The Variance of Identity-by-Descent Sharing in the Wright–Fisher Model

Widespread sharing of long, identical-by-descent (IBD) genetic segments is a hallmark of populations that have experienced recent genetic drift. Detection of these IBD segments has recently become feasible, enabling a wide range of applications from phasing and imputation to demographic inference. Here, we study the distribution of IBD sharing in the Wright–Fisher model. Specifically, using coalescent theory, we calculate the variance of the total sharing between random pairs of individuals. We then investigate the cohort-averaged sharing: the average total sharing between one individual and the rest of the cohort. We find that for large cohorts, the cohort-averaged sharing is distributed approximately normally. Surprisingly, the variance of this distribution does not vanish even for large cohorts, implying the existence of “hypersharing” individuals. The presence of such individuals has consequences for the design of sequencing studies, since, if they are selected for whole-genome sequencing, a larger fraction of the cohort can be subsequently imputed. We calculate the expected gain in power of imputation by IBD and subsequently in power to detect an association, when individuals are either randomly selected or specifically chosen to be the hypersharing individuals. Using our framework, we also compute the variance of an estimator of the population size that is based on the mean IBD sharing and the variance in the sharing between inbred siblings. Finally, we study IBD sharing in an admixture pulse model and show that in the Ashkenazi Jewish population the admixture fraction is correlated with the cohort-averaged sharing.IN isolated populations, even purported unrelated individuals often share genetic material that is identical-by-descent (IBD). Traditionally, the term IBD sharing referred to coancestry at a single site (or autozygosity, in the case of a diploid individual) and was widely investigated as a measure of the degree of inbreeding in a population (Hartl and Clark 2006). Recent years have brought dramatic increases in the quantity and density of available genetic data and, together with new computational tools, these data have enabled the detection of IBD sharing of entire genomic segments (see, e.g., Purcell et al. 2007; Kong et al. 2008; Albrechtsen et al. 2009; Gusev et al. 2009; Browning and Browning 2011; Carr et al. 2011; Brown et al. 2012). The availability of IBD detection tools that are efficient enough to detect shared segments in large cohorts has resulted in numerous applications, from demographic inference (Davison et al. 2009; Palamara et al. 2012) and characterization of populations (Gusev et al. 2012a) to selection detection (Albrechtsen et al. 2010), relatedness detection and pedigree reconstruction (Huff et al. 2011; Kirkpatrick et al. 2011; Stevens et al. 2011; Henn et al. 2012), prioritization of individuals for sequencing (Gusev et al. 2012b), inference of HLA type (Setty et al. 2011), detection of haplotypes associated with a disease or a trait (Akula et al. 2011; Gusev et al. 2011; Browning and Thompson 2012), imputation (Uricchio et al. 2012), and phasing (Palin et al. 2011).Recently, some of us used coalescent theory to calculate several theoretical quantities of IBD sharing under a number of demographic histories. Then, shared segments were detected in real populations, and their demographic histories were inferred (Palamara et al. 2012). Here, we expand upon Palamara et al. (2012) to investigate additional aspects of the stochastic variation in IBD sharing. Specifically, we provide a precise calculation for the variance of the total sharing in the Wright–Fisher model, either between a random pair of individuals or between one individual and all others in the cohort.Understanding the variation in IBD sharing is an important theoretical characterization of the Wright–Fisher model, and additionally, it has several practical applications. For example, it can be used to calculate the variance of an estimator of the population size that is based on the sharing between random pairs. In a different domain, the variance in IBD sharing is needed to accurately assess strategies for sequencing study design, specifically, in prioritization of individuals to be sequenced. This is because imputation strategies use IBD sharing between sequenced individuals and genotyped, not-sequenced individuals to increase the number of effective sequences analyzed in the association study (Palin et al. 2011; Gusev et al. 2012b; Uricchio et al. 2012).In the remainder of this article, we first review the derivation of the mean fraction of the genome shared between two individuals (Palamara et al. 2012). We then calculate the variance of this quantity, using coalescent theory with recombination. We provide a number of approximations, one of which results in a surprisingly simple expression, which is then generalized to a variable population size and to the sharing of segments in a length range. We also numerically investigate the pairwise sharing distribution and provide an approximate fit. We then turn to the average total sharing between each individual and the entire cohort. We show that this quantity, which we term the cohort-averaged sharing, is approximately normally distributed, but is much wider than naively expected, implying the existence of hypersharing individuals. We consider several applications: the number of individuals needed to be sequenced to achieve a certain imputation power and the implications to disease mapping, inference of the population size based on the total sharing, and the variance of the sharing between siblings. We finally calculate the mean and the variance of the sharing in an admixture pulse model and show numerically that admixture results in a broader than expected cohort-averaged sharing. Therefore, large variance of the cohort-averaged sharing can indicate admixture. In the Ashkenazi Jewish population, we show that the cohort-averaged sharing is strongly anticorrelated with the fraction of European ancestry.     

