A minimal descriptor of an ancestral recombinations graph

Background

Processing cDNA microarray images is a crucial step in gene expression analysis, since any errors in early stages affect subsequent steps, leading to possibly erroneous biological conclusions. When processing the underlying images, accurately separating the sub-grids and spots is extremely important for subsequent steps that include segmentation, quantification, normalization and clustering.

Results

We propose a parameterless and fully automatic approach that first detects the sub-grids given the entire microarray image, and then detects the locations of the spots in each sub-grid. The approach, first, detects and corrects rotations in the images by applying an affine transformation, followed by a polynomial-time optimal multi-level thresholding algorithm used to find the positions of the sub-grids in the image and the positions of the spots in each sub-grid. Additionally, a new validity index is proposed in order to find the correct number of sub-grids in the image, and the correct number of spots in each sub-grid. Moreover, a refinement procedure is used to correct possible misalignments and increase the accuracy of the method.

Conclusions

Extensive experiments on real-life microarray images and a comparison to other methods show that the proposed method performs these tasks fully automatically and with a very high degree of accuracy. Moreover, unlike previous methods, the proposed approach can be used in various type of microarray images with different resolutions and spot sizes and does not need any parameter to be adjusted.     

Constructing minimal ancestral recombination graphs.

By viewing the ancestral recombination graph as defining a sequence of trees, we show how possible evolutionary histories consistent with given data can be constructed using the minimum number of recombination events. In contrast to previously known methods, which yield only estimated lower bounds, our method of detecting recombination always gives the minimum number of recombination events if the right kind of rooted trees are used in our algorithm. A new lower bound can be defined if rooted trees with fewer constraints are used. As well as studying how often it actually is equal to the minimum, we test how this new lower bound performs in comparison to some other lower bounds. Our study indicates that the new lower bound is an improvement on earlier bounds. Also, using simulated data, we investigate how well our method can recover the actual site-specific evolutionary relationships. In the presence of recombination, using a single tree to describe the evolution of the entire locus clearly leads to lower average recovery percentages than does our method. Our study shows that recovering the actual local tree topologies can be done more accurately than estimating the actual number of recombination events.     

Protein content of minimal and ancestral ribosome

Minimal genome approaches seek to define the smallest gene complement compatible with modern-type cellular life on Earth. A consensus of computational and experimental approaches indicates that a minimal genome is close to 300 protein-coding genes, if a rich medium is provided for cell growth. I relate ribosomal gene content in completely sequenced genomes to ribosomal subunit structure and approximate the protein components of the putative minimal ribosome and the ribosome of the Last Universal Common Ancestor of Life. Both sets contain between 35 and 40 proteins. There is evidence of protein-protein and protein-RNA displacement in the evolution of both ribosomal subunits.     

Gene mapping via the ancestral recombination graph

We present a multilocus gene mapping method based on linkage disequilibrium, which uses the ancestral recombination graph to model the history of sequences that may harbor an influential variant. We describe the construction of a recurrence equation used to make inferences about the location of a trait-influencing mutation. We demonstrate how a Monte Carlo algorithm combined with a local importance sampling scheme can be used for mapping. We explain how to simulate the timing of events in the coalescent in the presence of recombination and mutation, which accomodates variable population size. We provide an example to illustrate the use of the method, which can be easily extended to more general situations. Although the method is computationally intensive and variation in the likelihood profiles can occur, the method offers a great deal of promise.     

The conditional ancestral selection graph with strong balancing selection

Using a heuristic separation-of-time-scales argument, we describe the behavior of the conditional ancestral selection graph with very strong balancing selection between a pair of alleles. In the limit as the strength of selection tends to infinity, we find that the ancestral process converges to a neutral structured coalescent, with two subpopulations representing the two alleles and mutation playing the role of migration. This agrees with a previous result of Kaplan et al., obtained using a different approach. We present the results of computer simulations to support our heuristic mathematical results. We also present a more rigorous demonstration that the neutral conditional ancestral process converges to the Kingman coalescent in the limit as the mutation rate tends to infinity.     

The structured ancestral selection graph and the many-demes limit

We show that the unstructured ancestral selection graph applies to part of the history of a sample from a population structured by restricted migration among subpopulations, or demes. The result holds in the limit as the number of demes tends to infinity with proportionately weak selection, and we have also made the assumptions of island-type migration and that demes are equivalent in size. After an instantaneous sample-size adjustment, this structured ancestral selection graph converges to an unstructured ancestral selection graph with a mutation parameter that depends inversely on the migration rate. In contrast, the selection parameter for the population is independent of the migration rate and is identical to the selection parameter in an unstructured population. We show analytically that estimators of the migration rate, based on pairwise sequence differences, derived under the assumption of neutrality should perform equally well in the presence of weak selection. We also modify an algorithm for simulating genealogies conditional on the frequencies of two selected alleles in a sample. This permits efficient simulation of stronger selection than was previously possible. Using this new algorithm, we simulate gene genealogies under the many-demes ancestral selection graph and identify some situations in which migration has a strong effect on the time to the most recent common ancestor of the sample. We find that a similar effect also increases the sensitivity of the genealogy to selection.     

