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Amount of variation between a canonical gene sequence in various samples

Amount of variation between a canonical gene sequence in various samples



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Suppose there is a GeneBank DNA sequence listed that produces a specific enzyme in a specific species of plant. e.g. A terpene Synthase.

Now if someone samples various trees of the same species would one expect to get the exact same sequence each time? Or is a certain amount of variation expected from tree to tree?

The drift behind my question is: Obviously not all tress of the same species are exactly identical in phenotype. So are the causative factors seen in sequence variations of various enzymes etc.? Or can we expect the various samples to have exactly identical amino acid / DNA sequences for particular genes / enzymes.

e.g. e.g. Take this specific sequence: http://www.uniprot.org/uniprot/E3W202 If I sample from various trees of this same species and sequence this particular gene how much variation should I expect? Or would they be almost 100% identical?


Your question is quite vague so I can only give you a vague answer saying what I would expect given only the information of your question.

The vagueness mainly comes from the huge amount of functional sequences in the genome, particularly also in enzyme-coding genes, each being more or less conserved. You say

I am surprised that there is no information of how much of a within species variation there is in enzyme sequence. I am having a hard time getting this info. too.

I would say that there is no feasible way of studying this question. You will find different selective constraints on every single enzyme and breaking this down to DNA this means that every single locus can be target of different selective pressures. And even if you figured out how to answer that question comprehensively for a given species (which probably will not happen), generalising it to every single species in every ecological niche, with every possible population history and so on is close to impossible. That is why one studies sequence diversity/conservation in model organisms and mostly on a per-gene basis.

In general, without knowing any background of a species and enzyme, I would however expect two things when looking at molecular variation between individuals of that species. These are merely based on general evolutionary principles and the nature of the genetic code. Keep in mind that these are trends, meaning that many genes will match these expectations but some definitely will not due to lineage-specific evolution.

First, I would expect generally high levels of amino acid conservation (but not always identity) especially in functional enzymes of core pathways. However, this depends on the function of the gene product. If the gene is a target of balancing selection, which maintains genetic variation within a population, there can also be considerable amino acid variation.

Second, there will generally be higher levels of DNA variation because of mutations with little or no fitness effect (synonymous variation or intronic variation which tends to have lower selective pressure).

To relate this to your last question: even though I would always expect a general amount of variation, even in the amino acid sequence of core enzymes, this variation will probably not be the main reason why you see different phenotypes. Phenotypic plasticity - the differential response of a given genotype to a given environment - is often stronger in plants than in animals as plants are stationary organisms. This plasticity will probably be the main cause of striking phenotypic differences between individuals.


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Background

Ribosomal profiling, the genome-wide sequencing of ribosome-protected RNA fragments (Ribo-Seq), has been increasing our understanding of a crucial event in all living genomes: protein translation [1, 2]. Ribo-Seq results show that there exists a noticeable level of non-canonical translation in eukaryotes. This can arise from non-AUG codons, from polycistronic transcripts, and from unannotated small open reading frames of less than 100 codons (smORFs or sORFs) [3,4,5].

At the same time, the comparison of RNA-Seq and Ribo-Seq for the same biological samples allows the transcriptome-wide study of an important but often forgotten regulatory process in genome function: the regulation of translation. Typically, expression of an mRNA transcript is equated with the automatic translation of any encoded canonical ORF (of more than 100 codons). However, translation is not automatic, but is regulated, often with great relevance for organismal function, both under normal and altered conditions [6,7,8,9,10]. Translation regulation is also a key aspect of development in all animals [11] and has been studied extensively in Drosophila [12,13,14]. Drosophila embryogenesis is a highly coordinated and complex process that is completed in a time span of just 24 h [15]. During the first 2 h after egg laying (AEL), there is absence of transcription from the zygotic genome and the key developmental processes, such as establishment of the primary antero-posterior and dorso-ventral axes, are controlled purely through the translational regulation of maternal mRNA previously laid down in the egg [16, 17]. After this initial period, the embryo undergoes a “maternal to zygotic transition,” whereby the transcription and translation of the zygotic genome takes over the maternal products, a process also found in nematodes, echinoderms, and vertebrates [13, 18,19,20]. Nonetheless, the impact of translational regulation at the genome-wide scale on the whole of Drosophila embryogenesis has not yet been revealed.

Ribo-Seq results regarding non-canonical and regulated translation have been the subject of debate. While it has become accepted that both processes may occur more extensively than previously thought, there is no consensus on the actual fraction of smORFs and non-canonical ORFs whose translation is shown by Ribo-Seq [21,22,23,24,25]. The Ribo-Seq debate centers on the asymmetry between these numbers and other translational evidence, and on the interpretation of the Ribo-Seq results themselves. The most widely used counterpart of Ribo-Seq is proteomics, but the numbers of proteins and peptides detected by proteomics consistently fall short of those detected by Ribo-Seq, especially regarding non-canonical translation. For example, the most thorough proteomics study to date covering the whole Drosophila melanogaster life-cycle has detected less than 40% of all unique canonical proteins [26]. This number is further reduced to 30% of annotated smORF polypeptides, while we have previously reported that 80% of canonical and small ORFs show clear Ribo-Seq evidence of translation in a single embryonic cell line [23]. However, Ribo-Seq detects ribosomal binding, not actual peptide production. There is not a universally agreed Ribo-Seq metric unequivocally identifying productive, biologically relevant translation, as opposed to other processes such as low-level background translation, ribosomal scanning and nonsense-mediated-decay surveillance, or stochastic ribosomal binding. Bioinformatically, it is accepted that ribosomal binding above a certain level, and especially, binding showing tri-nucleotide periodicity in phase with codon triplets (phasing or framing), indicates translation of an ORF [1, 2]. A biochemical approach is to introduce modifications to the ribosomal-RNA purification, to ensure that only ribosomes engaged in productive translation are selected. For example, Ribo-Seq of polysomes (RNAs bound by several ribosomes), given that the sequential translation of polyadenylated, capped and circularized mRNAs by several ribosomes is a supramolecular feature of productive translation, excludes single ribosomes (which could be involved in low-level translation but also in other activities) [23, 27]. We have called this latter approach Poly-Ribo-Seq [23].

Here we present an in vivo Poly-Ribo-Seq study covering a time-course of Drosophila melanogaster embryogenesis. We have both improved our experimental Poly-Ribo-Seq and the subsequent data analysis pipeline, to obtain unprecedented levels of Ribo-Seq efficiency (reads mapped to ORFs) and quality, including codon framing as the hallmark of productive, biologically meaningful translation. Thus, we can ascertain translation and its regulation in vivo and across development for both canonical and non-canonical ORFs. We detect the translation of thousands of non-annotated ORFs and identify hundreds of mRNAs whose translation is highly regulated during embryogenesis. However, our results also reveal reproducible ribosomal binding not resulting in productive translation. This non-productive ribosomal binding seems to be especially prevalent amongst upstream short ORFs located in the 5′ mRNA leaders, and amongst canonical ORFs during the activation of the zygotic translatome at the maternal to zygotic transition. We suggest that this type of ribosomal binding might be due to either cis-regulatory ribosomal activity, or to defective ribosomal scanning of ORFs outside periods of productive translation.


What is RFLP?

Restriction Fragment Length Polymorphisms (RFLPs) is a molecular marker used in molecular biology for the identification of genetic variation in homologous DNA sequences. It is the first genetic marker developed for DNA fingerprinting. All organisms produce unique DNA profiles when restricted with specific restriction enzymes. RFLP serves as an important tool in producing unique DNA profiles of individuals and detection of genetic variation among them. When DNA samples are digested with specific restriction endonucleases, it yields different DNA profiles which are unique to each individual. Therefore, the principal of this method is the detection of genetic variation among organisms by restricting homologous DNA with specific restriction enzymes and analysis of the fragment length polymorphism via gel electrophoresis and blotting. Blotting patterns are unique to each organism and characterize the specific genotypes.

Following steps are involved with RFLP.

  1. Isolation of sufficient amount of DNA from samples
  2. Fragmentation of the DNA samples with specific restriction endonucleases into short sequence
  3. Separation of the resulted fragments with different lengths by agarose gel electrophoresis.
  4. Transfer of the gel profile into a membrane by Southern blotting
  5. Hybridization of the membrane with labeled probes and analysis of the fragment length polymorphism in each profile

RFLP has various applications such as diagnosis of inheritance diseases, genome mapping, criminal identification in forensic studies, paternity testing, etc.

