Measures for the exceptionality of gene order in conserved genomic regions. (English) Zbl 1194.62115
Summary: We propose in this article three measures for quantifying the exceptionality of gene order in conserved genomic regions found by the reference region approach. The three measures are based on the transposition distance in the permutation group. We obtain analytic expressions for their distribution in the case of a random uniform permutation, i.e., under the null hypothesis of random gene order. Our results can be used to increase the power of the significance tests for gene clusters which take into account only the proximity of the orthologous genes and not their order.
MSC:
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
| 92C40 | Biochemistry, molecular biology |
| 92D10 | Genetics and epigenetics |
Keywords:
gene order comparison; distance between permutations; transposition distance; exact distribution; random uniform permutation; conserved genomic regions; reference region approachReferences:
| [1] | Berestycki, N.; Durrett, R., A phase transition in the random transposition random walk, Probab. Theory Related Fields, 136, 203-233 (2006) · Zbl 1102.60005 |
| [2] | Bergeron, A.; Corteel, S.; Raffinot, M., The algorithmic of gene teams, (Lecture Notes in Comput. Sci., vol. 2452 (2002)), 464-476 · Zbl 1016.68618 |
| [3] | Christie, D. A., Sorting permutations by block-interchanges, Inform. Process. Lett., 60, 165-169 (1996) · Zbl 0900.68232 |
| [4] | Comtet, L., Advanced Combinatorics: The Art of Finite and Infinite Expansions (1974), Reidel Publishing Company: Reidel Publishing Company Dordrecht, Holland · Zbl 0283.05001 |
| [5] | Danchin, E.; Pontarotti, P., Statistical evidence for a more than 800-million-year-old evolutionarily conserved genomic region in our genome, J. Mol. Evol., 59, 587-597 (2004) |
| [6] | Diaconis, P., Group Representations in Probability and Statistics (1988), Institute of Mathematical Statistics: Institute of Mathematical Statistics Hayward · Zbl 0695.60012 |
| [7] | Doignon, J.-P.; Labarre, A., On Hultman numbers, J. Integer Seq., 10 (2007), Article 07.6.2 · Zbl 1138.05301 |
| [8] | Durand, D.; Sankoff, D., Tests for gene clustering, J. Comput. Biol., 10, 453-482 (2003) |
| [9] | Eriksen, N.; Hultman, A., Estimating the expected reversal distance after a fixed number of reversals, Adv. in Appl. Math., 32, 439-453 (2004) · Zbl 1051.92029 |
| [10] | Glaz, J.; Naus, J.; Wallenstein, S., Scan Statistics (2001), Springer-Verlag: Springer-Verlag New York · Zbl 0983.62075 |
| [11] | Hoberman, R.; Durand, D., The incompatible desiderata of gene cluster properties, (Lect. Notes in Bioinform., vol. 3678 (2005)), 73-87 |
| [12] | Hoberman, R.; Sankoff, D.; Durand, D., The statistical analysis of spatially clustered genes under the maximum gap criterion, J. Comput. Biol., 12, 1083-1102 (2005) |
| [13] | Huntington, R. J.; Naus, J., A simpler expression for \(k\) th nearest neighbor coincidence probabilities, Ann. Probab., 3, 894-896 (1975) · Zbl 0316.60014 |
| [14] | Li, Z.; Wang, L.; Zhang, K., Algorithmic approaches for genome rearrangement: a review, IEEE Trans. Syst. Man Cybernet. Part C, 36, 636-648 (2006) |
| [15] | Naus, J., Probabilities for a generalized birthday problem, J. Amer. Statist. Assoc., 69, 810-815 (1974) · Zbl 0292.60032 |
| [16] | Raghupathy, N.; Durand, D., Individual gene cluster statistics in noisy maps, (Lect. Notes in Bioinform., vol. 3678 (2005)), 106-120 |
| [17] | Sankoff, D.; Haque, L., Power boosts for clusters tests, (Lecture Notes in Comput. Sci., vol. 3678 (2005)), 121-130 |
| [18] | Sankoff, D.; Haque, L., The distribution of genomic distance between random genomes, J. Comput. Biol., 13, 1005-1012 (2006) |
| [19] | Xu, W.; Sankoff, D., Tests for gene clusters satisfying the generalized adjacency criterion, (Lect. Notes in Bioinform., vol. 5167 (2008)), 152-160 |
| [20] | Xu, W.; Zheng, C.; Sankoff, D., Paths and cycles in breakpoint graphs of random multichromosomal genomes, (Lect. Notes in Bioinform., vol. 4205 (2006)), 51-62 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
