The spread of infectious diseases in spatially structured populations: an invasory pair approximation

The invasion of new species and the spread of emergent infectious diseases in spatially structured populations has stimulated the study of explicit spatial models such as cellular automata, network models and lattice models. However, the analytic intractability of these models calls for the development of tractable mathematical approximations that can capture the dynamics of discrete, spatially-structured populations. Here we explore moment closure approximations for the invasion of an SIS epidemic on a regular lattice. We use moment closure methods to derive an expression for the basic reproductive number, R(0), in a lattice population. On lattices, R(0) should be bounded above by the number of neighbors per individual. However, we show that conventional pair approximations actually predict unbounded growth in R(0) with increasing transmission rates. To correct this problem, we propose an 'invasory' pair approximation which yields a relatively simple expression for R(0) that remains bounded above, and also predicts R(0) values from lattice model simulations more accurately than conventional pair and triple approximations. The invasory pair approximation is applicable to any spatial model, since it takes into account characteristics of invasions that are common to all spatially structured populations.     

Assessing the Exceptionality of Coloured Motifs in Networks

Various methods have been recently employed to characterise the structure of biological networks. In particular, the concept of network motif and the related one of coloured motif have proven useful to model the notion of a functional/evolutionary building block. However, algorithms that enumerate all the motifs of a network may produce a very large output, and methods to decide which motifs should be selected for downstream analysis are needed. A widely used method is to assess if the motif is exceptional, that is, over- or under-represented with respect to a null hypothesis. Much effort has been put in the last thirty years to derive -values for the frequencies of topological motifs, that is, fixed subgraphs. They rely either on (compound) Poisson and Gaussian approximations for the motif count distribution in Erdös-Rényi random graphs or on simulations in other models. We focus on a different definition of graph motifs that corresponds to coloured motifs. A coloured motif is a connected subgraph with fixed vertex colours but unspecified topology. Our work is the first analytical attempt to assess the exceptionality of coloured motifs in networks without any simulation. We first establish analytical formulae for the mean and the variance of the count of a coloured motif in an Erdös-Rényi random graph model. Using simulations under this model, we further show that a Pólya-Aeppli distribution better approximates the distribution of the motif count compared to Gaussian or Poisson distributions. The Pólya-Aeppli distribution, and more generally the compound Poisson distributions, are indeed well designed to model counts of clumping events. Altogether, these results enable to derive a -value for a coloured motif, without spending time on simulations.     

Allelic Diversity and Its Implications for the Rate of Adaptation

Genetic variation is usually estimated empirically from statistics based on population gene frequencies, but alternative statistics based on allelic diversity (number of allelic types) can provide complementary information. There is a lack of knowledge, however, on the evolutionary implications attached to allelic-diversity measures, particularly in structured populations. In this article we simulated multiple scenarios of single and structured populations in which a quantitative trait subject to stabilizing selection is adapted to different fitness optima. By forcing a global change in the optima we evaluated which diversity variables are more strongly correlated with both short- and long-term adaptation to the new optima. We found that quantitative genetic variance components for the trait and gene-frequency-diversity measures are generally more strongly correlated with short-term response to selection, whereas allelic-diversity measures are more correlated with long-term and total response to selection. Thus, allelic-diversity variables are better predictors of long-term adaptation than gene-frequency variables. This observation is also extended to unlinked neutral markers as a result of the information they convey on the demographic population history. Diffusion approximations for the allelic-diversity measures in a finite island model under the infinite-allele neutral mutation model are also provided.     

Algorithms for extracting structured motifs using a suffix tree with an application to promoter and regulatory site consensus identification.

