus. Multiple nucleosomes, connected to each other like beads on a...Show moreThe nucleosome core particle is at the lowest level of DNA compaction, a mechanism that enables the DNA to fit inside the cell nucleus. Multiple nucleosomes, connected to each other like beads on a string, can stack tightly together to form the chromatin fiber. The compact form of this structure hinders external proteins and enzymes from accessing the nucleosomal DNA and using them in fundamental DNA processes. Nucleosome breathing is a process in which access is facilitated by the transient unwrapping of the nucleosome, thereby exposing the otherwise occluded DNA. This thesis investigates the nucleosome breathing mechanism in a dinucleosome system, a sub-structure of the chromatin fiber where two identical nucleosomes with varying DNA sequence are connected by a piece of linker DNA of varying length. The accessibility of the nucleosomal binding sites is modelled through a statistical model, expressing the breathing process in terms of the adsorption energy of the binding sites and the elasticity of the bent DNA in a dinucleosome configuration. The elastic energy of the bent linker DNA and nucleosomal DNA during the breathing process is estimated through a Monte-Carlo simulation. The results make clear that binding sites in such a dinucleosome structure are much more accessible than binding sites in a mononucleosome. Our findings show that the length of the linker DNA and the sequence of the nucleosomes are a determining factor of the dinucleosome configuration, thereby suggesting that these parameters play an important role in regulating the accessibility of higher order structures such as the chromatin fiber.Show less
DNA methylation is the phenomenon where a methyl group attaches to the nucleotide cytosine or adenine. We study CpG methylation and specifically its role in nucleosome positioning. Methylation...Show moreDNA methylation is the phenomenon where a methyl group attaches to the nucleotide cytosine or adenine. We study CpG methylation and specifically its role in nucleosome positioning. Methylation changes the mechanical properties of the CpG step and therefore the mechanical affinity of DNA to form nucleosomes. We use a rigid base pair model to emulate DNA where the mechanical and geometric properties of a base pair step depend on which base pairs it is made of. A 147 base pair long piece of DNA is forced into the shape known for wrapped DNA inside a nucleosome by attaching it to the nucleosome core proteins at 28 positions. Monte Carlo simulations then allow us to measure various quantities like the average energy of a given sequence or the occurrence rate of certain base pair triplets. The latter is used to inform a trinucleotide Markov model that generates free energy landscapes. From these landscapes we calculate free energy it takes to place a nucleosome at any position close to transcription start site of genes. On average human genes attract nucleosomes around their transcription start sites. We find in this thesis that methylation turns these nucleosome attractive regions into nucleosome expelling regions. We also study the role of entropy in nucleosome positioning by comparing energy landscapes to free energy landscapes. These comparisons show that at higher temperatures entropy becomes non-negligible. We propose a model that could generate energy landscapes at much lower calculational cost, a tool that can be useful in studying the role of entropy in nucleosome positioning on a genome wide scale.Show less
Nucleosomes can influence gene regulation by acting as repressors when located on top of genes. Because of this, nucleosome positioning has been the subject of many studies. One of the determinants...Show moreNucleosomes can influence gene regulation by acting as repressors when located on top of genes. Because of this, nucleosome positioning has been the subject of many studies. One of the determinants of nucleosome positioning is the DNA sequence itself as the mechanical properties of a sequence determine its binding affinity. A recent study showed that it is theoretically possible to change coding sequences to increase binding affinity thereby affecting nucleosome positioning. This can be seen as the multiplexing of genetic and mechanical information. By using a probabilistic model, we now investigate if gene sequences can be altered synonymously to place a nucleosome with base pair precision. By exchanging synonymous codons through a modified Monte Carlo simulation, the mechanical properties of the DNA are altered while keeping the genetic code intact. We find that for 93.7\% of the nucleosome positions on S. cerevisiae genes a minimum of the nucleosome energy landscape can be reached, allowing for the placement of a nucleosome. Additionally, we examined synonymous codon usage in regions of high nucleosome occupancy in the C. elegans genome. It appears that the choice in codon is biased mostly favouring codons with a higher GC content (as this correlates with nucleosome occupancy), but not exclusively. This might be an indication of a selective pressure to synonymously alter DNA in order to facilitate nucleosome binding.Show less
