Alternative splicing enriched cDNA libraries identify breast cancer-associated transcripts

Background: Alternative splicing (AS) is a central mechanism in the generation of genomic complexity and is a major contributor to transcriptome and proteome diversity. Alterations of the splicing process can lead to deregulation of crucial cellular processes and have been associated with a large spectrum of human diseases. Cancer-associated transcripts are potential molecular markers and may contribute to the development of more accurate diagnostic and prognostic methods and also serve as therapeutic targets. Alternative splicing-enriched cDNA libraries have been used to explore the variability generated by alternative splicing. In this study, by combining the use of trapping heteroduplexes and RNA amplification, we developed a powerful approach that enables transcriptome-wide exploration of the AS repertoire for identifying AS variants associated with breast tumor cells modulated by ERBB2 (HER-2/neu) oncogene expression. Results: The human breast cell line (C5.2) and a pool of 5 ERBB2 over-expressing breast tumor samples were used independently for the construction of two AS-enriched libraries. In total, 2,048 partial cDNA sequences were obtained, revealing 214 alternative splicing sequence-enriched tags (ASSETs). A subset with 79 multiple exon ASSETs was compared to public databases and reported 138 different AS events. A high success rate of RT-PCR validation (94.5%) was obtained, and 2 novel AS events were identified. The influence of ERBB2-mediated expression on AS regulation was evaluated by capillary electrophoresis and probe-ligation approaches in two mammary cell lines (Hb4a and C5.2) expressing different levels of ERBB2. The relative expression balance between AS variants from 3 genes was differentially modulated by ERBB2 in this model system. Conclusions: In this study, we presented a method for exploring AS from any RNA source in a transcriptome-wide format, which can be directly easily adapted to next generation sequencers. We identified AS transcripts that were differently modulated by ERBB2-mediated expression and that can be tested as molecular markers for breast cancer. Such a methodology will be useful for completely deciphering the cancer cell transcriptome diversity resulting from AS and for finding more precise molecular markers.

SOME PROPERTIES OF THE MULTIPLICITY SEQUENCE FOR ARBITRARY IDEALS

In this work we prove that the Achilles-Manaresi multiplicity sequence, like the classical Hilbert-Samuel multiplicity, is additive with respect to the exact sequence of modules. We also prove the associativity formula for his mulitplicity sequence. As a consequence, we give new proofs for two results already known. First, the Achilles-Manaresi multiplicity sequence is an invariant up to reduction, a result first proved by Ciuperca. Second, I subset of J is a reduction of (J,M) if and only if c(0)(I(p), M(p)) = c(0)(J(p), M(p)) for all p is an element of Spec(A), a result first proved by Flenner and Manaresi.

Gene Expression Complex Networks: Synthesis, Identification, and Analysis

Thanks to recent advances in molecular biology, allied to an ever increasing amount of experimental data, the functional state of thousands of genes can now be extracted simultaneously by using methods such as cDNA microarrays and RNA-Seq. Particularly important related investigations are the modeling and identification of gene regulatory networks from expression data sets. Such a knowledge is fundamental for many applications, such as disease treatment, therapeutic intervention strategies and drugs design, as well as for planning high-throughput new experiments. Methods have been developed for gene networks modeling and identification from expression profiles. However, an important open problem regards how to validate such approaches and its results. This work presents an objective approach for validation of gene network modeling and identification which comprises the following three main aspects: (1) Artificial Gene Networks (AGNs) model generation through theoretical models of complex networks, which is used to simulate temporal expression data; (2) a computational method for gene network identification from the simulated data, which is founded on a feature selection approach where a target gene is fixed and the expression profile is observed for all other genes in order to identify a relevant subset of predictors; and (3) validation of the identified AGN-based network through comparison with the original network. The proposed framework allows several types of AGNs to be generated and used in order to simulate temporal expression data. The results of the network identification method can then be compared to the original network in order to estimate its properties and accuracy. Some of the most important theoretical models of complex networks have been assessed: the uniformly-random Erdos-Renyi (ER), the small-world Watts-Strogatz (WS), the scale-free Barabasi-Albert (BA), and geographical networks (GG). The experimental results indicate that the inference method was sensitive to average degree k variation, decreasing its network recovery rate with the increase of k. The signal size was important for the inference method to get better accuracy in the network identification rate, presenting very good results with small expression profiles. However, the adopted inference method was not sensible to recognize distinct structures of interaction among genes, presenting a similar behavior when applied to different network topologies. In summary, the proposed framework, though simple, was adequate for the validation of the inferred networks by identifying some properties of the evaluated method, which can be extended to other inference methods.

