The Relationship Between FST and the Frequency of the Most Frequent Allele

F_ST is frequently used as a summary of genetic differentiation among groups. It has been suggested that F_ST depends on the allele frequencies at a locus, as it exhibits a variety of peculiar properties related to genetic diversity: higher values for biallelic single-nucleotide polymorphisms (SNPs) than for multiallelic microsatellites, low values among high-diversity populations viewed as substantially distinct, and low values for populations that differ primarily in their profiles of rare alleles. A full mathematical understanding of the dependence of F_ST on allele frequencies, however, has been elusive. Here, we examine the relationship between F_ST and the frequency of the most frequent allele, demonstrating that the range of values that F_ST can take is restricted considerably by the allele-frequency distribution. For a two-population model, we derive strict bounds on F_ST as a function of the frequency M of the allele with highest mean frequency between the pair of populations. Using these bounds, we show that for a value of M chosen uniformly between 0 and 1 at a multiallelic locus whose number of alleles is left unspecified, the mean maximum F_ST is ∼0.3585. Further, F_ST is restricted to values much less than 1 when M is low or high, and the contribution to the maximum F_ST made by the most frequent allele is on average ∼0.4485. Using bounds on homozygosity that we have previously derived as functions of M, we describe strict bounds on F_ST in terms of the homozygosity of the total population, finding that the mean maximum F_ST given this homozygosity is 1 − ln 2 ≈ 0.3069. Our results provide a conceptual basis for understanding the dependence of F_ST on allele frequencies and genetic diversity and for interpreting the roles of these quantities in computations of F_ST from population-genetic data. Further, our analysis suggests that many unusual observations of F_ST, including the relatively low F_ST values in high-diversity human populations from Africa and the relatively low estimates of F_ST for microsatellites compared to SNPs, can be understood not as biological phenomena associated with different groups of populations or classes of markers but rather as consequences of the intrinsic mathematical dependence of F_ST on the properties of allele-frequency distributions.DIFFERENTIATION among groups is one of the fundamental subjects of the field of population genetics. Comparisons of the level of variation among subpopulations with the level of variation in the total population have been employed frequently in population-genetic theory, in statistical methods for data analysis, and in empirical studies of distributions of genetic variation. Wright’s (Wright 1951) fixation indices, and F_ST in particular, have been central to this effort.Wright’s F_ST was originally defined as the correlation between two randomly sampled gametes from the same subpopulation when the correlation of two randomly sampled gametes from the total population is set to zero. Several definitions of F_ST or F_ST-like quantities are now available, relying on a variety of different conceptual formulations but all measuring some aspect of population differentiation (e.g., Charlesworth 1998; Holsinger and Weir 2009). Many authors have claimed that one or another formulation of F_ST is affected by levels of genetic diversity or by allele frequencies, either because the range of F_ST is restricted by these quantities or because these quantities affect the degree to which F_ST reflects population differentiation (e.g., Charlesworth 1998; Nagylaki 1998; Hedrick 1999, 2005; Long and Kittles 2003; Jost 2008; Ryman and Leimar 2008; Long 2009; Meirmans and Hedrick 2011). For example, Nagylaki (1998) and Hedrick (1999) argued that measures of F_ST may be poor measures of genetic differentiation when the level of diversity is high. Charlesworth (1998) suggested that F_ST can be inflated when diversity is low, arguing that F_ST might not be appropriate for comparing loci with substantially different levels of variation. In a provocative recent article, Jost (2008) used the diversity dependence of forms of F_ST to question their utility as differentiation measures at all.One definition that is convenient for mathematical assessment of the relationship of an F_ST-like quantity and allele frequencies is the quantity labeled G_ST by Nei (1973), which for a given locus measures the difference between the heterozygosity of the total (pooled) population, h_T, and the mean heterozygosity across subpopulations, h_S, divided by the heterozygosity of the total population:GST=hT−hShT.(1)In terms of the homozygosity of the total population, H_T = 1 − h_T, and the mean homozygosity across subpopulations, H_S = 1 − h_S, we can writeGST=HS−HT1−HT.(2)The Wahlund (1928) principle guarantees that H_S ≥ H_T and, therefore, because H_S ≤ 1 and for a polymorphic locus with finitely many alleles, 0 < H_T < 1, G_ST lies in the interval [0,1].Using G_ST for their definition of F_ST, Hedrick (1999, 2005) and Long and Kittles (2003) pointed out that because h_T < 1, F_ST cannot exceed the mean homozygosity across subpopulations, H_S:F_ST = 1 ? h_S/h_T < 1 ? h_S = H_S.(3)Hedrick (2005) obtained this result by considering a set of K equal-sized subpopulations, in which each allele is private to a single subpopulation. In the limit as K → ∞, a stronger upper bound on F_ST as a function of H_S and K reduces to Equation 3 (see also Jin and Chakraborty 1995 and Long and Kittles 2003).While Hedrick (1999, 2005) and Long and Kittles (2003) have clarified the relationship between F_ST and the mean homozygosity H_S across subpopulations, their approaches do not easily illuminate the connection between F_ST and allele frequencies themselves. A formal understanding of the relationship between F_ST and allele frequencies would make it possible to more fully understand the behavior of F_ST in situations where markers of interest differ substantially in allele frequencies or levels of genetic diversity. Our recent work on the relationship between homozygosity and the frequency of the most frequent allele (Rosenberg and Jakobsson 2008; Reddy and Rosenberg 2012) provides a mathematical approach for formal investigation of bounds on population-genetic statistics in terms of allele frequencies. In this article, we therefore seek to thoroughly examine the dependence of F_ST on allele frequencies by investigating the upper bound on F_ST in terms of the frequency M of the most frequent allele across a pair of populations. We derive bounds on F_ST given the frequency of the most frequent allele and bounds on the frequency of the most frequent allele given F_ST. We consider loci with arbitrarily many alleles in a pair of subpopulations. Using theory for the bounds on homozygosity given the frequency of the most frequent allele, we obtain strict bounds on F_ST given the homozygosity of the total population. Our analysis clarifies the relationships among F_ST, allele frequencies, and homozygosity, providing explanations for peculiar observations of F_ST that can be attributed to allele-frequency dependence.     

