1D periodic potentials with gaps vanishing at k=0

Appearance of energy bands and gaps in the dispersion relations of a periodic potential is a standard feature of Quantum Mechanics. We investigate the class of one-dimensional periodic potentials for which all gaps vanish at the center of the Brillouin zone. We characterize them through a necessary and sufficient condition. Potentials of the form we focus on arise in different fields of Physics, from supersymmetric Quantum Mechanics, to Korteweg-de Vries equation theory and classical diffusion problems. The O.D.E. counterpart to this problem is the characterisation of periodic potentials for which coexistence occur of linearly independent solutions of the corresponding Schroedinger equation (Hill's equation). This result is placed in perspective of the previous related results available in the literature.Comment: 29 pages, 4 figures, version accepted for publication in Memoirs on Differential Equations and Mathematical Physic

ShoRAH: estimating the genetic diversity of a mixed sample from next-generation sequencing data

<p>Abstract</p> <p>Background</p> <p>With next-generation sequencing technologies, experiments that were considered prohibitive only a few years ago are now possible. However, while these technologies have the ability to produce enormous volumes of data, the sequence reads are prone to error. This poses fundamental hurdles when genetic diversity is investigated.</p> <p>Results</p> <p>We developed ShoRAH, a computational method for quantifying genetic diversity in a mixed sample and for identifying the individual clones in the population, while accounting for sequencing errors. The software was run on simulated data and on real data obtained in wet lab experiments to assess its reliability.</p> <p>Conclusions</p> <p>ShoRAH is implemented in C++, Python, and Perl and has been tested under Linux and Mac OS X. Source code is available under the GNU General Public License at <url>http://www.cbg.ethz.ch/software/shorah</url>.</p

Highly Sensitive and Specific Detection of Rare Variants in Mixed Viral Populations from Massively Parallel Sequence Data

Viruses diversify over time within hosts, often undercutting the effectiveness of host defenses and therapeutic interventions. To design successful vaccines and therapeutics, it is critical to better understand viral diversification, including comprehensively characterizing the genetic variants in viral intra-host populations and modeling changes from transmission through the course of infection. Massively parallel sequencing technologies can overcome the cost constraints of older sequencing methods and obtain the high sequence coverage needed to detect rare genetic variants (<1%) within an infected host, and to assay variants without prior knowledge. Critical to interpreting deep sequence data sets is the ability to distinguish biological variants from process errors with high sensitivity and specificity. To address this challenge, we describe V-Phaser, an algorithm able to recognize rare biological variants in mixed populations. V-Phaser uses covariation (i.e. phasing) between observed variants to increase sensitivity and an expectation maximization algorithm that iteratively recalibrates base quality scores to increase specificity. Overall, V-Phaser achieved >97% sensitivity and >97% specificity on control read sets. On data derived from a patient after four years of HIV-1 infection, V-Phaser detected 2,015 variants across the ∼10 kb genome, including 603 rare variants (<1% frequency) detected only using phase information. V-Phaser identified variants at frequencies down to 0.2%, comparable to the detection threshold of allele-specific PCR, a method that requires prior knowledge of the variants. The high sensitivity and specificity of V-Phaser enables identifying and tracking changes in low frequency variants in mixed populations such as RNA viruses

Prevalence and predictors for homo- and heterosubtypic antibodies against influenza a virus

Background: The effectiveness of trivalent influenza vaccination has been confirmed in several studies. To date, it is not known whether repeated exposure and vaccination to influenza promote production of cross-reactive anti-bodies. Furthermore, how strains encountered earlier in life imprint the immune response is currently poorly understood. Methods: To determine the prevalence for human homo- and heterosubtypic antibody responses, we scruti-nized serum samples from 305 healthy volunteers for hemagglutinin-binding and -neutralizing antibodies against several strains and subtypes of influenza A. Statistical analyses were then performed to establish the association of measured values with potential predictors. Results: It was found that vaccination not only promoted higher binding and neutralizing antibody titers to homosubtypic in fluenza isolates but also increased heterosubtypic human immune responses. Both binding and neutralizing antibody titers in relation with age of the donors mirrored the course of the different influenza strain circulation during the last century. Advanced age appeared to be of advantage for both binding and neutralizing titers to most subtypes. In contrast, the first virus subtype encountered was found to imprint to some degree subsequent antibody responses. Antibodies to recent strains, however, primarily seemed to be promoted by vaccination. Conclusions: We provide evidence that vaccinations stimulate both homo- and heterosubtypic immune responses in young and middle-aged as well as more senior individuals. Our analyses suggest that influenza vaccinations not only prevent infection against currently circulating strains but can also stimulate broader humoral immune responses that potentially attenuate infections with zoonotic or antigenically shifted strains