Figure 02: RFLP genotyping


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Endoplasmic reticulum

<p>Manually curated information which has been propagated from a related experimentally characterized protein.</p> <p><a href="/manual/evidences#ECO:0000250">More. </a></p> Manual assertion inferred from sequence similarity to i

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Manual assertion inferred from sequence similarity to i

Cytosol
Endoplasmic reticulum
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Background

Alternative splicing (AS) is an important posttranscriptional process enabling a single gene to generate multiple different transcripts, also called isoforms [1, 2]. AS can increase the proteome diversity as well as modulate the stability of mRNAs by means of downstream RNA quality control (QC) mechanisms, which include nonsense-mediated decay (NMD) of the transcripts that possess premature termination codons and nuclear retention and elimination (NRE) of transcripts that contain introns [3]. In eukaryotes, the AS process removes introns from the nuclear pre-mRNAs with the help of the spliceosome, which can recognize conserved short consensus sequences within the introns and at intron-exon boundaries. More specifically, conserved dinucleotides located at the first two and the last two positions of introns in the pre-mRNAs are recognized by the spliceosome [4].

In higher eukaryotes, there are two types of identified spliceosome complex that catalyze the pre-mRNA splicing [5]. The majority of pre-mRNA introns (U2-type introns) are excised by the U2-dependent, major spliceosome that is found in all eukaryotes, whereas approximately 0.35% of human introns (U12-type introns) were removed by the U12-dependent, minor spliceosome that is found in only a subset of organisms [6,7,8]. Approximately 700 to 800 genes containing U12-type introns were identified in the human genome [9]. Unlike U2-type introns, the U12-type introns lack a polypyrimidine tract that is located upstream of the 3′ splice site (ss) however, the U12-type introns have highly conserved sequences located at their 5′ ss as well as branch sites [6]. It was found that, within the same gene, the U12-type introns co-occur with the U2-type introns, but the U12-type introns are spliced more slowly, suggesting the role of U12-type splicing in a rate-limiting step in gene expression [10]. The U12-dependent spliceosome is composed of the U11, U12, U4atac, and U6atac snRNPs, which are the functional homologs of the U1, U2, U4, and U6 in the U2-dependent spliceosome, respectively. Both U2-type and U12-type spliceosomes have the U5 snRNP [5, 8]. Although U2-type and U12-type spliceosomes have most of their protein components shared, seven protein components are unique and associated with the U11/U12 di-snRNP so that the U11/U12 di-snRNP can recognize the branch point sequences and the 5′ splice sites of the U12-type introns [8].

Mutations in the U12-type spliceosome, either in specific snRNA or in protein components, can cause diseases of very narrow tissue-specific consequences [11, 12]. Three patients possess severe isolated growth hormone deficiency (IGHD) and pituitary hypoplasia that arise from the biallelic mutations in the RNPC3 gene that encodes the 65 kDa protein component of the U12-type spliceosome [12]. Mutations in specific regions in the U4atac snRNA cause microcephalic osteodysplastic primordial dwarfism type I (MOPD I), also called Taybi-Linder syndrome (TALS). The mutations most probably result in distortion of the phylogenetically conserved stem-loop (SL) structure formed by U4atac snRNA. The distortion prevents the normal binding of a 15.5 K protein component of the spliceosome to the SL structure, thereby causing a series of downstream consequences, and eventually accumulating the immature pre-mRNAs that carry unspliced U12-type introns [13].

MicroRNA (miRNA) are small, non-coding RNA that serve as genetic regulatory elements in animals by silencing, and in rare cases enhancing, other mRNA transcripts. These single-stranded RNA are approximately 22 nucleotides in length and are involved in many processes throughout the body [14, 15]. These small mature miRNA are processed from longer pre-miRNA. Pre-miRNA forms a stem and loop structure that is processed by two RNase III enzymes: Drosha and Dicer [16]. Regulation mediated by miRNA targets mature mRNA in the cytoplasm, the miRNA will bind to the 3’UTR of the target mRNA. This binding can help to stabilize the targeted transcript but is usually followed by the interaction with RISC complex which leads to degradation of the mRNA, by this process miRNA is able to effectively silence the translation of its target [17]. Beyond degradation, miRNA also physically impairs the binding of the mRNA to the ribosome [14, 15]. It is estimated that more than 60% of all protein coding genes are regulated by miRNAs by these methods [18]. As such, miRNA has been implicated in many different complex diseases.

These diseases include many cancers, neurological diseases, cardiovascular disease, and other inheritable diseases. In cancer miRNA expression profiles have been well documented with many differences in expression between normal and tumor tissue. Typically this is shown by an overall downregulation of miRNA in tumor tissues [19]. miRNAs are able to act as either tumor suppressor genes or oncogenes depending on the targets of the specific miRNA [20,21,22,23]. The development of neurons is highly influenced by the presence of miRNA [24]. As such, the misregulation of miRNA has been implicated in Parkinson’s disease, Alzheimer’s disease, Down’s syndrome, and many other diseases [25,26,27,28,29,30,31,32,33]. The involvement of miRNA in cardiovascular diseases is similar to their involvement in neurological diseases - changes in miRNA expression can lead to arrhythmias, vascular abnormalities, unrestricted muscular growth, hypertension, and can lead to death if completely removed [34,35,36,37,38,39,40,41,42]. Other diseases that have been associated with miRNA include 5q syndrome, ICF syndrome, Rett’s syndrome, Crohn’s disease, and even deafness [43,44,45,46,47,48]. With the implications of miRNA in a multitude of complex diseases they have become important for targeted therapies and potential indicators of these diseases making them an important target for further study.

Given that such types of non-canonical splicing events of short mRNA regions and U12-type intron are important across biological systems and diseases, there is an urgent need to develop methodologies for identifying all possible non-canonical short splicing regions in cytoplasm and also looking for U12-type spliced isoforms. Most existing tools for detecting next-generation sequencing-based splicing events focus on generic splicing events. Consequently, non-canonical splicing events of short mRNA regions occurring within the cytosol and U12-type events have not yet been thoroughly investigated using bioinformatics approaches in conjunction with next-generation technologies at a genome-wide level.

We have developed a novel bioinformatics pipeline method named the Read-Split-Walk (RSW) [49] and Read-Split-Run (RSR) [50] for detecting non-canonical, short, splicing regions using RNA-Seq data. In this study, we have advanced the algorithm with an improved running speed and memory usage. We have applied RSF on human ENCODE data to characterize U12 splicing and study miRNA signatures in spliced sequences.


Author information

Present address: Novartis Institutes for Biomedical Research, Cambridge, MA, USA

These authors equally contributed: Brittany C. Michel, Andrew R. D’Avino and Seth H. Cassel.

Affiliations

Department of Pediatric Oncology, Dana–Farber Cancer Institute and Harvard Medical School, Boston, MA, USA

Brittany C. Michel, Andrew R. D’Avino, Seth H. Cassel, Nazar Mashtalir, Zachary M. McKenzie, Matthew J. McBride, Alfredo M. Valencia, Joshua Pan, Hayley J. Zullow, Nora Fortoul & Cigall Kadoch

Broad Institute of MIT and Harvard, Cambridge, MA, USA

Brittany C. Michel, Andrew R. D’Avino, Seth H. Cassel, Nazar Mashtalir, Matthew J. McBride, Alfredo M. Valencia, Joshua Pan, David I. Remillard, Caleb A. Lareau, Hayley J. Zullow & Cigall Kadoch

Biomedical and Biological Sciences Program, Harvard Medical School, Boston, MA, USA

Brittany C. Michel, Seth H. Cassel, Joshua Pan, Caleb A. Lareau & Hayley J. Zullow

Medical Scientist Training Program, Harvard Medical School, Boston, MA, USA

Seth H. Cassel & Hayley J. Zullow

Chemical Biology Program, Harvard Medical School, Boston, MA, USA

Matthew J. McBride, Alfredo M. Valencia & David I. Remillard

Foghorn Therapeutics, Inc., Cambridge, MA, USA

Qianhe Zhou, Michael Bocker, Luis M. M. Soares & Ho Man Chan

Department of Cancer Biology, Dana–Farber Cancer Institute, Boston, MA, USA

Department of Medical Oncology, Dana-Farber Cancer Institute , Boston, MA, United States

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Contributions

B.C.M., A.R.D., S.H.C., and C.K. conceived and designed the study. B.C.M. designed and performed most experiments, A.R.D. performed all bioinformatic analyses and statistical calculations. S.H.C. designed and performed GLTSCR1/1L biochemistry and contributed to ChIP-seq interpretation and analysis, Z.M.M. performed GLTSCR1/1L biochemistry, N.M. and J.P. were involved in the design and execution of experiments pertaining to ncBAF biochemistry, M.J.M, and A.M.V. were involved in the design and execution of synovial sarcoma and MRT experiments, and J.P. contributed to the analysis and interpretation of large-scale dependency data. D.I.R. synthesized dBRD9 and assisted in experimental design using dBRD9, and H.J.Z. and N.F. assisted with conducting GLTSCR1/1L biochemistry experiments. H.M.C., Q.Z. and M.B. directed the CRISPR tiling experiments and L.M.M.S. performed bioinformatic analyses of these datasets. C.A.L contributed important insights and aided in data analysis and interpretation. N.S.G. and J.E.B. supervised the development of the dBRD9 small molecule. B.C.M., A.R.D., S.H.C. and C.K. wrote the manuscript.

