SINE Family Research Articles

Regularity for Semilinear Neutral Hyperbolic Equations with Cosine Families

The purpose of this paper is to obtain the regularity for solutions of semilinear neutral hyperbolic equations with the nonlinear convolution. The principal operator is the infinitesimal generator of a cosine and sine families. In order to show a variation of constant formula for solutions, we make of using the nature of cosine and sine families.

New results on controllability of fractional evolution systems with order $ \alpha\in (1,2) $

This paper addresses some interesting results of mild solutions to fractional evolution systems with order \begin{document}$ \alpha\in (1,2) $\end{document} in Banach spaces as well as the controllability problem. Firstly, we deduce a new representation of solution operators and give a new concept of mild solutions for the objective equations by the Laplace transform and Mainardi's Wright-type function, and then we proceed to establish a new compact result of the solution operators when the sine family is compact. Secondly, the controllability results of mild solutions are obtained. Finally, an example is presented to illustrate the main results.

Hagfish genome reveals parallel evolution of 7SL RNA-derived SINEs

BackgroundShort interspersed elements (SINEs) are ubiquitous components of eukaryotic genomes. SINEs are composite transposable elements that are mobilized by non-long terminal repeat (non-LTR) retrotransposons, also called long interspersed elements (LINEs). The 3′ part of SINEs usually originated from that of counterpart non-LTR retrotransposons. The 5′ part of SINEs mostly originated from small RNA genes. SINE1 is a group of SINEs whose 5′ part originated from 7SL RNA, and is represented by primate Alu and murine B1. Well-defined SINE1 has been found only from Euarchontoglires, a group of mammals, in contrast to the wide distribution of SINE2, which has a tRNA-derived sequence, from animals to plants to protists. Both Alu and B1 are mobilized by L1-type non-LTR retrotransposons, which are the only lineage of autonomous non-LTR retrotransposons active in these mammalian lineages.ResultsHere a new lineage of SINE1 is characterized from the seashore hagfish Eptatretus burgeri genome. This SINE1 family, designated SINE1-1_EBu, is young, and is transposed by RTE-type non-LTR retrotransposon, not L1-type. Comparison with other SINE families from hagfish indicated the birth of SINE1-1_EBu through chimera formation of a 7SL RNA-derived sequence and an older tRNA-derived SINE family. It reveals parallel evolution of SINE1 in two vertebrate lineages with different autonomous non-LTR retrotransposon partners. The comparison between two SINE1 lineages supports that the RNA secondary structure of the Alu domain of 7SL RNA is required for the efficient retrotransposition.ConclusionsThe hagfish SINE1 is the first evident SINE1 family found outside of Euarchontoglires. Independent evolution of SINE1 with similar RNA secondary structure originated in 7SL RNA indicates the functional importance of 7SL RNA-derived sequence in the proliferation of SINEs.

Bounded type Siegel disks of a family of sine families

We prove that for any positive integer n, there is a polynomial P(z) with degree n such that the entire function G(z)=P(sin⁡(z)) has a bounded type Siegel disk bounded by a quasi-circle in the plane which passes through at least one critical point of G. In addition, let 0<θ<1 be an irrational number of bounded type. We prove that for any integer k≥0, the boundary of the Siegel disk of G(z)=∫0sin⁡(z)e2πiθ(1−s2)kds centered at the origin is a quasi-circle passing through exactly two critical points π/2 and −π/2 with multiplicity k+1, respectively.

Implicit analytic solutions for a nonlinear fractional partial differential beam equation

Analytic solutions in implicit form are derived for a nonlinear partial differential equation (PDE) with fractional derivative elements, which can model the dynamics of a deterministically excited Euler-Bernoulli beam resting on a viscoelastic foundation. Specifically, the initial-boundary value problem for the corresponding PDE is reduced to an initial value problem for a nonlinear ordinary differential equation in a Hilbert space. Next, by employing the cosine and sine families of operators, a variation of parameters representation of the solution map is introduced. Due to the presence of a nonlinear term, a local fixed point theorem is employed to prove the local existence and uniqueness of the solution. Relying on the regularity properties of cosine and sine families, taking into account the form of the nonlinear term, and considering the properties of the fractional derivative, the solution map of the abstract problem is cast into a derivative-free analytic solution in implicit-form for the initial boundary value problem. Results corresponding to the limiting purely elastic and purely viscous cases are also provided. The herein developed technique and derived implicit form solutions can be construed as generalizations of available results in the literature to account for fractional derivative elements. This is of significant importance given the vast utilization of fractional calculus modeling in modern engineering mechanics, and in viscoelastic material behavior in particular.

