Long-distance electron transport in individual, living cable bacteria.

Electron transport within living cells is essential for energy conservation in all respiring and photosynthetic organisms. While a few bacteria transport electrons over micrometer distances to their surroundings, filaments of cable bacteria are hypothesized to conduct electric currents over centimeter distances. We used resonance Raman microscopy to analyze cytochrome redox states in living cable bacteria. Cable-bacteria filaments were placed in microscope chambers with sulfide as electron source and oxygen as electron sink at opposite ends. Along individual filaments a gradient in cytochrome redox potential was detected, which immediately broke down upon removal of oxygen or laser cutting of the filaments. Without access to oxygen, a rapid shift toward more reduced cytochromes was observed, as electrons were no longer drained from the filament but accumulated in the cellular cytochromes. These results provide direct evidence for long-distance electron transport in living multicellular bacteria.

polyDFEv2.0: testing for invariance of the distribution of fitness effects within and across species.

SUMMARY: Distribution of fitness effects (DFE) of mutations can be inferred from site frequency spectrum (SFS) data. There is mounting interest to determine whether distinct genomic regions and/or species share a common DFE, or whether evidence exists for differences among them. polyDFEv2.0 fits multiple SFS datasets at once and provides likelihood ratio tests for DFE invariance across datasets. Simulations show that testing for DFE invariance across genomic regions within a species requires models accounting for distinct sources of heterogeneity (chance and genuine difference in DFE) underlying differences in SFS data in these regions. Not accounting for this will result in the spurious detection of DFE differences. AVAILABILITY AND IMPLEMENTATION: polyDFEv2.0 is implemented in C and is accompanied by a series of R functions that facilitate post-processing of the output. It is available as source code and compiled binaries under a GNU General Public License v3.0 from https://github.com/paula-tataru/polyDFE. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Statistical Inference in the Wright-Fisher Model Using Allele Frequency Data.

The Wright­Fisher model provides an elegant mathematical framework for understanding allele frequency data. In particular, the model can be used to infer the demographic history of species and identify loci under selection. A crucial quantity for inference under the Wright­Fisher model is the distribution of allele frequencies (DAF). Despite the apparent simplicity of the model, the calculation of the DAF is challenging. We review and discuss strategies for approximating the DAF, and how these are used in methods that perform inference from allele frequency data. Various evolutionary forces can be incorporated in the Wright­Fisher model, and we consider these in turn. We begin our review with the basic bi-allelic Wright­Fisher model where random genetic drift is the only evolutionary force. We then consider mutation, migration, and selection. In particular, we compare diffusion-based and moment-based methods in terms of accuracy, computational efficiency, and analytical tractability. We conclude with a brief overview of the multi-allelic process with a general mutation model.

One size fits all? Direct evidence for the heterogeneity of genetic drift throughout the genome.

Effective population size (Ne) is a central parameter in population and conservation genetics. It measures the magnitude of genetic drift, rates of accumulation of inbreeding in a population, and it conditions the efficacy of selection. It is often assumed that a single Ne can account for the evolution of genomes. However, recent work provides indirect evidence for heterogeneity in Ne throughout the genome. We study this by examining genome-wide diversity in the Danish Holstein cattle breed. Using the differences in allele frequencies over a single generation, we directly estimated Ne among autosomes and smaller windows within autosomes. We found statistically significant variation in Ne at both scales. However, no correlation was found between the detected regional variability in Ne, and proxies for the intensity of linked selection (local recombination rate, gene density), or the presence of either past strong selection or current artificial selection on traits of economic value. Our findings call for further caution regarding the wide applicability of the Ne concept for understanding quantitatively processes such as genetic drift and accumulation of consanguinity in both natural and managed populations.

diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals.

UNLABELLED: We present a tool, diCal-IBD, for detecting identity-by-descent (IBD) tracts between pairs of genomic sequences. Our method builds on a recent demographic inference method based on the coalescent with recombination, and is able to incorporate demographic information as a prior. Simulation study shows that diCal-IBD has significantly higher recall and precision than that of existing single-nucleotide polymorphism-based IBD detection methods, while retaining reasonable accuracy for IBD tracts as small as 0.1 cM. AVAILABILITY: http://sourceforge.net/projects/dical-ibd.

