The diffusive spread of alleles in heterogeneous populations

The spread of genes and individuals through space in populations is relevant in many biological contexts. I study, via systems of reaction-diffusion equations, the spatial spread of advantageous alleles through structured populations. The results show that the temporally asymptotic rate of spread of an advantageous allele, a kind of invasion speed, can be approximated for a class of linear partial differential equations via a relatively simple formula, c = 2 square root of (rD), that is reminiscent of a classic formula attributed to R. A. Fisher. The parameters r and D represent an asymptotic growth rate and an average diffusion rate, respectively, and can be interpreted in terms of eigenvalues and eigenvectors that depend on the population's demographic structure. The results can be applied, under certain conditions, to a wide class of nonlinear partial differential equations that are relevant to a variety of ecological and evolutionary scenarios in population biology. I illustrate the approach for computing invasion speed with three examples that allow for heterogeneous dispersal rates among different classes of individuals within model populations.     

The iron cycle and oxidative stress in the lung

Iron is critical for many aspects of cellular function, but it can also generate reactive oxygen species that can damage biological macromolecules. To limit oxidative stress, iron acquisition and its distribution must be tightly regulated. In the lungs, which are continuously exposed to the atmosphere, the risk of oxidative damage is particularly high because of the high oxygen concentration and the presence of significant amounts of catalytically active iron in atmospheric particulates. An effective system of metal detoxification must exist to minimize the associated generation of oxidative stress in the lungs. Here we summarize the evidence that a number of specific proteins that control iron uptake in the gastrointestinal tract are also employed in the lung to transport iron into epithelial cells and sequester it in a catalytically inactive form in ferritin. Furthermore, these and other proteins facilitate ferritin release from lung cells to the epithelial and bronchial lining fluids for clearance by the mucociliary system or to the reticuloendothelial system for long-term storage of iron. These pathways seem to be the primary mechanism for control of oxidative stress presented by iron in the respiratory tract.     

Separate pathways for cellular uptake of ferric and ferrous iron

Separate pathways for transport of nontransferrin ferric and ferrous iron into tissue cultured cells were demonstrated. Neither the ferric nor ferrous pathway was shared with either zinc or copper. Manganese shared the ferrous pathway but had no effect on cellular uptake of ferric iron. We postulate that ferric iron was transported into cells via beta(3)-integrin and mobilferrin (IMP), whereas ferrous iron uptake was facilitated by divalent metal transporter-1 (DMT-1; Nramp-2). These conclusions were documented by competitive inhibition studies, utilization of a beta(3)-integrin antibody that blocked uptake of ferric but not ferrous iron, development of an anti-DMT-1 antibody that blocked ferrous iron and manganese uptake but not ferric iron, transfection of DMT-1 DNA into tissue culture cells that showed enhanced uptake of ferrous iron and manganese but neither ferric iron nor zinc, hepatic metal concentrations in mk mice showing decreased iron and manganese but not zinc or copper, and data showing that the addition of reducing agents to tissue culture media altered iron binding to proteins of the IMP and DMT-1 pathways. Although these experiments show ferric and ferrous iron can enter cells via different pathways, they do not indicate which pathway is dominant in humans.     

Comparison of molecular breeding values based on within- and across-breed training in beef cattle

Background

Although the efficacy of genomic predictors based on within-breed training looks promising, it is necessary to develop and evaluate across-breed predictors for the technology to be fully applied in the beef industry. The efficacies of genomic predictors trained in one breed and utilized to predict genetic merit in differing breeds based on simulation studies have been reported, as have the efficacies of predictors trained using data from multiple breeds to predict the genetic merit of purebreds. However, comparable studies using beef cattle field data have not been reported.

Methods

Molecular breeding values for weaning and yearling weight were derived and evaluated using a database containing BovineSNP50 genotypes for 7294 animals from 13 breeds in the training set and 2277 animals from seven breeds (Angus, Red Angus, Hereford, Charolais, Gelbvieh, Limousin, and Simmental) in the evaluation set. Six single-breed and four across-breed genomic predictors were trained using pooled data from purebred animals. Molecular breeding values were evaluated using field data, including genotypes for 2227 animals and phenotypic records of animals born in 2008 or later. Accuracies of molecular breeding values were estimated based on the genetic correlation between the molecular breeding value and trait phenotype.

