AR-quiver approach to affine canonical basis elements

AbstractThis is the continuation of [Y. Li, Affine quivers of type A˜n and canonical bases, math.QA/0501175]. We describe the affine canonical basis elements in the case when the affine quiver has arbitrary orientation. This generalizes the description in [G. Lusztig, Affine quivers and canonical bases, Publ. Math. Inst. Hautes Études Sci. 76 (1992) 111–163]

Large deletion estimates.

<p>Estimated deletion size deviation and false negative rate for different true deletion sizes of (A) 100, (B) 500, and (C) 1000 bp. For each deletion length and each coverage of 5, 12, 24, 48, 96, and 144×, a boxplot summarizes the deviations of the estimated to the true deletion size in 100 simulated samples. The blue line represents the number of false negative predicted deletions in each of the 100 samples.</p

Viral Quasispecies Assembly via Maximal Clique Enumeration

<div><p>Virus populations can display high genetic diversity within individual hosts. The intra-host collection of viral haplotypes, called viral quasispecies, is an important determinant of virulence, pathogenesis, and treatment outcome. We present HaploClique, a computational approach to reconstruct the structure of a viral quasispecies from next-generation sequencing data as obtained from bulk sequencing of mixed virus samples. We develop a statistical model for paired-end reads accounting for mutations, insertions, and deletions. Using an iterative maximal clique enumeration approach, read pairs are assembled into haplotypes of increasing length, eventually enabling global haplotype assembly. The performance of our quasispecies assembly method is assessed on simulated data for varying population characteristics and sequencing technology parameters. Owing to its paired-end handling, HaploClique compares favorably to state-of-the-art haplotype inference methods. It can reconstruct error-free full-length haplotypes from low coverage samples and detect large insertions and deletions at low frequencies. We applied HaploClique to sequencing data derived from a clinical hepatitis C virus population of an infected patient and discovered a novel deletion of length 357±167 bp that was validated by two independent long-read sequencing experiments. HaploClique is available at <a href="https://github.com/armintoepfer/haploclique" target="_blank">https://github.com/armintoepfer/haploclique</a>. A summary of this paper appears in the proceedings of the RECOMB 2014 conference, April 2-5.</p></div

Global haplotype assembly results.

<p>Minimum, maximum, and mean read lengths (A) and the total number of reads (B) for the global haplotype assembly of the lab-mix, for the first 13 and the last iteration (30).</p

Max-clique enumeration and edge definitions.

<p>(A) Example of a read alignment graph based on the insert size criterion. Alignments of read pairs are shown in gray and the corresponding nodes in the graph representation are depicted in blue. The four bottom-most alignment pairs stem from a haplotype harboring a deletion (shown in orange in the reference genome) and therefore display a larger insert size than the remaining alignment pairs. Note that the four deletion-indicating alignment pairs form a max-clique (circled in orange). (B) Illustration of the compatible gaps condition of the sequence similarity criterion. Two reads and are aligned against the reference (left). This induces a direct read-to-read alignment of and (right). Case (1): No gaps in the reference alignments lead to a gapless read-to-read alignment, which renders the pair of reads an edge candidate. Case (2): Gaps in the reference alignment lead to gaps in the read-to-read alignment, excluding the possibility of an edge. See also <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003515#pcbi.1003515.s006" target="_blank">Figure S6</a> in the appendix for more complicated cases involving gaps.</p

Global haplotype assembly comparison.

<p>Global haplotype assembly comparison of HaploClique with the software packages ShoRAH <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003515#pcbi.1003515-Zagordi3" target="_blank">[33]</a>, PredictHaplo <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003515#pcbi.1003515-Prabhakaran1" target="_blank">[14]</a>, and QuRe <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003515#pcbi.1003515-Prosperi1" target="_blank">[16]</a>. We report the estimated variant frequencies and, in parenthesis, the maximal length of the reconstructed haplotypes relative to the genome length, for each of the five variants. In the remaining columns, the average error rate (computed as the number of mistaken nucleotides, divided by the length of the haplotype computed), the total number of reconstructed haplotypes, and the precision (percentage of perfectly reconstructed haplotypes weighted by the respective estimated frequency) are reported. See <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003515#s5" target="_blank">Methods</a> for more details on frequency estimation.</p

Clustering results among the 50 GT1a ATAHC sequences: genetic distance, percentage of sequences, tree, patristic distance and bootstrap values.

<p><i>Panel i</i>: The genetic distance distribution is shown for both ATAHC sequences (dark colour) and Los Alamos HCV database reference sequences (clear colour). The vertical dotted lines represent the thresholds for clustering, which were estimated by determining the point of overlap/uncertainty region between the two curves of most-closely related (ATAHC sequences) and distantly related (both ATAHC and LANL sequences) for each HCV region. <i>Panel ii</i> shows the ATAHC clustering patterns using Cluster Picker with bootstrap support threshold fixed at 90% and maximum genetic distance threshold varied between 0.01 and 0.08 (colour lines: ATAHC sequences; grey lines: LANL reference sequences). Plain lines represent the percentage of clustered sequences; dot lines correspond to average cluster size. The vertical dot line indicates the clustering threshold (as per panel i) used to determine the percentage of clustered sequences and average cluster size (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0131437#pone.0131437.t001" target="_blank">Table 1</a>). <i>Panel iii</i> shows the phylloclade with participants highlighted when defined as part of a cluster with the clustering threshold (panel i) and bootstrap support above 90% criteria (Cluster Picker).</p

Weighted Robinson-Foulds tree distances among HCV regions compared to the Core-E2_NS5B tree have been compared to mean genetic distance of ATAHC HCV sequences.

<p>First values from weighted Robinson-Foulds tree distances computed by RAxML1.3 from HCV regions compared to the region Core-E2 concatenated to NS5B as reference with length of 1684bp and a mean genetic distance of 0.076).</p

Mean genetic distance versus length of HCV regions.

<p>Relationship between mean genetic distance and length of HCV regions used in this project (squares for concatenated regions; circles for single regions). Regions with high mean genetic distance and longer size are preferable for phylogenetic analysis.</p

Clustering characteristics of different HCV subregions, derived from the Core-HVR1 amplicon and NS5B.

<p>*: Sequence length after alignment and gaps deletion;</p><p>^$:Genetic distance calculated with ATAHC sequences;</p><p>^#:Genetic distance threshold estimated from ATAHC pairwise distance distribution;</p><p>^&:Percentage of sequence clustered using region genetic distance threshold using cluster picker and bootstrap at 90%;</p><p>^@: Percentage of sequence clustered using pairwise distance threshold (without any bootstrap threshold);</p><p>^‡: ATAHC sequences with LANL reference sequences.</p><p>Characteristics of each subregion were determined after sequence alignment and gaps deletion, including sequence length, H77 sequence location within HCV, genetic diversity calculated from P. Simmonds (as per <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0131437#pone.0131437.g001" target="_blank">Fig 1</a>).;clustering threshold estimated from the genetic distance distribution; percentage of sequences clustered at threshold; average cluster size; average patristic distance of identified clusters; average bootstrap values of identified clusters; percentage of sequences clustered using pairwise distance threshold and no bootstrap support.</p