Increased levels of (class switched) memory B cells in peripheral blood of current smokers

There is increasing evidence that a specific immune response contributes to the pathogenesis of COPD. B-cell follicles are present in lung tissue and increased anti-elastin titers have been found in plasma of COPD patients. Additionally, regulatory T cells (Tregs) have been implicated in its pathogenesis as they control immunological reactions. We hypothesize that the specific immune response in COPD is smoke induced, either by a direct effect of smoking or as a result of smoke-induced lung tissue destruction (i.e. formation of neo-epitopes or auto antigens). Furthermore, we propose that Tregs are involved in the suppression of this smoke-induced specific immune response.The presence of B cells, memory B cells and Tregs was assessed by flow cytometry in peripheral blood of 20 COPD patients and 29 healthy individuals and related to their current smoking status.COPD patients had lower (memory) B-cell percentages and higher Treg percentages in peripheral blood than healthy individuals, with a significant negative correlation between these cells. Interestingly, current smokers had higher percentages of (class-switched) memory B cells than ex-smokers and never smokers, irrespective of COPD.This increase in (class-switched) memory B cells in current smokers is intriguing and suggests that smoke-induced neo-antigens may be constantly induced in the lung. The negative correlation between B cells and Tregs in blood is in line with previously published observations that Tregs can suppress B cells. Future studies focusing on the presence of these (class switched) memory B cells in the lung, their antigen specificity and their interaction with Tregs are necessary to further elucidate the specific B-cell response in COPD.     

<Emphasis Type="Italic">In vitro</Emphasis> and <Emphasis Type="Italic">ex vivo</Emphasis> effect of hyaluronic acid on erythrocyte flow properties

Background  

Hyaluronic acid (HA) is present in many tissues; its presence in serum may be related to certain inflammatory conditions, tissue damage, sepsis, liver malfunction and some malignancies. In the present work, our goal was to investigate the significance of hyaluronic acid effect on erythrocyte flow properties. Therefore we performed in vitro experiments incubating red blood cells (RBCs) with several HA concentrations. Afterwards, in order to corroborate the pathophysiological significance of the results obtained, we replicated the in vitro experiment with ex vivo RBCs from diagnosed rheumatoid arthritis (RA) patients, a serum HA-increasing pathology.     

Assessment of the relative contribution of asexual propagation in a population of the coral-excavating sponge Cliona delitrix from the Bahamas

Cliona delitrix is a very destructive coral-excavating sponge in Caribbean coral reef systems, particularly for Montastraea species. Little is known about how these excavating sponges propagate across coral reefs. In this study a hypothesis was tested that coral breakage caused by the bioeroding activity facilitates the asexual propagation of this sponge and in turn favors the spread of the most aggressive sponge genotypes. An allozyme analysis, involving 12 loci systems of 52 sponge individuals from a total of 13 Montastraea heads, found that no two sponges possessed identical multi-locus genotypes. Contrary to the pattern expected for fragmenting species, the incidence of clonality and asexual propagation at the population level was minimal. The lack of correlation between genetic and physical distances for the studied sponges also suggests that population maintenance appears to derive from larval dispersal, with a spatial range of dispersal larger than the average distance between the coral heads (10–10² m).     