This paper introduces two exact algorithms for extracting conserved structured motifs from a set of DNA sequences. Structured motifs may be described as an ordered collection of p > or = 1 "boxes" (each box corresponding to one part of the structured motif), p substitution rates (one for each box) and p - 1 intervals of distance (one for each pair of successive boxes in the collection). The contents of the boxes--that is, the motifs themselves--are unknown at the start of the algorithm. This is precisely what the algorithms are meant to find. A suffix tree is used for finding such motifs. The algorithms are efficient enough to be able to infer site consensi, such as, for instance, promoter sequences or regulatory sites, from a set of unaligned sequences corresponding to the noncoding regions upstream from all genes of a genome. In particular, both algorithms time complexity scales linearly with N2n where n is the average length of the sequences and N their number. An application to the identification of promoter and regulatory consensus sequences in bacterial genomes is shown.     

Estimation and efficient computation of the true probability of recurrence of short linear protein sequence motifs in unrelated proteins

Background  

Large datasets of protein interactions provide a rich resource for the discovery of Short Linear Motifs (SLiMs) that recur in unrelated proteins. However, existing methods for estimating the probability of motif recurrence may be biased by the size and composition of the search dataset, such that p-value estimates from different datasets, or from motifs containing different numbers of non-wildcard positions, are not strictly comparable. Here, we develop more exact methods and explore the potential biases of computationally efficient approximations.     

An overview on the distribution of word counts in Markov chains.

In this paper, we give an overview about the different results existing on the statistical distribution of word counts in a Markovian sequence of letters. Results concerning the number of overlapping occurrences, the number of renewals and the number of clumps will be presented. Counts of single words and also multiple words are considered. Most of the results are approximations as the length of the sequence tends to infinity. We will see that Gaussian approximations switch to (compound) Poisson approximations for rare words. Modeling DNA sequences or proteins by stationary Markov chains, these results can be used to study the statistical frequency of motifs in a given sequence.     

Density-structured models for plant population dynamics

Density-structured models are structured population models in which the state variable is the proportion of populations or sites in a small number of discrete density states. Although such models have rarely been used, they have the advantage that they are straightforward to parameterize, make few assumptions about population dynamics, and permit rapid data collection using coarse density assessment. In this article, we highlight their use in relating population dynamics to environmental variation and their robustness to measurement error. We show that density-structured models are able to accurately represent population dynamics under a wide range of conditions. We look at the effects of including a persistent seedbank and describe numerical approximations for the mean and variance of population size. For simulated data, we determine the extent to which the underlying continuous process may be inferred from density-structured data. Finally, we discuss issues of parameter estimation and applications for which these types of models may be useful.     

Species assembly in model ecosystems, I: Analysis of the population model and the invasion dynamics

Recently we have introduced a simplified model of ecosystem assembly (Capitán et al., 2009) for which we are able to map out all assembly pathways generated by external invasions in an exact manner. In this paper we provide a deeper analysis of the model, obtaining analytical results and introducing some approximations which allow us to reconstruct the results of our previous work. In particular, we show that the population dynamics equations of a very general class of trophic-level structured food-web have an unique interior equilibrium point which is globally stable. We show analytically that communities found as end states of the assembly process are pyramidal and we find that the equilibrium abundance of any species at any trophic level is approximately inversely proportional to the number of species in that level. We also find that the per capita growth rate of a top predator invading a resident community is key to understand the appearance of complex end states reported in our previous work. The sign of these rates allows us to separate regions in the space of parameters where the end state is either a single community or a complex set containing more than one community. We have also built up analytical approximations to the time evolution of species abundances that allow us to determine, with high accuracy, the sequence of extinctions that an invasion may cause. Finally we apply this analysis to obtain the communities in the end states. To test the accuracy of the transition probability matrix generated by this analytical procedure for the end states, we have compared averages over those sets with those obtained from the graph derived by numerical integration of the Lotka-Volterra equations. The agreement is excellent.     

