A generalization of substitution evolution models of nucleotides to genetic motifs.

We generalize here the classical stochastic substitution models of nucleotides to genetic motifs of any size. This generalized model gives the analytical occurrence probabilities of genetic motifs as a function of a substitution matrix containing up to three formal parameters (substitution rates) per motif site and of an initial occurrence probability vector of genetic motifs. The evolution direction can be direct (past-present) or inverse (present-past). This extension has been made due to the identification of a Kronecker relation between the nucleotide substitution matrices and the motif substitution matrices. The evolution models for motifs of size 4 (tetranucleotides) and 5 (pentanucleotides) are now included in the SEGM (Stochastic Evolution of Genetic Motifs) web server.

Genome evolution by transformation, expansion and contraction (GETEC).

We propose here the GETEC (Genome Evolution by Transformation, Expansion and Contraction) model of gene evolution based on substitution, insertion and deletion of genetic motifs. The GETEC model unifies two classes of evolution models: models of substitution, insertion and deletion of nucleotides as function of time (Lèbre and Michel, 2010) and sequence length (Lèbre and Michel, 2012), and models of symmetric substitution of genetic motifs as function of time (Benard and Michel, 2011). Evolution of genetic motifs based on substitution, insertion and deletion is modeled by a differential equation whose analytical solutions give an expression of the genetic motif occurrence probabilities as a function of time or sequence length, as well as in direct time direction (past-present) or inverse time direction (present-past). Evolution models with "substitution only", i.e. without insertion and deletion, and with "insertion and deletion only", i.e. without substitution, are particular cases of the GETEC model. We have also developed a research software for computing the analytical solutions of the GETEC model. It is freely accessible at http://icube-bioinfo.u-strasbg.fr/webMathematica/GETEC/ or via the web site http://dpt-info.u-strasbg.fr/∼michel/.

Challenges with using primer IDs to improve accuracy of next generation sequencing.

Next generation sequencing technologies, like ultra-deep pyrosequencing (UDPS), allows detailed investigation of complex populations, like RNA viruses, but its utility is limited by errors introduced during sample preparation and sequencing. By tagging each individual cDNA molecule with barcodes, referred to as Primer IDs, before PCR and sequencing these errors could theoretically be removed. Here we evaluated the Primer ID methodology on 257,846 UDPS reads generated from a HIV-1 SG3Δenv plasmid clone and plasma samples from three HIV-infected patients. The Primer ID consisted of 11 randomized nucleotides, 4,194,304 combinations, in the primer for cDNA synthesis that introduced a unique sequence tag into each cDNA molecule. Consensus template sequences were constructed for reads with Primer IDs that were observed three or more times. Despite high numbers of input template molecules, the number of consensus template sequences was low. With 10,000 input molecules for the clone as few as 97 consensus template sequences were obtained due to highly skewed frequency of resampling. Furthermore, the number of sequenced templates was overestimated due to PCR errors in the Primer IDs. Finally, some consensus template sequences were erroneous due to hotspots for UDPS errors. The Primer ID methodology has the potential to provide highly accurate deep sequencing. However, it is important to be aware that there are remaining challenges with the methodology. In particular it is important to find ways to obtain a more even frequency of resampling of template molecules as well as to identify and remove artefactual consensus template sequences that have been generated by PCR errors in the Primer IDs.

Computation of direct and inverse mutations with the SEGM web server (Stochastic Evolution of Genetic Motifs): an application to splice sites of human genome introns.

We present here the SEGM web server (Stochastic Evolution of Genetic Motifs) in order to study the evolution of genetic motifs both in the direct evolutionary sense (past-present) and in the inverse evolutionary sense (present-past). The genetic motifs studied can be nucleotides, dinucleotides and trinucleotides. As an example of an application of SEGM and to understand its functionalities, we give an analysis of inverse mutations of splice sites of human genome introns. SEGM is freely accessible at http://lsiit-bioinfo.u-strasbg.fr:8080/webMathematica/SEGM/SEGM.html directly or by the web site http://dpt-info.u-strasbg.fr/~michel/. To our knowledge, this SEGM web server is to date the only computational biology software in this evolutionary approach.