Quantum Mechanics as Asymptotics of Solutions of Generalized Kramers Equation

We consider the process of diffusion scattering of a wave function given on the phase space. In this process the heat diffusion is considered only along momenta. We write down the modified Kramers equation describing this situation. In this model, the usual quantum description arises as asymptotics of this process for large values of resistance of the medium per unit of mass of particle. It is shown that in this case the process passes several stages. During the first short stage, the wave function goes to one of "stationary" values. At the second long stage, the wave function varies in the subspace of "stationary" states according to the Schrodinger equation. Further, dissipation of the process leads to decoherence, and any superposition of states goes to one of eigenstates of the Hamilton operator. At the last stage, the mixed state of heat equilibrium (the Gibbs state) arises due to the heat influence of the medium and the random transitions among the eigenstates of the Hamilton operator. Besides that, it is shown that, on the contrary, if the resistance of the medium per unit of mass of particle is small, then in the considered model, the density of distribution of probability $\rho =|\phi |^2$ satisfies the standard Liouville equation, as in classical statistical mechanics.Comment: 18 page

Promising markers of CIMP+ colon tumors identified on the basis of TCGA data analysis

CIMP+ (CpG­Island Methylator Phenotype) tumors are characterized by dense methylation of promoter CpG islands of many genes at once and represent a separate group of malignant neoplasms of the colon. Despite the fact that the diagnostics of CIMP+ tumors has a significant prognostic value, an effective set of markers has not been developed yet. For the identification of CpG sites, the methylation level of which could be used to detect CIMP+ tumors, an analysis of expression and methylation profiles of 297 primary colon tumors and 38 histologically normal tissues paired to them, which are presented in the TCGA (The Cancer Genome Atlas) project database, was performed by us using the CrossHub tool created previously. We developed the scoring, which takes into account the methylation level of CpG sites, their location, and the expression level of the corresponding genes. It was revealed that the methylation status of CpG sites of the AMOTL1, ZNF43, ZNF134, and CHFR genes is a promising marker of CIMP+ tumors. Moreover, specific regions of promoters of these genes, the methylation level of which was associated with the examined phenotype, were identified. To verify the obtained data in independent sampling, first, the quantitative PCR was used to assess the relative mRNA level of the AMOTL1, ZNF43, ZNF134, and CHFR genes in 30 paired (tumor/histologically normal tissue) colon samples. For all the genes, a frequent (50–60 % of cases) and significant (2–30­fold) expression decrease was revealed. Then, the bisulfite conversion of DNA followed by cloning and sequencing was applied to examine the methylation status of CpG sites that were selected as the result of bioinformatics analysis. We observed a high methylation level (β­value = 0.3–0.9) of the CpG sites in the samples with simultaneous downregulation of all 4 genes and a low methylation level (β­value = 0.0–0.2) in the samples with the unchanged expression level of 4 genes and in histologically normal tissues. Thus, the methylation status of the CpG sites of promoter regions of the AMOTL1, ZNF43, ZNF134, and CHFR genes is a promising potential marker of CIMP+ colon tumors

Pan-Cancer Analysis of TCGA Data Revealed Promising Reference Genes for qPCR Normalization

Quantitative PCR (qPCR) remains the most widely used technique for gene expression evaluation. Obtaining reliable data using this method requires reference genes (RGs) with stable mRNA level under experimental conditions. This issue is especially crucial in cancer studies because each tumor has a unique molecular portrait. The Cancer Genome Atlas (TCGA) project provides RNA-Seq data for thousands of samples corresponding to dozens of cancers and presents the basis for assessment of the suitability of genes as reference ones for qPCR data normalization. Using TCGA RNA-Seq data and previously developed CrossHub tool, we evaluated mRNA level of 32 traditionally used RGs in 12 cancer types, including those of lung, breast, prostate, kidney, and colon. We developed an 11-component scoring system for the assessment of gene expression stability. Among the 32 genes, PUM1 was one of the most stably expressed in the majority of examined cancers, whereas GAPDH, which is widely used as a RG, showed significant mRNA level alterations in more than a half of cases. For each of 12 cancer types, we suggested a pair of genes that are the most suitable for use as reference ones. These genes are characterized by high expression stability and absence of correlation between their mRNA levels. Next, the scoring system was expanded with several features of a gene: mutation rate, number of transcript isoforms and pseudogenes, participation in cancer-related processes on the basis of Gene Ontology, and mentions in PubMed-indexed articles. All the genes covered by RNA-Seq data in TCGA were analyzed using the expanded scoring system that allowed us to reveal novel promising RGs for each examined cancer type and identify several “universal” pan-cancer RG candidates, including SF3A1, CIAO1, and SFRS4. The choice of RGs is the basis for precise gene expression evaluation by qPCR. Here, we suggested optimal pairs of traditionally used RGs for 12 cancer types and identified novel promising RGs that demonstrate high expression stability and other features of reliable and convenient RGs (high expression level, low mutation rate, non-involvement in cancer-related processes, single transcript isoform, and absence of pseudogenes)

The evolution and expression of the snaR family of small non-coding RNAs

We recently identified the snaR family of small non-coding RNAs that associate in vivo with the nuclear factor 90 (NF90/ILF3) protein. The major human species, snaR-A, is an RNA polymerase III transcript with restricted tissue distribution and orthologs in chimpanzee but not rhesus macaque or mouse. We report their expression in human tissues and their evolution in primates. snaR genes are exclusively in African Great Apes and some are unique to humans. Two novel families of snaR-related genetic elements were found in primates: CAS (catarrhine ancestor of snaR), limited to Old World Monkeys and apes; and ASR (Alu/snaR-related), present in all monkeys and apes. ASR and CAS appear to have spread by retrotransposition, whereas most snaR genes have spread by segmental duplication. snaR-A and snaR-G2 are differentially expressed in discrete regions of the human brain and other tissues, notably including testis. snaR-A is up-regulated in transformed and immortalized human cells, and is stably bound to ribosomes in HeLa cells. We infer that snaR evolved from the left monomer of the primate-specific Alu SINE family via ASR and CAS in conjunction with major primate speciation events, and suggest that snaRs participate in tissue- and species-specific regulation of cell growth and translation

Structural architecture of the human long non-coding RNA, steroid receptor RNA activator

While functional roles of several long non-coding RNAs (lncRNAs) have been determined, the molecular mechanisms are not well understood. Here, we report the first experimentally derived secondary structure of a human lncRNA, the steroid receptor RNA activator (SRA), 0.87 kB in size. The SRA RNA is a non-coding RNA that coactivates several human sex hormone receptors and is strongly associated with breast cancer. Coding isoforms of SRA are also expressed to produce proteins, making the SRA gene a unique bifunctional system. Our experimental findings (SHAPE, in-line, DMS and RNase V1 probing) reveal that this lncRNA has a complex structural organization, consisting of four domains, with a variety of secondary structure elements. We examine the coevolution of the SRA gene at the RNA structure and protein structure levels using comparative sequence analysis across vertebrates. Rapid evolutionary stabilization of RNA structure, combined with frame-disrupting mutations in conserved regions, suggests that evolutionary pressure preserves the RNA structural core rather than its translational product. We perform similar experiments on alternatively spliced SRA isoforms to assess their structural features