Corresponding author


Amount of variation between a canonical gene sequence in various samples - Biology

Temporal genetic structure in a poecilogonous polychaete: the interplay of developmental mode and environmental stochasticity

Speciation and evolutionary genetics

14 1 12 http://www.biomedcentral.com/1471-2148/14/12

2014 Kesäniemi et al. licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( http://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Creative Commons Public Domain Dedication waiver ( http://creativecommons.org/publicdomain/zero/1.0/ ) applies to the data made available in this article, unless otherwise stated. Pygospio elegans Poecilogony Population genetics Developmental mode Genetic drift Temporal Sweepstakes reproductive success Full-sibs

Temporal variation in the genetic structure of populations can be caused by multiple factors, including natural selection, stochastic environmental variation, migration, or genetic drift. In benthic marine species, the developmental mode of larvae may indicate a possibility for temporal genetic variation: species with dispersive planktonic larvae are expected to be more likely to show temporal genetic variation than species with benthic or brooded non-dispersive larvae, due to differences in larval mortality and dispersal ability. We examined temporal genetic structure in populations of Pygospio elegans , a poecilogonous polychaete with within-species variation in developmental mode. P. elegans produces either planktonic, benthic, or intermediate larvae, varying both among and within populations, providing a within-species test of the generality of a relationship between temporal genetic variation and larval developmental mode.

In contrast to our expectations, our microsatellite analyses of P. elegans revealed temporal genetic stability in the UK population with planktonic larvae, whereas there was variation indicative of drift in temporal samples of the populations from the Baltic Sea, which have predominantly benthic and intermediate larvae. We also detected temporal variation in relatedness within these populations. A large temporal shift in genetic structure was detected in a population from the Netherlands, having multiple developmental modes. This shift could have been caused by local extiction due to extreme environmental conditions and (re)colonization by planktonic larvae from neighboring populations.

In our study of P. elegans , temporal genetic variation appears to be due to not only larval developmental mode, but also the stochastic environment of adults. Large temporal genetic shifts may be more likely in marine intertidal habitats (e.g. North Sea and Wadden Sea) which are more prone to environmental stochasticity than the sub-tidal Baltic habitats. Sub-tidal and/or brackish (less saline) habitats may support smaller P. elegans populations and these may be more susceptible to the effects of random genetic drift. Moreover, higher frequencies of asexual reproduction and the benthic larval developmental mode in these populations leads to higher relatedness and contributes to drift. Our results indicate that a general relationship between larval developmental mode and temporal genetic variation may not exist.

Since the planktonic, benthic and intermediate larval developmental modes of P. elegans differ in the number of larvae produced per female, the duration of brooding time within capsules and the duration of the planktonic period, as well as in the size of larvae at release from the capsules and the presence or absence of larval swimming setae, the larvae developing via these different modes are expected to differ in their dispersal potential and their susceptibility to predation. As a result, developmental mode of larvae may affect the population genetic structure of P. elegans both spatially 42 and temporally. Although somewhat higher population genetic connectivity is found among P. elegans populations with planktonic larvae, overall a pattern of significant spatial population genetic structure and low connectivity has been found among European P. elegans populations 42 . Moreover, asexual reproduction or mixed strategies of reproduction could affect population genetic structure 42 52 53 .

Sample collection and DNA analyses

Years sampled (number of genotyped individuals)

Observed developmental modes*

Pygospio elegans sampling locations (st = sub-tidal, it = intertidal), population codes, and years sampled, with number of individuals genotyped per sample in parentheses. Salinity measured at each location, qualitative estimates of worm density and observed larval developmental modes are noted, with the most common developmental mode listed first.

*Observed larval developmental modes: B = benthic, I = intermediate, P = planktonic.

Marine intertidal sand and mud flats in the Wadden Sea (NET) and North Sea (UK) were also sampled. In both, sediment sampling was done during low tide when the sediment and worm tubes were partly exposed. In the Netherlands, we sampled a mudflat from the mainland side of Schiermonnikoog Island (site NET) and in the UK, the Drum Sands sand flat (near Edinburgh, Scotland) was sampled (Table  1 ). Even though we did not measure density of P. elegans during our collection, the difference between the intertidal marine sites and the sub-tidal Baltic Sea sites was striking. In UK and NET, the worm density was high with densely packed P. elegans tubes. In contrast, the distribution of worms was patchy and worm density was noticeably lower in the Baltic Sea. Densities from 150 to 2800 ind. m 2 have been observed in the Northern Baltic Sea previously (pers. obs. CB), whereas 11 000 ind. m 2 is common at the UK site 40 41 .

Adult worms were preserved individually in ethanol until DNA extraction. DNA was extracted using Qiagen chemicals and a Kingfisher magnetic processor (Thermo Fisher Scientific), after which the samples were genotyped using eight highly polymorphic microsatellite markers following protocols described in 54 .

To examine proportions of genetic variation explained by both spatial and temporal variation, analysis of molecular variance (AMOVA) was performed with two different sample sets using Arlequin (20 000 permutations). First, an analysis was carried out grouping the samples according to sample year (4 groups: 2008, 2009, 2010 and 2011). Second, the samples were grouped according to population (7 groups: temporal samples from the same population combined). To further investigate temporal genetic variation within the different populations, pair-wise FST values (using Arlequin and 10 000 permutations) and Jost’s 59 pairwise Dest values were calculated (using the R package DEMEtics, 3000 permutations 60 ) among the temporal samples within each population (temporal FST/Dest). Pair-wise comparisons of FST were also calculated among populations collected in the same year (2008, 2009, 2010). Linearized pair-wise FST values were analyzed with PCA in GenAlEx v. 6.5 61 to visualize differences among the samples and populations.

Genetic variation in the temporal samples is summarized in Table  2 . Genetic diversity was relatively high in most populations, lowest in Finland (FIF, HE from 0.614 to 0.655) and highest in the UK (HE from 0.797 to 0.799). There were fluctuations in allelic richness and heterozygosity among samples within most populations, with UK, DKR and FIF showing the most consistent values among samples (Table  2 ). Fluctuations in diversity did not follow any particular pattern. For example, in DKV diversity (HE, gene diversity, allelic richness) was lower in 2010 compared to the previous years, but in DKH diversity was higher in 2010 than in previous years. Most fluctuations in genetic diversity within populations were not of high magnitude, except in DKV, where there was a decline in variation from 2008 to 2010, and in NET, where there was a noticeable increase in variation in the 2011 sample. The fluctuations among samples within a population are indicated best by the numbers of private alleles (alleles observed only in one temporal sample) which were calculated for each population separately and, unlike allelic richness, are not comparable among populations but only among temporal samples within a population. Most extreme increases in the number of private alleles were seen in DKH from 2008 to 2010 (3.5 to 5.3), and in NET from the 2009 and 2010 samples (2.0 and 2.3, respectively) to the 2011 sample (4.4, Table  2 ). Overall, allelic richness was highest in UK, the population with only planktonic larvae, in line with our findings from a previous study of additional populations from a broader geographic scale 42 .

