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.genome organization ͉ polymer model ͉ chromatin folding T he chromatin fiber inside the interphase nucleus of higher eukaryotes is folded and compacted on several length scales. On the smallest scale the basic filament is formed by wrapping double-stranded DNA around a histone protein octamer, forming a nucleosomal unit every Ϸ200 bp. This beads-on-a-string type filament in turn condenses to a fiber of 30-nm diameter, which detailed organization is still under debate (1-3). At bigger length scales the spatial organization of chromatin in the interphase nucleus is even more unclear. Imaging techniques do not allow one to directly follow the folding path of the chromatin fiber in the interphase nucleus. Therefore, indirect approaches have been used to obtain information about chromatin folding. One way, pursued in this study, is fluorescence in situ hybridization (FISH) to measure the relationship between the physical distance between genomic sequence elements (in m) and their genomic distance (in megabases). There have been several attempts to explain the folding of chromatin in the interphase nucleus using polymer models. The strength of polymer models is their ability to make predictions on the structure of chromatin by pointing out the driving forces for observed folding motifs. These predictions can then be tested experimentally. However, a polymer model that is able to explain chromatin folding spanning differen...
Chromatin folding inside the interphase nucleus of eukaryotic cells is done on multiple scales of length and time. Despite recent progress in understanding the folding motifs of chromatin, the higher-order structure still remains elusive. Various experimental studies reveal a tight connection between genome folding and function. Chromosomes fold into a confined subspace of the nucleus and form distinct territories. Chromatin looping seems to play a dominant role both in transcriptional regulation as well as in chromatin organization and has been assumed to be mediated by long-range interactions in many polymer models. However, it remains a crucial question which mechanisms are necessary to make two chromatin regions become co-located, i.e. have them in spatial proximity. We demonstrate that the formation of loops can be accomplished solely on the basis of diffusional motion. The probabilistic nature of temporary contacts mimics the effects of proteins, e.g. transcription factors, in the solvent. We establish testable quantitative predictions by deriving scale-independent measures for comparison to experimental data. In this Dynamic Loop (DL) model, the co-localization probability of distant elements is strongly increased compared to linear non-looping chains. The model correctly describes folding into a confined space as well as the experimentally observed cell-to-cell variation. Most importantly, at biological densities, model chromosomes occupy distinct territories showing less inter-chromosomal contacts than linear chains. Thus, dynamic diffusion-based looping, i.e. gene co-localization, provides a consistent framework for chromatin organization in eukaryotic interphase nuclei.
Remarkably little is known about the higher-order folding motifs of the chromatin fibre inside the cell nucleus. Folding depends among others on local gene density and transcriptional activity and plays an important role in gene regulation. Strikingly, at fibre lengths above 5 to 10 Mb the measured mean square distance˙R 2¸b etween any two points on the chromatin fibre is independent of polymer length. We propose a polymer model that can explain this levelling-off by means of random looping. We derive an analytical expression for the mean square displacement between two arbitrary beads. Here the average is taken over the thermal ensemble with a fixed but random loop configuration, while quenched averaging over the ensemble of different loop configurationswhich turns out to be equivalent to averaging over an ensemble of random matrices -is performed numerically. A detailed investigation of this model shows that loops on all scales are necessary to fit experimental data.
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