The joint sequencing of related genomes has become an important means to discover rare variants. Normal-tumor genome pairs are routinely sequenced together to find somatic mutations and their associations with different cancers. Parental and sibling genomes reveal de novo germline mutations and inheritance patterns related to Mendelian diseases.Acute lymphoblastic leukemia (ALL) is the most common paediatric cancer and the leading cause of cancer-related death among children. With the aim of uncovering the full spectrum of germline and somatic genetic alterations in childhood ALL genomes, we conducted whole-exome re-sequencing on a unique cohort of over 120 exomes of childhood ALL quartets, each comprising a patient's tumor and matched-normal material, and DNA from both parents. We developed a general probabilistic model for such quartet sequencing reads mapped to the reference human genome. The model is used to infer joint genotypes at homologous loci across a normal-tumor genome pair and two parental genomes.We describe the algorithms and data structures for genotype inference, model parameter training. We implemented the methods in an open-source software package (QUADGT) that uses the standard file formats of the 1000 Genomes Project. Our method's utility is illustrated on quartets from the ALL cohort.

Protein-coding genes in eukaryotes are interrupted by introns, but intron densities widely differ between eukaryotic lineages. Vertebrates, some invertebrates and green plants have intron-rich genes, with 6-7 introns per kilobase of coding sequence, whereas most of the other eukaryotes have intron-poor genes. We reconstructed the history of intron gain and loss using a probabilistic Markov model (Markov Chain Monte Carlo, MCMC) on 245 orthologous genes from 99 genomes representing the three of the five supergroups of eukaryotes for which multiple genome sequences are available. Intron-rich ancestors are confidently reconstructed for each major group, with 53 to 74% of the human intron density inferred with 95% confidence for the Last Eukaryotic Common Ancestor (LECA). The results of the MCMC reconstruction are compared with the reconstructions obtained using Maximum Likelihood (ML) and Dollo parsimony methods. An excellent agreement between the MCMC and ML inferences is demonstrated whereas Dollo parsimony introduces a noticeable bias in the estimations, typically yielding lower ancestral intron densities than MCMC and ML. Evolution of eukaryotic genes was dominated by intron loss, with substantial gain only at the bases of several major branches including plants and animals. The highest intron density, 120 to 130% of the human value, is inferred for the last common ancestor of animals. The reconstruction shows that the entire line of descent from LECA to mammals was intron-rich, a state conducive to the evolution of alternative splicing.

UNLABELLED: Malin is a software package for the analysis of eukaryotic gene structure evolution. It provides a graphical user interface for various tasks commonly used to infer the evolution of exon-intron structure in protein-coding orthologs. Implemented tasks include the identification of conserved homologous intron sites in protein alignments, as well as the estimation of ancestral intron content, lineage-specific intron losses and gains. Estimates are computed either with parsimony, or with a probabilistic model that incorporates rate variation across lineages and intron sites. AVAILABILITY: Malin is available as a stand-alone Java application, as well as an application bundle for MacOS X, at the website http://www.iro.umontreal.ca/~csuros/introns/malin/. The software is distributed under a BSD-style license.

Computational Biology recently published an article about spliceosomal intron evolution by Nguyen, Yoshihama, and Kenmochi [1].The authors were unaware of some earlier independent results.Foremostly, the main point of the article-that of estimating the density of potential intron sites-is not novel.It was described more than three months earlier [2].The numerical results are virtually identical in the two publications, which is not surprising, since they apply the same model to the same data [3].A recent article points to the model's validity.Raible and coauthors [4] report that introns in the protostome Platynereis dumerilii are almost as abundant as in humans, and many introns are in homologous positions between the two species.The shared positions indicate that at most one-third of human introns were gained in the vertebrate lineage, in agreement with the estimates of [2] and [1].In contrast, parsimony estimates [3] should change significantly when including P. dumerilii.To estimate ancestral intron losses and gains, Nguyen and coauthors use an exponential-time procedure, which is practical only for a few species.In reality, the estimation can be done in linear time [2], as described briefly below.We are modeling intron presence and absence in homologous sites across organisms related by a known phylogeny.Presence and absence are encoded by 1 and 0, respectively.Introns evolve independently, by a Markov model for a binary character.On branch e, an intron is lost with probability p e (1 !0) and an intron is gained with probability p e (0 ! 1) at every site.Assuming a continuous-time Markov process,

