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]

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

Flow chart describing the selection of ATAHC participants for inclusion in this analysis.

<p>Among the ATAHC participants (n = 163), 143 samples were tested and sequences were generated for Core-E2 and NS5B regions. 50 participants with both Core-E2 and NS5B sequences were used for clustering analysis.</p

Heatmap of the number of clustered sequences present among different HCV regions using genetic distance and clustering threshold criteria and illustrated in a phylogram using Core-E2 region.

<p>Sequences with a pairwise distance below the genetic threshold were identified as part of a cluster. The colours represent the number of regions which consistently identified each sequence in a cluster. A phylogram based on the Core-E2 analysis highlights sequences that are included/excluded of cluster depending of the region selected.</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

HCV amplicons and regions used for clustering analysis.

<p>The genetic variability between each region was estimated using the diagrammatic representation of the HCV genome from [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0131437#pone.0131437.ref050" target="_blank">50</a>] as shown in mean pairwise distance from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0131437#pone.0131437.g001" target="_blank">Fig 1</a> (black line). The black line represents the genetic diversity across the length of HCV RNA [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0131437#pone.0131437.ref050" target="_blank">50</a>]. The red lines represent the amplicons generated with the in-house Core-E2 protocol (1534bp) and the NS5B method published by Murphy <i>et al</i>. (360bp) [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0131437#pone.0131437.ref015" target="_blank">15</a>]. The colour rectangles show the location of the sequences used for clustering analysis: the full Core-E2 amplicon; same sequence trimmed to E1 with partial HVR1; with HVR1 removed; E1 alone, without HVR1; NS5B; Core. Every sequence from the 5’ region was analysed alone and also concatenated to NS5B. Full length sequences from naïve GT1a patients available from LANL were trimmed to identical regions to be used as reference sequences.</p