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Chromosomes in the nucleus assemble into hierarchies of 3D domains that, during interphase, share essential features with a knot-free condensed polymer known as the fractal globule (FG). The FG-like chromosome likely affects macromolecular transport, yet its characteristics remain poorly understood. Using computer simulations and scaling analysis, we show that the 3D folding and macromolecular size of the chromosomes determine their transport characteristics. Large-scale subdiffusion occurs at a critical particle size where the network of accessible volumes is critically connected. Condensed chromosomes have connectivity networks akin to simple Bernoulli bond percolation clusters, regardless of the polymer models. However, even if the network structures are similar, the tracer’s walk dimension varies. It turns out that the walk dimension depends on the network topology of the accessible volume and dynamic heterogeneity of the tracer’s hopping rate. We find that the FG structure has a smaller walk dimension than other random geometries, suggesting that the FG-like chromosome structure accelerates macromolecular diffusion and target-search.

Animals use the Polycomb system to epigenetically repress developmental genes. The repression requires trimethylation of lysine 27 of histone H3 (H3K27me3) by Polycomb Repressive Complex 2 (PRC2), but the dynamics of this process is poorly understood. To bridge the gap, we developed a computational model that forecasts H3K27 methylation in Drosophila with high temporal resolution and spatial accuracy of contemporary experimental techniques. Using this model, we show that pools of methylated H3K27 in dividing cells are defined by the effective concentration of PRC2 and the replication frequency. We find that the allosteric stimulation by preexisting H3K27me3 makes PRC2 better in methylating developmental genes as opposed to indiscriminate methylation throughout the genome. Applied to Drosophila development, our model argues that, in this organism, the intergenerationally inherited H3K27me3 does not “survive” rapid cycles of embryonic chromatin replication and is unlikely to transmit the memory of epigenetic repression to the offspring. Our model is adaptable to other organisms, including mice and humans. Computational forecasts of histone methylation shed light on the intergenerational inheritance of epigenetic repression.

Cells regulate fates and complex body plans using spatiotemporal signaling cascades that al- ter gene expression. Enhancers, short DNA sequences (50-150 base pairs), help coordinate these cascades by attracting regulatory proteins to enhance the transcription of distal genes by bind- ing to promoters. In humans, there are hundreds of thousands of enhancers dispersed across the genome, which poses a challenging coordination task to prevent unintended gene activation. To mit- igate this problem, the genome contains additional DNA elements, insulators, that block enhancer- promoter interactions. However, there is an open problem with how the insulation works, especially as enhancer-insulator pairs may be separated by millions of base pairs. Based on recent empirical data from Hi-C experiments, this paper proposes a new mechanism that challenges the common paradigm that rests on specific insulator-insulator interactions. Instead, this paper introduces a stochastic looping model where enhancers bind weakly to surrounding chromatin. After calibrating the model to experimental data, we use simulations to study the broad distribution of hitting times between an enhancer and a promter when there are blocking insulators. In some cases, there is a large difference between average and most probable hitting times, making it difficult to assign a typical time scale, hinting at highly defocused regulation times. We also map our computational model onto a resetting problem that allows us to derive several analytical results. Besides offering new insights into enhancer-insulator interactions, our paper advances the understanding of gene regulatory networks and causal connections between genome folding and gene activation.