Generating confidence intervals on biological networks

BACKGROUND

In the analysis of networks we frequently require the statistical significance of some network statistic, such as measures of similarity for the properties of interacting nodes. The structure of the network may introduce dependencies among the nodes and it will in general be necessary to account for these dependencies in the statistical analysis. To this end we require some form of Null model of the network: generally rewired replicates of the network are generated which preserve only the degree (number of interactions) of each node. We show that this can fail to capture important features of network structure, and may result in unrealistic significance levels, when potentially confounding additional information is available.

METHODS

We present a new network resampling Null model which takes into account the degree sequence as well as available biological annotations. Using gene ontology information as an illustration we show how this information can be accounted for in the resampling approach, and the impact such information has on the assessment of statistical significance of correlations and motif-abundances in the Saccharomyces cerevisiae protein interaction network. An algorithm, GOcardShuffle, is introduced to allow for the efficient construction of an improved Null model for network data.

RESULTS

We use the protein interaction network of S. cerevisiae; correlations between the evolutionary rates and expression levels of interacting proteins and their statistical significance were assessed for Null models which condition on different aspects of the available data. The novel GOcardShuffle approach results in a Null model for annotated network data which appears better to describe the properties of real biological networks.

CONCLUSION

An improved statistical approach for the statistical analysis of biological network data, which conditions on the available biological information, leads to qualitatively different results compared to approaches which ignore such annotations. In particular we demonstrate the effects of the biological organization of the network can be sufficient to explain the observed similarity of interacting proteins.

Evolution at the system level: the natural history of protein interaction networks

Recent work leading to new insights into the molecular architecture underlying complex cellular phenotypes enables researchers to investigate evolutionary processes in unprecedented detail. Protein interaction network data, which are now available for an increasing number of species, promise new insights and there have been many recent studies investigating evolutionary aspects of these interaction networks, from mathematical studies of growing networks to detailed phylogenetic surveys of proteins in their interaction network context. Here, we review the spectrum of such approaches, and assess issues associated with analyzing such data from an evolutionary perspective. Currently, such analyses are statistically challenging, but could link present initiatives in systems biology with results and methodologies that have developed in evolutionary biology over the past 60 years.

Evidence for an apartheid-like social structure in early Anglo-Saxon England

The role of migration in the Anglo-Saxon transition in England remains controversial. Archaeological and historical evidence is inconclusive, but current estimates of the contribution of migrants to the English population range from less than 10000 to as many as 200000. In contrast, recent studies based on Y-chromosome variation posit a considerably higher contribution to the modern English gene pool (50-100%). Historical evidence suggests that following the Anglo-Saxon transition, people of indigenous ethnicity were at an economic and legal disadvantage compared to those having Anglo-Saxon ethnicity. It is likely that such a disadvantage would lead to differential reproductive success. We examine the effect of differential reproductive success, coupled with limited intermarriage between distinct ethnic groups, on the spread of genetic variants. Computer simulations indicate that a social structure limiting intermarriage between indigenous Britons and an initially small Anglo-Saxon immigrant population provide a plausible explanation of the high degree of Continental male-line ancestry in England.

Multi-model inference of network properties from incomplete data

It has previously been shown that subnets differ from global networks from which they are sampled for all but a very limited number of theoretical network models. These differences are of qualitative as well as quantitative nature, and the properties of subnets may be very different from the corresponding properties in the true, unobserved network. Here we propose a novel approach which allows us to infer aspects of the true network from incomplete network data in a multi-model inference framework. We develop the basic theoretical framework, including procedures for assessing confidence intervals of our estimates and evaluate the performance of this approach in simulation studies and against subnets drawn from the presently available PIN network data in Saccaromyces cerevisiae. We then illustrate the potential power of this new approach by estimating the number of interactions that will be detectable with present experimental approaches in sfour eukaryotic species, inlcuding humans. Encouragingly, where independent datasets are available we obtain consistent estimates from different partial protein interaction networks. We conclude with a discussion of the scope of this approaches and areas for further research

Induction and Function of the Phage Shock Protein Extracytoplasmic Stress Response in Escherichia coli

The phage shock protein (Psp) F regulon response in Escherichia coli is thought to be induced by impaired inner membrane integrity and an associated decrease in proton motive force (pmf). Mechanisms by which the Psp system detects the stress signal and responds have so far remained undetermined. Here we demonstrate that PspA and PspG directly confront a variety of inducing stimuli by switching the cell to anaerobic respiration and fermentation and by down-regulating motility, thereby subtly adjusting and maintaining energy usage and pmf. Additionally, PspG controls iron usage. We show that the Psp-inducing protein IV secretin stress, in the absence of Psp proteins, decreases the pmf in an ArcB-dependent manner and that ArcB is required for amplifying and transducing the stress signal to the PspF regulon. The requirement of the ArcB signal transduction protein for induction of psp provides clear evidence for a direct link between the physiological redox state of the cell, the electron transport chain, and induction of the Psp response. Under normal growth conditions PspA and PspD control the level of activity of ArcB/ArcA system that senses the redox/metabolic state of the cell, whereas under stress conditions PspA, PspD, and PspG deliver their effector functions at least in part by activating ArcB/ArcA through positive feedback.