Linkage disequilibrium, gene trees and selfing: an ancestral recombination graph with partial self-fertilization

It is shown that partial self-fertilization can be introduced into neutral population genetic models with recombination as a simple change in the scaling of the parameters. This means that statistical and computational methods that have been developed under the assumption of random mating can be used without modification, provided the appropriate parameter changes are made. An important prediction is that all forms of linkage disequilibrium will be more extensive in selfing species. The implications of this are discussed.     

A graph theoretic approach to the development of minimal phylogenetic trees

Summary The problem of determining the minimal phylogenetic tree is discussed in relation to graph theory. It is shown that this problem is an example of the Steiner problem in graphs which is to connect a set of points by a minimal length network where new points can be added. There is no reported method of solving realistically-sized Steiner problems in reasonable computing time. A heuristic method of approaching the phylogenetic problem is presented, together with a worked example with 7 mammalian cytochrome c sequences. It is shown in this case that the method develops a phylogenetic tree that has the smallest possible number of amino acid replacements. The potential and limitations of the method are discussed. It is stressed that objective methods must be used for comparing different trees. In particular it should be determined how close a given tree is to a mathematically determined lower bound. A theorem is proved which is used to establish a lower bound on the length of any tree and if a tree is found with a length equal to the lower bound, then no shorter tree can exist.     

The ancestral graph and gene genealogy under frequency-dependent selection.

Minority-advantage frequency-dependent selection has been proposed as the cause for the high level of observed polymorphism in some self/nonself-recognition systems. We present a mathematically rigorous derivation of the ancestral graph for a sample of genes that evolved according to a haploid infinite-alleles model of minority-advantage frequency-dependent selection. In the case of sufficiently weak selection, the gene genealogy can be extracted from the ancestral graph. We demonstrate that the gene genealogy under this model is identical to that obtained for a diploid model with heterozygote advantage. The case of strong selection is exemplified by a one-locus haploid self-incompatibility system; in this context, we investigate the number of alleles that can be maintained in a spatial versus a non-spatial habitat. Finally, we compare gametophytic self-incompatibility to the haploid self-incompatibility model.     

Effect of epistasis and linkage on fixation probability in three-locus models: an ancestral recombination-selection graph approach

We study the probability of ultimate fixation of a single new mutant arising in an individual chosen at random at a locus linked to two other loci carrying previously arisen mutations. This is done using the Ancestral Recombination-Selection Graph (ARSG) in a finite population in the limit of a large population size, which is also known as the Ancestral Influence Graph (AIG). An analytical expansion of the fixation probability with respect to population-scaled recombination rates and selection intensities is obtained. The coefficients of the expansion are expressed in terms of the initial state of the population and the epistatic interactions among the selected loci. Under the assumption of weak selection at tightly linked loci, the sign of the leading term, which depends on the signs of epistasis and initial linkage disequilibrium, determines whether an increase in recombination rates increases the chance of ultimate fixation of the new mutant. If mutants are advantageous, this is the case when epistasis is positive or null and the initial linkage disequilibrium is negative, which is an expected state in a finite population under directional selection. Moreover, this is also the case for a neutral mutant modifier coding for higher recombination rates if the same conditions hold at the selected loci. Under the same conditions, deleterious mutants are disfavored for ultimate fixation and neutral modifiers for higher recombination rates still favored. The recombination rates between the modifier locus and the selected loci do not come into play in the leading terms of the approximation for the fixation probability, but they do in higher-order terms.     

Fixation probability in a two-locus model by the ancestral recombination-selection graph

We use the ancestral influence graph (AIG) for a two-locus, two-allele selection model in the limit of a large population size to obtain an analytic approximation for the probability of ultimate fixation of a single mutant allele A. We assume that this new mutant is introduced at a given locus into a finite population in which a previous mutant allele B is already segregating with a wild type at another linked locus. We deduce that the fixation probability increases as the recombination rate increases if allele A is either in positive epistatic interaction with B and allele B is beneficial or in no epistatic interaction with B and then allele A itself is beneficial. This holds at least as long as the recombination fraction and the selection intensity are small enough and the population size is large enough. In particular this confirms the Hill-Robertson effect, which predicts that recombination renders more likely the ultimate fixation of beneficial mutants at different loci in a population in the presence of random genetic drift even in the absence of epistasis. More importantly, we show that this is true from weak negative epistasis to positive epistasis, at least under weak selection. In the case of deleterious mutants, the fixation probability decreases as the recombination rate increases. This supports Muller's ratchet mechanism to explain the accumulation of deleterious mutants in a population lacking recombination.     

Evolution of the ancestral recombination graph along the genome in case of selective sweep

We consider the genome of a sample of n individuals taken at the end of a selective sweep, which is the fixation of an advantageous allele in the population. When the selective advantage is high, the genealogy at a locus under selective sweep can be approximated by a comb with n teeth. However, because of recombinations during the selective sweep, the hitchhiking effect decreases as the distance from the selected site increases, so that far from this locus, the tree can be approximated by a Kingman coalescent tree, as in the neutral case. We first give the distribution of the tree at a given locus. Then we focus on the evolution of this tree along the genome. Since this tree-valued process is not Markovian, we study the evolution of the Ancestral Recombination Graph along the genome in case of selective sweep.     