Programmed cell death during development of cowpea (Vigna unguiculata (L.) Walp.) seed coat

The seed coat develops primarily from maternal tissues and comprises multiple cell layers at maturity, providing a metabolically dynamic interface between the developing embryo and the environment during embryogenesis, dormancy and germination of seeds. Seed coat development involves dramatic cellular changes, and the aim of this research was to investigate the role of programmed cell death (PCD) events during the development of seed coats of cowpea [Vigna unguiculata (L.) Walp.]. We demonstrate that cells of the developing cowpea seed coats undergo a programme of autolytic cell death, detected as cellular morphological changes in nuclei, mitochondria, chloroplasts and vacuoles, DNA fragmentation and oligonucleosome accumulation in the cytoplasm, and loss of membrane viability. We show for the first time that classes 6 and 8 caspase‐like enzymes are active during seed coat development, and that these activities may be compartmentalized by translocation between vacuoles and cytoplasm during PCD events.     

Population density of the Réunion Grey White-eye Zosterops borbonicus within the summit ecosystems of Réunion,Mascarene Islands

Assessing population density is crucial for studying the ecology and evolutionary biology of species as well as for conservation purposes. Here we used point count methods to infer population density in a single-island endemic passerine bird, the Réunion Grey White-eye Zosterops borbonicus, that displays striking evidence of differentiation at a small spatial scale. Population density was estimated at 5.17 birds ha^?1 (CL 4.85–5.50), a value somewhat higher than previously believed. This estimation provides the first detailed estimation of bird population density in the vulnerable summit ecosystems of Réunion and will possibly allow a better understanding of the evolutionary causes of this plumage colour variation.     

Efficiency of population structures for mapping of Mendelian and imprinted quantitative trait loci in outbred pigs using variance component methods

In a simulation study different designs for a pure line pig population were compared for efficiency of mapping QTL using the variance component method. Phenotypes affected by a Mendelian QTL, a paternally expressed QTL, a maternally expressed QTL or by a QTL without an effect were simulated. In all alternative designs 960 progeny were phenotyped. Given the limited number of animals there is an optimum between the number of families and the family size. Estimation of Mendelian and parentally expressed QTL is more efficient in a design with large family sizes. Too small a number of sires should be avoided to minimize chances of sires to be non-segregating. When a large number of families is used, the number of haplotypes increases which reduces the accuracy of estimating the QTL effect and thereby reduces the power to show a significant QTL and to correctly position the QTL. Dense maps allow for smaller family size due to exploitation of LD-information. Given the different possible modes of inheritance of the QTL using 8 to16 boars, two litters per dam was optimal with respect to determining significance and correct location of the QTL for a data set consisting of 960 progeny. The variance component method combining linkage disequilibrium and linkage analysis seems to be an appropriate choice to analyze data sets which vary in marker density and which contain complex family structures.     

Domain-based identification and analysis of glutamate receptor ion channels and their relatives in prokaryotes

Voltage-gated and ligand-gated ion channels are used in eukaryotic organisms for the purpose of electrochemical signaling. There are prokaryotic homologues to major eukaryotic channels of these sorts, including voltage-gated sodium, potassium, and calcium channels, Ach-receptor and glutamate-receptor channels. The prokaryotic homologues have been less well characterized functionally than their eukaryotic counterparts. In this study we identify likely prokaryotic functional counterparts of eukaryotic glutamate receptor channels by comprehensive analysis of the prokaryotic sequences in the context of known functional domains present in the eukaryotic members of this family. In particular, we searched the nonredundant protein database for all proteins containing the following motif: the two sections of the extracellular glutamate binding domain flanking two transmembrane helices. We discovered 100 prokaryotic sequences containing this motif, with a wide variety of functional annotations. Two groups within this family have the same topology as eukaryotic glutamate receptor channels. Group 1 has a potassium-like selectivity filter. Group 2 is most closely related to eukaryotic glutamate receptor channels. We present analysis of the functional domain architecture for the group of 100, a putative phylogenetic tree, comparison of the protein phylogeny with the corresponding species phylogeny, consideration of the distribution of these proteins among classes of prokaryotes, and orthologous relationships between prokaryotic and human glutamate receptor channels. We introduce a construct called the Evolutionary Domain Network, which represents a putative pathway of domain rearrangements underlying the domain composition of present channels. We believe that scientists interested in ion channels in general, and ligand-gated ion channels in particular, will be interested in this work. The work should also be of interest to bioinformatics researchers who are interested in the use of functional domain-based analysis in evolutionary and functional discovery.     

Autoantibody systems in rheumatoid arthritis: specificity, sensitivity and diagnostic value

The diagnosis of rheumatoid arthritis (RA) is primarily based on clinical symptoms, so it is often difficult to diagnose RA in very early stages of the disease. A disease-specific autoantibody that could be used as a serological marker would therefore be very useful. Most autoimmune diseases are characterized by a polyclonal B-cell response targeting multiple autoantigens. These immune responses are often not specific for a single disease. In this review, the most important autoantibody/autoantigen systems associated with RA are described and their utility as a diagnostic and prognostic tool, including their specificity, sensitivity and practical application, is discussed. We conclude that, at present, the antibody response directed to citrullinated antigens has the most valuable diagnostic and prognostic potential for RA.