Are there rearrangement hotspots in the human genome?

Abstract

In a landmark paper, Nadeau and Taylor [18] formulated the random breakage model (RBM) of chromosome evolution that postulates that there are no rearrangement hotspots in the human genome. In the next two decades, numerous studies with progressively increasing levels of resolution made RBM the de facto theory of chromosome evolution. Despite the fact that RBM had prophetic prediction power, it was recently refuted by Pevzner and Tesler [4], who introduced the fragile breakage model (FBM), postulating that the human genome is a mosaic of solid regions (with low propensity for rearrangements) and fragile regions (rearrangement hotspots). However, the rebuttal of RBM caused a controversy and led to a split among researchers studying genome evolution. In particular, it remains unclear whether some complex rearrangements (e.g., transpositions) can create an appearance of rearrangement hotspots. We contribute to the ongoing debate by analyzing multi-break rearrangements that break a genome into multiple fragments and further glue them together in a new order. In particular, we demonstrate that (1) even if transpositions were a dominant force in mammalian evolution, the arguments in favor of FBM still stand, and (2) the "gene deletion" argument against FBM is flawed.

Figure 1. The Breakpoint Graph

The breakpoint graph G(P,Q) of a two-chromosomal genome P = (+ a + b − c) (−d + e) and a unichromosomal genome Q = (+a + b – e + c − d) represented as two black-obverse cycles and a gray-obverse cycle, correspondingly.

Figure 2. Different Types of 2-Breaks

A 2-break on edges (u,v) and (x,y) corresponding to (A) reversal: the edges belong to the same black-obverse cycle that is rearranged after 2-break; (B) fission: the edges belong to the same black-obverse cycle that is split by 2-break; and (C) translocation/fusion: the edges belong to different black-obverse cycles that are joined by 2-break.

Figure 3. Example of a 3-Break That Corresponds to a Transposition

A 3-break on edges (u,v), (x,y) and (z,t) corresponding to a transposition of the segment y…t from one chromosome to another. A transposition cuts off a segment of one chromosome and inserts it into the same or another chromosome. A transposition of a segment π_iπ_i+1…π_j of a chromosome π₁…π_i-1π_iπ_i+1…π_jπ_j+1…π_k-1π_k…π_n into a position k of the same chromosome results in a chromosome π₁…π_i-1π_j+1…π_k-1π_iπ_i+1…π_jπ_κ…π_n. For chromosomes π = π₁…π_m and σ = σ₁…σ_n, a transposition of a segment π_iπ_i+1…π_j of chromosome π into a position k in the chromosome σ results in chromosomes π₁…π_i-1π_j+1π_j+2…π_m and σ₁…σ_k-1π_iπ_i+1…π_jσ_k…σ._n. Underlining shows a piece of chromosome that was transposed from one chromosome to another.

Figure 4. Breakpoint Re-Use Rate as a Function of the Number of Complete 3-Breaks

A lower bound for the breakpoint re-use rate as a function of the number of complete 3-breaks in a series of 3-breaks between the circularized human and mouse genomes based on 281 conserved segments from [46]. In the case of linear genomes, the plot is similar, with the breakpoint re-use rate of ≈0.1 lower than in the circular case [47]. In particular, even in the extreme case when the number of transpositions is not limited, the breakpoint re-use rate of ≈1.31 is still higher than the breakpoint re-use rate expected for RBM (see [4]).

Figure 5. Breakpoint Re-Use Rate as a Function of θ, the Proportion of the Elements Deleted

(A) Breakpoint re-use rate for parameters n = 100 (m = 5, 12, 20, 32, and 48) and n = 1,000 (m = 50, 120, 200, 320, and 480), where n stands for the number of elements (genes) and m stands for the number of reversals. Since we reproduced simulations in [7], this figure and Figure 1 from [7] are identical. Detailed description (including pseudocode) of this simulation is given in [20]. (B) Breakpoint re-use rate for parameters n = 25,000 (m = 50, 120, 200, 320, and 480).

Figure 6. Distribution of Synteny Block Sizes

(A) Synteny block sizes (for a permutation with 1,000 elements after 320 reversals) do not fit the exponential distribution expected from RBM. (B) Synteny block sizes (for a permutation with 25,000 elements after 320 reversals) fit the exponential distribution expected from RBM.

Figure 7. Breakpoint Re-Use Rate as a Function of σ, the Maximal Size of Deleted Synteny Blocks, and Its Distribution at σ = 0.00033

(A) Breakpoint re-use rate as a function of the maximal size of deleted synteny blocks (as the proportion of the whole genome length). Deletion of blocks shorter than 1 Mb as in [4] (assuming that the human genome is ≈3,000 Mb long, σ = 1 Mb/3,000 Mb ≈ 0.00033) results in low breakpoint re-use (≈1.2). The plot shows simulations for a genome with 25,000 genes and 320 reversals (in this case, σ = 0.00033 corresponds to deleting all synteny blocks shorter than nine genes). (B) The distribution of breakpoint re-use at σ = 0.00033 with a mean of 1.23 and a standard deviation of 0.02 (100,000 simulations). The maximum breakpoint re-use rate in this simulation was 1.33, and it appeared only once.

Figure 8. Distribution of the Synteny Block Sizes between the Human and Mouse Genomes

Distribution of the synteny block sizes between the human and mouse genomes based on (A) 281 synteny blocks from [46] with extra 190 “hidden” short synteny blocks as predicted in [4] (this figure corresponds to Figure 1, center panel in [4]); and (B) 566 human–mouse synteny blocks derived from 1,338 multispecies conserved segments in [22]. The large number of confirmed short synteny blocks (leftmost bar in [B]) is already in conflict with the exponential distribution imposed by RBM. Moreover, the leftmost bar in (B) represents only the currently known short synteny blocks and does not even account for still unknown “hidden” synteny blocks that may have evaded the computational techniques in [22].