用原图-对偶图法设计内部间隔最小的自然保护区

生境破碎是导致生物多样性损失的重要原因之一,在设计自然保护区时设法减少生境破碎是提高保护区有效性的重要方法.由于经济资源或地理因素制约不可能把连续的大片土地都划为保护区时,设计一个由相互分离的几部分组成的保护区是更为现实的做法.选择地块组成内部间隔最小的保护区是减少破碎化的一个重要途径,但结合空间特征的保护区地块选择模...     

Group representation of genetic recombinations

An algebraic representation of operations of genetic recombinations is illustrated. It is shown that the recombinations between chromosomes in the two-strand model can be represented by groups, in the sense of the theory of groups. Recombinations between chromosomes with inversions and a translocation are considered as well as cases without them. It is found that the groups derived from such cases are Abelianp-groups (p=2) and that the types of the Abelian groups for the various pairs of chromosomes are different from each other. Differences among those recombination groups are illustrated by showing the sets of generators of the various groups, which generate the corresponding recombination groups by multiplication.     

The distribution of surviving blocks of an ancestral genome

What is the chance that some part of a stretch of genome will survive? In a population of constant size, and with no selection, the probability of survival of some part of a stretch of map length y < 1 approaches y/log(yt/2) for log(yt) > or = 1. Thus, the whole genome is certain to be lost, but the rate of loss is extremely slow. This solution extends to give the whole distribution of surviving block sizes as a function of time. We show that the expected number of blocks at time t is 1+yt and give expressions for the moments of the number of blocks and the total amount of genome that survives for a given time. The solution is based on a branching process and assumes complete interference between crossovers, so that each descendant carries only a single block of ancestral material. We consider cases where most individuals carry multiple blocks, either because there are multiple crossovers in a long genetic map, or because enough time has passed that most individuals in the population are related to each other. For species such as ours, which have a long genetic map, the genome of any individual which leaves descendants (approximately 80% of the population for a Poisson offspring number with mean two) is likely to persist for an extremely long time, in the form of a few short blocks of genome.     

Haplotypes histories as pathways of recombinations

MOTIVATION: The diversity of a haplotype, represented as a string of polymorphic sites along a DNA sequence, increases exponentially with the number of sites if recombinations are taking place. Reconstructing the history of recombinations compared with that of the polymorphic sites is thus extremely difficult. However, in the human genome, because of the relatively simple pattern of haplotype diversity dominated by a few ancestral haplotypes, the complexity of the recombinational network can be reduced, thus making its reconstruction feasible. We focus on the problem of inferring the recombination pathways starting with putative ancestral haplotypes and leading to new rare recombinant haplotypes. RESULTS: We describe classes of recombinations that represent the whole set of minimal recombination pathways leading to a new haplotype. We present an O(n(2)) algorithm that outputs such representative recombination pathways. We apply it to haplotypes of the 8 kb dystrophin gene segment dys44. AVAILABILITY: A software implementing the algorithm and some other extentions has been developed on a Java platform (JDK 1.3.1). It is freely available at http://www.iro.umontreal.ca/~mabrouk/     

Evidence for an ancestral core structure in nucleotide-binding proteins with the type A motif

Many proteins that bind purine nucleotide triphosphates have a type A sequence motif. Only two classes of structures for such proteins are so far available from X-ray crystallography. We examined the tertiary structures of representatives of the two classes, porcine cytoplasmic adenylate kinase and Escherichia coli translational elongation factor Tu. Comparison of the two proteins suggests that the A motif may be just one part of a larger common core structure consisting of four parallel strands of beta-sheet sandwiched between four alpha-helices. This compact core structure comprises over one half of each protein. We speculate that A motif proteins have diverged from a common ancestor having this core structure.     

The split genes of Nanoarchaeum equitans are an ancestral character

The introns early hypothesis predicts that introns were fundamental in assembling the first genes. In Nanoarchaeum equitans some genes are split into two. If these split genes were the ancestral forms, as suggested by the introns early hypothesis, then the end-beginning of the two parts of the split protein in a multiple alignment with the orthologous proteins from the Eukarya and Arachaea domains should make a clear prediction on where the intron in the homologous eukaryotic gene should be positioned. The analysis has shown that the introns are in this position, which is therefore predictable on the basis of the split proteins of N. equitans. This corroborates the hypothesis that the split genes of N. equitans are the plesiomorphic forms of these genes. If true, this would show that the origin of genes was polyphyletic as the monophyletic origin hypothesis would deny the existence, in a real organism, of these ancestral (split) genes, which imply that they were assembled late on and after the domains of life were established. Furthermore, it would seem that hyperthermophily is also an ancestral trait because it is linked to a split gene in N. equitans.