Oxfold: kinetic folding of RNA using stochastic context-free grammars and evolutionary information.

MOTIVATION: Many computational methods for RNA secondary structure prediction, and, in particular, for the prediction of a consensus structure of an alignment of RNA sequences, have been developed. Most methods, however, ignore biophysical factors, such as the kinetics of RNA folding; no current implementation considers both evolutionary information and folding kinetics, thus losing information that, when considered, might lead to better predictions. RESULTS: We present an iterative algorithm, Oxfold, in the framework of stochastic context-free grammars, that emulates the kinetics of RNA folding in a simplified way, in combination with a molecular evolution model. This method improves considerably on existing grammatical models that do not consider folding kinetics. Additionally, the model compares favourably to non-kinetic thermodynamic models.

Cable bacteria with electric connection to oxygen attract flocks of diverse bacteria.

Cable bacteria are centimeter-long filamentous bacteria that conduct electrons via internal wires, thus coupling sulfide oxidation in deeper, anoxic sediment with oxygen reduction in surface sediment. This activity induces geochemical changes in the sediment, and other bacterial groups appear to benefit from the electrical connection to oxygen. Here, we report that diverse bacteria swim in a tight flock around the anoxic part of oxygen-respiring cable bacteria and disperse immediately when the connection to oxygen is disrupted (by cutting the cable bacteria with a laser). Raman microscopy shows that flocking bacteria are more oxidized when closer to the cable bacteria, but physical contact seems to be rare and brief, which suggests potential transfer of electrons via unidentified soluble intermediates. Metagenomic analysis indicates that most of the flocking bacteria appear to be aerobes, including organotrophs, sulfide oxidizers, and possibly iron oxidizers, which might transfer electrons to cable bacteria for respiration. The association and close interaction with such diverse partners might explain how oxygen via cable bacteria can affect microbial communities and processes far into anoxic environments.

Evolving stochastic context--free grammars for RNA secondary structure prediction.

BACKGROUND: Stochastic Context-Free Grammars (SCFGs) were applied successfully to RNA secondary structure prediction in the early 90s, and used in combination with comparative methods in the late 90s. The set of SCFGs potentially useful for RNA secondary structure prediction is very large, but a few intuitively designed grammars have remained dominant. In this paper we investigate two automatic search techniques for effective grammars - exhaustive search for very compact grammars and an evolutionary algorithm to find larger grammars. We also examine whether grammar ambiguity is as problematic to structure prediction as has been previously suggested. RESULTS: These search techniques were applied to predict RNA secondary structure on a maximal data set and revealed new and interesting grammars, though none are dramatically better than classic grammars. In general, results showed that many grammars with quite different structure could have very similar predictive ability. Many ambiguous grammars were found which were at least as effective as the best current unambiguous grammars. CONCLUSIONS: Overall the method of evolving SCFGs for RNA secondary structure prediction proved effective in finding many grammars that had strong predictive accuracy, as good or slightly better than those designed manually. Furthermore, several of the best grammars found were ambiguous, demonstrating that such grammars should not be disregarded.

Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains.

BACKGROUND: Continuous time Markov chains (CTMCs) is a widely used model for describing the evolution of DNA sequences on the nucleotide, amino acid or codon level. The sufficient statistics for CTMCs are the time spent in a state and the number of changes between any two states. In applications past evolutionary events (exact times and types of changes) are unaccessible and the past must be inferred from DNA sequence data observed in the present. RESULTS: We describe and implement three algorithms for computing linear combinations of expected values of the sufficient statistics, conditioned on the end-points of the chain, and compare their performance with respect to accuracy and running time. The first algorithm is based on an eigenvalue decomposition of the rate matrix (EVD), the second on uniformization (UNI), and the third on integrals of matrix exponentials (EXPM). The implementation in R of the algorithms is available at http://www.birc.au.dk/~paula/. CONCLUSIONS: We use two different models to analyze the accuracy and eight experiments to investigate the speed of the three algorithms. We find that they have similar accuracy and that EXPM is the slowest method. Furthermore we find that UNI is usually faster than EVD.

polyDFE: Inferring the Distribution of Fitness Effects and Properties of Beneficial Mutations from Polymorphism Data.