Stability of closed gaps for the alternating Kronig-Penney Hamiltonian

We consider the Kronig-Penney model for a quantum crystal with equispaced periodic delta-interactions of alternating strength. For this model all spectral gaps at the centre of the Brillouin zone are known to vanish, although so far this noticeable property has only been proved through a very delicate analysis of the discriminant of the corresponding ODE and the associated monodromy matrix. We provide a new, alternative proof by showing that this model can be approximated, in the norm resolvent sense, by a model of regular periodic interactions with finite range for which all gaps at the centre of the Brillouin zone are still vanishing. In particular this shows that the vanishing gap property is stable in the sense that it is present also for the "physical" approximants and is not only a feature of the idealised model of zero-range interactions. \ua9 2015, Springer Basel

Sequential Bottlenecks Drive Viral Evolution in Early Acute Hepatitis C Virus Infection

Hepatitis C is a pandemic human RNA virus, which commonly causes chronic infection and liver disease. The characterization of viral populations that successfully initiate infection, and also those that drive progression to chronicity is instrumental for understanding pathogenesis and vaccine design. A comprehensive and longitudinal analysis of the viral population was conducted in four subjects followed from very early acute infection to resolution of disease outcome. By means of next generation sequencing (NGS) and standard cloning/Sanger sequencing, genetic diversity and viral variants were quantified over the course of the infection at frequencies as low as 0.1%. Phylogenetic analysis of reassembled viral variants revealed acute infection was dominated by two sequential bottleneck events, irrespective of subsequent chronicity or clearance. The first bottleneck was associated with transmission, with one to two viral variants successfully establishing infection. The second occurred approximately 100 days post-infection, and was characterized by a decline in viral diversity. In the two subjects who developed chronic infection, this second bottleneck was followed by the emergence of a new viral population, which evolved from the founder variants via a selective sweep with fixation in a small number of mutated sites. The diversity at sites with non-synonymous mutation was higher in predicted cytotoxic T cell epitopes, suggesting immune-driven evolution. These results provide the first detailed analysis of early within-host evolution of HCV, indicating strong selective forces limit viral evolution in the acute phase of infection

Inferring viral quasispecies spectra from 454 pyrosequencing reads

<p>Abstract</p> <p>Background</p> <p>RNA viruses infecting a host usually exist as a set of closely related sequences, referred to as quasispecies. The genomic diversity of viral quasispecies is a subject of great interest, particularly for chronic infections, since it can lead to resistance to existing therapies. High-throughput sequencing is a promising approach to characterizing viral diversity, but unfortunately standard assembly software was originally designed for single genome assembly and cannot be used to simultaneously assemble and estimate the abundance of multiple closely related quasispecies sequences.</p> <p>Results</p> <p>In this paper, we introduce a new <b>Vi</b>ral <b>Sp</b>ectrum <b>A</b>ssembler (ViSpA) method for quasispecies spectrum reconstruction and compare it with the state-of-the-art ShoRAH tool on both simulated and real 454 pyrosequencing shotgun reads from HCV and HIV quasispecies. Experimental results show that ViSpA outperforms ShoRAH on simulated error-free reads, correctly assembling 10 out of 10 quasispecies and 29 sequences out of 40 quasispecies. While ShoRAH has a significant advantage over ViSpA on reads simulated with sequencing errors due to its advanced error correction algorithm, ViSpA is better at assembling the simulated reads after they have been corrected by ShoRAH. ViSpA also outperforms ShoRAH on real 454 reads. Indeed, 7 most frequent sequences reconstructed by ViSpA from a real HCV dataset are viable (do not contain internal stop codons), and the most frequent sequence was within 1% of the actual open reading frame obtained by cloning and Sanger sequencing. In contrast, only one of the sequences reconstructed by ShoRAH is viable. On a real HIV dataset, ShoRAH correctly inferred only 2 quasispecies sequences with at most 4 mismatches whereas ViSpA correctly reconstructed 5 quasispecies with at most 2 mismatches, and 2 out of 5 sequences were inferred without any mismatches. ViSpA source code is available at <url>http://alla.cs.gsu.edu/~software/VISPA/vispa.html</url>.</p> <p>Conclusions</p> <p>ViSpA enables accurate viral quasispecies spectrum reconstruction from 454 pyrosequencing reads. We are currently exploring extensions applicable to the analysis of high-throughput sequencing data from bacterial metagenomic samples and ecological samples of eukaryote populations.</p

