Brownian Motion of Radioactive Particles: Derivation and Monte Carlo Test of Spatial and Temporal Distributions

Stochastic processes such as diffusion can be analyzed by means of a partial differential equation of the Fokker-Planck type (FPE), which yields a transition probability density, or by a stochastic differential equation of the Langevin type (LE), which yields the time evolution of a statistical process variable. Provided the stochastic process is continuous and certain boundary conditions are met, the two approaches yield equivalent information. However, Brownian motion of radioactively decaying particles is not a continuous process because the Brownian trajectories abruptly terminate when the particle decays. Recent analysis of the Brownian motion of decaying particles by both approaches has led to different mean-square displacements. In this paper, we demonstrate the complete equivalence of the two approaches by 1) showing quantitatively and operationally how the probability densities and statistical moments predicted by the FPE and LE relate to one another, 2) verifying that both approaches lead to identical statistical moments at all orders, and 3) confirming that the analytical solution to the FPE accurately describes the Brownian trajectories obtained by Monte Carlo simulations based on the LE. The analysis in this paper addresses both the spatial distribution of the particles (i.e. the question of displacement as a function of diffusion time) and the temporal distribution (i.e. the question of first-passage time to fixed absorbing boundaries)

Genomic insights into triple-negative and HER2-positive breast cancers using isogenic model systems

Introduction In general, genomic signatures of breast cancer subtypes have little or no overlap owing to the heterogeneous genetic backgrounds of study samples. Thus, obtaining a reliable signature in the context of isogenic nature of the cells has been challenging and the precise contribution of isogenic triple negative breast cancer (TNBC) versus non-TNBC remains poorly defined. Methods We established isogenic stable cell lines representing TNBC and Human Epidermal Growth Factor Receptor 2 positive (HER2+) breast cancers by introducing HER2 in TNBC cell lines MDA-MB-231 and MDA-MB-468. We examined protein level expression and functionality of the transfected receptor by treatment with an antagonist of HER2. Using microarray profiling, we obtained a comprehensive gene list of differentially expressed between TNBC and HER2+ clones. We identified and validated underlying isogenic components using qPCR and also compared results with expression data from patients with similar breast cancer subtypes. Results We identified 544 and 1087 statistically significant differentially expressed genes between isogenic TNBC and HER2+ samples in MDA-MB-231 and MDA-MB-468 backgrounds respectively and a shared signature of 49 genes. By comparing results from MDA-MB-231 and MDA-MB-468 backgrounds with two patient microarray datasets, we identified 17 and 22 common genes with same expression trend respectively. Additionally, we identified 56 and 78 genes from MDA-MB-231 and MDA-MB-468 comparisons respectively present in our published RNA-seq data. Conclusions Using our unique model system, we have identified an isogenic gene expression signature between TNBC and HER2+ breast cancer. A portion of our results was also verified in patient data samples, indicating an existence of isogenic element associated with HER2 status between genetically heterogeneous breast cancer samples. These findings may potentially contribute to the development of molecular platform that would be valuable for diagnostic and therapeutic decision for TNBC and in distinguishing it from HER2+ subtype

Analysis for co-occurring sequence features identifies link between common synonymous variant and an early-terminated NPC1 isoform

Direct assessment of allelic phase for DNA and RNA features of diploid genomes has been challenging for Sanger sequencing, due to its allele-conflating base-calling signal. Massively parallel sequencing technologies are based on the generation of a continuous copy of a single strand sequence segments, thus preserving the allelic relation between the features of the original molecules. We have performed a transcriptome-wide search for co-occurrence of variant nucleotides and exon-intron boundaries positioned within the length of a single sequencing read. Analysis of 75 human transcriptomes from retinal pigment epithelia (RPE), glioblastoma, low-grade brain tumor, breast cancer and colon cancer, have identified an association between the synonymous variant rs1140458 and an early-terminated NPC1 isoform lacking exons 19–25. Higher proportion of molecules bearing the variant nucleotide (versus the reference) incorporates the intron (P \u3c0.0001), which turns the last codon of exon 18 into a stop codon. The significance is highest in RPE cells (P = 3.88 × 10−12). NPC1 protein is involved in the control of the cholesterol trafficking. NPC1 mutations lead, in an autosomal recessive manner, to the neurological disorder Niemann-Pick syndrome type C (NP-C), and, ablation of NPC1 causes age-progressive retinal degeneration in mice and drosophila. The vast majority of the NP-C causative variants consist of missense/nonsense substitutions, small indels, and, intronic splice variants. Rs1140458 is a common exonic synonymous substitution that has never been linked to alternative splicing or pathogenicity. Our analysis suggests that rs1140458 may affect the levels of the functional NPC1 protein, and to contribute to some of the cholesterol-implicated cellular phenotype