An algorithmic Friedman-Pippenger theorem on tree embeddings and applications

An (n, d)-expander is a graph G = (V, E) such that for every X subset of V with vertical bar X vertical bar <= 2n - 2 we have vertical bar Gamma(G)(X) vertical bar >= (d + 1) vertical bar X vertical bar. A tree T is small if it has at most n vertices and has maximum degree at most d. Friedman and Pippenger (1987) proved that any ( n; d)- expander contains every small tree. However, their elegant proof does not seem to yield an efficient algorithm for obtaining the tree. In this paper, we give an alternative result that does admit a polynomial time algorithm for finding the immersion of any small tree in subgraphs G of (N, D, lambda)-graphs Lambda, as long as G contains a positive fraction of the edges of Lambda and lambda/D is small enough. In several applications of the Friedman-Pippenger theorem, including the ones in the original paper of those authors, the (n, d)-expander G is a subgraph of an (N, D, lambda)-graph as above. Therefore, our result suffices to provide efficient algorithms for such previously non-constructive applications. As an example, we discuss a recent result of Alon, Krivelevich, and Sudakov (2007) concerning embedding nearly spanning bounded degree trees, the proof of which makes use of the Friedman-Pippenger theorem. We shall also show a construction inspired on Wigderson-Zuckerman expander graphs for which any sufficiently dense subgraph contains all trees of sizes and maximum degrees achieving essentially optimal parameters. Our algorithmic approach is based on a reduction of the tree embedding problem to a certain on-line matching problem for bipartite graphs, solved by Aggarwal et al. (1996).

On the resilience of long cycles in random graphs

In this paper we determine the local and global resilience of random graphs G(n,p) (p >> n(-1)) with respect to the property of containing a cycle of length at least (1 - alpha)n. Roughly speaking, given alpha > 0, we determine the smallest r(g) (G, alpha) with the property that almost surely every subgraph of G = G(n,p) having more than r(g) (G, alpha)vertical bar E(G)vertical bar edges contains a cycle of length at least (1 - alpha)n (global resilience). We also obtain, for alpha < 1/2, the smallest r(l) (G, alpha) such that any H subset of G having deg(H) (v) larger than r(l) (G, alpha) deg(G) (v) for all v is an element of V(G) contains a cycle of length at least (1 - alpha)n (local resilience). The results above are in fact proved in the more general setting of pseudorandom graphs.

Gibbs random graphs on point processes

Consider a discrete locally finite subset Gamma of R(d) and the cornplete graph (Gamma, E), with vertices Gamma and edges E. We consider Gibbs measures on the set of sub-graphs with vertices Gamma and edges E` subset of E. The Gibbs interaction acts between open edges having a vertex in common. We study percolation properties of the Gibbs distribution of the graph ensemble. The main results concern percolation properties of the open edges in two cases: (a) when Gamma is sampled from a homogeneous Poisson process; and (b) for a fixed Gamma with sufficiently sparse points. (c) 2010 American Institute of Physics. [doi:10.1063/1.3514605]

Induced Modules for Affine Lie Algebras

We study induced modules of nonzero central charge with arbitrary multiplicities over affine Lie algebras. For a given pseudo parabolic subalgebra P of an affine Lie algebra G, our main result establishes the equivalence between a certain category of P-induced G-modules and the category of weight P-modules with injective action of the central element of G. In particular, the induction functor preserves irreducible modules. If P is a parabolic subalgebra with a finite-dimensional Levi factor then it defines a unique pseudo parabolic subalgebra P(ps), P subset of P(ps). The structure of P-induced modules in this case is fully determined by the structure of P(ps)-induced modules. These results generalize similar reductions in particular cases previously considered by V. Futorny, S. Konig, V. Mazorchuk [Forum Math. 13 (2001), 641-661], B. Cox [Pacific J. Math. 165 (1994), 269-294] and I. Dimitrov, V. Futorny, I. Penkov [Comm. Math. Phys. 250 (2004), 47-63].

