Intragenic DNA methylation: implications of this epigenetic mechanism for cancer research

Epigenetics is the study of all mechanisms that regulate gene transcription and genome stability that are maintained throughout the cell division, but do not include the DNA sequence itself. The best-studied epigenetic mechanism to date is DNA methylation, where methyl groups are added to the cytosine base within cytosine–guanine dinucleotides (CpG sites). CpGs are frequently clustered in high density (CpG islands (CGIs)) at the promoter of over half of all genes. Current knowledge of transcriptional regulation by DNA methylation centres on its role at the promoter where unmethylated CGIs are present at most actively transcribed genes, whereas hypermethylation of the promoter results in gene repression. Over the last 5 years, research has gradually incorporated a broader understanding that methylation patterns across the gene (so-called intragenic or gene body methylation) may have a role in transcriptional regulation and efficiency. Numerous genome-wide DNA methylation profiling studies now support this notion, although whether DNA methylation patterns are a cause or consequence of other regulatory mechanisms is not yet clear. This review will examine the evidence for the function of intragenic methylation in gene transcription, and discuss the significance of this in carcinogenesis and for the future use of therapies targeted against DNA methylation

A NSFD discretization of two-dimensional singularly perturbed semilinear convection-diffusion problems

Despite the availability of an abundant literature on singularly perturbed problems, interest toward non-linear problems has been limited. In particular, parameter-uniform methods for singularly perturbed semilinear problems are quasi-non-existent. In this article, we study a two-dimensional semilinear singularly perturbed convection-diffusion problems. Our approach requires linearization of the continuous semilinear problem using the quasilinearization technique. We then discretize the resulting linear problems in the framework of non-standard finite difference methods. A rigorous convergence analysis is conducted showing that the proposed method is first-order parameter-uniform convergent. Finally, two test examples are used to validate the theoretical findings

The S phase checkpoint promotes the Smc5/6 complex dependent SUMOylation of Pol2, the catalytic subunit of DNA polymerase ε

Replication fork stalling and accumulation of single-stranded DNA trigger the S phase checkpoint, a signalling cascade that, in budding yeast, leads to the activation of the Rad53 kinase. Rad53 is essential in maintaining cell viability, but its targets of regulation are still partially unknown. Here we show that Rad53 drives the hyper-SUMOylation of Pol2, the catalytic subunit of DNA polymerase ε, principally following replication forks stalling induced by nucleotide depletion. Pol2 is the main target of SUMOylation within the replisome and its modification requires the SUMO-ligase Mms21, a subunit of the Smc5/6 complex. Moreover, the Smc5/6 complex co-purifies with Pol ε, independently of other replisome components. Finally, we map Pol2 SUMOylation to a single site within the N-terminal catalytic domain and identify a SUMO-interacting motif at the C-terminus of Pol2. These data suggest that the S phase checkpoint regulate Pol ε during replication stress through Pol2 SUMOylation and SUMO-binding abilit

Global diversification of a tropical plant growth form: environmental correlates and historical contingencies in climbing palms

Tropical rain forests (TRF) are the most diverse terrestrial biome on Earth, but the diversification dynamics of their constituent growth forms remain largely unexplored. Climbing plants contribute significantly to species diversity and ecosystem processes in TRF. We investigate the broad-scale patterns and drivers of species richness as well as the diversification history of climbing and non-climbing palms (Arecaceae). We quantify to what extent macroecological diversity patterns are related to contemporary climate, forest canopy height and paleoclimatic changes. We test whether diversification rates are higher for climbing than non-climbing palms and estimate the origin of the climbing habit. Climbers account for 22% of global palm species diversity mostly concentrated in Southeast Asia. Global variation in climbing palm species richness can be partly explained by past and present-day climate and rain forest canopy height, but regional differences in residual species richness after accounting for current and past differences in environment suggest a strong role of historical contingencies in climbing palm diversification. Climbing palms show a higher net diversification rate than non-climbers. Diversification analysis of palms detected a diversification rate increase along the branches leading to the most species-rich clade of climbers. Ancestral character reconstructions revealed that the climbing habit originated between early Eocene and Miocene. These results imply that changes from non-climbing to climbing habit may have played an important role in palm diversification, resulting in the origin of one fifth of all palm species. We suggest that, in addition to current climate and paleoclimatic changes after the late Neogene, present-day diversity of climbing palms can be explained by morpho-anatomical innovations, the biogeographic history of Southeast Asia, and/or ecological opportunities due to the diversification of high-stature dipterocarps in Asian TRFs