Allelic Selection of Amplicons in Glioblastoma Revealed by Combining Somatic and Germline Analysis

Cancer is a disease driven by a combination of inherited risk alleles coupled with the acquisition of somatic mutations, including amplification and deletion of genomic DNA. Potential relationships between the inherited and somatic aspects of the disease have only rarely been examined on a genome-wide level. Applying a novel integrative analysis of SNP and copy number measurements, we queried the tumor and normal-tissue genomes of 178 glioblastoma patients from the Cancer Genome Atlas project for preferentially amplified alleles, under the hypothesis that oncogenic germline variants will be selectively amplified in the tumor environment. Selected alleles are revealed by allelic imbalance in amplification across samples. This general approach is based on genetic principles and provides a method for identifying important tumor-related alleles. We find that SNP alleles that are most significantly overrepresented in amplicons tend to occur in genes involved with regulation of kinase and transferase activity, and many of these genes are known contributors to gliomagenesis. The analysis also implicates variants in synapse genes. By incorporating gene expression data, we demonstrate synergy between preferential allelic amplification and expression in DOCK4 and EGFR. Our results support the notion that combining germline and tumor genetic data can identify regions relevant to cancer biology.     

The association of Sam68 with Vav1 contributes to tumorigenesis

Vav1 functions in the hematopoietic system as a specific GDP/GTP nucleotide exchange factor regulated by tyrosine phosphorylation. An intact C-terminal SH3 domain of Vav1 (Vav1SH3C) was shown to be necessary for Vav1-induced transformation, yet the associating protein(s) necessary for this activity have not yet been identified. Using a proteomics approach, we identified Sam68 as a Vav1SH3C-associating protein. Sam68 (Src-associated in mitosis of 68 kD) belongs to the heteronuclear ribonucleoprotein particle K (hnRNP-K) homology (KH) domain family of RNA-binding proteins. The Vav1/Sam68 interaction was observed in vitro and in vivo. Mutants of Vav1SH3C previously shown to lose their transforming potential did not associate with Sam68. Co-expression of Vav1 and Sam68 in Jurkat T cells led to increased localization of Vav1 in the nucleus and changes in cell morphology. We then tested the contribution of Sam68 to known functions of Vav1, such as focus-forming in NIH3T3 fibroblasts and NFAT stimulation in T cells. Co-expression of oncogenic Vav1 with Sam68 in NIH3T3 fibroblasts resulted in a dose-dependent increase in foci, yet no further enhancement of NFAT activity was observed in Jurkat T cells, as compared to cells overexpressing only Vav1 or Sam68. Our results strongly suggest that Sam68 contributes to transformation by oncogenic Vav1.     

Can we predict butterfly diversity along an elevation gradient from space?

An important challenge in ecology is to predict patterns of biodiversity across eco‐geographical gradients. This is particularly relevant in areas that are inaccessible, but are of high research and conservation value, such as mountains. Potentially, remotely‐sensed vegetation indices derived from satellite images can help in predicting species diversity in vast and remote areas via their relationship with two of the major factors that are known to affect biodiversity: productivity and spatial heterogeneity in productivity. Here, we examined whether the Normalized Difference Vegetation Index (NDVI) can be used effectively to predict changes in butterfly richness, range size rarity and beta diversity along an elevation gradient. We examined the relationship between butterfly diversity and both the mean NDVI within elevation belts (a surrogate of productivity) and the variability in NDVI within and among elevation belts (surrogates for spatial heterogeneity in productivity). We calculated NDVI at three spatial extents, using a high spatial resolution QuickBird satellite image. We obtained data on butterfly richness, rarity and beta diversity by field sampling 100 m quadrats and transects between 500 and 2200 m in Mt Hermon, Israel. We found that the variability in NDVI, as measured both within and among adjacent elevation belts, was strongly and significantly correlated with butterfly richness. Butterfly range size rarity was strongly correlated with the mean and the standard deviation of NDVI within belts. In our system it appears that it is spatial heterogeneity in productivity rather than productivity per se that explained butterfly richness. These results suggest that remotely‐sensed data can provide a useful tool for assessing spatial patterns of butterfly richness in inaccessible areas. The results further indicate the importance of considering spatial heterogeneity in productivity along elevation gradients, which has no lesser importance than productivity in shaping richness and rarity, especially at the local scale.     