RNA sequencing of cancer reveals novel splicing alterations

Breast cancer transcriptome acquires a myriad of regulation changes, and splicing is critical for the cell to “tailor-make” specific functional transcripts. We systematically revealed splicing signatures of the three most common types of breast tumors using RNA sequencing: TNBC, non-TNBC and HER2-positive breast cancer. We discovered subtype specific differentially spliced genes and splice isoforms not previously recognized in human transcriptome. Further, we showed that exon skip and intron retention are predominant splice events in breast cancer. In addition, we found that differential expression of primary transcripts and promoter switching are significantly deregulated in breast cancer compared to normal breast. We validated the presence of novel hybrid isoforms of critical molecules like CDK4, LARP1, ADD3, and PHLPP2. Our study provides the first comprehensive portrait of transcriptional and splicing signatures specific to breast cancer sub-types, as well as previously unknown transcripts that prompt the need for complete annotation of tissue and disease specific transcriptome

RNA2DNAlign: nucleotide resolution allele asymmetries through quantitative assessment of RNA and DNA paired sequencing data.

We introduce RNA2DNAlign, a computational framework for quantitative assessment of allele counts across paired RNA and DNA sequencing datasets. RNA2DNAlign is based on quantitation of the relative abundance of variant and reference read counts, followed by binomial tests for genotype and allelic status at SNV positions between compatible sequences. RNA2DNAlign detects positions with differential allele distribution, suggesting asymmetries due to regulatory/structural events. Based on the type of asymmetry, RNA2DNAlign outlines positions likely to be implicated in RNA editing, allele-specific expression or loss, somatic mutagenesis or loss-of-heterozygosity (the first three also in a tumor-specific setting). We applied RNA2DNAlign on 360 matching normal and tumor exomes and transcriptomes from 90 breast cancer patients from TCGA. Under high-confidence settings, RNA2DNAlign identified 2038 distinct SNV sites associated with one of the aforementioned asymetries, the majority of which have not been linked to functionality before. The performance assessment shows very high specificity and sensitivity, due to the corroboration of signals across multiple matching datasets. RNA2DNAlign is freely available from http://github.com/HorvathLab/NGS as a self-contained binary package for 64-bit Linux systems

Novel insights into breast cancer genetic variance through RNA sequencing

Using RNA sequencing of triple-negative breast cancer (TNBC), non-TBNC and HER2-positive breast cancer sub-types, here we report novel expressed variants, allelic prevalence and abundance, and coexpression with other variation, and splicing signatures. To reveal the most prevalent variant alleles, we overlaid our findings with cancer- and population-based datasets and validated a subset of novel variants of cancer-related genes: ESRP2, GBP1, TPP1, MAD2L1BP, GLUD2 and SLC30A8. As a proof-of-principle, we demonstrated that a rare substitution in the splicing coordinator ESRP2(R353Q) impairs its ability to bind to its substrate FGFR2 pre-mRNA. In addition, we describe novel SNPs and INDELs in cancer relevant genes with no prior reported association of point mutations with cancer, such as MTAP and MAGED1. For the first time, this study illustrates the power of RNA-sequencing in revealing the variation landscape of breast transcriptome and exemplifies analytical strategies to search regulatory interactions among cancer relevant molecules

J Nepal Health Res Counc 2008 Oct;6(13):117-9 Glycogen Rich Clear Cell Carcinoma of Breast

A 37 years old woman presented with a palpable mass in outer upper quadrant of the right breast. Excision biopsy showed Glycogen rich clear cell carcinoma (GRCCC) based on histological, PAS staining and immunohistochemical staining findings Histologically, most of tumor cells were clear cell type with variable intracytopasmic PAS positivity Immunohistochemically, the tumor was positive for progesterone receptor and vimention and foceally positive for cytokeratin and negative for estrogen receptor and S100. The patient underwent right quadrantectomy with right axillary clearance. This case was in stage IIa (T2N0Mx) and Elston and Ellis histological grade 2(Scores 3+2+1=6). GRCCC is a rare variant of breast carcinoma, with incidence calculated to be 1.4 to 3 % and reports indicated a poorer prognosis for patient with GRCCC than those with usual breast cancer. Key words: breast, cancer glycogen rich clear cell carcinom