Directed Network Motifs in Alzheimer’s Disease and Mild Cognitive Impairment

Directed network motifs are the building blocks of complex networks, such as human brain networks, and capture deep connectivity information that is not contained in standard network measures. In this paper we present the first application of directed network motifs in vivo to human brain networks, utilizing recently developed directed progression networks which are built upon rates of cortical thickness changes between brain regions. This is in contrast to previous studies which have relied on simulations and in vitro analysis of non-human brains. We show that frequencies of specific directed network motifs can be used to distinguish between patients with Alzheimer’s disease (AD) and normal control (NC) subjects. Especially interesting from a clinical standpoint, these motif frequencies can also distinguish between subjects with mild cognitive impairment who remained stable over three years (MCI) and those who converted to AD (CONV). Furthermore, we find that the entropy of the distribution of directed network motifs increased from MCI to CONV to AD, implying that the distribution of pathology is more structured in MCI but becomes less so as it progresses to CONV and further to AD. Thus, directed network motifs frequencies and distributional properties provide new insights into the progression of Alzheimer’s disease as well as new imaging markers for distinguishing between normal controls, stable mild cognitive impairment, MCI converters and Alzheimer’s disease.     

Localized transfection on arrays of magnetic beads coated with PCR products

High-throughput gene analysis would benefit from new approaches for delivering DNA or RNA into cells. Here we describe a simple system that allows any molecular biology laboratory to carry out multiple, parallel cell transfections on microscope coverslip arrays. By using magnetically defined positions and PCR product-coated paramagnetic beads, we achieved transfection in a variety of cell lines. Beads may be added to the cells at any time, allowing both spatial and temporal control of transfection. Because the beads may be coated with more than one gene construct, the method can be used to achieve cotransfection within single cells. Furthermore, PCR-generated mutants may be conveniently screened, bypassing cloning and plasmid purification steps. We illustrated the applicability of the method by screening combinatorial peptide libraries, fused to GFP, to identify previously unknown cellular localization motifs. In this way, we identified several localizing peptides, including structured localization signals based around the scaffold of a single C2H2 zinc finger.     

Context-sensitivity of isosteric substitutions of non-Watson–Crick basepairs in recurrent RNA 3D motifs

Sequence variation in a widespread, recurrent, structured RNA 3D motif, the Sarcin/Ricin (S/R), was studied to address three related questions: First, how do the stabilities of structured RNA 3D motifs, composed of non-Watson–Crick (non-WC) basepairs, compare to WC-paired helices of similar length and sequence? Second, what are the effects on the stabilities of such motifs of isosteric and non-isosteric base substitutions in the non-WC pairs? And third, is there selection for particular base combinations in non-WC basepairs, depending on the temperature regime to which an organism adapts? A survey of large and small subunit rRNAs from organisms adapted to different temperatures revealed the presence of systematic sequence variations at many non-WC paired sites of S/R motifs. UV melting analysis and enzymatic digestion assays of oligonucleotides containing the motif suggest that more stable motifs tend to be more rigid. We further found that the base substitutions at non-Watson–Crick pairing sites can significantly affect the thermodynamic stabilities of S/R motifs and these effects are highly context specific indicating the importance of base-stacking and base-phosphate interactions on motif stability. This study highlights the significance of non-canonical base pairs and their contributions to modulating the stability and flexibility of RNA molecules.     

Formation of the Arabidopsis pentatricopeptide repeat family

In Arabidopsis (Arabidopsis thaliana) the 466 pentatricopeptide repeat (PPR) proteins are putative RNA-binding proteins with essential roles in organelles. Roughly half of the PPR proteins form the plant combinatorial and modular protein (PCMP) subfamily, which is land-plant specific. PCMPs exhibit a large and variable tandem repeat of a standard pattern of three PPR variant motifs. The association or not of this repeat with three non-PPR motifs at their C terminus defines four distinct classes of PCMPs. The highly structured arrangement of these motifs and the similar repartition of these arrangements in the four classes suggest precise relationships between motif organization and substrate specificity. This study is an attempt to reconstruct an evolutionary scenario of the PCMP family. We developed an innovative approach based on comparisons of the proteins at two levels: namely the succession of motifs along the protein and the amino acid sequence of the motifs. It enabled us to infer evolutionary relationships between proteins as well as between the inter- and intraprotein repeats. First, we observed a polarized elongation of the repeat from the C terminus toward the N-terminal region, suggesting local recombinations of motifs. Second, the most N-terminal PPR triple motif proved to evolve under different constraints than the remaining repeat. Altogether, the evidence indicates different evolution for the PPR region and the C-terminal one in PCMPs, which points to distinct functions for these regions. Moreover, local sequence homogeneity observed across PCMP classes may be due to interclass shuffling of motifs, or to deletions/insertions of non-PPR motifs at the C terminus.     