The possible evolutionary trajectories a population can follow is determined by the fitness effects of new mutations. Their relative frequencies are best specified through a distribution of fitness effects (DFE) that spans deleterious, neutral, and beneficial mutations. As such, the DFE is key to several aspects of the evolution of a population, and particularly the rate of adaptive molecular evolution (α). Inference of DFE from patterns of polymorphism and divergence has been a longstanding goal of evolutionary genetics.polyDFE provides a flexible statistical framework to estimate the DFE and α from site frequency spectrum (SFS) data. Several probability distributions can be fitted to the data to model the DFE. The method also jointly estimates a series of nuisance parameters that model the effect of unknown demography as well data imperfections, in particular possible errors in polarizing SNPs. This chapter is organized as a tutorial for polyDFE. We start by briefly reviewing the concept of DFE, α, and the principles underlying the method, and then provide an example using central chimpanzees data (Tataru et al., Genetics 207(3):1103-1119, 2017; Bataillon et al., Genome Biol Evol 7(4):1122-1132, 2015) to guide the user through the different steps of an analysis: formatting the data as input to polyDFE, fitting different models, obtaining estimates of parameters uncertainty and performing statistical tests, as well as model averaging procedures to obtain robust estimates of model parameters.

Comparison of the Full Distribution of Fitness Effects of New Amino Acid Mutations Across Great Apes.

The distribution of fitness effects (DFE) is central to many questions in evolutionary biology. However, little is known about the differences in DFE between closely related species. We use >9000 coding genes orthologous one-to-one across great apes, gibbons, and macaques to assess the stability of the DFE across great apes. We use the unfolded site frequency spectrum of polymorphic mutations (n = 8 haploid chromosomes per population) to estimate the DFE. We find that the shape of the deleterious DFE is strikingly similar across great apes. We confirm that effective population size (Ne ) is a strong predictor of the strength of negative selection, consistent with the nearly neutral theory. However, we also find that the strength of negative selection varies more than expected given the differences in Ne between species. Across species, mean fitness effects of new deleterious mutations covaries with Ne , consistent with positive epistasis among deleterious mutations. We find that the strength of negative selection for the smallest populations, bonobos and western chimpanzees, is higher than expected given their Ne This may result from a more efficient purging of strongly deleterious recessive variants in these populations. Forward simulations confirm that these findings are not artifacts of the way we are inferring Ne and DFE parameters. All findings are replicated using only GC-conservative mutations, thereby confirming that GC-biased gene conversion is not affecting our conclusions.

Regmex: a statistical tool for exploring motifs in ranked sequence lists from genomics experiments.

BACKGROUND: Motif analysis methods have long been central for studying biological function of nucleotide sequences. Functional genomics experiments extend their potential. They typically generate sequence lists ranked by an experimentally acquired functional property such as gene expression or protein binding affinity. Current motif discovery tools suffer from limitations in searching large motif spaces, and thus more complex motifs may not be included. There is thus a need for motif analysis methods that are tailored for analyzing specific complex motifs motivated by biological questions and hypotheses rather than acting as a screen based motif finding tool. METHODS: We present Regmex (REGular expression Motif EXplorer), which offers several methods to identify overrepresented motifs in ranked lists of sequences. Regmex uses regular expressions to define motifs or families of motifs and embedded Markov models to calculate exact p-values for motif observations in sequences. Biases in motif distributions across ranked sequence lists are evaluated using random walks, Brownian bridges, or modified rank based statistics. A modular setup and fast analytic p value evaluations make Regmex applicable to diverse and potentially large-scale motif analysis problems. RESULTS: We demonstrate use cases of combined motifs on simulated data and on expression data from micro RNA transfection experiments. We confirm previously obtained results and demonstrate the usability of Regmex to test a specific hypothesis about the relative location of microRNA seed sites and U-rich motifs. We further compare the tool with an existing motif discovery tool and show increased sensitivity. CONCLUSIONS: Regmex is a useful and flexible tool to analyze motif hypotheses that relates to large data sets in functional genomics. The method is available as an R package (https://github.com/muhligs/regmex).

