Robert Schöpflin

Probing the elasticity of DNA on short length scales by modeling supercoiling under tension.

The wormlike-chain (WLC) model is widely used to describe the energetics of DNA bending. Motivated by recent experiments, alternative, so-called subelastic chain models were proposed that predict a lower elastic energy of highly bent DNA conformations. Until now, no unambiguous verification of these models has been obtained because probing the elasticity of DNA on short length scales remains challenging. Here we investigate the limits of the WLC model using coarse-grained Monte Carlo simulations to model the supercoiling of linear DNA molecules under tension. At a critical supercoiling density, the DNA extension decreases abruptly due to the sudden formation of a plectonemic structure. This buckling transition is caused by the large energy required to form the tightly bent end-loop of the plectoneme and should therefore provide a sensitive benchmark for model evaluation. Although simulations based on the WLC energetics could quantitatively reproduce the buckling measured in magnetic tweezers experiments, the buckling almost disappears for the tested linear subelastic chain model. Thus, our data support the validity of a harmonic bending potential even for small bending radii down to 3.5 nm.

Exploring the Conformational Space of Chromatin Fibers and Their Stability by Numerical Dynamic Phase Diagrams

The three-dimensional structure of chromatin affects DNA accessibility and is therefore a key regulator of gene expression. However, the path of the DNA between consecutive nucleosomes, and the resulting chromatin fiber organization remain controversial. The conformational space available for the folding of the nucleosome chain has been analytically described by phase diagrams with a two-angle model, which describes the chain trajectory by a DNA entry-exit angle at the nucleosome and a torsion angle between consecutive nucleosomes. Here, a novel type of numerical phase diagrams is introduced that relates the geometric phase space to the energy associated with a given chromatin conformation. The resulting phase diagrams revealed differences in the energy landscape that reflect the probability of a given conformation to form in thermal equilibrium. Furthermore, we investigated the effects of entropy and additional degrees of freedom in the dynamic phase diagrams by performing Monte Carlo simulations of the initial chain trajectories. Using our approach, we were able to demonstrate that conformations that initially were geometrically impossible could evolve into energetically favorable states in thermal equilibrium due to DNA bending and torsion. In addition, dynamic phase diagrams were applied to identify chromatin fibers that reflect certain experimentally determined features.

Modeling nucleosome position distributions from experimental nucleosome positioning maps

MOTIVATION Recent experimental advancements allow determining positions of nucleosomes for complete genomes. However, the resulting nucleosome occupancy maps are averages of heterogeneous cell populations. Accordingly, they represent a snapshot of a dynamic ensemble at a single time point with an overlay of many configurations from different cells. To study the organization of nucleosomes along the genome and to understand the mechanisms of nucleosome translocation, it is necessary to retrieve features of specific conformations from the population average. RESULTS Here, we present a method for identifying non-overlapping nucleosome configurations that combines binary-variable analysis and a Monte Carlo approach with a simulated annealing scheme. In this manner, we obtain specific nucleosome configurations and optimized solutions for the complex positioning patterns from experimental data. We apply the method to compare nucleosome positioning at transcription factor binding sites in different mouse cell types. Our method can model nucleosome translocations at regulatory genomic elements and generate configurations for simulations of the spatial folding of the nucleosome chain. AVAILABILITY Source code, precompiled binaries, test data and a web-based test installation are freely available at http://bioinformatics.fh-stralsund.de/nucpos/

Modeling Effects of Nucleosome Positioning in Short and Long Chromatin Fibers

In eukaryotes DNA is associated with proteins in a complex structure termed chromatin. The basic packaging unit of chromatin is the nucleosome in which DNA is wrapped around a histone octamer. The mechanisms of the folding of DNA into chromatin are still under debate. Experiments indicate that chromatin has different packaging conditions connected to distinct activation states. Experimental evidence showed that packaging and activation states are closely linked to positions of nucleosomes on the DNA which are actively regulated.To improve the understanding of the interplay between nucleosome positions and chromatin structure we applied computer simulations of a coarse-grained chromatin model including fundamental physical properties such as elasticity, electrostatics and nucleosome interactions. We calculated the effect of nucleosome positioning on the structure of polynucleosomes of different length scales, up to the size of a gene locus. We compared chromatin models based on synthetic positions with models based on experimentally derived nucleosome positions from cells at different stages of cell differentiation. Simulation results revealed a significant influence of nucleosome positions on the three dimensional structure of chromatin.

Modeling Long Chromatin Fibers based on In-Vivo Nucleosome Positioning Maps

In the nucleus of eukaryotes DNA is wrapped around histone proteins forming so-called nucleosomes, the basic unit of chromatin. This packaging controls DNA accessibility, thus influences directly gene expression, DNA repair and recombination. The precise structure of chromatin in-vivo is still under debate, because experimental probing of chromatin in the nucleus remains difficult and evidence for proposed models is rare. The majority of theoretical models imply a uniform nucleosome repeat length. However, in-vivo nucleosomes exhibit more irregular patterns. It has been shown that the internucleosomal distance has a great impact on the local and global structure of the chromatin arrangement.Here we investigate the influence of nucleosome positioning on the three-dimensional chromatin structure by modeling chromatin fibers comprising more than 1000 nucleosomes. The spacing of nucleosomes was based on in-vivo nucleosome positioning maps from mouse embryonic stem cells and differentiated cells derived from these. We determined non-overlapping nucleosome configurations from MNase assisted high throughput sequencing assays by a simulation procedure. In the next step, we derived a three-dimensional coarse-grained chromatin model from nucleosome positioning data, including fundamental physical properties like elasticity, electrostatics and nucleosome interactions. To improve the understanding of how structural differences and function are linked, we simulate models of gene-clusters at different stages of cell differentiation.