Results

With one exception, the estimated genetic correlations of within-breed molecular breeding values with trait phenotype were greater than 0.28 when evaluated in the breed used for training. Most estimated genetic correlations for the across-breed trained molecular breeding values were moderate (> 0.30). When molecular breeding values were evaluated in breeds that were not in the training set, estimated genetic correlations clustered around zero.

Conclusions

Even for closely related breeds, within- or across-breed trained molecular breeding values have limited prediction accuracy for breeds that were not in the training set. For breeds in the training set, across- and within-breed trained molecular breeding values had similar accuracies. The benefit of adding data from other breeds to a within-breed training population is the ability to produce molecular breeding values that are more robust across breeds and these can be utilized until enough training data has been accumulated to allow for a within-breed training set.     

Cryptic structure and niche divergence within threatened Galápagos giant tortoises from southern Isabela Island

Although Galápagos giant tortoises are an icon for both human-mediated biodiversity losses and conservation management successes, populations of two species on southern Isabela Island (Chelonoidis guntheri, and C. vicina) remain threatened by hunting and persistence of feral animals. Conservation management of these tortoises has been hampered by lack of clarity regarding their taxonomy, ecological and morphological diversity, and the spatial distribution of evolutionarily significant units that may exist. Analyses of 16 microsatellite loci did not group samples according to current taxonomy. Instead, three (rather than two) genetic clusters were revealed. We show that the three regions of southern Isabela associated with these genetic clusters are significantly different in their ecological niches, which could suggest that ecological divergence may have shaped patterns of genetic differentiation in these tortoises. Furthermore, results suggest limited recent gene flow among sampled localities and between each of the three regions associated with genetic clusters. We discuss the need for further research on the ecological factors shaping the genetic and morphological diversity of southern Isabela tortoises. We suggest that current strategies whereby populations are managed separately are warranted pending further study, but due to mixed ancestry we recommend that Cerro Paloma tortoises be excluded from management programs.     

Mitochondria represent another locale for the divalent metal transporter 1 (DMT1)

The divalent metal transporter (DMT1) is well known for its roles in duodenal iron absorption across the apical enterocyte membrane, in iron efflux from the endosome during transferrin-dependent cellular iron acquisition, as well as in uptake of non-transferrin bound iron in many cells. Recently, using multiple approaches, we have obtained evidence that the mitochondrial outer membrane is another subcellular locale of DMT1 expression. While iron is of vital importance for mitochondrial energy metabolism, its delivery is likely to be tightly controlled due to iron''s damaging redox properties. Here we provide additional support for a role of DMT1 in mitochondrial iron acquisition by immunofluorescence colocalization with mitochondrial markers in cells and isolated mitochondria, as well as flow cytometric quantification of DMT1-positive mitochondria from an inducible expression system. Physiological consequences of mitochondrial DMT1 expression are discussed also in consideration of other DMT1 substrates, such as manganese, relevant to mitochondrial antioxidant defense.     

Integrated Genomic and Epigenomic Analysis of Breast Cancer Brain Metastasis

The brain is a common site of metastatic disease in patients with breast cancer, which has few therapeutic options and dismal outcomes. The purpose of our study was to identify common and rare events that underlie breast cancer brain metastasis. We performed deep genomic profiling, which integrated gene copy number, gene expression and DNA methylation datasets on a collection of breast brain metastases. We identified frequent large chromosomal gains in 1q, 5p, 8q, 11q, and 20q and frequent broad-level deletions involving 8p, 17p, 21p and Xq. Frequently amplified and overexpressed genes included ATAD2, BRAF, DERL1, DNMTRB and NEK2A. The ATM, CRYAB and HSPB2 genes were commonly deleted and underexpressed. Knowledge mining revealed enrichment in cell cycle and G2/M transition pathways, which contained AURKA, AURKB and FOXM1. Using the PAM50 breast cancer intrinsic classifier, Luminal B, Her2+/ER negative, and basal-like tumors were identified as the most commonly represented breast cancer subtypes in our brain metastasis cohort. While overall methylation levels were increased in breast cancer brain metastasis, basal-like brain metastases were associated with significantly lower levels of methylation. Integrating DNA methylation data with gene expression revealed defects in cell migration and adhesion due to hypermethylation and downregulation of PENK, EDN3, and ITGAM. Hypomethylation and upregulation of KRT8 likely affects adhesion and permeability. Genomic and epigenomic profiling of breast brain metastasis has provided insight into the somatic events underlying this disease, which have potential in forming the basis of future therapeutic strategies.     

