This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Generalized Gene Adjacencies, Graph Bandwidth, and Clusters in Yeast Evolution
April-June 2009 (vol. 6 no. 2)
pp. 213-220
Qian Zhu, University of Ottawa, Ottawa
Zaky Adam, University of Ottawa, Ottawa
Vicky Choi, Virginia Tech, Blacksburg
David Sankoff, University of Ottawa, Ottawa
We present a parameterized definition of gene clusters that allows us to control the emphasis placed on conserved order within a cluster. Though motivated by biological rather than mathematical considerations, this parameter turns out to be closely related to the bandwidth parameter of a graph. Our focus will be on how this parameter affects the characteristics of clusters: how numerous they are, how large they are, how rearranged they are, and to what extent they are preserved from ancestor to descendant in a phylogenetic tree. We infer the latter property by dynamic programming optimization of the presence of individual edges at the ancestral nodes of the phylogeny. We apply our analysis to a set of genomes drawn from the Yeast Gene Order Browser.

[1] A. Bergeron, S. Corteel, and M. Raffinot, “The Algorithmic of Gene Teams,” Proc. Second Int'l Workshop Bioinformatics (WABI '02), D. Gusfield and R. Guigo, eds., pp.464-476, 2002.
[2] K.P. Byrne and K.H. Wolfe, “The Yeast Gene Order Browser: Combining Curated Homology and Syntenic Context Reveals Gene Fate in Polyploid Species,” Genome Research, vol. 15, pp.1456-1461, 2005.
[3] B. Dujon etal., “Genome Evolution in Yeasts,” Nature, vol. 430, pp.35-44, 2004.
[4] J. Felsenstein, Inferring Phylogenies. Sinauer Assoc., 2004.
[5] A. George, “Computer Implementation of the Finite Element Method,” Technical Report STAN-CS-71-208, Computer Science Dept., Stanford Univ., 1971.
[6] E.M. Gurari and I.H. Sudborough, “Improved Dynamic Programming Algorithms for Bandwidth Minimization and the Mincut Linear Arrangement Problem,” J. Algorithms, vol. 5, pp.531-546, 1984.
[7] R. Hoberman, D. Sankoff, and D. Durand, “The Statistical Analysis of Spatially Clustered Genes under the Maximum Gap Criterion,” J. Computational Biology, vol. 12, pp.1081-1100, 2005.
[8] J. Liu and A. Sherman, “Comparative Analysis of the Cuthill-Mckee and the Reverse Cuthill-Mckee Ordering Algorithms for Sparse Matrices,” SIAM J. Numerical Analysis, vol. 13, pp.198-213, 1975.
[9] C.H. Papadimitriou, “The NP-Completeness of the Bandwidth Minimization Problem,” Computing, vol. 16, pp.263-270, 1976.
[10] J. Saxe, “Dynamic-Programming Algorithms for Recognizing Small-Band-Width Graphs in Polynomial Time,” SIAM J. Algebraic and Discrete Methods, vol. 1, pp.363-369, 1980.
[11] X. Xu and D. Sankoff, “Tests for Gene Clusters Satisfying the Generalized Adjacency Criterion,” Proc. Brazilian Symp. Bioinformatics (BSB '08), A.L.C. Bazzan, M. Craven, and N. F. Martins,eds., pp.152-160, 2008.

Index Terms:
Comparative genomics, gene clusters, yeast, evolution, phylogeny, genome rearrangements, graph bandwidth, dynamic programming, Saccharomyces cerevisiae, Candida glabrata, Ashbya gossypii, Kluyveromyces waltii, Kluyveromyces lactis.
Citation:
Qian Zhu, Zaky Adam, Vicky Choi, David Sankoff, "Generalized Gene Adjacencies, Graph Bandwidth, and Clusters in Yeast Evolution," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 6, no. 2, pp. 213-220, April-June 2009, doi:10.1109/TCBB.2008.121
Usage of this product signifies your acceptance of the Terms of Use.