Genetic diversity and sibship patterns in the temporal samples

PrivateARwithin site

Observed (HO) and expected (HE) heterozygosity, gene diversity (GD) and allelic richness (AR) based on a sample size of 40 for each sample (here, N = number of genes used in the rarefaction method of HP-rare). Private allele richness (PrivateAR) was calculated for temporal samples of each population separately (here, N [in italics] varies among populations, making the values comparable only among temporal samples within a population). Inbreeding coefficients (FIS, with significant values in italics) were calculated for each temporal sample. Number of full-sib families (FS) estimated within each temporal sample and within the combined dataset for each population (all) are listed. Samples marked with *have families consisting of more than two members (see text). In the combined data sets, cross-year full-sib families were found unless indicated.

Temporal and spatial genetic structure

AMOVA analyses (Table  3 ) indicated that the variation among the different populations was significant (3.61% of variation explained), and that this population structure was similar in different years (AMOVA grouping samples by year showed non-significant variation among years). Similarly, global FST values in different years were not significantly different (2008: 0.034, 2009: 0.046, 2010: 0.029, P =𔁚.617). Genetic structure between populations was also evident in our analysis of (within year) population pair-wise FST but there was temporal variation in structure among the Baltic Sea populations (Additional file 1 ). For example, in Denmark, most population pair-wise comparisons within a year were significant, however in 2010, DKV and DKH have non-significant pair-wise FST. In Finland, the pair-wise FST values between FIA and FIF are low each year (FST <𔁚.01), and significant in 2008 and 2010, but not in 2009 (Additional file 1 ).

AMOVA results of spatial and temporal variation in Pygospio elegans

Temporal groups (samples grouped by year)

Temporal groups consist of samples from different populations grouped by sampling year (4 groups: 2008, 2009, 2010, 2011) and spatial groups consist of temporal samples grouped according to population (7 groups).

Among populations within years

Geographical groups (samples grouped by population)

Among temporal samples within populations

Pair-wise FSTvalues for among populations comparisons within years. These results show significant genetic structure among the populations: the few exceptions are among some geographically close populations (as described in the text).

When the temporal samples were grouped according to population in AMOVA (Table  3 ), we found not only significant among population (spatial) variation (2.85% of variation explained), but also low but significant temporal variation within populations (0.85%). To clarify how specific temporal samples differed, we examined the samples from each population separately in pair-wise comparisons of FST and Dest (Table  4 ). In these analyses, significant differences were found between temporal samples in some but not all populations, and the FST and Dest values were generally low. There were no differences in temporal samples from UK and DKH. When significant differences between temporal samples were indicated, these were found between samples taken in subsequent years (2009 vs. 2010 in FIF, NET, DKR and DKV) as well as between samples from longer time periods (2008 vs. 2010 in FIA). Analysis of either FST or Dest indicated the same patterns of differentiation, except in DKR (Table  4 ). The largest differences among temporal samples was seen in the NET population, in which the 2011 sample was significantly differentiated from the two previous samples (2009 and 2010), which did not differ from each other (FST and Dest). Likewise, PCA analysis of linearized FST showed that in most cases, temporal samples from the same population clustered together (Additional file 2 ). However, NET2011 did not cluster with other temporal samples from NET and was placed between clusters of the Danish and UK samples, not grouping clearly with either (Additional file 2 ).

Temporal pair-wise FST/Dest values for samples within each population

Results of PCA analysis on linearized pair-wise FST. Differences among the temporal samples and populations are visualized.

Additional NET2011 FST/Dest analyses

Pair-wise FST/Dest values comparing the NET2011 sample (in bold) to previous temporal samples at the same site, as well as samples collected from two Dutch (NLB2010 & NLH2010) and two French (FRC2010 & FRS2010) populations in the previous year (data from 42 ) and to four 2010 samples from this study (DKR2010 DKV2010 DKH2010 UK2010).

Results of the STRUCTURE analysis used to clarify relationship of the NET2011 sample (K =𔁝)

Results of the STRUCTURE analysis used to clarify relationship of the NET2011 sample (K =𔁝). Each column in the barplot represents an individual genotype with cluster assignment denoted by different colours. Note the clear difference in assignment between the NET2011 sample and previously sampled individuals at the same location. NET2011 clusters together with samples collected from two Dutch and two French populations sampled in 2010 (data from 42 ) and is distinct from UK samples (this study).

Sibship analysis and relatedness

Full-sibs were found within almost all temporal samples, but not in FIF and UK (Table  2 ). In most samples, full-sibs were pairs of individuals, but larger families were found in two Danish populations. In DKR2009 and DKV2009 samples, full-sib families of five and three individuals, respectively, were identified. In NET, full-sib pairs were seen in 2009 (one pair) and 2010 (four pairs), but none were observed in the 2011 sample. When temporal samples within a population were combined to identify cross-year full-sibs, typically the same full-sib families were identified as in the analyses of each temporal sample separately, but also additional full-sib families were seen. However, cross-year full-sibs (full-sib pairs or families consisting of individuals from different temporal samples) were found only in three Baltic Sea populations (FIA, DKR and DKV). In the analyses of DKR and DKV, in addition to full-sib pairs, two larger cross-year full-sib families were identified (DKR: families of five and four individuals, DKV: families of three and four individuals). Even though no full-sib families were identified in the temporal samples in FIF and UK when they were analyzed separately, in each of these populations one full-sib pair was identified when the temporal samples were combined. In both cases, the full-sibs identified were individulas within a single temporal sample (no cross-year full-sibs), indicating the effect of sample size on identifying potentially highly related individuals.

Mean relatedness values for each sample are shown in Figure  2 . In Finland and UK, the values were relatively stable among temporal samples, and the largest fluctuations were seen in two Danish sites (DKR & DKH) and in Netherlands. In DKR, the relatedness was significantly higher in 2009 compared to the 2010 sample (Mann–Whitney U test P =𔁚.031). In NET, the 2011 sample relatedness is significantly lower than in the previous years (NET 2010 & NET 2011: Mann–Whitney U -test P =𔁚.014 NET 2009 & NET 2011: P =𔁚.002), while 2009 and 2010 values were similar (Mann–Whitney U -test P =𔁚.432). In other sites, the relatedness values among temporal samples (pair-wise tests) were not significantly different.

Mean relatedness of individuals in the temporal samples

Mean relatedness of individuals in the temporal samples. Relatedness estimates (with 95% confidence intervals) were calculated in ML-Relate taking potential null alleles into account. Population codes and sampling years are described in Table  1 . Symbols are used to separate populations (same symbols are used for temporal samples within a population).

Effective population size

The different methods used for estimating contemporary Ne produced somewhat different results (Table  6 ): MLNE estimation assuming no gene flow resulted in the highest estimates, whereas the same method allowing migration (MLNEopen) gave the lowest estimates. Overall, the values were low in comparison to estimations of population census sizes based on the densities of P. elegans in our sampling sites. Also, the 95% confidence intervals were wide and overlapping estimates for the different populations. With MLNE (without migration) the Ne estimations were similar in most sites (ranging from 142.1 to 355.5) except in UK, where a higher Ne was estimated (1117.8). With the Moment based temporal method (MBT), there was more variation among the estimates for the Baltic Sea populations, but the confidence intervals were overlapping, so the differences in estimated Ne are not significant. However, when comparing NET and the UK, the UK site has significantly higher Ne when estimated by MBT and MNLEopen methods. The overall trend seen in data is that the Ne estimates were highest in the strictly planktonic population, UK, and lowest in NET.


Amount of variation between a canonical gene sequence in various samples - Biology

The fungal genus Mixia (Protomycetaceae, Taphrinales, Ascomycetes) was introduced by Kramer [ 1 ] based on a single species, Taphrina osmundae [ 2 ], parasitic on fronds of the Japanese royal fern Osmunda japonica in Japan. Subsequently, the new family Mixiaceae (Protomycetales) was also proposed by Kramer [ 3 ] to accommodate the single genus Mixia . In those days, almost all mycologists believed that Mixia is a member of the ascomycetes, related to the species of the Protomycetales or Taphrinales. In 1995, it was reported that Mixia osmundae is not a member of Ascomycota but of Basidiomycota, based on molecular (18S rRNA sequence analysis) and morphological (light microscopic, standard electron microscopic and transmission electron microscopic observations on sporogenous cells) characters [ 4 ]. According to the classification of Assembling the Fungal Tree of Life (AFTOL), at present, M. osmundae has been accommodated in the Mixiales, Mixiomycetes, Pucciniomycotina and Basidiomycota, [ 5 ] and has no close relatives [ 6 ]. It takes a unique position in basidiomycete phylogeny as an enigmatic fungus. We previously reported an initial genome assembly of this species comprising 4408 contigs (a total of 3 019 501 nt) [ 7 ].

