Mathematics, Department of

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A Methodological Framework for the Reconstruction of Contiguous Regions of Ancestral Genomes and Its Application to Mammalian Genomes

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2008-11
Abstract: 

The reconstruction of ancestral genome architectures and gene orders from homologies between extant species is a long-standing problem, considered by both cytogeneticists and bioinformaticians. A comparison of the two approaches was recently investigated and discussed in a series of papers, sometimes with diverging points of view regarding the performance of these two approaches. We describe a general methodological framework for reconstructing ancestral genome segments from conserved syntenies in extant genomes. We show that this problem, from a computational point of view, is naturally related to physical mapping of chromosomes and benefits from using combinatorial tools developed in this scope. We develop this framework into a new reconstruction method considering conserved gene clusters with similar gene content, mimicking principles used in most cytogenetic studies, although on a different kind of data. We implement and apply it to datasets of mammalian genomes. We perform intensive theoretical and experimental comparisons with other bioinformatics methods for ancestral genome segments reconstruction. We show that the method that we propose is stable and reliable: it gives convergent results using several kinds of data at different levels of resolution, and all predicted ancestral regions are well supported. The results come eventually very close to cytogenetics studies. It suggests that the comparison of methods for ancestral genome reconstruction should include the algorithmic aspects of the methods as well as the disciplinary differences in data aquisition.

Document type: 
Article
File(s): 

Wavelength Isolation Sequence Design

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2013-05
Abstract: 

A recent paper by Jedwab and Wodlinger renewed interest in aproblem of multislit spectrometer design rst proposed by Golay in1951 but subsequently forgotten. It is shown that Golay's formulationof the problem in terms of 0/1 binary sequences is unduly restrictive.By relaxing the restrictions, in nitely many spectrometer designs sat-isfying all the original physical criteria can be found. Three construc-tions for such spectrometer designs are presented, involving Golombrulers and variants. These constructions explain all nontrivial exam-ples involving at most 26 slits.

Document type: 
Article

Consistency-Based Detection of Potential Tumor-Specific Deletions in Matched Normal/Tumor Genomes

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2011
Abstract: 

Background: Structural variations in human genomes, such as insertions, deletion, or rearrangements, play animportant role in cancer development. Next-Generation Sequencing technologies have been central in providingways to detect such variations. Most existing methods however are limited to the analysis of a single genome, and itis only recently that the comparison of closely related genomes has been considered. In particular, a few recentworks considered the analysis of data sets obtained by sequencing both tumor and healthy tissues of the samecancer patient. In that context, the goal is to detect variations that are specific to exactly one of the genomes, forexample to differentiate between patient-specific and tumor-specific variations. This is a difficult task, especially whenfacing the additional challenge of the possible contamination of healthy tissues by tumor cells and conversely.Results: In the current work, we analyzed a data set of paired-end short-reads, obtained by sequencing tumortissues and healthy tissues, both from the same cancer patient. Based on a combinatorial notion of conflictbetween deletions, we show that in the tumor data, more deletions are predicted than there could actually be in adiploid genome. In contrast, the predictions for the data from normal tissues are almost conflict-free. We designedand applied a method, specific to the analysis of such pooled and contaminated data sets, to detect potentialtumor-specific deletions. Our method takes the deletion calls from both data sets and assigns reads from themixed tumor/normal data to the normal one with the goal to minimize the number of reads that need to bediscarded to obtain a set of conflict-free deletion clusters. We observed that, on the specific data set we analyze,only a very small fraction of the reads needs to be discarded to obtain a set of consistent deletions.Conclusions: We present a framework based on a rigorous definition of consistency between deletions and theassumption that the tumor sample also contains normal cells. A combined analysis of both data sets based on thismodel allowed a consistent explanation of almost all data, providing a detailed picture of candidate patient- andtumor-specific deletions.

Document type: 
Article

Prediction of 492 Human Protein Kinase Substrate Specificities

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2011
Abstract: 

Background: Complex intracellular signaling networks monitor diverse environmental inputs to evoke appropriateand coordinated effector responses. Defective signal transduction underlies many pathologies, including cancer,diabetes, autoimmunity and about 400 other human diseases. Therefore, there is high impetus to define thecomposition and architecture of cellular communications networks in humans. The major components ofintracellular signaling networks are protein kinases and protein phosphatases, which catalyze the reversiblephosphorylation of proteins. Here, we have focused on identification of kinase-substrate interactions throughprediction of the phosphorylation site specificity from knowledge of the primary amino acid sequence of thecatalytic domain of each kinase.Results: The presented method predicts 488 different kinase catalytic domain substrate specificity matrices in 478typical and 4 atypical human kinases that rely on both positive and negative determinants for scoring individualphosphosites for their suitability as kinase substrates. This represents a marked advancement over existing methodssuch as those used in NetPhorest (179 kinases in 76 groups) and NetworKIN (123 kinases), which consider onlypositive determinants for kinase substrate prediction. Comparison of our predicted matrices with experimentallyderivedmatrices from about 9,000 known kinase-phosphosite substrate pairs revealed a high degree ofconcordance with the established preferences of about 150 well studied protein kinases. Furthermore for many ofthe better known kinases, the predicted optimal phosphosite sequences were more accurate than the consensusphosphosite sequences inferred by simple alignment of the phosphosites of known kinase substrates.Conclusions: Application of this improved kinase substrate prediction algorithm to the primary structures of over23, 000 proteins encoded by the human genome has permitted the identification of about 650, 000 putativephosphosites, which are posted on the open source PhosphoNET website (http://www.phosphonet.ca).