Prediction and Experimental Characterization of nsSNPs Altering Human PDZ-Binding Motifs

Single nucleotide polymorphisms (SNPs) are a major contributor to genetic and phenotypic variation within populations. Non-synonymous SNPs (nsSNPs) modify the sequence of proteins and can affect their folding or binding properties. Experimental analysis of all nsSNPs is currently unfeasible and therefore computational predictions of the molecular effect of nsSNPs are helpful to guide experimental investigations. While some nsSNPs can be accurately characterized, for instance if they fall into strongly conserved or well annotated regions, the molecular consequences of many others are more challenging to predict. In particular, nsSNPs affecting less structured, and often less conserved regions, are difficult to characterize. Binding sites that mediate protein-protein or other protein interactions are an important class of functional sites on proteins and can be used to help interpret nsSNPs. Binding sites targeted by the PDZ modular peptide recognition domain have recently been characterized. Here we use this data to show that it is possible to computationally identify nsSNPs in PDZ binding motifs that modify or prevent binding to the proteins containing the motifs. We confirm these predictions by experimentally validating a selected subset with ELISA. Our work also highlights the importance of better characterizing linear motifs in proteins as many of these can be affected by genetic variations.     

GGGCTA repeats can fold into hairpins poorly unfolded by replication protein A: a possible origin of the length-dependent instability of GGGCTA variant repeats in human telomeres

Human telomeres are composed of GGGTTA repeats and interspersed with variant repeats. The GGGCTA variant motif was identified in the proximal regions of human telomeres about 10 years ago and was shown to display a length-dependent instability. In parallel, a structural study showed that four GGGCTA repeats folded into a non-canonical G-quadruplex (G4) comprising a Watson–Crick GCGC tetrad. It was proposed that this non-canonical G4 might be an additional obstacle for telomere replication. In the present study, we demonstrate that longer GGGCTA arrays fold into G4 and into hairpins. We also demonstrate that replication protein A (RPA) efficiently binds to GGGCTA repeats structured into G4 but poorly binds to GGGCTA repeats structured into hairpins. Our results (along with results obtained with a more stable variant motif) suggest that GGGCTA hairpins are at the origin of GGGCTA length-dependent instability. They also suggest, as working hypothesis, that failure of efficient binding of RPA to GGGCTA structured into hairpins might be involved in the mechanism of GGGCTA array instability. On the basis of our present and past studies about telomeric G4 and their interaction with RPA, we propose an original point of view about telomeric G4 and the evolution of telomeric motifs.     

Do conformational biases of simple helical junctions influence RNA folding stability and specificity?

Structured RNAs must fold into their native structures and discriminate against a large number of alternative ones, an especially difficult task given the limited information content of RNA''s nucleotide alphabet. The simplest motifs within structured RNAs are two helices joined by nonhelical junctions. To uncover the fundamental behavior of these motifs and to elucidate the underlying physical forces and challenges faced by structured RNAs, we computationally and experimentally studied a tethered duplex model system composed of two helices joined by flexible single- or double-stranded polyethylene glycol tethers, whose lengths correspond to those typically observed in junctions from structured RNAs. To dissect the thermodynamic properties of these simple motifs, we computationally probed how junction topology, electrostatics, and tertiary contact location influenced folding stability. Small-angle X-ray scattering was used to assess our predictions. Single- or double-stranded junctions, independent of sequence, greatly reduce the space of allowed helical conformations and influencing the preferred location and orientation of their adjoining helices. A double-stranded junction guides the helices along a hinge-like pathway. In contrast, a single-stranded junction samples a broader set of conformations and has different preferences than the double-stranded junction. In turn, these preferences determine the stability and distinct specificities of tertiary structure formation. These sequence-independent effects suggest that properties as simple as a junction''s topology can generally define the accessible conformational space, thereby stabilizing desired structures and assisting in discriminating against misfolded structures. Thus, junction topology provides a fundamental strategy for transcending the limitations imposed by the low information content of RNA primary sequence.     

