An Algorithm for Counting the Number of 2n2^n-Periodic Binary Sequences with Fixed kk-Error Linear Complexity

The linear complexity and $k$-error linear complexity of sequences are important measures of the strength of key-streams generated by stream ciphers. The counting function of a sequence complexity measure gives the number of sequences with given complexity measure value and it is useful to determine the expected value and variance of a given complexity measure of a family of sequences. Fu et al. studied the distribution of $2^n$-periodic binary sequences with 1-error linear complexity in their SETA 2006 paper and peoples have strenuously promoted the solving of this problem from $k=2$ to $k=4$ step by step. Unfortunately, it still remains difficult to obtain the solutions for larger $k$ and the counting functions become extremely complex when $k$ become large. In this paper, we define an equivalent relation on error sequences. We use a concept of \textit{cube fragment} as basic modules to construct classes of error sequences with specific structures. Error sequences with the same specific structures can be represented by a single \textit{symbolic representation}. We introduce concepts of \textit{trace}, \textit{weight trace} and \textit{orbit} of sets to build quantitative relations between different classes. Based on these quantitative relations, we propose an algorithm to automatically generate symbolic representations of classes of error sequences, calculate \textit{coefficients} from one class to another and compute \textit{multiplicity} of classes defined based on specific equivalence on error sequences. This algorithm can efficiently get the number of sequences with given $k$-error linear complexity. The time complexity of this algorithm is $O(2^{k\log k})$ in the worst case which does not depend on the period $2^n$

Transcription-associated mutation promotes RNA complexity in highly expressed genes - a major new source of selectable variation

Alternatively spliced transcript isoforms are thought to play a critical role for functional diversity. However, the mechanism generating the enormous diversity of spliced transcript isoforms remains unknown, and its biological significance remains unclear. We analyzed transcriptomes in saker falcons, chickens, and mice to show that alternative splicing occurs more frequently, yielding more isoforms, in highly expressed genes. We focused on hemoglobin in the falcon, the most abundantly expressed genes in blood, finding that alternative splicing produces 10-fold more isoforms than expected from the number of splice junctions in the genome. These isoforms were produced mainly by alternative use of de novo splice sites generated by transcription-associated mutation (TAM), not by the RNA editing mechanism normally invoked. We found that high expression of globin genes increases mutation frequencies during transcription, especially on nontranscribed DNA strands. After DNA replication, transcribed strands inherit these somatic mutations, creating de novo splice sites, and generating multiple distinct isoforms in the cell clone. Bisulfate sequencing revealed that DNA methylation may counteract this process by suppressing TAM, suggesting DNA methylation can spatially regulate RNA complexity. RNA profiling showed that falcons living on the high Qinghai–Tibetan Plateau possess greater global gene expression levels and higher diversity of mean to high abundance isoforms (reads per kilobases per million mapped reads ≥18) than their low-altitude counterparts, and we speculate that this may enhance their oxygen transport capacity under low-oxygen environments. Thus, TAM-induced RNA diversity may be physiologically significant, providing an alternative strategy in lifestyle evolution

In Vivo Disruption of TGF-β Signaling by Smad7 in Airway Epithelium Alleviates Allergic Asthma but Aggravates Lung Carcinogenesis in Mouse

BACKGROUND: TGF-beta has been postulated to play an important role in the maintenance of epithelial homeostasis and the development of epithelium-derived cancers. However, most of previous studies are mainly focused on the function of TGF-beta in immune cells to the development of allergic asthma and how TGF-beta signaling in airway epithelium itself in allergic inflammation is largely unknown. Furthermore, the in vivo TGF-beta function specifically in the airway epithelium during lung cancer development has been largely elusive. METHODOLOGY/PRINCIPAL FINDINGS: To evaluate the in vivo contribution of TGF-beta signaling in lung epithelium to the development of allergic disease and lung cancer, we generated a transgenic mouse model with Smad7, an intracellular inhibitor of TGF-beta signaling, constitutively expressed in mouse airway Clara cells using a mouse CC10 promoter. The mice were subjected to the development of OVA-induced allergic asthma and urethane-induced lung cancer. The Smad7 transgenic animals significantly protected from OVA-induced asthma, with reduced airway inflammation, airway mucus production, extracellular matrix deposition, and production of OVA-specific IgE. Further analysis of cytokine profiles in lung homogenates revealed that the Th2 cytokines including IL-4, IL-5 and IL-13, as well as other cytokines including IL-17, IL-1, IL-6, IP10, G-CSF, and GM-CSF were significantly reduced in the transgenic mice upon OVA induction. In contrast, the Smad7 transgenic animals had an increased incidence of lung carcinogenesis when subjected to urethane treatment. CONCLUSION/SIGNIFICANCE: These studies, therefore, demonstrate for the first time the in vivo function of TGF-beta signaling specifically in airway epithelium during the development of allergic asthma and lung cancer