In the present study, we refined the genome assembly with additional sequencing, and annotated coding genes and their transcription start sites (TSSs), based, respectively, on RNA-seq [ 8 ] and the oligo-capping method [ 9 ] by using the Illumina GAIIx sequencer. For the annotated genome, we created a detailed nucleosome map by sequencing more than 60 million mono- and dinucleosomal DNA fragments, and investigated the nucleosomal organization around genes showing distinct levels of expression.

A nucleosome consists of an octamer of histones, around which genomic DNA is wrapped in 1.65 turns [ 10 ]. In recent years, studies have revealed a large number of patterns and rules for nucleosomes in relation to transcriptional activity. Recent findings include strong conservation of the nucleosome positions in gene promoter regions when compared with other genomic regions [ 11 – 14 ], and distinct conservation in nucleosome positioning between gene promoter and gene body regions [ 15 ], leading to proposals to use nucleosome positioning to categorize gene promoters [ 16 , 17 ]. Although in vitro studies revealed the influence of DNA sequences of core histones on nucleosome positioning, in vivo studies have demonstrated that ATP-dependent trans-acting factors play a major role in arranging nucleosomes in living cells [ 18 – 23 ]. All these patterns and rules observed in nucleosome positioning on active gene promoters suggest a functional link to transcription, and there is a clear correlation between nucleosome positioning and gene expression. It remains to be determined, however, whether changes in nucleosome positioning are a major driving force in the evolution of gene expression [ 16 , 24 , 25 ] or not [ 26 , 27 ].

Previous comparative studies of nucleosome positions were performed mainly using Saccharomycotina species (ascomycetous yeasts) [ 16 , 24 – 27 ]. Although some genome sequences of Basidiomycota species have been published [ 28 – 35 ], there is no nucleosome mapping data for the basidiomycetes. Comparison of nucleosome positioning between the ascomycetes and phylogenetically distant M. osmundae is expected to provide valuable information about the issue (i.e . whether nucleosome positioning is a major force in the evolution of gene expression). In this study, we identified mono- and dinucleosome positions on the genome of M. osmundae and investigated their features around the TSSs in relation to the level of transcriptional activity.

3. Results and discussion 3.1. Comparison of coding genes between Mixia osmundae and other fungal species

Assembly of the newly sequenced and previous datasets resulted in 283 contigs (a total of 13 393 708 nt). These 283 DNA sequences have been deposited to the DDBJ database under accession numbers BABT02000001–BABT02000283. On the newly assembled genome, 6726 protein-coding sequences (CDSs) were identified by using RNA-seq (see §5 and electronic supplementary material, table S1).

The 6726 protein-coding sequences were aligned to the protein sequences of 80 fungal organisms using the BLASTP program in Fungal Genomes Central at NCBI ( http://www.ncbi.nlm.nih.gov/projects/genome/guide/fungi/ electronic supplementary material, table S2). The BLASTP search revealed that 5399 (80.3%) of the 6726 CDSs had similar amino acid sequences with E -value < 10 −5 among the fungal genes. Among the 5399 sequences, 4908 (90.9%), 402 (7.4%), 55 (1.0%) and 34 (0.6%) showed the highest similarity with proteins of Basidiomycota, Pezizomycotina (Ascomycota), Saccharomycotina (Ascomycota) and Taphrinomycotina (Ascomycota), respectively ( figure 1 ). At the genus level, 1213 (22.5%), 753 (13.9%) and 665 (12.3%) showed the highest similarity with proteins of genera Melampsora , Rhodotorula and Puccinia , respectively ( figure 1 ). As these three genera belong to Pucciniomycotina in Basidiomycota, M. osmundae is probably a member of Pucciniomycotina. Figure 1.

Pie chart of the genera with which each CDS of Mixia osmundae showed the highest similarity. The BLASTP program at NCBI ( http://blast.ncbi.nlm.nih.gov/Blast.cgi ) was used for the protein sequence similarity search. A total of 5399 CDSs ( E -value < 10 −5 ) were analysed.

3.2. Comparison of size distribution of mono- and dinucleosomes of Mixia osmundae with Aspergillus fumigatus and Saccharomyces cerevisiae

We determined the positions of the 30 381 113 mono- (range 80–230 nt) and 27 443 027 dinucleosomes (range 200–400 nt) on the genome of M. osmundae by mapping the mono- and dinucleosomal DNA fragments sequenced by the Illumina GAIIx. The nucleosome position data can be downloaded at http://www.iu.a.u-tokyo.ac.jp/

hnishida/data_Mixia.zip . The size distribution of the mononucleosomal DNA fragments had two peaks at 132 and 150 nt, whereas that of the dinucleosomal DNA fragments had only a single peak at 300 nt ( figure 2 ). Figure 2.

Histograms of ( a ) mononucleosomal and ( b ) dinucleosomal DNA fragment lengths of Mixia osmundae . The 30 386 916 mononucleosomal and 27 740 353 dinucleosomal DNA fragments were mapped to the genome. The distribution of the mononucleosomal DNA fragment lengths showed two peaks at 132 and 150 nt, whereas that of the dinucleosomal DNA fragment lengths showed only a single peak at 300 nt.

As we reported previously, the double-peak distribution of mononucleosomal DNA fragments was observed in the filamentous ascomycete Aspergillus fumigatus [ 36 ]. The distribution of A. fumigatus mononucleosomal DNA fragments had two peaks at 135 and 150 nt [ 36 ]. In contrast, Saccharomyces cerevisiae had only a single peak at 163 nt [ 37 ]. In addition, the average mononucleosomal DNA length of 12 Saccharomycotina species is between 160 and 175 nt [ 16 ]. The nucleosomal DNA fragment length distribution depends on the micrococcal nuclease (MNase) treatment [ 38 ]. Based on the DNA ladder pattern on the agarose gel electrophoresis (electronic supplementary material, figure S1), we recognized that the digestion levels of MNase are similar between M. osmundae and S. cerevisiae . Thus, although A. fumigatus is phylogenetically closer to Saccharomycotina than M. osmundae , the distribution shape and size of mononucleosomal DNA fragments suggest that M. osmundae is closer to A. fumigatus than the ascomycetous yeasts (Saccharomycotina). This result adds support to the hypothesis that nucleosome positioning in fungal species has evolved primarily through neutral drift [ 26 , 27 ] and therefore fungi have species-specific nucleosome arrangements.

As we observed a loss of the longer peak at 150 nt in the highly transcribed (50 genes of highest level of expression) gene promoters of A. fumigatus [ 36 ], we examined whether the size of the mononucleosomes changes between the 50 genes of highest and lowest levels of expression in the upstream and downstream regions of the TSSs. However, in M. osmundae , the mononucleosomal DNA length distribution remained nearly invariant between distinct expression levels in both the upstream and downstream regions of the TSSs (electronic supplementary material, figure S2). The Mann–Whitney U -test yielded p -values of >0.7 and >0.11, respectively, for the upstream and downstream regions of the TSSs.

3.3. Comparison of dinucleosomes suggests a longer linker region in Mixia osmundae than in Aspergillus fumigatus

Prolonged treatment with MNase results in nearly complete cleavage of the total chromatin into mononucleosomes [ 39 ], suggesting that MNase-digested dinucleosomes are precursors of mononucleosomes [ 40 ]. Thus, dinucleosomal DNA fragments consist of two mononucleosomal DNAs and the linker DNA they flank. The distribution of dinucleosomal DNA lengths of M. osmundae had a single peak at 300 nt, whereas that of A. fumigatus had only a single peak at 285 nt [ 36 ]. As the mononucleosomal DNA lengths are nearly the same between the two fungi, the nucleosomal linker DNA lengths of M. osmundae appear to be approximately 15 nt longer than those of A. fumigatus .

3.4. Sizes of the mono- and dinucleosomes converge to their canonical sizes with increasing level of piles

To investigate potential differences in the nucleosome sizes between loosely and well-positioned nucleosomes, we examined how the double-peak distribution of mononucleosome lengths changes with increasing pile level (see §5). Interestingly, the sizes of both short- and long-mononucleosome groups converged to their respective mean sizes as the piles increased ( figure 3 ). This convergence to the mean size was also observed in highly positioned dinucleosomes ( figure 4 ). These sizes to which highly positioned mono- and dinucleosomes converge may be their canonical sizes taken to optimize functionality related to transcription, and the increase of the canonical portion may be required to optimize the nucleosome organization for the processes. Figure 3.