Performance of Ultra-Deep Pyrosequencing in Analysis of HIV-1 pol Gene Variation

INTRODUCTION: Ultra-deep pyrosequencing (UDPS) has been used to detect minority variants within HIV-1 populations. Some aspects of the quality and reproducibility of UDPS have been previously evaluated, but comprehensive studies are still needed. PRINCIPAL FINDING: In this study the UDPS technology (FLX platform) was evaluated by analyzing a 120 base pair fragment of the HIV-1 pol gene from plasma samples from two patients and artificial mixtures of molecular clones. UDPS was performed using an optimized experimental protocol and an in-house data cleaning strategy. Nine samples and mixtures were analyzed and the average number of reads per sample was 19,404 (range 8,858-26,846). The two patient plasma samples were analyzed twice and quantification of viral variants was found to be highly repeatable for variants representing >0.27% of the virus population, whereas some variants representing 0.11-0.27% were detected in only one of the two UDPS runs. Bland-Altman analysis showed that a repeated measurement would have a 95% likelihood to lie approximately within ±0.5 log(10) of the initial estimate. A similar level of agreement was observed for variant frequency estimates in forward vs. reverse sequencing direction, but here the agreement was higher for common variants than for rare variants. UDPS following PCR amplification with alternative primers indicated that some variants may be incorrectly quantified due to primer-related selective amplification. Finally, the in vitro recombination rate during PCR was evaluated using artificial mixtures of clones and was found to be low. The most abundant in vitro recombinant represented 0.25% of all UDPS reads. CONCLUSION: This study demonstrates that this UDPS protocol results in low experimental noise and high repeatability, which is relevant for future research and clinical use of the UDPS technology. The low rate of in vitro recombination suggests that this UDPS system can be used to study genetic variants and mutational linkage

Efficient error correction for next-generation sequencing of viral amplicons

<p>Abstract</p> <p>Background</p> <p>Next-generation sequencing allows the analysis of an unprecedented number of viral sequence variants from infected patients, presenting a novel opportunity for understanding virus evolution, drug resistance and immune escape. However, sequencing in bulk is error prone. Thus, the generated data require error identification and correction. Most error-correction methods to date are not optimized for amplicon analysis and assume that the error rate is randomly distributed. Recent quality assessment of amplicon sequences obtained using 454-sequencing showed that the error rate is strongly linked to the presence and size of homopolymers, position in the sequence and length of the amplicon. All these parameters are strongly sequence specific and should be incorporated into the calibration of error-correction algorithms designed for amplicon sequencing.</p> <p>Results</p> <p>In this paper, we present two new efficient error correction algorithms optimized for viral amplicons: (i) k-mer-based error correction (KEC) and (ii) empirical frequency threshold (ET). Both were compared to a previously published clustering algorithm (SHORAH), in order to evaluate their relative performance on 24 experimental datasets obtained by 454-sequencing of amplicons with known sequences. All three algorithms show similar accuracy in finding true haplotypes. However, KEC and ET were significantly more efficient than SHORAH in removing false haplotypes and estimating the frequency of true ones.</p> <p>Conclusions</p> <p>Both algorithms, KEC and ET, are highly suitable for rapid recovery of error-free haplotypes obtained by 454-sequencing of amplicons from heterogeneous viruses.</p> <p>The implementations of the algorithms and data sets used for their testing are available at: <url>http://alan.cs.gsu.edu/NGS/?q=content/pyrosequencing-error-correction-algorithm</url></p