A likelihood approach to analysis of network data

Biological, sociological, and technological network data are often analyzed by using simple summary statistics, such as the observed degree distribution, and nonparametric bootstrap procedures to provide an adequate null distribution for testing hypotheses about the network. In this article we present a full-likelihood approach that allows us to estimate parameters for general models of network growth that can be expressed in terms of recursion relations. To handle larger networks we have developed an importance sampling scheme that allows us to approximate the likelihood and draw inference about the network and how it has been generated, estimate the parameters in the model, and perform parametric bootstrap analysis of network data. We illustrate the power of this approach by estimating growth parameters for the Caenorhabditis elegans protein interaction network.

Localized breakdown in linkage disequilibrium does not always predict sperm crossover hot spots in the human MHC class II region

To investigate the relationship between meiotic crossover hot spots and block-like linkage disequilibrium (LD), we have extended our high-resolution studies of the human MHC class II region to a 90-kb segment upstream of the HLA-DOA gene. LD blocks in this region are not as well defined as in the neighboring 210-kb DNA segment but do show two regions of LD breakdown in which coalescent analysis indicates substantial historical recombination. Sperm crossover analysis of one region revealed a novel localized hot spot similar in intensity and morphology to most other MHC hot spots. Crossovers at this hot spot are not obviously affected by a large insertion/deletion polymorphism near the hot spot. The second region of LD breakdown, within the DPB1 gene, shows an extremely low level of sperm crossover activity and does not contain a sperm crossover hot spot. These results highlight the complexity of LD patterns and the importance of experimentally verifying crossover hot spots.

Sampling properties of random graphs: the degree distribution

We discuss two sampling schemes for selecting random subnets from a network, random sampling and connectivity dependent sampling, and investigate how the degree distribution of a node in the network is affected by the two types of sampling. Here we derive a necessary and sufficient condition that guarantees that the degree distributions of the subnet and the true network belong to the same family of probability distributions. For completely random sampling of nodes we find that this condition is satisfied by classical random graphs; for the vast majority of networks this condition will, however, not be met. We furthermore discuss the case where the probability of sampling a node depends on the degree of a node and we find that even classical random graphs are no longer closed under this sampling regime. We conclude by relating the results to real Eschericia coli protein interaction network data.

Gene expression profiles of Blumeria graminis indicate dynamic changes to primary metabolism during development of an obligate biotrophic pathogen

cDNA microarrays of Blumeria graminis f sp hordei transcript profiles during the asexual development cycle reveal the dynamics of global gene expression as the fungus germinates, penetrates, feeds on its host, and produces masses of conidia for dispersal. The expression profiles of genes encoding enzymes involved in primary metabolism show that there is a striking degree of coordinate regulation of some of the genes in the same pathway. In one example, genes encoding several glycolytic enzymes are significantly upregulated as mature appressoria form and also in infected epidermis, which contain fungal haustoria. In another example, mRNAs for lipid degrading enzymes are initially expressed at high levels in the conidia and the early germination stages and decrease significantly later. We discuss these results and draw inferences on the metabolic status of this obligate biotrophic fungus as it infects its host and completes its life cycle.

Subnets of scale-free networks are not scale-free: sampling properties of networks

Most studies of networks have only looked at small subsets of the true network. Here, we discuss the sampling properties of a network's degree distribution under the most parsimonious sampling scheme. Only if the degree distributions of the network and randomly sampled subnets belong to the same family of probability distributions is it possible to extrapolate from subnet data to properties of the global network. We show that this condition is indeed satisfied for some important classes of networks, notably classical random graphs and exponential random graphs. For scale-free degree distributions, however, this is not the case. Thus, inferences about the scale-free nature of a network may have to be treated with some caution. The work presented here has important implications for the analysis of molecular networks as well as for graph theory and the theory of networks in general.