The sizes of both short and long mononucleosome groups converged to their respective mean sizes as the number of piles increased. Normalized distributions of mononucleosomal DNA fragments were compared between distinct pile levels. The same number (27 801) of mononucleosomal DNA fragments was used to compute the frequency distribution of each pile subset. The Mann–Whitney U -test yielded p -values of 0.005 or less in all the pairwise size comparisons. Red line, 10 piles yellow line, 5 piles green line, 3 piles blue line, 2 piles black line, 1 pile.

The sizes of dinucleosomes converged to the mean size with increasing pile level. Normalized distributions of dinucleosomal DNA fragments were compared between distinct pile levels. The same number (24 798) of dinucleosomal DNA fragments was used to compute the frequency distribution of each pile subset. The Mann–Whitney U -test yielded p -values of 0.0008 or less in all the pairwise size comparisons. Red line, 10 piles yellow line, 5 piles green line, 3 piles blue line, 2 piles black line, 1 pile.

3.5. The dinucleosome position profile clarifies nucleosome depletion and suggests a longer linker DNA region in the upstream region of transcription start sites

The midpoint of a mononucleosome corresponds to the centre of the nucleosome core, whereas the midpoint of a dinucleosome lies in the linker DNA region flanked by two nucleosomes. Therefore, the peaks and bottoms of the midpoint profile of the mononucleosomes ( figure 5 ) coincide, respectively, with the bottoms and peaks of the midpoint profile of dinucleosomes ( figure 6 ). On the other hand, the interval between neighbouring peaks in the midpoint profile of dinucleosomes ( figure 6 ) was identical to that of mononucleosomes ( figure 5 ), indicating that the dinucleosomal DNA fragments were generated at random by MNase digestion. This result supports that MNase-digested dinucleosomes are precursors of mononucleosomes [ 40 ]. Figure 5.

Profiles of the midpoints of highly positioned mononucleosomes of Mixia osmundae around the transcription start sites. The position profile of midpoints of highly positioned mononucleosomes in the vicinity of the TSS is compared between the three groups of genes showing distinct levels of expression. The nucleosomal midpoints of five or more piles were used.

Profiles of the midpoints of highly positioned dinucleosomes of Mixia osmundae around the transcription start sites. The position profile of midpoints of highly positioned dinucleosomes in the vicinity of the TSS is compared between the three groups of genes showing distinct levels of expression. The nucleosomal midpoints of five or more piles were used.

The nucleosome organization of M. osmundae around the TSSs ( figure 5 ) was nearly identical to that of S. cerevisiae [ 18 , 23 ]. The highest peak of mononucleosome midpoints is found at position +1 on the downstream side of the TSS. Peak height decreases as the position moves away from the TSS on both the up- and downstream sides. The nucleosome position profile was sharper in the downstream region than in the upstream region of the TSS. Interestingly, in the upstream region of the TSS, genes with low expression levels showed a more clear phasing pattern of nucleosomes than genes with high levels of expression ( figure 5 see §5 for the three sets of genes showing distinct levels of expression).

Nucleosome depletion upstream of the TSS was observed as a loss of dinucleosomes mapped at the positions −1 and +1. Note that the degree of loss of dinucleosomes mapped at the −1 and +1 positions increased with increasing level of gene expression. A χ 2 test of frequencies of dinucleosomes mapped around position −1 (−200 to −1 nt from the TSS) yielded p -values of approximately 0 and <10 −15 , respectively, between the gene sets of low and medium expression levels, and between the sets of medium and high expression levels. The loss of dinucleosomes mapped to the −1 and +1 positions strongly suggests that MNase digests chromatins near nucleosome-depleted regions more quickly than other regions. It was supported by the fact that the interval size between the peaks of the −1 and +1 positions in the nucleosome midpoint profile ( figure 5 ) was longer than the others.

3.6. Mono- and dinucleosome organization around the translational termination sites

Since a previous study reported a phasing pattern of nucleosomes around the transcription termination sites for a subset of yeast genes [ 41 ], we examined the mono- and dinucleosome organization around the 3′ ends of ORFs of the three gene sets of distinct expression levels. Some phasing was observed in regions internal to genes in both mono- and dinuceosome maps for the gene group of high expression (electronic supplementary material, figures S3 and S4). In addition, we found a prominent phasing of the nucleosome penultimate to the 3′ end of ORF, as observed earlier [ 41 ]. Surprisingly, the dinucleomes were clearly depleted in regions immediately downstream of the 3′ ends of ORFs. This notable depletion of dinucleosomes near the translational termination sites supports the regulation mechanism of terminal nuclesomes in transcriptional termination [ 42 ], and may be related to disassembling of the terminating RNA polymerase, assembling of anti-sense pre-initiation complexes and/or a gene looping mediated by transcription factor IIB (TFIIB) [ 41 ].

3.7. Enriched and depleted dinucleotide sequences in and around Mixia osmundae mono- and dinucleosomes

Previous studies reported that sequences rich in guanine (G) and cytosine (C) favour core nucleosomes, while sequences rich in adenine (A) and thymine (T) disfavour them, although some variations of preferred sequences exist between species [ 25 ]. We examined the biases of all 16 dinucleotide sequences in and around the midpoints of the mono- and dinucleosome positions by comparing the profiles of distances to the closest dinucleotides (see electronic supplementary material, figure S5, for definition of the closest dinucleotide). The enriched and depleted dinucleotides in and around the midpoints of the mononucleosome of M. osmundae showed features common to those of humans [ 22 ] (i.e. G/C-rich and A/T-rich sequences tend to be enriched, respectively, at the centres and edges of the mononucleosomes). We also examined dinucleotide enrichment in and around the dinucleosomes. Interestingly, there were clear preferences of dinucleotides associated with dinucleosomes, and the dinucleotides enriched or depleted at the midpoints of dinucleosomes differed from those found in and around the midpoints of mononucleosomes (figures 7 and 8 ). We believe this is the first report of DNA sequence preference of the nucleosomal linker DNA regions, inferred from the direct DNA sequence data. The dinucleotide sequence distributions are very different between the nucleosome-bound region and the nucleosomal linker region (figures 7 and 8 ). For example, the dinucleotide sequences CC, CG, GC and GG are enriched in the nucleosomal linker regions ( figure 8 ), while AT and TA are depleted in the nucleosomal linker regions ( figure 8 ). These dinucleotide sequences, AT and TA, are enriched in the nucleosome core regions ( figure 7 ), while they become enriched in regions away from the midpoints of dinucleosomes towards their edges ( figure 8 see electronic supplementary material, figure S6, for the profile in extended regions from the midpoints). Figure 7.

Enriched and depleted dinucleotides around the midpoints of highly positioned mononucleosomes of Mixia osmundae . Composite profiles of the distances between midpoints of highly positioned (five or more piles) mononucleosomes and their closest dinucleotides are shown. The x - and y -axes represent, respectively, the position relative to the TSS and the normalized frequencies of the distances from the nucleosomal midpoints to the closest dinucleotides. The frequencies of the distances were normalized to the average frequencies at all the genome positions and each of the 16 profiles was normalized to 100.

Enriched and depleted dinucleotides around the midpoints of highly positioned dinucleosomes of Mixia osmundae . Composite profiles of the distances between midpoints of highly positioned (five or more piles) dinucleosomes and their closest dinucleotides are shown. The x - and y -axes represent, respectively, the position relative to the TSS and the normalized frequencies of the distances from the midpoints of dinucleosomes to the closest dinucleotides. The frequencies of the distances were normalized to the average frequencies at all the genome positions and each of the 16 profiles was normalized to 100.

Since previous studies [ 43 , 44 ] used dinucleotide frequencies around the nucleosome midpoints to identify the dinucleotides favoured or disfavoured by the nucleosome cores, we also examined the dinucleotide frequencies around the highly positioned nucleosome midpoints (as shown in electronic supplementary material, figures S7 and S8). Some dinucleotides showed profiles distinct from that of distances to the closest dinucleotides. For example, enrichment of CC, CG, GC and GG found in the profile of distances to the closest dinucleotides was not observed in that of dinucleotide frequencies around midpoints of mononucleosomes, and depletion of AA and TT in the profile of distances to the closest dinucleotides is not observed in that of dinucleotide frequencies around the midpoints of dinucleosomes. This difference occurred since only a single dinucleotide closest to the midpoint of a nucleosome was considered in the profile of distances to the closest dinucleotides, whereas all the dinucleotides in regions flanking the midpoint were counted in computing dinucleotide frequencies. Thus, this difference between the two profiles indicates which of the closest dinucleotide to a position or the overall distribution around the position is a major determinant in the positioning of nucleosomes. Since many previous studies reported the enrichment of C/G-rich dinucleotides and depletion of A/T-rich dinucleotides in the nucleosome cores, this observation suggests that the closest dinucleotide is more important than its overall distribution in nucleosome positioning.