Document type: 
Article

A Novel Approach to Modelling Water Transport and Drug Diffusion Through the Stratum Corneum

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2010
Abstract: 

Background: The potential of using skin as an alternative path for systemicallyadministering active drugs has attracted considerable interest, since the creation ofnovel drugs capable of diffusing through the skin would provide a great steptowards easily applicable -and more humane- therapeutic solutions. However, fordrugs to be able to diffuse, they necessarily have to cross a permeability barrier: thestratum corneum (SC), the uppermost set of skin layers. The precise mechanism bywhich drugs penetrate the skin is generally thought to be diffusion of moleculesthrough this set of layers following a “tortuous pathway” around corneocytes, i.e.impermeable dead cells.Results: In this work, we simulate water transport and drug diffusion using a threedimensionalporous media model. Our numerical simulations show that diffusiontakes place through the SC regardless of the direction and magnitude of the fluidpressure gradient, while the magnitude of the concentrations calculated areconsistent with experimental studies.Conclusions: Our results support the possibility for designing arbitrary drugs capableof diffusing through the skin, the time-delivery of which is solely restricted by theirdiffusion and solubility properties.

Document type: 
Article

Wavelength Isolation Sequence Design: Supplementary Data

Peer reviewed: 
No, item is not peer reviewed.
Date created: 
2013-01-04
Abstract: 

This technical report accompanies the paper J. Jedwab and M. Strange. Wavelength isolation sequence design. Submitted to IEEE Trans. Inform. Theory, 2012. It gives a complete listing of the inequivalent nontrivial wavelength isolation sequence triples(WISTs) of length at most 26 and their corresponding aperiodic cross correlations.

Document type: 
Technical Report
File(s): 

The Cellular Dynamics of Bone Remodeling: a Mathematical Model

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2010
Abstract: 

The mechanical properties of vertebrate bone are largely determined by a processwhich involves the complex interplay of three different cell types. This process is called bone remodelingand occurs asynchronously at multiple sites in the mature skeleton. The cells involvedare bone resorbing osteoclasts, bone matrix producing osteoblasts, and mechanosensing osteocytes.These cells communicate with each other by means of autocrine and paracrine signaling factors andoperate in complex entities, the so-called bone multicellular units (BMUs). To investigate the BMUdynamics in silico, we develop a novel mathematical model resulting in a system of nonlinear partialdifferential equations (PDEs) with time delays. The model describes the osteoblast and osteoclastpopulations together with the dynamics of the key messenger molecule RANKL and its decoy receptorOPG. Scaling theory is used to address parameter sensitivity and predict the emergence ofpathological remodeling regimes. The model is studied numerically in one and two space dimensionsusing finite difference schemes in space and explicit delay equation solvers in time. The computationalresults are in agreement with in vivo observations and provide new insights into the role ofthe RANKL/OPG pathway in the spatial regulation of bone remodeling.

Document type: 
Article

An integral representation of the Green’s function for a linear array of acoustic point sources

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2010
Abstract: 

We present a new algorithm for the evaluation of the periodized Green’s function fora linear array of acoustic point sources such as those arising in the analysis of linearray loudspeakers. A variety of classical algorithms (based on spatial and spectralrepresentations, Ewald transformation, etc.) have been implemented in the past toevaluate these acoustic fields. However as we show, these methods become unstableand/or impractically expensive as the frequency of use of the sources increases. Herewe introduce a new numerical scheme that overcomes some of these limitations allowingfor simulations at unprecedentally large frequencies. The method is based ona new integral representation derived from the classic spatial form, and on suitablefurther manipulations of the relevant integrands to render the integrals amenable toefficient and accurate approximations through standard quadrature formulas. Weinclude a variety of numerical results that demonstrate that our algorithm comparesfavorably with several classical method both for points close to the line where thepoles are located and at high-frequencies while remaining competitive with them inevery other instance.

Document type: 
Article

On the Well-Posedness of the Stochastic Allen-Cahn Equation in Two Dimensions

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2011-12-31
Abstract: 

White noise-driven nonlinear stochastic partial differential equations (SPDEs) of parabolic type are frequently used to model physical and biological systems in space dimensions d = 1,2,3. Whereas existence and uniqueness of weak solutions to these equations are well established in one dimension, the situation is different for d \geq 2. Despite their popularity in the applied sciences, higher dimensional versions of these SPDE models are generally assumed to be ill-posed by the mathematics community. We study this discrepancy on the specific example of the two dimensional Allen-Cahn equation driven by additive white noise. Since it is unclear how to define the notion of a weak solution to this equation, we regularize the noise and introduce a family of approximations. Based on heuristic arguments and numerical experiments, we conjecture that these approximations exhibit divergent behavior in the continuum limit. The results strongly suggest that a series of published numerical studies are problematic: shrinking the mesh size in these simulations does not lead to the recovery of a physically meaningful limit.

Document type: 
Article

Numerical Integration for High Order Pyramidal Elements

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2011
Abstract: 

We examine the effect of numerical integration on the accuracy of high order conformingpyramidal finite element methods. Non-smooth shape functions are indispensable to the construction ofpyramidal elements, and this means the conventional treatment of numerical integration, which requiresthat the finite element approximation space is piecewise polynomial, cannot be applied. We developan analysis that allows the finite element approximation space to include non-smooth functions andshow that, despite this complication, conventional rules of thumb can still be used to select appropriatequadrature methods on pyramids. Along the way, we present a new family of high order pyramidalfinite elements for each of the spaces of the de Rham complex.

Document type: 
Article