Reduction in accuracy of genomic prediction for ordered categorical data compared to continuous observations

Background

Accuracy of genomic prediction depends on number of records in the training population, heritability, effective population size, genetic architecture, and relatedness of training and validation populations. Many traits have ordered categories including reproductive performance and susceptibility or resistance to disease. Categorical scores are often recorded because they are easier to obtain than continuous observations. Bayesian linear regression has been extended to the threshold model for genomic prediction. The objective of this study was to quantify reductions in accuracy for ordinal categorical traits relative to continuous traits.

Methods

Efficiency of genomic prediction was evaluated for heritabilities of 0.10, 0.25 or 0.50. Phenotypes were simulated for 2250 purebred animals using 50 QTL selected from actual 50k SNP (single nucleotide polymorphism) genotypes giving a proportion of causal to total loci of.0001. A Bayes C π threshold model simultaneously fitted all 50k markers except those that represented QTL. Estimated SNP effects were utilized to predict genomic breeding values in purebred (n = 239) or multibreed (n = 924) validation populations. Correlations between true and predicted genomic merit in validation populations were used to assess predictive ability.

Results

Accuracies of genomic estimated breeding values ranged from 0.12 to 0.66 for purebred and from 0.04 to 0.53 for multibreed validation populations based on Bayes C π linear model analysis of the simulated underlying variable. Accuracies for ordinal categorical scores analyzed by the Bayes C π threshold model were 20% to 50% lower and ranged from 0.04 to 0.55 for purebred and from 0.01 to 0.44 for multibreed validation populations. Analysis of ordinal categorical scores using a linear model resulted in further reductions in accuracy.

Conclusions

Threshold traits result in markedly lower accuracy than a linear model on the underlying variable. To achieve an accuracy equal or greater than for continuous phenotypes with a training population of 1000 animals, a 2.25 fold increase in training population size was required for categorical scores fitted with the threshold model. The threshold model resulted in higher accuracies than the linear model and its advantage was greatest when training populations were smallest.     

A class of Bayesian methods to combine large numbers of genotyped and non-genotyped animals for whole-genome analyses

Background

To obtain predictions that are not biased by selection, the conditional mean of the breeding values must be computed given the data that were used for selection. When single nucleotide polymorphism (SNP) effects have a normal distribution, it can be argued that single-step best linear unbiased prediction (SS-BLUP) yields a conditional mean of the breeding values. Obtaining SS-BLUP, however, requires computing the inverse of the dense matrix G of genomic relationships, which will become infeasible as the number of genotyped animals increases. Also, computing G requires the frequencies of SNP alleles in the founders, which are not available in most situations. Furthermore, SS-BLUP is expected to perform poorly relative to variable selection models such as BayesB and BayesC as marker densities increase.

Methods

A strategy is presented for Bayesian regression models (SSBR) that combines all available data from genotyped and non-genotyped animals, as in SS-BLUP, but accommodates a wider class of models. Our strategy uses imputed marker covariates for animals that are not genotyped, together with an appropriate residual genetic effect to accommodate deviations between true and imputed genotypes. Under normality, one formulation of SSBR yields results identical to SS-BLUP, but does not require computing G or its inverse and provides richer inferences. At present, Bayesian regression analyses are used with a few thousand genotyped individuals. However, when SSBR is applied to all animals in a breeding program, there will be a 100 to 200-fold increase in the number of animals and an associated 100 to 200-fold increase in computing time. Parallel computing strategies can be used to reduce computing time. In one such strategy, a 58-fold speedup was achieved using 120 cores.

Discussion

In SSBR and SS-BLUP, phenotype, genotype and pedigree information are combined in a single-step. Unlike SS-BLUP, SSBR is not limited to normally distributed marker effects; it can be used when marker effects have a t distribution, as in BayesA, or mixture distributions, as in BayesB or BayesC π. Furthermore, it has the advantage that matrix inversion is not required. We have investigated parallel computing to speedup SSBR analyses so they can be used for routine applications.

Electronic supplementary material

The online version of this article (doi:10.1186/1297-9686-46-50) contains supplementary material, which is available to authorized users.