Genome-Wide Identification of Microsatellites and Transposable Elements in the Dromedary Camel Genome Using Whole-Genome Sequencing Data.

Transposable elements (TEs) along with simple sequence repeats (SSRs) are prevalent in eukaryotic genome, especially in mammals. Repetitive sequences form approximately one-third of the camelid genomes, so study on this part of genome can be helpful in providing deeper information from the genome and its evolutionary path. Here, in order to improve our understanding regarding the camel genome architecture, the whole genome of the two dromedaries (Yazdi and Trodi camels) was sequenced. Totally, 92- and 84.3-Gb sequence data were obtained and assembled to 137,772 and 149,997 contigs with a N50 length of 54,626 and 54,031 bp in Yazdi and Trodi camels, respectively. Results showed that 30.58% of Yazdi camel genome and 30.50% of Trodi camel genome were covered by TEs. Contrary to the observed results in the genomes of cattle, sheep, horse, and pig, no endogenous retrovirus-K (ERVK) elements were found in the camel genome. Distribution pattern of DNA transposons in the genomes of dromedary, Bactrian, and cattle was similar in contrast with LINE, SINE, and long terminal repeat (LTR) families. Elements like RTE-BovB belonging to LINEs family in cattle and sheep genomes are dramatically higher than genome of dromedary. However, LINE1 (L1) and LINE2 (L2) elements cover higher percentage of LINE family in dromedary genome compared to genome of cattle. Also, 540,133 and 539,409 microsatellites were identified from the assembled contigs of Yazdi and Trodi dromedary camels, respectively. In both samples, di-(393,196) and tri-(65,313) nucleotide repeats contributed to about 42.5% of the microsatellites. The findings of the present study revealed that non-repetitive content of mammalian genomes is approximately similar. Results showed that 9.1 Mb (0.47% of whole assembled genome) of Iranian dromedary’s genome length is made up of SSRs. Annotation of repetitive content of Iranian dromedary camel genome revealed that 9,068 and 11,544 genes contain different types of TEs and SSRs, respectively. SSR markers identified in the present study can be used as a valuable resource for genetic diversity investigations and marker-assisted selection (MAS) in camel-breeding programs.

A note on temporal regularity of second order difference equations

This work deals with the study of maximal ℓp‐regularity of a pair (A,B) of bounded linear operators on a complex Banach space associated to the second order difference equation un + 2 = Bun + 1 + Aun + fn, where f is a given sequence on . We obtain results of characterization based on spectral analysis of the discrete sine family, which is the resolvent family of this equation.

T time for ADAR: ADAR1 is required for T cell self-tolerance.

ADAR1, an RNA‐editing enzyme, plays a key role in preventing self‐RNAs from triggering autoinflammatory responses. In this issue of EMBO reports , Nakahama and colleagues uncover a novel role for ADAR1 in T cells [1]. The authors report that in T cells, ADAR1‐mediated suppression of type I interferon‐stimulated gene (ISG) expression is required for thymic T cell self‐tolerance and prevention of colitis. These findings establish a novel function of ADAR1 in T cells and suggest that autoreactive T cells may contribute to disease symptoms in autoinflammatory disorders.

