Skip Navigation



Bioinformatics Advance Access published online on January 5, 2006
Bioinformatics, doi:10.1093/bioinformatics/btk001
This Article
Right arrow Advance Access manuscript (PDF) Freely available
Right arrow All Versions of this Article:
22/6/708    most recent
btk001v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Catanzaro, D.
Right arrow Articles by Milinkovitch, M. C.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Catanzaro, D.
Right arrow Articles by Milinkovitch, M. C.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author (2006). Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org
Received November 4, 2005
Revised November 29, 2005
Accepted December 9, 2005

Article

A nonlinear optimization procedure to estimate GTR-distances

Daniele Catanzaro 1, Raffaele Pesenti 2, and Michel C. Milinkovitch 1 *

1 Laboratory of Evolutionary Genetics, Institute for Molecular Biology and Medicine (IBMM), Université Libre de Bruxelles, CP300, Rue Jeener et Brachet 12, B-6041, Gosselies, Belgium
2 DINFO, Dipartimento di Ingegneria Informatica, University of Palermo, Viale delle Scienze I-90128 Palermo, Italy

* To whom correspondence should be addressed.
Michel C. Milinkovitch, E-mail: mcmilink{at}ulb.ac.be


  Abstract

Motivation: The general-time-reversible (GTR) model is one of the most popular models of nucleotide substitution because it constitutes a good trade-off between mathematical tractability and biological reality. However, when it is applied for inferring evolutionary distances, the GTR model seems more prone to inapplicability than more restrictive time-reversible models. Although it has been previously noted that the causes for intractability are caused by the impossibility of computing the logarithm of a matrix characterised by negative eigenvalues, the issue has not been investigated further.

Results: Here, we formally characterize the mathematical conditions, and discuss their biological interpretation, that lead to the inapplicability of the GTR model. We investigate the relations between, on one hand, the occurrence of negative eigenvalues and, on the other hand, both sequence length and sequence divergence. We then propose a possible re-formulation of previous procedures in terms of a non-linear optimization problem. We analytically investigate the effect of our approach on the estimated evolutionary distances and transition probability matrix. Finally, we provide an analysis on the goodness of the solution we propose. A numerical example is discussed.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.