Abstract
One fundamental problem of bioinformatics is the computational recognition of DNA and RNA binding sites. Given a set of short DNA or RNA sequences of equal length such as transcription factor binding sites or RNA splice sites, the task is to learn a pattern from this set that allows the recognition of similar sites in another set of DNA or RNA sequences. Permuted Markov (PM) models and permuted variable length Markov (PVLM) models are two powerful models for this task, but the problem of finding an optimal PM model or PVLM model is NP-hard. While the problem of finding an optimal PM model or PVLM model of order one is equivalent to the traveling salesman problem (TSP), the problem of finding an optimal PM model or PVLM model of order two is equivalent to the quadratic TSP (QTSP). Several exact algorithms exist for solving the QTSP, but it is unclear if these algorithms are capable of solving QTSP instances resulting from RNA splice sites of at least 150 base pairs in a reasonable time frame. Here, we investigate the performance of three exact algorithms for solving the QTSP for ten datasets of splice acceptor sites and splice donor sites of five different species and find that one of these algorithms is capable of solving QTSP instances of up to 200 base pairs with a running time of less than two days.
Highlights
Gene regulation in higher organisms is accomplished at several levels such as transcriptional regulation and post-transcriptional regulation by several cellular processes such as transcription initiation and RNA splicing
The computational recognition of RNA splice sites is an important task in bioinformatics, and two popular models for this task are permuted Markov models and permuted variable length Markov models
Learning permuted Markov models and permuted variable length Markov models is NP-hard and, a challenging problem for the recognition of RNA splice sites, because it could be shown that sequences of at least 150 bp surrounding the splice sites should be taken into account for a reliable recognition of RNA splice sites
Summary
Gene regulation in higher organisms is accomplished at several levels such as transcriptional regulation and post-transcriptional regulation by several cellular processes such as transcription initiation and RNA splicing. Many approaches for the computational recognition of transcription factor binding sites or RNA splice sites rely on statistical models, and two popular models for this task are permuted Markov (PM). It would be desirable to develop exact algorithms capable of learning PM models and PVLM models for RNA splice sites of at least 150 bp in practically acceptable running times. For PM models and PVLM models of order one, the task of learning the maximum likelihood model results in the traditional Hamiltonian path problem (HPP) or the related traditional traveling salesman problem (TSP). For more powerful PM models and PVLM models of order two, the task of learning the maximum likelihood model results in the quadratic Hamiltonian path problem (QHPP) or the related quadratic traveling salesman problem (QTSP), which are extensions of the traditional linear HPP and TSP, respectively.
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