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Extensive Monte Carlo simulations are presented for the bond-fluctuation model on three-dimensional simple cubic lattices. High statistics data are obtained for polymer volume fractions Φ in the range $0.025 \leqslant \Phi \leqslant 0.500$ and chain lengths N in the range $20 \leqslant N \leqslant 200$, making use of a parallel computer containing 80 transputers. The simulation technique takes into account both excluded volume interactions and entanglement restrictions, while otherwise the chains are non-interacting and athermal. The simulation data are analysed in terms of the de Gennes scaling concepts, describing the crossover from swollen coils in the dilute limit to gaussian coils in semidilute and concentrated solution. The crossover scaling functions for the chain linear dimensions and for the decay of the structure factor are estimated and compared to corresponding theoretical and experimental results in the literature. Also the dynamics of the chains is studied in detail, and evidence for a gradual crossover from the Rouse model to a D ∼N-2 law for the diffusion constant is presented. This crossover is consistent with scaling only if a concentration-dependent segmental “friction coefficient" is introduced. Within this framework general agreement between these data, other simulations and experiment is found

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...