Evaluation of PANAMA and alternative methods on the simulated eQTL dataset.

<p>(<b>a,b</b>) number of recovered <i>cis</i> and <i>trans</i> associations as a function of the chosen false discovery rate cutoff. To circumvent biases due to linkage, at most one association per chromosome and gene is counted. (<b>c</b>) Receiver Operating Characteristics (ROC) for recovering true simulated associations, depicting the true positive rate (TPR) as a function of the permitted false positive rate (FPR). (<b>d</b>) inflation factors, defined as , indicating either inflated p-value distributions () or deflation () of the respective tests statistics. (<b>e</b>) Area under the ROC curve for alternative simulated datasets, subsampling certain fractions of number of simulated <i>trans</i> association. (<b>f</b>) Area under the ROC curve for alternative simulated datasets, subsampling the number of simulated confounding factors.</p

Illustration of the PANAMA model.

<p>(<b>a</b>) Representation of the linear model used by PANAMA to correct for the effect of confounding factors. (<b>b</b>) Alternative settings of confounders in relation to true genetic signals: First, orthogonality between confounders and genetics. The variation in the gene expression levels (green arrow) can be better explained by the SNP (blue arrow). Second, statistical overlap between variation explained by confounders and the genetic variation as often found in <i>trans</i> hotspots. Gene expression variation can be equally well explained as genetic or due to a confounding factor. Previous methods focus in the first setting, while PANAMA is able to handle both situations. (<b>c</b>) PANAMA applied to the yeast eQTL dataset. Pronounced <i>trans</i> regulators that overlap with the learnt confounding factors are highlighted in red.</p

Clustering forces could play a major role in the pairing of small chromosomes.

<p>The output of distances between alleles on a pair of chromosomes modelled on chromosome I of <i>S. cerevisiae</i>. The white and yellow lines are mean distances (from 177,000 randomly selected trajectories) plotted from one end of the chromosome between 300 equidistant notional allelic loci, expressed as a proportion of the nuclear diameter. The black area denotes standard deviation. The arrowhead on the X-axis indicates the position of the centromere. The mean distances for No Tether have been included on other graphs in white for comparison. For each chromosome layout used samples of telomere distributions (from 500 nuclei using the shorter persistence length) are indicated by the red dots in the nuclear spheres to the left. Diagrams showing telomere distributions use a sample of 500 cells for each conditions. A sample of chromosome I of trajectories, including a wider range of Rabl conditions, is provided in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002496#pcbi.1002496.s001" target="_blank">Figs.s S1</a>, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002496#pcbi.1002496.s002" target="_blank">S2</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002496#pcbi.1002496.s007" target="_blank">S7</a>.</p

The mean distances between nonallelic loci on homologous chromosomes increases with the Tight Bouquet and increasing chromosome rigidity.

<p>The output of distances between alleles on a pair of chromosomes modelled on chromosome I of <i>S. cerevisiae</i> expressed in (A) interhomologue LDMs, the colour coding indicates distances between loci on homologous chromosomes, expressed as a proportion of nuclear diameter. The two chromosomes on the X- and Y-axis of the LDMs are homologous partners. X- and Y-axis intersections on the interhomologue LDMs represent distances between alleles (on the diagonal), and distances between nonallelic loci, which are off diagonal. Examples of such ectopic interactions are shown as areas on the LDMs adjacent to E^I, E^II, E^III. The circle in the LDM represents the position of the centromere. The graph indicates the use of the axes for those displayed in (B). (B) The interhomologue LDMs are organised with the same conditions described in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002496#pcbi-1002496-g006" target="_blank">Fig. 6</a>. The accompanying graphs reveal on the rank scores of the 300 mean allelic distances and the 89,700 mean ectopic distances collected into 299 bins (each bin containing the average of 300 ranked mean distances).</p

Intrachromosomal interactions are influenced by centromere and telomere location and persistence length – Chromosome I.

