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

Arsuaga J, Jayasinghe RG, Scharein RG, Segal MR, Stolz RH, Vazquez M - Front Mol Biosci (2015)

Bottom Line: A key characteristic of the fractal globule is the lack of topological complexity (knotting or inter-linking).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.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, University of California, Davis Davis, CA, USA ; Department of Molecular and Cellular Biology, University of California, Davis Davis, CA, USA.

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.

No MeSH data available.


Related in: MedlinePlus

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.
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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.

Mentions: Our approach is based on, and extends, the BFACF algorithm. BFACF is a dynamic Monte Carlo method acting on the space of self-avoiding polygons in the simple cubic lattice (Z3) by performing one of the three local moves described in Figure 1A (Aragão de Carvalho and Caracciolo, 1983; Aragão de Carvalho et al., 1983; Madras and Slade, 1996). The acceptance probabilities for each move, denoted by p(0), p(2), and p(−2), are a function of the fugacity per bond z, where 0≤z≤z0. Within this range, the choice of z determines the average length of the generated lattice polygons. Going beyond this range causes the average polygon length to diverge. In BFACF the equilibrium conformations are sampled from a Boltzmann distribution (reviewed in Madras and Slade, 1996), and the ergodicity classes are the knot types (Janse van Rensburg and Whittington, 1991).


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

Arsuaga J, Jayasinghe RG, Scharein RG, Segal MR, Stolz RH, Vazquez M - Front Mol Biosci (2015)

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.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4543886&req=5

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.
Mentions: Our approach is based on, and extends, the BFACF algorithm. BFACF is a dynamic Monte Carlo method acting on the space of self-avoiding polygons in the simple cubic lattice (Z3) by performing one of the three local moves described in Figure 1A (Aragão de Carvalho and Caracciolo, 1983; Aragão de Carvalho et al., 1983; Madras and Slade, 1996). The acceptance probabilities for each move, denoted by p(0), p(2), and p(−2), are a function of the fugacity per bond z, where 0≤z≤z0. Within this range, the choice of z determines the average length of the generated lattice polygons. Going beyond this range causes the average polygon length to diverge. In BFACF the equilibrium conformations are sampled from a Boltzmann distribution (reviewed in Madras and Slade, 1996), and the ergodicity classes are the knot types (Janse van Rensburg and Whittington, 1991).

Bottom Line: A key characteristic of the fractal globule is the lack of topological complexity (knotting or inter-linking).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.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, University of California, Davis Davis, CA, USA ; Department of Molecular and Cellular Biology, University of California, Davis Davis, CA, USA.

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.

No MeSH data available.


Related in: MedlinePlus