Inference of Distribution of Fitness Effects and Proportion of Adaptive Substitutions from Polymorphism Data.

The distribution of fitness effects (DFE) encompasses the fraction of deleterious, neutral, and beneficial mutations. It conditions the evolutionary trajectory of populations, as well as the rate of adaptive molecular evolution (α). Inferring DFE and α from patterns of polymorphism, as given through the site frequency spectrum (SFS) and divergence data, has been a longstanding goal of evolutionary genetics. A widespread assumption shared by previous inference methods is that beneficial mutations only contribute negligibly to the polymorphism data. Hence, a DFE comprising only deleterious mutations tends to be estimated from SFS data, and α is then predicted by contrasting the SFS with divergence data from an outgroup. We develop a hierarchical probabilistic framework that extends previous methods to infer DFE and α from polymorphism data alone. We use extensive simulations to examine the performance of our method. While an outgroup is still needed to obtain an unfolded SFS, we show that both a DFE, comprising both deleterious and beneficial mutations, and α can be inferred without using divergence data. We also show that not accounting for the contribution of beneficial mutations to polymorphism data leads to substantially biased estimates of the DFE and α We compare our framework with one of the most widely used inference methods available and apply it on a recently published chimpanzee exome data set.

Inference Under a Wright-Fisher Model Using an Accurate Beta Approximation.

The large amount and high quality of genomic data available today enable, in principle, accurate inference of evolutionary histories of observed populations. The Wright-Fisher model is one of the most widely used models for this purpose. It describes the stochastic behavior in time of allele frequencies and the influence of evolutionary pressures, such as mutation and selection. Despite its simple mathematical formulation, exact results for the distribution of allele frequency (DAF) as a function of time are not available in closed analytical form. Existing approximations build on the computationally intensive diffusion limit or rely on matching moments of the DAF. One of the moment-based approximations relies on the beta distribution, which can accurately describe the DAF when the allele frequency is not close to the boundaries (0 and 1). Nonetheless, under a Wright-Fisher model, the probability of being on the boundary can be positive, corresponding to the allele being either lost or fixed. Here we introduce the beta with spikes, an extension of the beta approximation that explicitly models the loss and fixation probabilities as two spikes at the boundaries. We show that the addition of spikes greatly improves the quality of the approximation. We additionally illustrate, using both simulated and real data, how the beta with spikes can be used for inference of divergence times between populations with comparable performance to an existing state-of-the-art method.

Algorithms for hidden markov models restricted to occurrences of regular expressions.

Hidden Markov Models (HMMs) are widely used probabilistic models, particularly for annotating sequential data with an underlying hidden structure. Patterns in the annotation are often more relevant to study than the hidden structure itself. A typical HMM analysis consists of annotating the observed data using a decoding algorithm and analyzing the annotation to study patterns of interest. For example, given an HMM modeling genes in DNA sequences, the focus is on occurrences of genes in the annotation. In this paper, we define a pattern through a regular expression and present a restriction of three classical algorithms to take the number of occurrences of the pattern in the hidden sequence into account. We present a new algorithm to compute the distribution of the number of pattern occurrences, and we extend the two most widely used existing decoding algorithms to employ information from this distribution. We show experimentally that the expectation of the distribution of the number of pattern occurrences gives a highly accurate estimate, while the typical procedure can be biased in the sense that the identified number of pattern occurrences does not correspond to the true number. We furthermore show that using this distribution in the decoding algorithms improves the predictive power of the model.