Population transcriptomes reveal synergistic responses of DNA polymorphism and RNA expression to extreme environments on the Qinghai-Tibetan Plateau in a predatory bird

Low oxygen and temperature pose key physiological challenges for endotherms living on the Qinghai–Tibetan Plateau (QTP). Molecular adaptations to high‐altitude living have been detected in the genomes of Tibetans, their domesticated animals and a few wild species, but the contribution of transcriptional variation to altitudinal adaptation remains to be determined. Here we studied a top QTP predator, the saker falcon, and analysed how the transcriptome has become modified to cope with the stresses of hypoxia and hypothermia. Using a hierarchical design to study saker populations inhabiting grassland, steppe/desert and highland across Eurasia, we found that the QTP population is already distinct despite having colonized the Plateau <2000 years ago. Selection signals are limited at the cDNA level, but of only seventeen genes identified, three function in hypoxia and four in immune response. Our results show a significant role for RNA transcription: 50% of upregulated transcription factors were related to hypoxia responses, differentiated modules were significantly enriched for oxygen transport, and importantly, divergent EPAS1 functional variants with a refined co‐expression network were identified. Conservative gene expression and relaxed immune gene variation may further reflect adaptation to hypothermia. Our results exemplify synergistic responses between DNA polymorphism and RNA expression diversity in coping with common stresses, underpinning the successful rapid colonization of a top predator onto the QTP. Importantly, molecular mechanisms underpinning highland adaptation involve relatively few genes, but are nonetheless more complex than previously thought and involve fine‐tuned transcriptional responses and genomic adaptation

Enhanced transcriptomic resilience following increased alternative splicing and differential isoform production between air pollution conurbations

Adversehealth outcomes caused by ambient particulate matter (PM) pollution occur in a 16progressive process, with neutrophils eliciting inflammation or pathogenesis. We investigated the 17toxico-transcriptomic mechanisms of PM in real-life settings by comparing healthy residents living 18in Beijing and Chengde, the opposing ends of a well-recognised air pollution (AP) corridor in China. 19Beijing recruits (BRs) uniquelyexpressed ~12,000 alternativesplicing (AS)-derived transcripts, 20largely elevating the proportion of transcripts significantly correlated with PM concentration. BRs 21expressed PM-associated isoforms (PMAIs) of PFKFB3and LDHA,encoding enzymes responsible 22for stimulatingand maintaining glycolysis. PMAIsof PFKFB3featured different COOH-terminals, 23targeting PFKFB3 to different sub-cellular functional compartments and stimulating glycolysis. 24PMAIs of LDHAhavelonger 3’UTRs relative to those expressed in Chengderecruits (CRs),allowing 25glycolysis maintenance by enhancing LDHAmRNA stability and translational efficiency. PMAIs 26weredirectly regulated by different HIF-1Aand HIF-1Bisoforms. BRs expressed more non-func-27tional Fasisoforms and a resultant reduction of intact Fasproportion is expectedto inhibit the trans-28mission of apoptotic signals and prolong neutrophil lifespan. BRs expressed both membrane-bound 29and soluble IL-6Risoforms insteadof only one in CRs. The presence of both IL-6Risoforms sug-30gested a higher migration capacity of neutrophils in BRs. PMAIs of HIF-1Aand PFKFB3were down-31regulated inChronic Obstructive Pulmonary Disease patients compared with BRs, implying HIF-1 32mediated defective glycolysis may mediate neutrophil dysfunction. PMAIs could explain large var-33iances of different phenotypes, highlighting their potential application as biomarkers and therapeu-34tic targets in PM-induced diseases, which remain poorly elucidated