Christian Münkel

Compartmentalization of interphase chromosomes observed in simulation and experiment.

Human interphase chromosomes were simulated as a flexible fiber with excluded volume interaction, which represents the chromatin fiber of each chromosome. For the higher-order structures, we assumed a folding into 120 kb loops and an arrangement of these loops into rosette-like subcompartments. Chromosomes consist of subcompartments connected by small fragments of chromatin. Number and size of subcompartments correspond with chromosome bands in early prophase. We observed essentially separated chromosome arms in both our model calculations and confocal laser scanning microscopy, and measured the same overlap in simulation and experiment. Overlap, number and size of chromosome 15 subcompartments of our model chromosomes agree with subchromosomal foci composed of either early or late replicating chromatin, which were observed at all stages of the cell cycle and possibly provide a functionally relevant unit of chromosome territory compartmentalization. Computed distances of chromosome specific markers both on Mb and 10-100 Mb scale agree with fluorescent in situ hybridization measurements under different preparation conditions.

Separate and variably shaped chromosome arm domains are disclosed by chromosome arm painting in human cell nuclei

Fluorescence in situ hybridization (FISH) with microdissection probes from human chromosomes 3 and 6 was applied to visualize arm and subregional band domains in human amniotic fluid cell nuclei. Confocal laser scanning microscopy and quantitative three-dimensional image analysis showed a pronounced variability of p- and q-arm domain arrangements and shapes. Apparent intermingling of neighbouring arm domains was limited to the domain surface. Three-dimensional distance measurements with pter and qter probes supported a high variability of chromosome territory folding.

The dynamical critical exponent of the two-, three- and five-dimensional kinetic Ising model

Abstract We present Monte Carlo simulation results for the dynamical critical exponent z of the two-, three- and five-dimensional kinetic Ising model. We used Glauber as well as Metropolis dynamics. Both type of dynamics lead to the same z-values in two and three dimensions. The z-values were calculated from the magnetization relaxation from an ordered state into the equilibrium state at Tc for very large systems (up to (169984)2, (3072)3 and (48)5). For the two-dimensional case we obtain z = 2.21 ± 0.03 and for the three-dimensional case z = 2.08 ± 0.03. For the five-dimensional Glauber case, the requirement z = 2 gives a critical point J/kBTc = 0.11391 from Monte Carlo simulations, whereas new series expansions with four more terms give 0.113935 ± 0.000015 for this ratio.

Three‐dimensional distribution of centromeric or paracentromeric heterochromatin of chromosomes 1, 7, 15 and 17 in human lymphocyte nuclei studied with light microscopic axial tomography

Light microscopic axial tomography was applied to examine the position of peri- or paracentromeric chromosomal targets in nuclei of PHA-stimulated human lymphocytes following two color fluorescence in situ hybridization with DNA probes for 1q12 and 15p or 7c and 17c. Evaluation of hybridized nuclei was performed in a glass capillary device. By turning the capillary around its longitudinal axis each nucleus could be viewed at any desired angle. To measure the true three-dimensional distance between two chromosomal targets, the nucleus was turned around until both targets were positioned in the same focal plane. Similarly, the true distance between a target region and the center of the nucleus was estimated. The results provide evidence for differences in the three-dimensional nuclear distribution of the target regions. In particular, 7c was positioned more peripherally than the other chromosomal targets. Experimental data were compared with several models for a distribution of chromosomal targets under topological constraints. These models take into account spatial limitations of the distribution of the chromosome territories which harbor the hybridized targets.