Can-SINE dynamics in the giant panda and three other Caniformia genomes

BackgroundAlthough repeat sequences constitute about 37% of carnivore genomes, the characteristics and distribution of repeat sequences among carnivore genomes have not been fully investigated. Based on the updated Repbase library, we re-annotated transposable elements (TEs) in four Caniformia genomes (giant panda, polar bear, domestic dog, and domestic ferret) and performed a systematic, genome-wide comparison focusing on the Carnivora-specific SINE family, Can-SINEs.ResultsWe found the majority of young recently integrated transposable elements are LINEs and SINEs in carnivore genomes. In particular, SINEC1_AMe, SINEC1B_AMe and SINEC_C1 are the top three most abundant Can-SINE subfamilies in the panda and polar bear genomes. Transposition in transposition analysis indicates that SINEC1_AMe and SINEC1B_AMe are the most active subfamilies in the panda and the polar bear genomes. SINEC2A1_CF and SINEC1A_CF subfamilies show a higher retrotransposition activity in the dog genome, and MVB2 subfamily is the most active Can-SINE in the ferret genome. As the giant panda is an endangered icon species, we then focused on the identification of panda specific Can-SINEs. With the panda-associated two-way genome alignments, we identified 250 putative panda-specific (PPS) elements (139 SINEC1_AMes and 111 SINEC1B_AMes) that inserted in the panda genome but were absent at the orthologous regions of the other three genomes. Further investigation of these PPS elements allowed us to identify a new Can-SINE subfamily, the SINEC1_AMe2, which was distinguishable from the current SINEC1_AMe consensus by four non-CpG sites. SINEC1_AMe2 has a high copy number (> 100,000) in the panda and polar bear genomes and the vast majority (> 96%) of the SINEC1_AMe2 elements have divergence rates less than 10% in both genomes.ConclusionsOur results suggest that Can-SINEs show lineage-specific retransposition activity in the four genomes and have an important impact on the genomic landscape of different Caniformia lineages. Combining these observations with results from the COSEG, Network, and target site duplication analysis, we suggest that SINEC1_AMe2 is a young mobile element subfamily and currently active in both the panda and polar bear genomes.

Implicit analytic solutions for the linear stochastic partial differential beam equation with fractional derivative terms

Analytic solutions in implicit-form are derived for a linear stochastic partial differential equation (SPDE) with fractional derivative terms, which can model the dynamics of a stochastically excited Euler–Bernoulli beam resting on a viscoelastic foundation. Specifically, the original initial–boundary value problem of the SPDE is reduced to an initial value problem of a second-order stochastic differential equation in an appropriate Hilbert space. Next, addressing the abstract Cauchy problem, employing cosine and sine families of operators, and representing the fractional derivative term in a suitable form, a variation of parameters treatment yields the solution in implicit-form. The limiting purely viscous and purely elastic modeling cases are also studied within the same framework. The herein proposed technique and derived implicit-form solutions can be construed as an extension of available results in the literature to account for fractional derivative terms. This generalization is of significant importance given the vast utilization of fractional calculus modeling in engineering mechanics, and in viscoelastic material behavior in particular. In this regard, the herein proposed analytical treatment also supplements existing more numerically oriented solution schemes available in the engineering mechanics literature.

Area of the complement of the fast escaping sets of a family of entire functions

Let $f$ be an entire function with the form $f(z)=P(e^z)/e^z$, where $P$ is a polynomial with degree at least $2$ and $P(0)\neq 0$. We prove that the area of the complement of the fast escaping set (hence the Fatou set) of $f$ in a horizontal strip of width $2\pi$ is finite. In particular, the corresponding result can be applied to the sine family $\alpha\sin(z+\beta)$, where $\alpha\neq 0$ and $\beta\in\mathbb{C}$.

Cross-Kingdom Commonality of a Novel Insertion Signature of RTE-Related Short Retroposons.

