symmetry S S Article Mathematical Algorithm for Identification of Eukaryotic Promoter Sequences Eugene V. Korotkov 1, * , Yulia. M. Suvorova 1 , Anna V. Nezhdanova 1 , Sofia E. Gaidukova 1 , Irina V. Yakovleva 1 , Anastasia M. Kamionskaya 1 and Maria A. Korotkova 2   Citation: Korotkov, E.V.; Suvorova, Y..M.; Nezhdanova, A.V.; Gaidukova, S.E.; Yakovleva, I.V.; Kamionskaya, A.M.; Korotkova, M.A. Mathematical Algorithm for Identification of Eukaryotic Promoter Sequences. Symmetry 2021, 13, 917. https:/ /doi.org/10.3390/sym13060917 Academic Editor: Laura Pop Received: 19 April 2021 Accepted: 18 May 2021 Published: 21 May 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Institute of Bioengineering, Federal Research Center of Biotechnology of the Russian Academy of Sciences, 119071 Moscow, Russia; suvorovay@biengi.ac.ru (Y.M.S.); anna-negdanova@mail.ru (A.V.N.); plasmid@yandex.ru (S.E.G.); iacgea@biengi.ac.ru (I.V.Y.); akatio@biengi.ac.ru (A.M.K.) 2 Institute of Cyber Intelligence Systems, National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), 115409 Moscow, Russia; makorotkova@mephi.ru * Correspondence: katrin2@biengi.ac.ru; Tel.: +79-26-724-8271 Abstract: Identification of promoter sequences in the eukaryotic genome, by computer methods, is an important task of bioinformatics. However, this problem has not been solved since the best algorithms have a false positive probability of 10 -3 –10 -4 per nucleotide. As a result of full genome analysis, there may be more false positives than annotated gene promoters. The probability of a false positive should be reduced to 10 -6 –10 -8 to reduce the number of false positives and increase the reliability of the prediction. The method for multi alignment of the promoter sequences was developed. Then, mathematical methods were developed for calculation of the statistically important classes of the promoter sequences. Five promoter classes, from the rice genome, were created. We developed promoter classes to search for potential promoter sequences in the rice genome with a false positive number less than 10 -8 per nucleotide. Five classes of promoter sequences contain 1740, 222, 199, 167 and 130 promoters, respectively. A total of 145,277 potential promoter sequences (PPSs) were identified. Of these, 18,563 are promoters of known genes, 87,233 PPSs intersect with transposable elements, and 37,390 PPSs were found in previously unannotated sequences. The number of false positives for a randomly mixed rice genome is less than 10 -8 per nucleotide. The method developed for detecting PPSs was compared with some previously used approaches. The developed mathematical method can be used to search for genes, transposable elements, and transcript start sites in eukaryotic genomes. Keywords: promoter; rice genome; dynamic programming; base correlation 1. Introduction The promoter sequences, in both prokaryotes and eukaryotes, are located up to the point of transcription initiation [1]. The site on the DNA from which the first RNA nu- cleotide is transcribed is called the +1 site. The so-called core promoter, with a length of 60–120 bases, stands out, and RNA polymerase binds to this DNA region [2,3]. A longer stretch of 600 bases from -499–+100 includes the core promoter, as well as the binding sites of various transcription factors [4]. “Further, we will focus only on eukaryotic promoter sequences. The promoter includes some motifs, which are short conservative sequences. The so-called TATA sequence is known, which occupies positions from -31–-26 nu- cleotides [5]. Additionally, the B recognition element is known, which is between -37 and 32 nucleotides in the promoter sequence. Short sequences have been found that provide binding of various protein factors to the promoter sequence [6]. Many of these sequences fall on the promoter region from +1–+40. The promoter sequence is not symmetrical” [7], thereby making the DNA polymerase begin transcription in the right direction. Promoter sequences are very different from each other [8–10]. This is as a result of the need to control the transcription of various genes. When transcription is initiated, the Symmetry 2021, 13, 917. https://doi.org/10.3390/sym13060917 https://www.mdpi.com/journal/symmetry