A Brownian dynamics model for the chromatin fiber

MOTIVATION We describe a Brownian dynamics model for the folding of the chromatin fiber based on the model of Woodcock et al. (Proc Natl Acad Sci USA, 90, 9021-9025, 1993). The model takes into account the elastic properties of the DNA as well as the electrostatic interaction and nucleosomal excluded-volume interaction. The solvent is described as a viscous medium, the electrostatic interactions by a screened Coulomb potential. RESULTS The hydrodynamic properties and their dependence on the solvents ionic strength are accurately reproduced by the model for nucleosome di- and tetramers. Ionic strength-dependent changes in mobility can be attributed to partial screening of the electrostatic repulsion between different segments of linker DNA. Formation of fiber-like structures occurs on time scales of several hundred microseconds for a linear configuration of 25 nucleosomes. The model was implemented by creating user-defined data types. Use of this so-called object-oriented paradigm allowed for a high degree of component reuse in simulation, analysis and visualization contexts. AVAILABILITY The described software is available on request from the authors. Additional information can be found on the WWW at http:/(/)www.dkfz-heidelberg.de/Macromol/ehrlich /chromatin.htm/.

Simulation of the distribution of chromosome targets in cell nuclei under topological constraints

Several models for the distribution of subchromosomal targets under topological constraints were developed which take into account that chromosomes occupy distinct, mutually exclusive territories in the cell nucleus. Nuclei and two pairs of chromosome territories of various size were modeled by spheres or ellipsoids under the simplified assumption that the entire set of chromosome territories present in a diploid cell nucleus completely fills the nuclear interior and that each territory occupies a fraction of the nuclear volume proportional to its DNA content. Monte Carlo simulations of the distribution of the territory gravity centers were performed taking into account the constraint of territory extension by the nuclear boundary and the constraint of territory self avoidance, i.e. territories should not intersect each other. In addition, various assumptions were made with regard to the location of point-like targets either within or at the surface of two ‘homologous’ model territories. For each assumption the distance between the two point-like targets and between each target and the center of the model nucleus was calculated in Monte Carlo simulations and in part also analytically. The distribution of point-like targets in model nuclei under the influence of these topological constraints depends on the shape of the model nucleus and shows strong deviations from a model often applied in previous studies. In this model the random distribution of point-like targets was described under the assumption that such targets are distributed uniformly and independently from each other within the nuclear space without any constraints except for the nuclear boundary. All models were applied to experimentally measured distributions of chromosomal subregions delineated by fluorescence in situ hybridization with subregion specific probes. We demonstrate that a neglect of geometrical constraints in the simulation of target distributions can lead to erroneous conclusions of whether experimental target distributions occur in a random manner or not.

Folding Transitions of Self-Avoiding Membranes.

The phase structure of self-avoiding polymerized membranes is studied by extensive Hybrid Monte Carlo simulations. Several folding transitions from the flat to a collapsed state are found. Using a suitable order parameter and finite size scaling theory, these transitions are shown to be of {\em first order}. The phase diagram in the temperature-field plane is given.

The Crumpling Transition of Dynamically Triangulated Random Surfaces

We present the crumpling transition in three-dimensional Euclidian space of dynamically triangulated random surfaces with edge extrinsic curvature and fixed topology of a sphere as well as simulations of a dynamically triangulated torus. We used longer runs than previous simulations and give new and more accurate estimates of critical exponents. Our data indicate a cusp singularity in the specific heat. The transition temperature, as well as the exponents are topology dependent

Visualization of polymer systems

The combination of computer simulations of polymer systems and three-dimensional scientific visualization of these systems is discussed in this paper.

Three-Dimensional Organization of Chromosome Territories and the Human Cell Nucleus

Despite the successful linear sequencing of the human genome its three-dimensional structure is widely unknown. However, the regulation of genes — their transcription and replication — has been shown to be closely connected to the three-dimensional organization of the genome and the cell nucleus. On the bases of polymer physics we have recently developed detailed and quantitative structural models for the folding of the 30 nm chromatin fiber within the human interphase cell nucleus. A quantitative test of several plausible theories resulted in a best agreement between computer simulations of chromosomes, cell nuclei and experiments for the so called Multi-Loop-Subcompartment (MLS) model. Results concern the following properties: overlap of chromosome territories, -arms, -bands, 3D spatial distances between genomic markers as function of their genomic separation in base pairs, fractal analyis of simulations, mass distribution of chromatin in cell nuclei and the fragmentation distribution of cellular DNA after irradiation with carbon ions. Thus in an anology to the Bauhaus principle that “form follows function”, analyzing in which form DNA is organized might help us to understand genomic function.