ON THE THREE-DIMENSIONAL BLASCHKE-LEBESGUE PROBLEM

The width of a closed convex subset of n-dimensional Euclidean space is the distance between two parallel supporting hyperplanes. The Blaschke-Lebesgue problem consists of minimizing the volume in the class of convex sets of fixed constant width and is still open in dimension n >= 3. In this paper we describe a necessary condition that the minimizer of the Blaschke-Lebesgue must satisfy in dimension n = 3: we prove that the smooth components of the boundary of the minimizer have their smaller principal curvature constant and therefore are either spherical caps or pieces of tubes (canal surfaces).

Can we make a Bohmian electron reach the speed of light, at least for one instant?

In Bohmian mechanics, a version of quantum mechanics that ascribes world lines to electrons, we can meaningfully ask about an electron's instantaneous speed relative to a given inertial frame. Interestingly, according to the relativistic version of Bohmian mechanics using the Dirac equation, a massive particle's speed is less than or equal to the speed of light, but not necessarily less. That is, there are situations in which the particle actually reaches the speed of light-a very nonclassical behavior. That leads us to the question of whether such situations can be arranged experimentally. We prove a theorem, Theorem 5, implying that for generic initial wave functions the probability that the particle ever reaches the speed of light, even if at only one point in time, is zero. We conclude that the answer to the question is no. Since a trajectory reaches the speed of light whenever the quantum probability current (psi) over bar gamma(mu)psi is a lightlike 4-vector, our analysis concerns the current vector field of a generic wave function and may thus be of interest also independently of Bohmian mechanics. The fact that the current is never spacelike has been used to argue against the possibility of faster-than-light tunneling through a barrier, a somewhat similar question. Theorem 5, as well as a more general version provided by Theorem 6, are also interesting in their own right. They concern a certain property of a function psi : R(4) -> C(4) that is crucial to the question of reaching the speed of light, namely being transverse to a certain submanifold of C(4) along a given compact subset of space-time. While it follows from the known transversality theorem of differential topology that this property is generic among smooth functions psi : R(4) -> C(4), Theorem 5 asserts that it is also generic among smooth solutions of the Dirac equation. (C) 2010 American Institute of Physics. [doi:10.1063/1.3520529]

Extremal problems on sum-free sets and coverings in tridimensional spaces

Given a prime power q, define c (q) as the minimum cardinality of a subset H of F 3 q which satisfies the following property: every vector in this space di ff ers in at most 1 coordinate from a multiple of a vector in H. In this work, we introduce two extremal problems in combinatorial number theory aiming to discuss a known connection between the corresponding coverings and sum-free sets. Also, we provide several bounds on these maps which yield new classes of coverings, improving the previous upper bound on c (q)

Modeling associations between genetic markers using Bayesian networks

Motivation: Understanding the patterns of association between polymorphisms at different loci in a population ( linkage disequilibrium, LD) is of fundamental importance in various genetic studies. Many coefficients were proposed for measuring the degree of LD, but they provide only a static view of the current LD structure. Generative models (GMs) were proposed to go beyond these measures, giving not only a description of the actual LD structure but also a tool to help understanding the process that generated such structure. GMs based in coalescent theory have been the most appealing because they link LD to evolutionary factors. Nevertheless, the inference and parameter estimation of such models is still computationally challenging. Results: We present a more practical method to build GM that describe LD. The method is based on learning weighted Bayesian network structures from haplotype data, extracting equivalence structure classes and using them to model LD. The results obtained in public data from the HapMap database showed that the method is a promising tool for modeling LD. The associations represented by the learned models are correlated with the traditional measure of LD D`. The method was able to represent LD blocks found by standard tools. The granularity of the association blocks and the readability of the models can be controlled in the method. The results suggest that the causality information gained by our method can be useful to tell about the conservability of the genetic markers and to guide the selection of subset of representative markers.

Singular Perturbation for the Discounted Continuous Control of Piecewise Deterministic Markov Processes

This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP`s) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space a""e (n) . The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter epsilon > 0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as epsilon goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as epsilon goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.

