Fast algorithms for efficient biosequence search

Summary

DNA sequencing and the following analysis of biosequences become a core procedure for many problems in biological research, such as medical diagnosis, development of target medicine, virology, forensic sciences, etc. Examples of biosequence search include the detection of mutations within human DNA in cancer studies and searching for matching patterns in microbial genomes.
With an ever-increasing volume of data to process, the development of efficient search algorithms becomes of paramount importance.

Seeding is one of the techniques which is extensively used in biosequence alignment problems to speed up the searching procedure. A few seeding algorithms have been proposed in the past years. The first seeds which have been suggested represent small contiguous matching patterns and explore the seed-and-extend paradigm. Later the idea has been developed into spaced seeds (binary/ternary), allowing mismatches.

Another technique is k-mers, a set of short matching patterns of length k which is often used in alignment-free methods.

However, finding optimal seeds/k-mers, which maximize efficiency, is still a topic for study. Usually, efficiency can be assessed as a compromise between the algorithm’s time complexity and its sensitivity (ratio of correctly aligned sequences). Different studies suggest different methods for increasing efficiency. Often the selection is based on a certain probabilistic model and pre-defined properties of seeds.

In this project, the student will look into the problem of generating optimal seeds/k-mers to improve the efficiency of biosequence searching algorithms. The focus will be made on the development of a mathematical framework to investigate and demonstrate the efficiency of suggested seeds’ structures.

It has been shown in [1] that spaced seeds may be more efficient than contiguous seeds. Other designs of seeding strategy have been suggested, such as adaptive seeds and minimisers to speed up the search at the price of decreasing sensitivity.

Seeds generators which produce seeds of a certain structure to satisfy given parameters have been proposed in [2] and [3]. The properties of optimal seeds have been investigated in [4] and a list of optimal seeds for predefined structural properties has been suggested.

An example of investigating an optimal parameter for k-mers in error correction tools can be found in [5].

[1] Keich Uri, Li Ming, Ma Bin, Tromp John, On spaced seeds for similarity search. Discrete Applied Mathematics. https://doi.org/10.1016/S0166-218X(03)00382-2

[2] Brejová, B., Brown, D. G., & Vinar, T. (2004). Optimal spaced seeds for homologous coding regions. Journal of bioinformatics and computational biology, 1(4), 595–610. https://doi.org/10.1142/s0219720004000326

[3] Kucherov, G., Noé, L., & Roytberg, M. (2006). A unifying framework for seed sensitivity and its application to subset seeds. Journal of bioinformatics and computational biology, 4(2), 553–569. https://doi.org/10.1142/s0219720006001977

[4] Valeriy Titarenko, Sofya Titarenko. PerFSeeB: Designing Long High-weight Single Spaced Seeds for Full Sensitivity Alignment with a Given Number of Mismatches, 15 November 2021, PREPRINT (Version 1) available at Research Square [https://doi.org/10.21203/rs.3.rs-1051543/v1]

[5] Sharma, A., Jain, P., Mahgoub, A. et al. Lerna: transformer architectures for configuring error correction tools for short- and long-read genome sequencing. BMC Bioinformatics 23, 25 (2022). https://doi.org/10.1186/s12859-021-04547-0

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