EXHAUSTIVE COMPUTATION OF EXACT DUPLICATIONS VIA SUPER AND NON-NESTED LOCAL MAXIMAL REPEATS

Abstract

We propose and implement a method to obtain all duplicated sequences (repeats) from a chromosome or whole genome. Unlike existing approaches our method makes it possible to simultaneously identify and classify repeats into super, local, and non-nested local maximal repeats. Computation veri¯cation demonstrates that maximal repeats for a genome of several gigabases can be identi¯ed in a reasonable time, enabling us to identi¯ed these maximal repeats for any sequenced genome. The algorithm used for the identi¯cation relies on enhanced su±x array data structure to achieve practical space and time e±ciency, to identify and classify the maximal repeats, and to perform further post-processing on the identi¯ed duplicated sequences. The simplicity and e®ectiveness of the implementation makes the method readily extendible to more sophisticated computations. Maxmers can be exhaustively accounted for in few minutes for genome sequences of dozen megabases in length and in less than a day or two for genome sequences of few gigabases in length. One application of duplicated sequence identi¯cation is to the study of duplicated sequence length distributions, which our found to exhibit for large lengths a persistent power-law behavior. Variation of estimated exponents of this power law are studied among di®erent species and successive assembly release versions of the same species. This makes the characterization of the power-law regime of sequenced genomes via maximal repeats identi¯cation and classi¯cation, an important task for the derivation of models that would help us to elucidate sequence duplication and genome evolution.

Human–chimpanzee alignment: Ortholog exponentials and paralog power laws

“…Were these C⇒T/G⇒A substitutions neutral, an exponential would have been anticipated. Yet, a qualitatively similar phenomenon (criterion II shifts algebraic criterion I curves to larger numbers and greater lengths, with minimal impact on shape) is observed for duplications within a genome [9,16,31].…”

“…However, please note that here our definitions of nested and non-nested CMRs are different from those of nested and non-nested local maxmers by E Taillefer and J Miller in[31].…”

“…CMR distributions obtained with criteria I through IV display sufficient qualitative similarity to one another that only exact match distributions are displayed in this manuscript. An example for human-chimpanzee alignment can be found in the supplement (see figure S9 in Supplementary Text S2); for other genome pairs corresponding plots may be found in [9,17,26,30,31].…”

How Evolution of Genomes Is Reflected in Exact DNA Sequence Match Statistics

“…MLDs computed from the self-alignment of many other genomes have been presented by Taillefer and Miller (2014) . These MLDs exhibit power laws with various exponent (from to ).…”

On the Natural Structure of Amino Acid Patterns in Families of Protein Sequences

“…We classify the different MR patterns in three disjoint subsets: a) Super Maximal Repetition (SMR): a sequence that occurs more than once in s, and each of its extensions occurs only once; b) Nested Maximal Repetition (NE): a MR where all of its occurrences are contained in a longer MR; and c) Non-Nested Maximal Repetition (NN): a MR where at least one of its occurrences are not contained in a longer MR and is not SMR. Formal details on these definitions are described in previous work 13 .…”