Extension of the core map of common bean with EST-SSR, RGA, AFLP, and putative functional markers

Microsatellites and gene-derived markers are still underrepresented in the core molecular linkage map of common bean compared to other types of markers. In order to increase the density of the core map, a set of new markers were developed and mapped onto the RIL population derived from the `BAT93` x `Jalo EEP558` cross. The EST-SSR markers were first characterized using a set of 24 bean inbred lines. On average, the polymorphism information content was 0.40 and the mean number of alleles per locus was 2.7. In addition, AFLP and RGA markers based on the NBS-profiling method were developed and a subset of the mapped RGA was sequenced. With the integration of 282 new markers into the common bean core map, we were able to place markers with putative known function in some existing gaps including regions with QTL for resistance to anthracnose and rust. The distribution of the markers over 11 linkage groups is discussed and a newer version of the common bean core linkage map is proposed.

Culture-Independent Assessment of Rhizobiales-Related Alphaproteobacteria and the Diversity of Methylobacterium in the Rhizosphere and Rhizoplane of Transgenic Eucalyptus

The rhizosphere is an ecosystem exploited by a variety of organisms involved in plant health and environmental sustainability. Abiotic factors influence microorganism-plant interactions, but the microbial community is also affected by expression of heterologous genes from host plants. In the present work, we assessed the community shifts of Alphaproteobacteria phylogenetically related to the Rhizobiales order (Rhizobiales-like community) in rhizoplane and rhizosphere soils of wild-type and transgenic eucalyptus. A greenhouse experiment was performed and the bacterial communities associated with two wild-type (WT17 and WT18) and four transgenic (TR-9, TR-15, TR-22, and TR-23) eucalyptus plant lines were evaluated. The culture-independent approach consisted of the quantification, by real-time polymerase chain reaction (PCR), of a targeted subset of Alphaproteobacteria and the assessment of its diversity using PCR-denaturing gradient gel electrophoresis (DGGE) and 16S rRNA gene clone libraries. Real-time quantification revealed a lesser density of the targeted community in TR-9 and TR-15 plants and diversity analysis by principal components analysis, based on PCR-DGGE, revealed differences between bacterial communities, not only between transgenic and nontransgenic plants, but also among wild-type plants. The comparison between clone libraries obtained from the transgenic plant TR-15 and wild-type WT17 revealed distinct bacterial communities associated with these plants. In addition, a culturable approach was used to quantify the Methylobacterium spp. in the samples where the identification of isolates, based on 16S rRNA gene sequences, showed similarities to the species Methylobacterium nodulans, Methylobacterium isbiliense, Methylobacterium variable, Methylobacterium fujisawaense, and Methylobacterium radiotolerans. Colonies classified into this genus were not isolated from the rhizosphere but brought in culture from rhizoplane samples, except for one line of the transgenic plants (TR-15). In general, the data suggested that, in most cases, shifts in bacterial communities due to cultivation of transgenic plants are similar to those observed when different wild-type cultivars are compared, although shifts directly correlated to transgenic plant cultivation may be found.

Two physically, functionally, and developmentally distinct peritoneal macrophage subsets

The peritoneal cavity (PerC) is a unique compartment within which a variety of immune cells reside, and from which macrophages (Mempty set) are commonly drawn for functional studies. Here we define two Mempty set subsets that coexist in PerC in adult mice. One, provisionally called the large peritoneal Mempty set (LPM), contains approximately 90% of the PerC Mempty set in unstimulated animals but disappears rapidly from PerC following lipopolysaccharide (LPS) or thioglycolate stimulation. These cells express high levels of the canonical Mempty set surface markers, CD11b and F4/80. The second subset, referred to as small peritoneal Mempty set (SPM), expresses substantially lower levels of CD11b and F4/80 but expresses high levels of MHC-II, which is not expressed on LPM. SPM, which predominates in PerC after LPS or thioglycolate stimulation, does not derive from LPM. Instead, it derives from blood monocytes that rapidly enter the PerC after stimulation and differentiate to mature SPM within 2 to 4 d. Both subsets show clear phagocytic activity and both produce nitric oxide (NO) in response to LPS stimulation in vivo. However, their responses to LPS show key differences: in vitro, LPS stimulates LPM, but not SPM, to produce NO; in vivo, LPS stimulates both subsets to produce NO, albeit with different response patterns. These findings extend current models of Mempty set heterogeneity and shed new light on PerC Mempty set diversity, development, and function. Thus, they introduce a new context for interpreting (and reinterpreting) data from ex vivo studies with PerC Mempty set.