A two-backbone polymer model for interphase chromosome geometry

Spatially confined folding of chromatin in the interphase nucleus

Genome function in higher eukaryotes involves major changes in the spatial organization of the chromatin fiber. Nevertheless, our understanding of chromatin folding is remarkably limited. Polymer models have been used to describe chromatin folding. However, none of the proposed models gives a satisfactory explanation of experimental data. In particularly, they ignore that each chromosome occupies a confined space, i.e., the chromosome territory. Here, we present a polymer model that is able to describe key properties of chromatin over length scales ranging from 0.5 to 75 Mb. This random loop (RL) model assumes a self-avoiding random walk folding of the polymer backbone and defines a probability P for 2 monomers to interact, creating loops of a broad size range. Model predictions are compared with systematic measurements of chromatin folding of the q-arms of chromosomes 1 and 11. The RL model can explain our observed data and suggests that on the tens-of-megabases length scale P is small, i.e., 10-30 loops per 100 Mb. This is sufficient to enforce folding inside the confined space of a chromosome territory. On the 0.5- to 3-Mb length scale chromatin compaction differs in different subchromosomal domains. This aspect of chromatin structure is incorporated in the RL model by introducing heterogeneity along the fiber contour length due to different local looping probabilities. The RL model creates a quantitative and predictive framework for the identification of nuclear components that are responsible for chromatin-chromatin interactions and determine the 3-dimensional organization of the chromatin fiber.

Conformation of replicated segments of chromosome fibres in human S-phase nucleus

Recent statistical analysis of the folding of G0/G1 chromosomes using fluorescence in situ hybridization (FISH) allowed development of a random walk/giant loop model of chromosome structure. According to this model there are two levels of organization of G0/G1 chromosome fibres. On the first level, the fibres are arranged in giant loops several Mbp in size, and within each loop the fibres are randomly folded. On the second level, the loop attachment sites form a chromosome backbone that also shows random folding. Newly replicated segments of mammalian chromosomes may be directly visualized at high resolution in S-phase nuclei using immunofluorescent methods and appear as worm-like fibres. In our earlier study, we analysed conformation of the fibres in human cells blocked for 16 h at the G1/S boundary with 5-fluorodeoxyuridine (FdU) and then released into S-phase by the addition of a DNA precursor. However, long treatment of cells with FdU induces very short replicons and may promote apoptosis. In this study we analysed conformation of the fibres in normally proliferating human cells that had not been blocked with FdU for a long time. It has been found that replicated chromosome fibres visualized just after 2 h of incubation of the cells with a non-radioactively labelled DNA precursor behave as flexible polymer chains without major constraints, and that their local conformation in the range of several microns of their contour length may be considered as random. Confocal analysis of human X chromosomes visualized in HeLa cells using FISH with a specific painting probe shows that in S-phase the chromosomes occupy distinct nuclear territories and their apparent size does not differ from that in non-S-phase cells. This observation indicates that the second level of chromosome organization also exists in S-phase chromosomes. It appears, therefore, that the random walk/giant loop model developed earlier for G0/G1 chromosomes is also valid for S-phase chromosomes.

A polymer model for the structural organization of chromatin loops and minibands in interphase chromosomes

A quantitative model of interphase chromosome higher-order structure is presented based on the isochore model of the genome and results obtained in the field of copolymer research. G1 chromosomes are approximated in the model as multiblock copolymers of the 30-nm chromatin fiber, which alternately contain two types of 0.5- to 1-Mbp blocks (R and G minibands) differing in GC content and DNA-bound proteins. A G1 chromosome forms a single-chain string of loop clusters (micelles), with each loop approximately 1-2 Mbp in size. The number of approximately 20 loops per micelle was estimated from the dependence of geometrical versus genomic distances between two points on a G1 chromosome. The greater degree of chromatin extension in R versus G minibands and a difference in the replication time for these minibands (early S phase for R versus late S phase for G) are explained in this model as a result of the location of R minibands at micelle cores and G minibands at loop apices. The estimated number of micelles per nucleus is close to the observed number of replication clusters at the onset of S phase. A relationship between chromosomal and nuclear sizes for several types of higher eukaryotic cells (insects, plants, and mammals) is well described through the micelle structure of interphase chromosomes. For yeast cells, this relationship is described by a linear coil configuration of chromosomes.