Current theoretical models fail to predict the topological complexity of the human genome

Abstract

Understanding the folding of the human genome is a key challenge of modern structural biology. The emergence of chromatin conformation capture assays (e.g., Hi-C) has revolutionized chromosome biology and provided new insights into the three dimensional structure of the genome. The experimental data are highly complex and need to be analyzed with quantitative tools. It has been argued that the data obtained from Hi-C assays are consistent with a fractal organization of the genome. A key characteristic of the fractal globule is the lack of topological complexity (knotting or inter-linking). However, the absence of topological complexity contradicts results from polymer physics showing that the entanglement of long linear polymers in a confined volume increases rapidly with the length and with decreasing volume. In vivo and in vitro assays support this claim in some biological systems. We simulate knotted lattice polygons confined inside a sphere and demonstrate that their contact frequencies agree with the human Hi-C data. We conclude that the topological complexity of the human genome cannot be inferred from current Hi-C data.

Keywords: BFACF; DNA knotting; Hi-C; chromosome organization; equilibrium globule; lattice models.

Figure 1

Computational methods used to generate BFACF globules. (A) BFACF moves: the 0-move (left) does not change the length of the conformation; the (+2)- and (-2)-moves (right) can add/remove an edge. (B) From left to right we illustrate a trefoil knot 3₁ smoothly embedded in R³, a minimal step lattice realization of 3₁, and the resulting BFACF globule. This BFACF globule is a 4000-step embedding of the knot within a sphere of radius 10.5 obtained using the modified BFACF algorithm described in Section 2. (C) Log-log plot of the contact probability as a function of contour length. The data are obtained as an average over 10,000 sampled BFACF globules with knot type 3₁. The slope of the linear fit is in excellent agreement with the experimental data of Lieberman-Aiden et al. (2009). (D) Contact probability curves for connected sums of trefoils (_31)n for n = 1, 20, 40, 60, 100, with slopes −1.085±0.003, −1.079±0.003, −0.919±0.011, −0.656±0.013, −0.558±0.035, respectively.