<p>(A) Output from the computer modeling (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002496#s3" target="_blank">Materials and Methods</a>) can be expressed in a heat map. The colours correspond to average distance between loci as a proportion of nuclear diameter. These are built up into locus distance maps (LDMs). The circles represent centromeres. The intersection between X- and Y-axes of the LDMs represents the distance between loci on the same chromosome. Different regions can be defined in the LDMs to examine how mean distances change between chromosome landmarks: such as between, (α) the centromere and interstitial region, (β) the centromere and a telomere (γ) opposite telomeres and (δ) interstitial regions on opposite arms. The graph provides a key for those displayed in (B). (B) LDMs are provided for a chromosome modelled on <i>S. cerevisiae</i> chromosome I (240 Kb) tested at two persistence lengths/rigidity and in four different configurations with respect to probable centromere and telomere location in the nucleus. In No Tether chromosome are located randomly in the nuclear volume, Centromere Tether means the centromere was located at the nuclear periphery, Telomeres Tethered means that both telomeres were tethered to the nuclear periphery at independent locations and Telomeres Tethered plus Clustering means there was an additional high chance of telomeres being located close to each. The two persistence lengths used to define flexibility were set at 0.2 µm and 2.0 µm and the nuclear diameter was set at 2 µm. Rank score graphs indicate the mean distances between loci collected into 300 bins after ranking. The data for No Tether is repeated in white lines for comparison to the yellow lines, which are the data for the other conditions. The black areas indicate standard deviation. Diagrams with showing the telomere distributions use a sample of 500 cells for each condition.</p

The mean distances between alleles are shorter when homologues are in a tight bouquet compared to non bouquet configurations.

<p>Comparison of rank scores for 300 mean distances between alleles on homologues with No Tether, Telomeres Tethered or in either Rabl or Tight Bouquet with flexible or rigid chromosomes. X-axis is rank score, Y-axis is mean distance as a proportion of nuclear diameter.</p

The influence of clustering forces over interhomologue distance for larger chromosomes is limited by distance from the tether site, and dependent on chromosome rigidity.

<p>The output of distances between alleles on a pair of chromosomes modelled on chromosome XVIs of <i>S. cerevisiae</i>. All aspects of the layout are as for <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002496#pcbi-1002496-g006" target="_blank">Fig. 6</a>. A sample of chromosome XVI of trajectories, including a wider range of Rabl conditions, is provided in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002496#pcbi.1002496.s003" target="_blank">Figs.s S3</a>, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002496#pcbi.1002496.s004" target="_blank">S4</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002496#pcbi.1002496.s007" target="_blank">S7</a>.</p

Chromosomes reorganise early in meiosis to form the bouquet structure.

<p>(A) During mitosis the nucleus divides and centromeres move towards the microtubule organiser (spindle pole body in <i>S. cereveisiae</i>). (B) The centromeres remain clustered and close to the nuclear envelope in the Rabl configuration. (C) During early meiosis the telomeres become attached via SUN/KASH proteins (not shown) to the nuclear envelope and then (D) cluster near the microtubule organising centre in the bouquet configuration.</p

Intrachromosomal interactions are influenced by centromere and telomere location and persistence length – Chromosome IV.

<p>Output from the computer modeling as described for <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002496#pcbi-1002496-g003" target="_blank">Fig. 3</a> using a chromosome modelled on <i>S. cerevisiae</i> chromosome IV (1530 Kb). All conditions are as described for <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002496#pcbi-1002496-g003" target="_blank">Fig. 3</a>.</p

Ectopic interactions between heterologous chromosomes are reduced by chromosome tethering, clustering and rigidity.

<p>The output of distances between alleles on a heterologous pair of chromosomes modelled on chromosome I and IV of <i>S. cerevisiae</i> expressed in (A) interheterologue LDMs, the colour coding indicates ectopic distances between loci on heterologous chromosomes, expressed as a proportion of nuclear diameter. The two chromosomes on the X- and Y-axis of the LDMs are proportional to the heterologous chromosome, and each contains 300 equidistant notional loci. The graph indicates the use of the axes for those displayed in (B). (B) The interheterologue LDMs are organised with the same conditions described in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002496#pcbi-1002496-g006" target="_blank">Fig. 6</a>. The accompanying graphs reveal the 90,000 mean ectopic distances, which were ranked and collected into 300 bins (each bin containing the average of 300 ranked mean distances). Allelic rank scores from data in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002496#pcbi-1002496-g009" target="_blank">Figs.s 9</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002496#pcbi-1002496-g010" target="_blank">10</a> are provided for comparison.</p