Testing Models For DNA Elasticity on Short Length Scales by Simulating DNA Supercoiling under Tension

The worm-like-chain (WLC) model is widely used to describe the energetics of DNA bending. However, for length scales much shorter than the persistence length the validity of a purely harmonic bending potential has been questioned by recent experiments. So-called sub-elastic chain (SEC) models were proposed that predict a lower elastic energy of highly bent DNA conformations. Until now, no unambiguous verification of these models has been obtained since probing the elasticity of DNA on short length scales remains challenging. Here we address this issue by modeling single molecule supercoiling experiments of DNA under tension using coarse-grained Monte Carlo simulations. Twisting of stretched DNA is accompanied by an abrupt decrease of the DNA extension at a critical supercoil density due to buckling of the molecule. This transition is caused by an energetic offset due to the strongly bent end-loop of the forming superhelical structure. While simulations based on WLC bending energetics could quantitatively reproduce the buckling measured in magnetic tweezers experiments, the buckling almost disappears for the tested linear SEC model. Thus, our data support the validity of a harmonic bending potential even for strongly bent DNA down to bending radii of 3.5 nm.

Computer Simulation of Chromatin: Interdependency Between Nucleosome Positions and Chromatin Structure

The three-dimensional structure of chromatin is a key factor for controlling DNA accessibility, replication and repair. Despite numerous experimental efforts many details of the spatial organization and structural regulation mechanisms of chromatin remain unclear.Most theoretical models of chromatin proposed in literature imply a periodical positioning and uniform occupancy of the fiber nucleosomes. However, recent studies suggest a dynamic rather than static nucleosome positioning, which is both actively regulated by chromatin-remodeling complexes (CRCs) and passively influenced by thermal fluctuations. These processes have been subject to intensive scientific work, yielding new insights into the function of CRCs and the biophysical properties of the histone-DNA interface. However, nucleosome positions are also influenced by energetic effects imposed by structural constraints inherent in the chromatin fiber, and, vice versa, nucleosome positioning impacts chromatin fiber structure as well.To investigate the effects of nucleosome repositioning, we carried out Monte Carlo simulations with a coarse-grained chromatin model incorporating elastic fiber properties as well as a detailed description of the electrostatic and internucleosomal interactions. We created computational fiber conformations based on experimental results. These fiber conformations were modified by repositioning nucleosomes by a range of base pair steps. After simulation, the chromatin energy landscape and shape were analyzed. We observed a significant energy barrier against nucleosome repositioning which is larger than thermal fluctuations but within the range of ATP-dependent biological processes. Moreover, analysis of fiber shape data revealed an increased kinking susceptibility of the fiber within the region proximate to a repositioned nucleosome. This behavior is accompanied by increased fiber flexibility within the same region.These findings facilitate a deeper understanding of the relation between nucleosome positions and chromatin fiber structure.

A Theoretical Description of DNA Plectonemes under Tension

Twisting a DNA molecule held under constant tension is accompanied by a transition from a linear to a plectonemic DNA configuration, in which part of the applied twist is absorbed in a superhelical structure. This is seen as a linear shortening of the DNA length with added turns after the transition. So far no theoretical description exists, which consistently describes the slope of the supercoiling curves as well as the torque in the plectonemic regime and its dependency on the applied force and the monovalent ion concentration in solution. Here, we present a simple model, in which the DNA is treated as a semiflexible rod. The energy of the plectonemic structure is calculated considering DNA bending, applied tension and electrostatic repulsion between the DNA strands but excluding fluctuations. We compare the predictions of our simple static theory with experimental supercoiling data, recorded with magnetic tweezers. We obtain an excellent agreement for the supercoiling slopes and the torque as function of force and monovalent ion concentration only if a reduced DNA charge is taken into account. We verify our theory using Monte-Carlo simulations, in which the same energetic terms are used. Surprisingly, the simple static model describes experimental data much better than more sophisticated models considering fluctuations, which considerably overestimate the torque of the plectonemic phase.

Monte Carlo Simulation of Supercoiled DNA at Buckling Transition

Recent studies of high resolution single molecule experiments yielded detailed information of DNA supercoiling under applied tension. Here we use Monte Carlo simulations with a coarse-grained DNA model to improve the understanding of these data. To reproduce experimental conditions, stretching, bending, twisting and electrostatic potentials were explicitly considered in the computer model.As in single-molecule experiments with magnetic tweezers, we carry out simulations for different applied forces and ionic strengths over a large range of applied supercoils. The simulations reproduce well the experimentally observed behavior: While initially the molecule extension remains almost constant upon twisting, a linear decrease in extension with added twist is observed, once a critical buckling torque is reached. At higher ionic strength this is caused by the formation of a superhelical, i.e. plectonemic, structure. At these conditions the buckling transition between stretched and plectonemic DNA is accompanied by a abrupt DNA length decrease. At low ionic strength however, the buckling phase vanishes and the formation of multiple loose DNA loops is preferred over a superhelical structure. Interestingly under these conditions, the torque does not remain constant anymore with added turns.Beyond an overall qualitative agreement, the MC simulations reproduce quantitatively most of the experimental parameters, if the interaction potentials are appropriately chosen. This includes the slope and torque of the linear decrease after buckling but also the jump size and the torque change during abrupt buckling. The computer model allows thereby new insights into the torsional and electrostatic behavior of supercoiled DNA. Further details not directly accessible in experiments like plectoneme geometry or singular energy distributions can easily be derived.