The zero-error capacity region of r-out-of-T user multiple-access OR channel is investigated. A family F of subsets of [n] = {1, ..., n} is an r-single-user-tracing superimposed code (r-SUT) if there exists such a single-user-tracing function /spl phi/:2/sup [n]/ /spl rarr/ F that for all F' /spl sube/ F with 1 /spl les/ |F'| /spl les/ r, /spl phi/(/spl cup//sub A/spl isin/F/'A) /spl isin/ F'. In this correspondence, we introduce the concept of these codes and give bounds on their rate. We also consider disjointly r-superimposed codes.

We investigate the zero-error capacity region of r-out of T user multiple access OR channel. A family /spl Fscr/ subsets of [n]={1, . . . ,n} is an r-single-user-tracing superimposed code (r-SUT) if there exists such a single-user-tracing function /spl phi/: 2/sup [n]//spl rarr//spl Fscr/ that for all /spl Fscr//spl sube//spl Fscr/ with |/spl Fscr/'|/spl les/r, /spl phi/(/spl cup//sub A/spl isin///spl Fscr//sub '/A)/spl isin//spl Fscr/'. In this paper we introduce the concept of these codes and investigate bounds on their rate. We also consider disjointly r-superimposed codes.

We examine the problem of finding maximum-scoring sets of disjoint segments in a sequence of scores. The problem arises in DNA and protein segmentation and in postprocessing of sequence alignments. Our key result states a simple recursive relationship between maximum-scoring segment sets. The statement leads to fast algorithms for finding such segment sets. We apply our methods to the identification of noncoding RNA genes in thermophiles.

We present a novel distance-based algorithm for evolutionary tree reconstruction. Our algorithm reconstructs the topology of a tree with n leaves in O(n2) time using O(n) working space. In the general Markov model of evolution the algorithm recovers the topology successfully with (1 — Ο(1)) probability from sequences with polynomial length in n. Moreover, for almost all trees, our algorithm achieves the same success probability on polylogarithmic sample sizes. The theoretical results are supported by simulation experiments involving trees with 500, 1895, and 3135 leaves. The topologies of the trees are recovered with high success from 2000 bp DNA sequences.

We give a greedy learning algorithm for reconstructing an evolutionary tree based on a certain harmonic average on triplets of terminal taxa. After the pairwise distances between terminal taxa are estimated from sequence data, the algorithm runs in $\smallbigO{\numtaxa^2}$ time using $\smallbigO{\numtaxa}$ work space, where $\numtaxa$ is the number of terminal taxa. These time and space complexities are optimal in the sense that the size of an input distance matrix is $\numtaxa^2$ and the size of an output tree is $\numtaxa$. Moreover, in the Jukes--Cantor model of evolution, the algorithm recovers the correct tree topology with high probability using sample sequences of length polynomial in (1) $\numtaxa$, (2) the logarithm of the error probability, and (3) the inverses of two small parameters.

The problem of modeling complicated data sequences, such as DNA or speech, often arises in practice.Most of the algorithms select a hypothesis from within a model class assuming that the observed sequence is the direct output of the underlying generation process.In this paper we consider the case when the output passes through a memoryless noisy channel before observation.In particular, we show that in the class of Markov chains with variable memory length, learning is affected by factors, which, despite being super-polynomial, are still small in some practical cases.Markov models with variable memory length, or probabilistic finite suffix automata, were introduced in learning theory by Ron, Singer and Tishby who also described a polynomial time learning algorithm [11, 12].We present a modification of the algorithm which uses a noise-corrupted sample and has knowledge of the noise structure.The same algorithm is still viable if the noise is not known exactly but a good estimation is available.Finally, some experimental results are presented for removing noise from corrupted English text, and to measure how the performance of the learning algorithm is affected by the size of the noisy sample and the noise rate.