Diffusion-Driven Looping Provides a Consistent Framework for Chromatin Organization

Abstract

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.

Complexity of chromatin folding is captured by the strings and binders switch model

“…Furthermore, although these models explain the plateau of the mean-square spatial distance, R 2 ðsÞ, at large s, they do not reproduce the behavior of the contact probability, P c ðsÞ, observed in Hi-C data, as does the SBS model. More recently, the possibility of transient interactions across a polymer has been studied in the dynamic loop (DL) model, which, to mimic the effects of bridging molecules, assigns an attachment probability to genomic regions that randomly meet in space (35). In agreement with the SBS model, the DL model can also reproduce the Hi-C exponent of P c ðsÞ.…”

“…In principle, K carries information about genomic locus-to-locus and cell-to-cell variations. Interestingly, K has been measured experimentally by FISH (9,34,35) and found to vary between 1.5 and 4.4, depending on the locus and cell type studied (Fig. 4A).…”

“…The experimental observations (9,34,35) Measurements of K from previous models produce a constant value of K. The randomly folded polymer (SAW) model produces K ¼ 1.5 (22). Previous polymer models that consider the effects of both specified chromatin loops at fixed lengths of 120 kb and 3 Mb (12,36), and the possibility of chromatin loops of all sizes (37), also produce constant K values.…”

Shape Transitions and Chiral Symmetry Breaking in the Energy Landscape of the Mitotic Chromosome

“…A complete understanding of chromosomal organization is challenging since the condensation of the chromosome into its dense mitotic form permits many different orderings and phase transitions. Owing to the large scale of the chromosome, we also can expect interesting non-equilibrium glassy dynamics and possible kinetic control of structure formation [5][6][7][8][9][10][11][12][13].Structural models of the mitotic chromosome have been proposed, including the radial loop model [4], the chromatin network model [14] and the hierarchical folding model [3]. These models often highlight the biologically specific role of protein molecules but the intrinsic properties of the DNA as a long highly helical molecule must also be at work.…”

“…A complete understanding of chromosomal organization is challenging since the condensation of the chromosome into its dense mitotic form permits many different orderings and phase transitions. Owing to the large scale of the chromosome, we also can expect interesting non-equilibrium glassy dynamics and possible kinetic control of structure formation [5][6][7][8][9][10][11][12][13].…”