Modeling the evolution space of breakage fusion bridge cycles with a stochastic folding process

Breakage-Fusion-Bridge cycles in cancer arise when a broken segment of DNA is duplicated and an end from each copy joined together. This structure then 'unfolds' into a new piece of palindromic DNA. This is one mechanism responsible for the localised amplicons observed in cancer genome data. The process has parallels with paper folding sequences that arise when a piece of paper is folded several times and then unfolded. Here we adapt such methods to study the breakage-fusion-bridge structures in detail. We firstly consider discrete representations of this space with 2-d trees to demonstrate that there are 2^(n(n-1)/2) qualitatively distinct evolutions involving n breakage-fusion-bridge cycles. Secondly we consider the stochastic nature of the fold positions, to determine evolution likelihoods, and also describe how amplicons become localised. Finally we highlight these methods by inferring the evolution of breakage-fusion-bridge cycles with data from primary tissue cancer samples

Computational Cancer Biology: An Evolutionary Perspective

ISSN:1553-734XISSN:1553-735

A hierarchical kinetic theory of birth, death, and fission in age-structured interacting populations

We study mathematical models describing the evolution of stochastic age-structured populations. After reviewing existing approaches, we develop a complete kinetic framework for age-structured interacting populations undergoing birth, death and fission processes in spatially dependent environments. We define the full probability density for the population-size age chart and find results under specific conditions. Connections with more classical models are also explicitly derived. In particular, we show that factorial moments for non-interacting processes are described by a natural generalization of the McKendrick-von Foerster equation, which describes mean-field deterministic behavior. Our approach utilizes mixed-type, multidimensional probability distributions similar to those employed in the study of gas kinetics and with terms that satisfy BBGKY-like equation hierarchies

Reconstructing cancer genomes from paired-end sequencing data

<p>Abstract</p> <p>Background</p> <p>A cancer genome is derived from the germline genome through a series of somatic mutations. Somatic structural variants - including duplications, deletions, inversions, translocations, and other rearrangements - result in a cancer genome that is a scrambling of intervals, or "blocks" of the germline genome sequence. We present an efficient algorithm for reconstructing the block organization of a cancer genome from paired-end DNA sequencing data.</p> <p>Results</p> <p>By aligning paired reads from a cancer genome - and a matched germline genome, if available - to the human reference genome, we derive: (i) a partition of the reference genome into intervals; (ii) adjacencies between these intervals in the cancer genome; (iii) an estimated copy number for each interval. We formulate the Copy Number and Adjacency Genome Reconstruction Problem of determining the cancer genome as a sequence of the derived intervals that is consistent with the measured adjacencies and copy numbers. We design an efficient algorithm, called Paired-end Reconstruction of Genome Organization (PREGO), to solve this problem by reducing it to an optimization problem on an interval-adjacency graph constructed from the data. The solution to the optimization problem results in an Eulerian graph, containing an alternating Eulerian tour that corresponds to a cancer genome that is consistent with the sequencing data. We apply our algorithm to five ovarian cancer genomes that were sequenced as part of The Cancer Genome Atlas. We identify numerous rearrangements, or structural variants, in these genomes, analyze reciprocal vs. non-reciprocal rearrangements, and identify rearrangements consistent with known mechanisms of duplication such as tandem duplications and breakage/fusion/bridge (B/F/B) cycles.</p> <p>Conclusions</p> <p>We demonstrate that PREGO efficiently identifies complex and biologically relevant rearrangements in cancer genome sequencing data. An implementation of the PREGO algorithm is available at <url>http://compbio.cs.brown.edu/software/</url>.</p

Detecting copy number status and uncovering subclonal markers in heterogeneous tumor biopsies

<p>Abstract</p> <p>Background</p> <p>Genomic aberrations can be used to determine cancer diagnosis and prognosis. Clinically relevant novel aberrations can be discovered using high-throughput assays such as Single Nucleotide Polymorphism (SNP) arrays and next-generation sequencing, which typically provide aggregate signals of many cells at once. However, heterogeneity of tumor subclones dramatically complicates the task of detecting aberrations.</p> <p>Results</p> <p>The aggregate signal of a population of subclones can be described as a linear system of equations. We employed a measure of allelic imbalance and total amount of DNA to characterize each locus by the copy number status (gain, loss or neither) of the strongest subclonal component. We designed simulated data to compare our measure to existing approaches and we analyzed SNP-arrays from 30 melanoma samples and transcriptome sequencing (RNA-Seq) from one melanoma sample.</p> <p>We showed that any system describing aggregate subclonal signals is underdetermined, leading to non-unique solutions for the exact copy number profile of subclones. For this reason, our illustrative measure was more robust than existing Hidden Markov Model (HMM) based tools in inferring the aberration status, as indicated by tests on simulated data. This higher robustness contributed in identifying numerous aberrations in several loci of melanoma samples. We validated the heterogeneity and aberration status within single biopsies by fluorescent <it>in situ </it>hybridization of four affected and transcriptionally up-regulated genes E2F8, ETV4, EZH2 and FAM84B in 11 melanoma cell lines. Heterogeneity was further demonstrated in the analysis of allelic imbalance changes along single exons from melanoma RNA-Seq.</p> <p>Conclusions</p> <p>These studies demonstrate how subclonal heterogeneity, prevalent in tumor samples, is reflected in aggregate signals measured by high-throughput techniques. Our proposed approach yields high robustness in detecting copy number alterations using high-throughput technologies and has the potential to identify specific subclonal markers from next-generation sequencing data.</p

Ultrasound evaluation of the abductor hallucis muscle: Reliability study

© 2008 Cameron et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licens

A Computational Framework Discovers New Copy Number Variants with Functional Importance

Structural variants which cause changes in copy numbers constitute an important component of genomic variability. They account for 0.7% of genomic differences in two individual genomes, of which copy number variants (CNVs) are the largest component. A recent population-based CNV study revealed the need of better characterization of CNVs, especially the small ones (<500 bp).We propose a three step computational framework (Identification of germline Changes in Copy Number or IgC2N) to discover and genotype germline CNVs. First, we detect candidate CNV loci by combining information across multiple samples without imposing restrictions to the number of coverage markers or to the variant size. Secondly, we fine tune the detection of rare variants and infer the putative copy number classes for each locus. Last, for each variant we combine the relative distance between consecutive copy number classes with genetic information in a novel attempt to estimate the reference model bias. This computational approach is applied to genome-wide data from 1250 HapMap individuals. Novel variants were discovered and characterized in terms of size, minor allele frequency, type of polymorphism (gains, losses or both), and mechanism of formation. Using data generated for a subset of individuals by a 42 million marker platform, we validated the majority of the variants with the highest validation rate (66.7%) was for variants of size larger than 1 kb. Finally, we queried transcriptomic data from 129 individuals determined by RNA-sequencing as further validation and to assess the functional role of the new variants. We investigated the possible enrichment for variant's regulatory effect and found that smaller variants (<1 Kb) are more likely to regulate gene transcript than larger variants (p-value = 2.04e-08). Our results support the validity of the computational framework to detect novel variants relevant to disease susceptibility studies and provide evidence of the importance of genetic variants in regulatory network studies