The nucleosome consists of a short stretch of DNA wrapped around a protein cylinder, and is the fundamental unit of chromatin, which compacts the DNA into the cell nucleus. The nucleosome is known...Show moreThe nucleosome consists of a short stretch of DNA wrapped around a protein cylinder, and is the fundamental unit of chromatin, which compacts the DNA into the cell nucleus. The nucleosome is known to transiently partially unwrap or 'breathe' \textit{in vitro}, exposing DNA which would otherwise be sterically inaccessible to enzymes. Breathing is investigated for its potential importance \textit{in vivo} in both essential DNA processes, and in higher-order chromatin organisation. In this thesis we present a two-parameter physical statistical model of the breathing process based on steric enzyme accessibility, the energetics of the bent DNA molecule, and the adsorption of the DNA upon the proteins. We estimate the elastic energy using Monte Carlo simulations of a coarse-grained model of the nucleosomal DNA, and we fit the model to the available experimental results. We find in agreement with experimental studies that site accessibility decays exponentially toward the centre sites, and that highly asymmetric breathing behaviour is possible due to the very sensitive dependence of breathing upon energy distribution, and in turn, sequence.Show less
As DNA contains the blue print of life, it is the subject of many studies. Comprehending DNA has lead to breakthroughs in both medical and scientific understanding. In medicine, DNA presents the...Show moreAs DNA contains the blue print of life, it is the subject of many studies. Comprehending DNA has lead to breakthroughs in both medical and scientific understanding. In medicine, DNA presents the possibility to make early diagnoses and find treatment; in science, genetic engineering has led to great advancements in agriculture, biology and nanotechnology. DNA is build up out of base pairs. The sequences of these base pairs store the essential genetic information for life to function. As such understanding the mechanical rules that govern the positioning of these base pairs is of paramount importance. This thesis aims to study the sequence dependence of the cyclization of small DNA rings by Monte Carlo simulation. Chapter one introduces the key concepts behind DNA rings and summarizes the paper that inspired this project. In chapter two we introduce our model in the context of Metropolis Monte Carlo simulations. Finally, we will present and discuss our results in chapter 3. This last chapter is divided into three parts. The first part discusses the initial tests and simulations performed with the different Monte Carlo moves. In the second part, the results of our simulation of the Rosanio et al. cyclization experiment are presented. The chapter concludes with a discussion of several simulations that were designed to generate interesting new results that might be hard to come by experimentally.Show less
Accessibility to nucleosomal dna is an important factor in transcription and gene expression. During transcription, rna polymerase exerts a force on the nucleosome under which the nucleosome...Show moreAccessibility to nucleosomal dna is an important factor in transcription and gene expression. During transcription, rna polymerase exerts a force on the nucleosome under which the nucleosome unwraps, and, as recently shown experimentally, this can happen asymmetrically. In this thesis, we show, using computer simulations of sequence-dependent coarse-grained dna, what causes this asymmetry. We will also show a proof of concept that we can design dna sequences that unwrap in a predetermined way.Show less
Often low copy number plasmids in bacterial cells exhibit active mechanisms to ensure stable inheritance. In this master thesis we investigate several models that aim to explain the equidistant...Show moreOften low copy number plasmids in bacterial cells exhibit active mechanisms to ensure stable inheritance. In this master thesis we investigate several models that aim to explain the equidistant positioning of pB171 plasmids in E. coli. In this system a walker type ATPase, ParA, forms filamentous structures on the nucleoid. Plasmids with attached ParB, a DNA binding protein, follow the retractive movement of ParA. We show that a polymer pulling model in which the plasmid detachment rate depends critically on the plasmid bound ParB levels can generate partitioning. Furthermore a recently proposed biased diffusion model in which the plasmid diffusion is influenced by the dynamic ParA concentration can direct motion towards mid cell. However the necessity of a high plasmid diffusion constant renders it unlikely to be the actual mechanism used by bacteria. A slight variation of this idea where diffusing oligomers pull on plasmids encounters the same problems as a biased diffusion model. The influence of polymer drag which depends on the length of the filament can be beneficial though it seems unlikely to be the sole mechanism to partition plasmids. Finally, in our favoured model we show that ParA polymers can position plasmids equidistantly with the assumption that ParA subunits bind along the filament and slide to the tip end, thereby influencing the polymerization rate critically.Show less