By effectively using the high-throughput datasets of mono- and dinucleosomal DNA fragments, we have identified characteristics of nucleosomal arrangement and linker DNA regions in the genome of the basidiomycete M. osmundae, which holds a unique phylogenic position in the evolution of fungal species. The double-peak distribution of mononucleosomal DNA lengths of M. osmundae resembles that of A. fumigatus and clearly differs from the single-peak distribution of ascomycetous yeasts. This strongly suggests that nucleosome positioning has evolved primarily through neutral drift in fungal species. Thus, the divergence of nucleosome positioning is not correlated with that of gene expression.

The profile of dinucleosomal midpoints around the TSS presents a unique view of the nucleosome-depleted region, which was observed as a loss of the first peak on the upstream side of the TSS. The degree of loss of the peak clearly correlates with gene expression levels. The loss of dinucleosomes mapped in the position upstream of the TSS implicates an extended size of linker DNAs in this region, and thus quicker digestion of the longer linkers when compared with those of other regions. Comparison of the phasing patterns of mono- and dinucleosomes around the TSS revealed random cleaving of dinucleosomal DNA fragments. This gives additional support to our previous observation that dinucleosomes are precursors of mononucleosomes prior to MNase digestion.

Importantly, we found clear sequence biases in linker DNA regions mapped by the midpoints of dinucleosomes. The propensity of the linkers to digestion is likely to be regulated at least in part by the arrangement of DNA sequences. This association of DNA sequences with uncleaved linkers, in addition to the unique arrangement of dinucleosomes near the TSS, may implicate some specific regulatory mechanism for the midpoint linkers of dinucleosomes.

We have demonstrated the great utility of dinucleosomes in investigating nucleosomal organization of the M. osmundae genome. Extension of this approach to other species and comparative studies will reveal important aspects of evolution of nucleosome organization.

5. Material and methods 5.1. Mixia osmundae culturing

Mixia osmundae IAM 14324 (i.e. JCM 22182, CBS 9802) was used in this study (for strain data, see [ 6 ]). The strain was cultivated in YM broth (yeast extract, 3 g malt extract, 3 g peptone, 5g dextrose, 10 g water, 1 l) at 25°C to an absorbance at 600 nm of 0.7 ml −1 .

Genome sequencing was performed using the massively parallel Roche GS FLX Titanium DNA sequencer. Assembly of the reads was performed using the N ewbler program (v. 2.3). The 5′-end sequences were determined using the oligo-capping method [ 9 ]. The cDNAs from total mRNA were sequenced using the Illumina Genome Analyzer IIx.

Cells were collected from 50 ml culture and resuspended in 250 µl of NP buffer (1 M sorbitol, 50 mM NaCl, 10 mM Tris–HCl at pH 7.4, 5 mM MgCl2, 1 mM CaCl2 and 0.075% Nonidet P40, with freshly added 1 mM β-mercaptoethanol and 500 µM spermidine). Cell suspensions were homogenized using a Covaris S2 manufacture. The homogenate was filled up to 2 ml with NP buffer and was divided into six aliquots of 300 μl each, and then MNase was added at concentrations of 0, 0.1, 0.5, 1, 3 and 5 U per sample. The digestion reactions were incubated at 37°C for 30 min, and were stopped by adding sodium dodecylsulphate to a final concentration of 1 per cent and ethylene diaminetetraacetic acid to a final concentration of 10 mM. Five microlitres of proteinase K solution (20 mg ml −1 ) was added and then the mixtures were incubated at 56°C for 1 h. Samples were phenol/chloroform-extracted, ethanol-precipitated and treated with RNase. To isolate the nucleosomal DNA fragments, electrophoresis was carried out on a 2 per cent agarose gel (electronic supplementary material, figure S1). The mononucleosomal and dinucleosomal DNA bands were excised and purified using the QIAquick Gel Extraction Kit (QIAGEN). Both ends (76 bases) of the DNA fragments treated with 5 U of MNase were sequenced using the Illumina GAIIx. The short read pairs were aligned to the genomic contigs of M. osmundae using SOAP2 [ 45 ]. Only uniquely mapped read pairs were used for the analysis.

5.4. Highly positioned mono- and dinucleosomes

Valouev et al . identified characteristics of mononucleosomes in the human genome, effectively using highly positioned nucleosomes, which were redundantly mapped (or piled) by high-throughput sequencing data of MNase-processed human genomic DNA [ 22 ]. They reported a profile of consistently positioned nucleosomes, correlation of phasograms (histograms of sizes of the nucleosome core + linker) with expression level, and sequence preferences associated with nucleosome cores. Following their approach, we investigated nucleosome positions redundantly mapped by the mono- and dinucleosome DNA fragments. Unless otherwise specified, we used subsets of the midpoints of mono- and dinucleosomes and positions of fragmental DNAs mapped by five or more sequence pairs (5-pile subsets) in the analyses (1 916 208 and 1 714 131 midpoints of mono- and dinucleosomal DNA fragments, respectively).

5.5. RNA-seq-based gene prediction

Using AUGUSTUS [ 46 ], a gene-prediction program based on alignment of expressed sequences to the genome, we determined the coding regions (CDSs) of the genes expressed on the genome of M. osmundae . We obtained 42 706 936 single reads (76 nt) by sequencing a total RNA sample of M. osmundae using Illumina GAIIx. Single reads of 34 962 178 could be aligned to the genome allowing five or less mismatches using BLAT [ 47 ]. Based on the coordinates mapped by the expressed sequences, AUGUSTUS predicted a total of 6569 genes (6462 complete and 107 partial genes). Since 148 genes showed alternative splicing forms, a total of 6726 transcripts were detected among the 6569 gene loci. We used the gene model trained for Ustilago , the closest basidiomycete to M. osmundae among those available in AUGUSTUS. A total of 13 546 fragments (1 kb each) of the M. osmundae genome contigs were aligned to the genome of Ustilago maydis 521 by BLAST [ 48 ]. About one-third (4157) of the 1 kb fragments of M. osmundae could be aligned to the Ustilagao genome at 68 ± 6% over 346 ± 230 nt.

5.6. Determination of levels of gene expression based on RNA-seq

The expression levels of the 6462 complete genes were determined based on the alignment of the RNA-seq reads to the genome. The expression level, in RPKM (reads mapped per kilobase of mature transcript per million of reads) [ 49 ], was computed counting the number of the reads mapped to the exons of each gene. According to the levels of expression thus determined, we made three gene groups of low (rank: 1–1000 0.2 ≦ RPKM ≦ 14.6), medium (rank: 2732–3731 41.3 ≦ RPKM ≦ 63.9) and high (rank: 5463–6462 199 ≦ RPKM ≦ 22 400) level of expression of an equal size (1000 genes each).

5.7. Mapping of transcriptional start sites by the oligo-capping method

We determined the TSS of the expressed genes on the genome of M. osmundae by mapping the 5′ ends of full-length cDNAs obtained by the oligo-capping method [ 9 ]. We generated 17 750 643 single reads (36 bp each) of the 5′ ends by Illumina GAIIx. In total, 10 642 239 of them could be aligned to the genome by SOAP2 [ 45 ]. Typical profiles of the TSSs mapped near the translation start sites (TRSs) determined by AUGUSTUS are shown in electronic supplementary material, figure S9. We searched for the position mapped by the largest number of short reads within the 1 kb upstream region of the TRS of each gene, and the upstream position most intensely mapped by the 5′-end reads was used as the TSS of the gene. The number of oligo-capped reads mapped within the 1 kb upstream region of the TRS highly correlated with the RPKM values determined by RNA-seq. The 1 kb upstream regions of the three gene groups of low, medium and high level of expression were mapped, respectively, by 170,440 and 3500 oligo-capped reads, on average.


Amount of variation between a canonical gene sequence in various samples - Biology

Kalyuzhnyi, Yurij V. Cummings, Peter T.