In multicellular organisms, such as vertebrates and flowering plants, horizontal transfer (HT) of genetic information is thought to be a rare event. However, recent findings unveiled unexpectedly frequent HT of RTE-clade LINEs. To elucidate the molecular footprints of the genomic integration machinery of RTE-related retroposons, the sequence patterns surrounding the insertion sites of plant Au-like SINE families were analyzed in the genomes of a wide variety of flowering plants. A novel and remarkable finding regarding target site duplications (TSDs) for SINEs was they start with thymine approximately one helical pitch (ten nucleotides) downstream of a thymine stretch. This TSD pattern was found in RTE-clade LINEs, which share the 3′-end sequence of these SINEs, in the genome of leguminous plants. These results demonstrably show that Au-like SINEs were mobilized by the enzymatic machinery of RTE-clade LINEs. Further, we discovered the same TSD pattern in animal SINEs from lizard and mammals, in which the RTE-clade LINEs sharing the 3′-end sequence with these animal SINEs showed a distinct TSD pattern. Moreover, a significant correlation was observed between the first nucleotide of TSDs and microsatellite-like sequences found at the 3′-ends of SINEs and LINEs. We propose that RTE-encoded protein could preferentially bind to a DNA region that contains a thymine stretch to cleave a phosphodiester bond downstream of the stretch. Further, determination of cleavage sites and/or efficiency of primer sites for reverse transcription may depend on microsatellite-like repeats in the RNA template. Such a unique mechanism may have enabled retroposons to successfully expand in frontier genomes after HT.

ALUternative Regulation for Gene Expression.

Alu elements belong to the primate-specific SINE family of retrotransposons and constitute almost 11% of the human genome. Alus are transcribed by RNA polymerase (Pol) III and are inserted back into the genome with the help of autonomous LINE retroelements. Since Alu elements are preferentially located near to or within gene-rich regions, they can affect gene expression by distinct mechanisms of action at both DNA and RNA levels. In this review we focus on recent advances of how Alu elements are pervasively involved in gene regulation. We discuss the impacts of Alu DNA sequences that are in close proximity to genes, Pol-III-transcribed free Alu RNAs, and Pol-II-transcribed Alu RNAs that are embedded within coding or noncoding RNA transcripts. The recent elucidation of Alu functions reveals previously underestimated roles of these selfish or junk DNA sequences in the human genome.

Control problems for semilinear second order equations with cosine families

This paper aims to obtain the approximate controllability for the second order nonlinear control systems with a strongly cosine family and the associated with sine family.

Enrichment analysis of Alu elements with different spatial chromatin proximity in the human genome.

Transposable elements (TEs) have no longer been totally considered as “junk DNA” for quite a time since the continual discoveries of their multifunctional roles in eukaryote genomes. As one of the most important and abundant TEs that still active in human genome, Alu, a SINE family, has demonstrated its indispensable regulatory functions at sequence level, but its spatial roles are still unclear. Technologies based on 3C (chromosome conformation capture) have revealed the mysterious three-dimensional structure of chromatin, and make it possible to study the distal chromatin interaction in the genome. To find the role TE playing in distal regulation in human genome, we compiled the new released Hi-C data, TE annotation, histone marker annotations, and the genome-wide methylation data to operate correlation analysis, and found that the density of Alu elements showed a strong positive correlation with the level of chromatin interactions (hESC: r = 0.9, P < 2.2 × 1016; IMR90 fibroblasts: r = 0.94, P < 2.2 × 1016) and also have a significant positive correlation with some remote functional DNA elements like enhancers and promoters (Enhancer: hESC: r = 0.997, P = 2.3 × 10−4; IMR90: r = 0.934, P = 2 × 10−2; Promoter: hESC: r = 0.995, P = 3.8 × 10−4; IMR90: r = 0.996, P = 3.2 × 10−4). Further investigation involving GC content and methylation status showed the GC content of Alu covered sequences shared a similar pattern with that of the overall sequence, suggesting that Alu elements also function as the GC nucleotide and CpG site provider. In all, our results suggest that the Alu elements may act as an alternative parameter to evaluate the Hi-C data, which is confirmed by the correlation analysis of Alu elements and histone markers. Moreover, the GC-rich Alu sequence can bring high GC content and methylation flexibility to the regions with more distal chromatin contact, regulating the transcription of tissue-specific genes.Electronic supplementary materialThe online version of this article (doi:10.1007/s13238-015-0240-7) contains supplementary material, which is available to authorized users.