HIV and the CCR5-Δ32 resistance allele

The combination of molecular biology, epidemiology, virology, evolutionary and population genetics has enabled us to understand the delicate interplay between HIV and the CCR5-Delta32 HIV resistance allele. We here review and collect from the different approaches to show how they can be combined to elucidate the interaction between host and pathogen genetics in this system. We will present an overview of the normal role of CCR5, its involvement in HIV, the molecular biology of the CCR5-Delta32 allele and its probable origins. By focusing on this well-documented and important system we hope to demonstrate the power that such a "holistic" approach might offer in the study of infectious diseases.

Allelic histories: positive selection on a HIV-resistance allele

The CCR5-Delta32 allele crucially determines the course of HIV infection and appears to be highly protective against the disease. Population genetic studies suggest that the allele has been under positive selection in Europe in the past. In a recent paper, Alison Galvani and Montgomery Slatkin collate the available evidence and use a mathematical model to strongly suggest that smallpox could have exerted sufficient selection pressure to explain the distribution of the allele across Europe. This is a beautiful example of the power of mathematical models in evolutionary genetics.

Haplotype diversity and SNP frequency dependence in the description of genetic variation

Haplotype diversity is controlled by a variety of processes, including mutation, recombination, marker ascertainment and demography. Understanding the extent to which genetic variation at physically linked loci is co-inherited is crucial for the design of the HapMap project and the correct interpretation of the resulting data. In the absence of an analytical theory extensive coalescent simulations are used to disentangle the influence of all of these factors on haplotype diversity. In addition to these qualitative insights, this study also demonstrates (i) that marker spacing and frequency profoundly influence observed levels of haplotype diversity; (ii) that the spectrum of haplotypes contains information about how exhaustively genetic variation in a region is described by a given marker set; and (iii) that so-called haplotype blocks can be generated due by the stochasticity inherent in the recombination process without having to assume variation in the recombination rate.

Estimating recombination rates from population-genetic data

Obtaining an accurate measure of how recombination rates vary across the genome has implications for understanding the molecular basis of recombination, its evolutionary significance and the distribution of linkage disequilibrium in natural populations. Although measuring the recombination rate is experimentally challenging, good estimates can be obtained by applying population-genetic methods to DNA sequences taken from natural populations. Statistical methods are now providing insights into the nature and scale of variation in the recombination rate, particularly in humans. Such knowledge will become increasingly important owing to the growing use of population-genetic methods in biomedical research.

Some notes on the combinatorial properties of haplotype tagging

Tagging haplotypes with a small number of genetic markers is becoming an increasingly interesting and important problem. Surprisingly little work has been done to characterize the mathematical framework of this problem. In this paper we present a mathematical frame, based on Boolean algebras, that adequately describe the structure of a set of genetic bi-allelic markers and the corresponding set of haplotypes. We derive a number of results that relate the number of markers required to tag a set of haplotypes to the set of markers themselves.

A Y chromosome census of the British Isles

The degree of population replacement in the British Isles associated with cultural changes has been extensively debated. Recent work has demonstrated that comparisons of genetic variation in the British Isles and on the European Continent can illuminate specific demographic processes in the history of the British Isles. For example, Wilson et al. used the similarity of Basque and Celtic Y chromosomes to argue for genetic continuity from the Upper Palaeolithic to the present in the paternal history of these populations (see also ). Differences in the Y chromosome composition of these groups also suggested genetic signatures of Norwegian influence in the Orkney Islands north of the Scottish mainland, an important center of Viking activities between 800 and 1300 A.D. More recently, Weale et al. argued for substantial Anglo-Saxon male migration into central England based on the analysis of eight British sample sets collected on an east-west transect across England and Wales. To provide a more complete assessment of the paternal genetic history of the British Isles, we have compared the Y chromosome composition of multiple geographically distant British sample sets with collections from Norway (two sites), Denmark, and Germany and with collections from central Ireland, representing, respectively, the putative invading and the indigenous populations. By analyzing 1772 Y chromosomes from 25 predominantly small urban locations, we found that different parts of the British Isles have sharply different paternal histories; the degree of population replacement and genetic continuity shows systematic variation across the sampled areas.

Balancing selection at the prion protein gene consistent with prehistoric kurulike epidemics

Kuru is an acquired prion disease largely restricted to the Fore linguistic group of the Papua New Guinea Highlands, which was transmitted during endocannibalistic feasts. Heterozygosity for a common polymorphism in the human prion protein gene (PRNP) confers relative resistance to prion diseases. Elderly survivors of the kuru epidemic, who had multiple exposures at mortuary feasts, are, in marked contrast to younger unexposed Fore, predominantly PRNP 129 heterozygotes. Kuru imposed strong balancing selection on the Fore, essentially eliminating PRNP 129 homozygotes. Worldwide PRNP haplotype diversity and coding allele frequencies suggest that strong balancing selection at this locus occurred during the evolution of modern humans.

