Alignment-free Sequence Comparison for Biologically Realistic Sequences of Moderate Length

Burden, Conrad J.; Jing, Junmei; Wilson, Susan R.

doi:10.2202/1544-6115.1724

Cited by 8 publications

(9 citation statements)

References 19 publications

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“…For instance, in previous studies of a database of cis-regulatory modelled as a set of i.i.d. sequences was successfully studied using the D 2 statistics simply by imposing PBCs on the sequences prior to calculating the D 2 (Forêt et al, 2009a;Burden et al, 2012).…”

Section: Discussionmentioning

confidence: 99%

“…In biological aplications of the analogous results for i.i.d. sequences (Forêt et al, 2009a;Burden et al, 2012) we have found generally that the PBCs are not an impediment, as they can simply be imposed on the sequences prior to calculating D 2 without without seriously affecting its efficacy as a measure of sequence similarity.…”

Section: Introductionmentioning

confidence: 89%

“…For m = n, it has been shown that the limiting distribution is normal in the regime k < 1/2 log b n + const. (Burden et al, 2008) and Pólya-Aeppli in the regime k > 2 log b n + const. (Lippert et al, 2002).…”

Section: Numerical Simulationsmentioning

confidence: 97%

“…The distributional properties of the D 2 statistic under the null hypothesis of sequences composed of independently and identically distributed (i.i.d.) letters have been studied extensively (Lippert et al, 2002;Forêt et al, 2006;Kantorovitz et al, 2006;Forêt et al, 2009b;Forêt et al, 2009a;Burden et al, 2012).…”

Section: Introductionmentioning

confidence: 99%

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The Distribution of Short Word Match Counts between Markovian Sequences

Burden¹,

Leopardi²,

Fôret

2013

Proceedings of the International Conference on Bioinformatics Models, Methods and Algorithms

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The D 2 statistic, which counts the number of word matches between two given sequences, has long been proposed as a measure of similarity for biological sequences. Much of the mathematically rigorous work carried out to date on the properties of the D 2 statistic has been restricted to the case of 'Bernoulli' sequences composed of identically and independently distributed letters. Here the properties of the distribution of this statistic for the biologically more realistic case of Markovian sequences is studied. The approach is novel in that Markovian dependency is defined for sequences with periodic boundary conditions, and this enables exact analytic formulae for the mean and variance to be derived. The formulae are confirmed using numerical simulations, and asymptotic approximations to the full distribution are tested.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 89%

Section: Numerical Simulationsmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Distribution of Short Word Match Counts between Markovian Sequences

Burden¹,

Leopardi²,

Fôret

2013

Proceedings of the International Conference on Bioinformatics Models, Methods and Algorithms

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“…Needleman to Fitch 65 in 1965 and later introduced as the first algorithm for full-length sequence alignment 66 . Applied to molecular sequences, all these approaches find regions of local identity (or similarity).…”

Section: Oligonucleotides and K-mersmentioning

confidence: 99%

Scalable alignment-free approaches in microbial phylogenomics

Bernard¹

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In the 1970s Carl Woese and colleagues discovered the third domain of life by comparing oligonucleotide catalogs of 16S/18S rRNAs. Four decades later, phylogenetic studies are mostly based on multiple sequence alignment (MSA) approaches. However, genome evolution in microbes involves highly dynamic molecular mechanisms including genome rearrangement and lateral genetic transfer (LGT). These mechanisms can potentially violate the implicit assumption of full-length contiguity in MSA. Furthermore, commonly used MSA-based approaches can necessitate the use of heuristic methods, e.g. Bayesian inference, in reconstructing phylogenies, and these may not be scalable to the quantity of existing and forthcoming genome data. In recent years, alignment-free (AF) methods have been developed as an alternative strategy to infer evolutionary relatedness based on shared subsequences of fixed length, known as k-mers, similarly to Woese's preliminary work. In this thesis, I aimed to study the complex evolution of microbial genomes with the development of novel AF approaches, and systematic assessment of the AF methods' potential for phylogenetic inference. This could potentially provide new insight onto microbial evolution and change the way we do phylogenomics, i.e. potentially lead to the development of "next-generation phylogenomics".The thesis starts with a brief overview of the diversity of microbial life, and the difficulties in understanding microbial evolution due to complex phenomena such as LGT or rearrangement. I explain how phylogenomic approaches can be used to understand microbial evolution, and describe distinct approaches based on MSA and AF.The second chapter is a literature review of the conceptual foundations of alignment-free approaches for the inference of phylogenetic relationships of genome sequences. I discuss the limitations of MSA-based approaches, introduce the concept of k-mers, present in detail the different families of alignment-free approaches and describe their applications to infer vertical and lateral phylogenetic signal among microbial genomes.The three result chapters are presented in the form of research papers, each with its own introduction, methods, results and discussion.

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