Polyadenylation of RNA transcribed from mammalian SINEs by RNA polymerase III: Complex requirements for nucleotide sequences

It is generally accepted that only transcripts synthesized by RNA polymerase II (e.g., mRNA) were subject to AAUAAA-dependent polyadenylation. However, we previously showed that RNA transcribed by RNA polymerase III (pol III) from mouse B2 SINE could be polyadenylated in an AAUAAA-dependent manner. Many species of mammalian SINEs end with the pol III transcriptional terminator (TTTTT) and contain hexamers AATAAA in their A-rich tail. Such SINEs were united into Class T+, whereas SINEs lacking the terminator and AATAAA sequences were classified as T−. Here we studied the structural features of SINE pol III transcripts that are necessary for their polyadenylation. Eight and six SINE families from classes T+ and T−, respectively, were analyzed. The replacement of AATAAA with AACAAA in T+ SINEs abolished the RNA polyadenylation. Interestingly, insertion of the polyadenylation signal (AATAAA) and pol III transcription terminator in T− SINEs did not result in polyadenylation. The detailed analysis of three T+ SINEs (B2, DIP, and VES) revealed areas important for the polyadenylation of their pol III transcripts: the polyadenylation signal and terminator in A-rich tail, β region positioned immediately downstream of the box B of pol III promoter, and τ region located upstream of the tail. In DIP and VES (but not in B2), the τ region is a polypyrimidine motif which is also characteristic of many other T+ SINEs. Most likely, SINEs of different mammals acquired these structural features independently as a result of parallel evolution.

Existence of solution of impulsive second order neutral integro- differential equations with state delay

This paper consists of two parts. The first part deals with the existence of a mild solution of a class of instantaneous impulsive second order partial neutral differential equations with state dependent delay. The second part studies the non-instantaneous impulsive conditions on the same problem. The Kuratowski measure of noncompactness and M\'onch fixed point theorem are used to prove the existence of the mild solution. We remove the restrictive conditions on the priori estimation available in literature. The compactness assumption on the associated cosine or sine family of operators, nonlinear terms and associated impulsive term are also not required in this paper. The noncompactness measure estimation, the Lipschitz conditions and compactness on the nonlinear functions are replaced by simple and natural assumptions. We introduce new non-instantaneous impulses with fixed delays. In the last section, we study examples to illustrate the result presented.

The 3D folding of metazoan genomes correlates with the association of similar repetitive elements.

The potential roles of the numerous repetitive elements found in the genomes of multi-cellular organisms remain speculative. Several studies have suggested a role in stabilizing specific 3D genomic contacts. To test this hypothesis, we exploited inter-chromosomal contacts frequencies obtained from Hi-C experiments and show that the folding of the human, mouse and Drosophila genomes is associated with a significant co-localization of several specific repetitive elements, notably many elements of the SINE family. These repeats tend to be the oldest ones and are enriched in transcription factor binding sites. We propose that the co-localization of these repetitive elements may explain the global conservation of genome folding observed between homologous regions of the human and mouse genome. Taken together, these results support a contribution of specific repetitive elements in maintaining and/or reshaping genome architecture over evolutionary times.

On PZ type Siegel disks of the sine family

We prove that for typical rotation numbers $0&lt;{\it\theta}&lt;1$, the boundary of the Siegel disk of $f_{{\it\theta}}(z)=e^{2{\it\pi}i{\it\theta}}\sin (z)$ centered at the origin is a Jordan curve which passes through exactly two critical points ${\it\pi}/2$ and $-{\it\pi}/2$.

Approximate Controllability of a Second Order Neutral Differential Equation with State Dependent Delay

This paper deals with the existence and uniqueness of mild solution and approximate controllability of a second order neutral partial differential equation with state dependent delay. The Hausdorff measure of noncompactness and Darbo Sadovskii theorem is used to prove the existence of mild solution of the system. Some restrictive conditions such as the compactness assumption on the associated cosine or sine family of operators and the Lipschitz conditions on the nonlinear functions are replaced by simple and natural assumptions. The conditions for approximate controllability are investigated for the distributed second order neutral system by assuming the approximate controllability of the corresponding linear system in a Hilbert space.