Energy landscape analysis of the development of the chromosome structure across the cell cycle

Abstract

During mitosis, there are significant structural changes in chromosomes. We used a maximum entropy approach to invert experimental Hi-C data to generate effective energy landscapes for chromosomal structures at different stages during the cell cycle. Modeled mitotic structures show a hierarchical organization of helices of helices. High-periodicity loops span hundreds of kilobases or less, while the other low-periodicity ones are larger in genomic separation, spanning several megabases. The structural ensembles reveal a progressive decrease in compartmentalization from interphase to mitosis, accompanied by the appearance of a second diagonal in prometaphase, indicating an organized array of loops. While there is a local tendency to form chiral helices, overall, no preferential left-handed or right-handed chirality appears to develop on the time scale of the cell cycle. Chromatin thus appears to be a liquid crystal containing numerous defects that anneal rather slowly.

Keywords: chromatin dynamics; energy landscape; mitotic chromosome.

Fig. 1.

Modeling chromosome structural changes across the cell cycle. (A) Representative 3D structures of chromosome 7 from DT40 chicken cells at different time points after release from G2 arrest. Structures are shown at information temperature 1.0 and are derived from the average over 3D ensembles of 200,000 structures. Colors represent the time evolution of chromosomes along the cell cycle. (B) Experimental (Lower triangle) and in silico (Upper triangle) Hi-C contact maps for chromosome 7 at different time points. (C) Contact probability as a function of genomic distance curves for chromosome 7 obtained from experimental (dashed gray) and simulated (colored) Hi-C data. (D) Compartmentalization saddle plots showing the A–B phase separation sharpness by averaging interaction frequencies between pairs of 100 kb bins ranked by their G2 eigenvector value.

Fig. 2.

Structural heterogeneity and helical ordering of chromosome 7 during the cell cycle. (A) Representative quenched structures of chromosome 7 at different time points after release from G2 arrest. Structures are colored according to their genomic position, with blue representing the beginning of the chromosome and red representing the end. (B) Orientation order parameter (OP) as a function of genomic distance for all simulated time points. The Orientation order parameter oscillates as a function of genomic distance, indicating the presence of fibril structures. (C) Fourier spectrum of the Orientation order parameter signals, showing the dominant frequencies of the helical turns in two regimes. The high-periodicity turns are on the order of a few hundred kilobases, while the low-periodicity turns correspond to the second band diagonal observed in the Hi-C maps in the order of megabases. (D) Coarsened structure based on the high-periodicity turns, highlighting the spiral organization of helices of helices in the mitotic chromosome.

Fig. 3.

Chiral symmetry breaking and helical ordering of chromosome 7 during the cell cycle. (A) Local collective chiral variable Fig. 3 along the annealing simulation for different time points across the cell cycle. Blue represents a right-handed twist, and red represents a left-handed twist. (B) Chromosome structures are colored based on their local chirality degree score for high-frequency helices. (C) Chirality for the coarsened chromosome structures, showing global twisting, especially at later time points. (D) Diffusion coefficient, defect propagation time, and defect lifespan analysis for structural ensemble simulated in $T=0.2$ (blue) and $T=1.0$ (gray).