Breaking functional connectivity into components: a novel approach using an individual-based model, and first outcomes

Landscape connectivity is a key factor determining the viability of populations in fragmented landscapes. Predicting 'functional connectivity', namely whether a patch or a landscape functions as connected from the perspective of a focal species, poses various challenges. First, empirical data on the movement behaviour of species is often scarce. Second, animal-landscape interactions are bound to yield complex patterns. Lastly, functional connectivity involves various components that are rarely assessed separately. We introduce the spatially explicit, individual-based model FunCon as means to distinguish between components of functional connectivity and to assess how each of them affects the sensitivity of species and communities to landscape structures. We then present the results of exploratory simulations over six landscapes of different fragmentation levels and across a range of hypothetical bird species that differ in their response to habitat edges. i) Our results demonstrate that estimations of functional connectivity depend not only on the response of species to edges (avoidance versus penetration into the matrix), the movement mode investigated (home range movements versus dispersal), and the way in which the matrix is being crossed (random walk versus gap crossing), but also on the choice of connectivity measure (in this case, the model output examined). ii) We further show a strong effect of the mortality scenario applied, indicating that movement decisions that do not fully match the mortality risks are likely to reduce connectivity and enhance sensitivity to fragmentation. iii) Despite these complexities, some consistent patterns emerged. For instance, the ranking order of landscapes in terms of functional connectivity was mostly consistent across the entire range of hypothetical species, indicating that simple landscape indices can potentially serve as valuable surrogates for functional connectivity. Yet such simplifications must be carefully evaluated in terms of the components of functional connectivity they actually predict.     

Tyrosine Residues at the Carboxyl Terminus of Vav1 Play an Important Role in Regulation of Its Biological Activity

The guanine nucleotide exchange factor (GEF) Vav1 is an essential signal transducer protein in the hematopoietic system, where it is expressed physiologically. It is also involved in several human malignancies. Tyrosine phosphorylation at the Vav1 amino terminus plays a central role in regulating its activity; however, the role of carboxyl terminal tyrosine residues is unknown. We found that mutation of either Tyr-826 (Y826F) or Tyr-841 (Y841F) to phenylalanine led to loss of Vav1 GEF activity. When these Vav1 mutants were ectopically expressed in pancreatic cancer cells lacking Vav1, they failed to induce growth in agar, indicating loss of transforming potential. Furthermore, although Y841F had no effect on Vav1-stimulated nuclear factor of activated T cells (NFAT) activity, Y826F doubled NFAT activity when compared with Vav1, suggesting that Tyr-826 mediates an autoinhibitory effect on NFAT activity. SH2 profiling revealed that Shc, Csk, Abl, and Sap associate with Tyr-826, whereas SH2-B, Src, Brk, GTPase-activating protein, and phospholipase C-γ associate with Tyr-841. Although the mutations in the Tyr-826 and Tyr-841 did not affect the binding of the carboxyl SH3 of Vav1 to other proteins, binding to several of the proteins identified by the SH2 profiling was lost. Of interest is Csk, which associates with wild-type Vav1 and Y841F, yet it fails to associate with Y826F, suggesting that loss of binding between Y826F and Csk might relieve an autoinhibitory effect, leading to increased NFAT. Our data indicate that GEF activity is critical for the function of Vav1 as a transforming protein but not for NFAT stimulation. The association of Vav1 with other proteins, detected by SH2 profiling, might affect other Vav1-dependent activities, such as NFAT stimulation.     

Gallium-desferrioxamine protects the cat retina against injury after ischemia and reperfusion

This study sought to determine whether gallium-desferrioxamine (Ga/DFO) can curb free radical formation and mitigate biochemical and electrophysiological parameters of injury in the cat retina subjected to ischemia followed by reperfusion.For the biochemical studies, cat eyes were subjected to 90 min of retinal ischemia followed by 5 min of reperfusion, and enucleation of one eye of each cat was used to measure retinal reperfusion injury. Before enucleation of fellow eyes, 2.5 mg/kg Ga/DFO was injected intravenously 5 min before reperfusion. The flux of hydroxyl radicals, as measured directly by conversion of salicylate to 2,3- and 2,5-dihydroxybenzoic acid (2,3- and 2,5-DHBA), was significantly lower in Ga/DFO-treated eyes. The mean normalized level of 2,3-DHBA (considered a specific marker of hydroxyl radicals) was 3.5 times higher in untreated eyes. Ga/DFO caused a significant reduction, by 2.56-fold, in lipid peroxidation, as reflected by levels of malondialdehyde. Ascorbic acid, a natural antioxidant present in the retina, is severely depleted in untreated eyes. In contrast, in Ga/DFO-treated eyes, levels were 10 times higher than the control. Energy charge was 2.38 times higher in treated eyes. Levels of purine catabolites (hypoxanthine, xanthine, and uric acid) that reflect excessive metabolism of purine nucleotides were approximately twice higher in untreated retinas. Electroretionographic studies, performed on a different subset of animals, substantiated the biochemical results. In Ga/DFO-treated eyes the amplitude of the mixed cone-rod response b-wave (as compared with fellow nonischemic eyes) fully recovered within 24 h after ischemia (b-wave ratio 1.04 +/- 0.09, [mean +/- SEM]) whereas ischemic/reperfused and nontreated eyes recovered to only 0.33 +/- 0. 05. The results show that severe biochemical and functional retinal injury occurs in cat eyes subjected to ischemia and reperfusion. These severe changes were significantly reduced by a single administration of Ga/DFO just before reperfusion. We hypothesize that the protection afforded by Ga/DFO is due to a combined effect of "Push-Pull" mechanisms interfering with transition metal-dependent and free radical-mediated injurious processes.