Demography, recombination hotspot intensity, and the block structure of linkage disequilibrium

BACKGROUND

Effective gene mapping based on genetic association data will require detailed knowledge of patterns of linkage disequilibrium (LD) in human populations. It has been recently suggested that linkage disequilibrium in humans may be organized in a block-like structure, with islands of high LD separated by regions of rapid breakdown of LD due to recombination hotspots. The experimental data to date, however, are limited, and fundamental questions remain about the implications of recombination rate heterogeneity. Here, we use computer simulations to evaluate how such heterogeneity influences patterns of LD, and we develop formal criteria to assess whether the patterns are functionally block like in the context of association mapping.

RESULTS

Our analyses suggest that, even in models of extreme recombination rate heterogeneity, some human populations will have a functionally block-like structure to the pattern of LD, but others will not, depending on their precise demographic histories. In fact, for many models, we find that, following an LD-generating event, populations may move through discrete phases that can be functionally described as pre-block, block, and post-block. An analysis of observed and expected patterns of LD surrounding hotspots within the MHC Class II region confirms these theoretical expectations.

CONCLUSIONS

Even if highly punctuated patterns of recombination are the rule, patterns of LD are still likely to show differences among populations and among genomic regions that are of practical importance in the design of genetic association studies. The notion that the average extent of LD is a useful concept for the design of association studies must be abandoned in light of the experimental and theoretical evidence.

Herpes viruses hedge their bets

Static latency is the hallmark of all herpes viruses. The varicella zoster virus, for instance, causes varicella (chickenpox), and after a latent phase of between 5 and 40 years, it can give rise to herpes zoster (shingles). This latency and the subsequent reactivation has intrigued and puzzled virologists. Although several factors have been suggested, it is unknown what triggers reactivation. However, latency can be explained with a simple evolutionary model. Here, we demonstrate that a simple, yet efficient, bet-hedging strategy might have evolved in a number of viruses, especially those belonging to the herpes virus family and most importantly in varicella zoster virus. We show that the evolution of latency can be explained by the population dynamics of infectious diseases in fluctuating host populations.

Genetic diversity and models of viral evolution for the hepatitis C virus

In this review we discuss the application of theoretical frameworks to the interpretation of viral gene sequence data, with particular reference to the hepatitis C virus (HCV). The increasing availability of such data means that it is now possible (and necessary) to proceed from simple qualitative models of viral evolution, to more quantitative frameworks based on statistical inference, notably population genetics and molecular phylogenetics. We argue that these approaches are invaluable tools to the virologist and are essential for understanding the dynamics of viral infection and the outcome of therapeutic strategies. We use several recent HCV data-sets to illustrate the methods.

Haplotype diversity and the block structure of linkage disequilibrium

Several recent studies indicate that patterns of linkage disequilibrium in the human genome cannot be reconciled with a uniform distribution of recombination events, but crossovers appear to be localized in short hot-spots that separate longer stretches of DNA. Markers within these low-recombination blocks show increased levels of linkage disequilibrium and very low haplotype diversity. This could simplify study of the genetic basis of complex diseases if causal variants are common.

Population genomics: ageing by association

Mutations in the gene Klotho lead to premature ageing in mice. Recent work on human genetic variation has identified an association between a particular allele of Klotho and human lifespan. A harbinger of things to come, this work illustrates the power and growth potential for association studies of human ageing.

A predominantly indigenous paternal heritage for the Austronesian-speaking peoples of insular Southeast Asia and Oceania

Modern humans reached Southeast Asia and Oceania in one of the first dispersals out of Africa. The resulting temporal overlap of modern and archaic humans-and the apparent morphological continuity between them-has led to claims of gene flow between Homo sapiens and H. erectus. Much more recently, an agricultural technology from mainland Asia spread into the region, possibly in association with Austronesian languages. Using detailed genealogical study of Y chromosome variation, we show that the majority of current Austronesian speakers trace their paternal heritage to Pleistocene settlers in the region, as opposed to more-recent agricultural immigrants. A fraction of the paternal heritage, however, appears to be associated with more-recent immigrants from northern populations. We also show that the northern Neolithic component is very unevenly dispersed through the region, with a higher contribution in Southeast Asia and a nearly complete absence in Melanesia. Contrary to claims of gene flow (under regional continuity) between H. erectus and H. sapiens, we found no ancestral Y chromosome lineages in a set of 1,209 samples. The finding excludes the possibility that early hominids contributed significantly to the paternal heritage of the region.