Contrasting patterns of local richness of seedlings, saplings and trees may have implications for regeneration in rainforest remnants

Remnants of lowland rainforest remain following deforestation, but the longer-term effects of fragmentation remain poorly understood, partly due to the long generation times of trees. We study rainforest trees in three size classes: seedlings (5 cm), that broadly reflect pre- and post-fragmentation communities, and we examine the impacts of fragmentation on forest regeneration in Sabah, Malaysian Borneo. We found that seedling richness (measured as the number of genera per plot) in fragments was about 30 percent lower than in plots in undisturbed forest, and about 20 percent lower than in an extensive tract of selectively logged forest, providing evidence of recruitment declines in fragments. Seedling richness was lowest in small, isolated, and disturbed fragments, potentially signalling an extinction debt given that these fragmentation impacts were not observed in trees. Unlike seedlings, saplings showed no declines in richness in fragments, suggesting that density dependent mortality (where rare individuals have a higher survival rate) and/or year-to-year variation in which species are recruiting could potentially compensate for the reductions in seedling richness we observed. Longer-term studies are required to determine whether sporadic or failed recruitment in small fragments will eventually translate into reduced richness of mature trees, or whether the processes that currently retain high sapling richness will continue in fragments

On Semi-Classical Orthogonal Polynomials Associated with a Modified Sextic Freud-Type Weight

Polynomials that are orthogonal with respect to a perturbation of the Freud weight function by some parameter, known to be modified Freudian orthogonal polynomials, are considered. In this contribution, we investigate certain properties of semi-classical modified Freud-type polynomials in which their corresponding semi-classical weight function is a more general deformation of the classical scaled sextic Freud weight |x|αexp(−cx6),c&gt;0,α&gt;−1. Certain characterizing properties of these polynomials such as moments, recurrence coefficients, holonomic equations that they satisfy, and certain non-linear differential-recurrence equations satisfied by the recurrence coefficients, using compatibility conditions for ladder operators for these orthogonal polynomials, are investigated. Differential-difference equations were also obtained via Shohat’s quasi-orthogonality approach and also second-order linear ODEs (with rational coefficients) satisfied by these polynomials. Modified Freudian polynomials can also be obtained via Chihara’s symmetrization process from the generalized Airy-type polynomials. The obtained linear differential equation plays an essential role in the electrostatic interpretation for the distribution of zeros of the corresponding Freudian polynomials.</jats:p

Unconditionally positive NSFD and classical finite difference schemes for biofilm formation on medical implant using Allen-Cahn equation

Abstract The study of biofilm formation is becoming increasingly important. Microbes that produce biofilms have complicated impact on medical implants. In this paper, we construct an unconditionally positive non-standard finite difference scheme for a mathematical model of biofilm formation on a medical implant. The unknowns in many applications reflect values that cannot be negative, such as chemical component concentrations or population numbers. The model employed here uses the bistable Allen-Cahn partial differential equation, which is a generalization of Fisher’s equation. We study consistency and convergence of the scheme constructed. We compare the performance of our scheme with a classical finite difference scheme using four numerical experiments. The technique used in the construction of unconditionally positive method in this study can be applied to other areas of mathematical biology and sciences. The results here elaborate the benefits of the non-standard approximations over the classical approximations in practical applications.</jats:p

On Semi-Classical Orthogonal Polynomials Associated with a Modified Sextic Freud-Type Weight

Polynomials that are orthogonal with respect to a perturbation of the Freud weight function by some parameter, known to be modified Freudian orthogonal polynomials, are considered. In this contribution, we investigate certain properties of semi-classical modified Freud-type polynomials in which their corresponding semi-classical weight function is a more general deformation of the classical scaled sextic Freud weight |x|&alpha;exp(&minus;cx6),c&gt;0,&alpha;&gt;&minus;1. Certain characterizing properties of these polynomials such as moments, recurrence coefficients, holonomic equations that they satisfy, and certain non-linear differential-recurrence equations satisfied by the recurrence coefficients, using compatibility conditions for ladder operators for these orthogonal polynomials, are investigated. Differential-difference equations were also obtained via Shohat&rsquo;s quasi-orthogonality approach and also second-order linear ODEs (with rational coefficients) satisfied by these polynomials. Modified Freudian polynomials can also be obtained via Chihara&rsquo;s symmetrization process from the generalized Airy-type polynomials. The obtained linear differential equation plays an essential role in the electrostatic interpretation for the distribution of zeros of the corresponding Freudian polynomials