Prediction of consensus structural motifs in a family of coregulated RNA sequences

Given a set of homologous or functionally related RNA sequences, the consensus motifs may represent the binding sites of RNA regulatory proteins. Unlike DNA motifs, RNA motifs are more conserved in structures than in sequences. Knowing the structural motifs can help us gain a deeper insight of the regulation activities. There have been various studies of RNA secondary structure prediction, but most of them are not focused on finding motifs from sets of functionally related sequences. Although recent research shows some new approaches to RNA motif finding, they are limited to finding relatively simple structures, e.g. stem-loops. In this paper, we propose a novel genetic programming approach to RNA secondary structure prediction. It is capable of finding more complex structures than stem-loops. To demonstrate the performance of our new approach as well as to keep the consistency of our comparative study, we first tested it on the same data sets previously used to verify the current prediction systems. To show the flexibility of our new approach, we also tested it on a data set that contains pseudoknot motifs which most current systems cannot identify. A web-based user interface of the prediction system is set up at http://bioinfo. cis.nctu.edu.tw/service/gprm/.     

Prediction of structured non-coding RNAs in the genomes of the nematodes Caenorhabditis elegans and Caenorhabditis briggsae

We present a survey for non-coding RNAs and other structured RNA motifs in the genomes of Caenorhabditis elegans and Caenorhabditis briggsae using the RNAz program. This approach explicitly evaluates comparative sequence information to detect stabilizing selection acting on RNA secondary structure. We detect 3,672 structured RNA motifs, of which only 678 are known non-translated RNAs (ncRNAs) or clear homologs of known C. elegans ncRNAs. Most of these signals are located in introns or at a distance from known protein-coding genes. With an estimated false positive rate of about 50% and a sensitivity on the order of 50%, we estimate that the nematode genomes contain between 3,000 and 4,000 RNAs with evolutionary conserved secondary structures. Only a small fraction of these belongs to the known RNA classes, including tRNAs, snoRNAs, snRNAs, or microRNAs. A relatively small class of ncRNA candidates is associated with previously observed RNA-specific upstream elements.     

Conservation of unfavorable sequence motifs that contribute to the chemokine quaternary state

In the chemokine family, we characterize two examples of evolutionarily conserved unfavorable sequence motifs that affect quaternary structure. In contrast to the straightforward action of favorable sequences, these unfavorable motifs produce interactions disfavoring one outcome to indirectly promote another one but should not be confused with the broad sampling produced by negative selection and/or design. To identify such motifs, we developed a statistically validated computational method combining structure and phylogeny. This approach was applied in an analysis of the alternate forms of homodimerization exhibited in the chemokine family. While the chemokine family exhibits the same tertiary fold, members of certain subfamilies, including CXCL8, form a homodimer across the beta1 strand whereas members of other subfamilies, including CCL4 and CCL2, form a homodimer on the opposite side of the chemokine fold. These alternate dimerization states suggest that CCL4 and CCL2 contain specific sequences that disfavor CXCL8 dimerization. Using our computational approach, we identified two evolutionarily conserved sequence motifs in the CC subfamilies: a drastic two-residue deletion (DeltaRV) and a simple point mutation (V27R). Cloned into the CXCL8 background, these two motifs were experimentally proven to confer a monomeric state. NMR analyses indicate that these variants are structured in solution and retain the chemokine fold. Structurally, the motifs retain a chemokine tertiary fold while introducing unfavorable quaternary interactions that inhibit CXCL8 dimerization. In demonstrating the success of our computational method, our results argue that these unfavorable motifs have been evolutionarily conserved to specifically disfavor one dimerization state and, as a result, indirectly contribute to favoring another.