The Blum-Høye [J. Stat. Phys. 19 317 (1978)] solution of the mean spherical approximation for a multicomponent multi-Yukawa hard-sphere fluid is extended to a polydisperse multi-Yukawa hard-sphere fluid. Our extension is based on the application of the orthogonal polynomial expansion method of Lado [Phys. Rev. E 54, 4411 (1996)]. Closed form analytical expressions for the structural and thermodynamic properties of the model are presented. They are given in terms of the parameters that follow directly from the solution . By way of illustration the method of solution is applied to describe the thermodynamic properties of the one- and two-Yukawa versions of the model.

Rasheed, Tabish Ahmad, Shabbir

Ab initio Hartree-Fock (HF), density functional theory (DFT) and second-order Møller-Plesset (MP2) methods were used to perform harmonic and anharmonic calculations for the biomolecule cytosine and its deuterated derivative. The anharmonic vibrational spectra were computed using the vibrational self-consistent field (VSCF) and correlation-corrected vibrational self-consistent field (CC-VSCF) methods. Calculated anharmonic frequencies have been compared with the argon matrix spectra reported in literature. The results were analyzed with focus on the properties of anharmonic couplings between pair of modes. A simple and easy to use formula for calculation of mode-mode coupling magnitudes has been derived. The key element in present approach is the approximation that only interactions between pairs of normal modes have been taken into account, while interactions of triples or more are neglected. FTIR and Raman spectra of solid state cytosine have been recorded in the regions 400-4000 cm(-1) and 60-4000 cm(-1), respectively. Vibrational analysis and assignments are based on calculated potential energy distribution (PED) values. Copyright 2010 Elsevier B.V. All rights reserved.

Jibrin, Sani Moksin, Mohd Maarof Husin, Mohd Shahril Zakaria, Azmi Hassan, Jumiah Talib, Zainal Abidin

Camera flash heating and the subsequent thermal wave propagation in a solid composite material is studied using the Laplace transform technique. Full-field rear surface temperature for a single-layer, two-layer and three-layer solid composites are obtained directly from the Laplace transform conversion tables as opposed to the tedious inversion process by integral transform method. This is achieved by first expressing the hyperbolic-transcendental equation in terms of negative exponentials of square root of s/α and expanded same in a series by the binomial theorem. Electrophoretic deposition (EPD) and dip coating processes were used to prepare three-layer solid composites consisting ZnO/Cu/ZnO and starch/Al/starch respectively. About 0.5ml of deionized water enclosed within an air-tight aluminium container serves as the third three layer sample (AL/water/AL). Thermal diffusivity experiments were carried out on all the three samples prepared. Using Scaled Levenberg-Marquardt algorithm, the approximate temperature curve for the three-layer solid composite is fitted with the corresponding experimental result. The agreement between the theoretical curve and the experimental data as well as that between the obtained thermal diffusivity values for the ZnO, aluminium and deionized water in this work and similar ones found in literature is found to be very good.

Holota, Petr Nesvadba, Otakar

The aim of this paper is to discuss the solution of the linearized gravimetric boundary value problem by means of the method of successive approximations . We start with the relation between the geometry of the solution domain and the structure of Laplace's operator. Similarly as in other branches of engineering and mathematical physics a transformation of coordinates is used that offers a possibility to solve an alternative between the boundary complexity and the complexity of the coefficients of the partial differential equation governing the solution . Laplace's operator has a relatively simple structure in terms of ellipsoidal coordinates which are frequently used in geodesy. However, the physical surface of the Earth substantially differs from an oblate ellipsoid of revolution, even if it is optimally fitted. Therefore, an alternative is discussed. A system of general curvilinear coordinates such that the physical surface of the Earth is imbedded in the family of coordinate surfaces is used. Clearly, the structure of Laplace's operator is more complicated in this case. It was deduced by means of tensor calculus and in a sense it represents the topography of the physical surface of the Earth. Nevertheless, the construction of the respective Green's function is more simple, if the solution domain is transformed. This enables the use of the classical Green's function method together with the method of successive approximations for the solution of the linear gravimetric boundary value problem expressed in terms of new coordinates. The structure of iteration steps is analyzed and where useful also modified by means of the integration by parts. Comparison with other methods is discussed.

The theory of positive-ion collection by a probe immersed in a low-pressure plasma was reviewed and extended by Allen et al. [Proc. Phys. Soc. 70, 297 (1957)]. The numerical computations for cylindrical and spherical probes in a sheath region were presented by F. F. Chen [J. Nucl. Energy C 7, 41 (1965)]. Here, in this paper, the sheath and presheath solutions for a cylindrical probe are matched through a numerical matching procedure to yield “matched” potential profile or “M solution .” The solution based on the Bohm criterion approach “B solution” is discussed for this particular problem. The comparison of cylindricalmore » probe characteristics obtained from the correct potential profile (M solution ) and the approximated Bohm-criterion approach are different. This raises questions about the correctness of cylindrical probe theories relying only on the Bohm-criterion approach. Also the comparison between theoretical and experimental ion current characteristics shows that in an argon plasma the ions motion towards the probe is almost radial.« less

The exact equation for sagitta of spherical surfaces is generalized to toric surfaces which include spherical and cylindrical surfaces as special cases. Lens thickness, therefore, can be calculated accurately anywhere on a lens even in cases of extreme spherical and cylindrical powers and large diameters. The sagittae of tire- and barrel-form toric surfaces differ off the principal meridians, as is shown by a numerical example. The same holds for pulley- and capstan-form toric surfaces. A general expression is given for thickness at an arbitrary point on a toric lens. Approximate expressions are derived and re-expressed in terms of matrices. The matrix provides an elegant means of generalizing equations for spherical surfaces and lenses to toric surfaces and lenses.

Smiga, Szymon Fabiano, Eduardo

We have developed a simplified coupled cluster (SCC) methodology, using the basic idea of scaled MP2 methods. The scheme has been applied to the coupled cluster double equations and implemented in three different non-iterative variants. This new method (especially the SCCD[3] variant, which utilizes a spin-resolved formalism) has been found to be very efficient and to yield an accurate approximation of the reference CCD results for both total and interaction energies of different atoms and molecules. Furthermore, we demonstrate that the equations determining the scaling coefficients for the SCCD[3] approach can generate non-empirical SCS-MP2 scaling coefficients which are in good agreement with previous theoretical investigations.

Bouallègue, Fayçal Ben Crouzet, Jean-François Comtat, Claude Fourcade, Marjolaine Mohammadi, Bijan Mariano-Goulart, Denis

This paper presents an extended 3-D exact rebinning formula in the Fourier space that leads to an iterative reprojection algorithm (iterative FOREPROJ), which enables the estimation of unmeasured oblique projection data on the basis of the whole set of measured data. In first approximation , this analytical formula also leads to an extended Fourier rebinning equation that is the basis for an approximate reprojection algorithm (extended FORE). These algorithms were evaluated on numerically simulated 3-D positron emission tomography (PET) data for the solution of the truncation problem, i.e., the estimation of the missing portions in the oblique projection data, before the application of algorithms that require complete projection data such as some rebinning methods (FOREX) or 3-D reconstruction algorithms (3DRP or direct Fourier methods). By taking advantage of all the 3-D data statistics, the iterative FOREPROJ reprojection provides a reliable alternative to the classical FOREPROJ method, which only exploits the low-statistics nonoblique data. It significantly improves the quality of the external reconstructed slices without loss of spatial resolution. As for the approximate extended FORE algorithm, it clearly exhibits limitations due to axial interpolations, but will require clinical studies with more realistic measured data in order to decide on its pertinence.

Gopalan, Giri Hrafnkelsson, Birgir Aðalgeirsdóttir, Guðfinna Jarosch, Alexander H. Pálsson, Finnur

Bayesian hierarchical modeling can assist the study of glacial dynamics and ice flow properties. This approach will allow glaciologists to make fully probabilistic predictions for the thickness of a glacier at unobserved spatio-temporal coordinates, and it will also allow for the derivation of posterior probability distributions for key physical parameters such as ice viscosity and basal sliding. The goal of this paper is to develop a proof of concept for a Bayesian hierarchical model constructed, which uses exact analytical solutions for the shallow ice approximation (SIA) introduced by Bueler et al. (2005). A suite of test simulations utilizing these exact solutions suggests that this approach is able to adequately model numerical errors and produce useful physical parameter posterior distributions and predictions. A byproduct of the development of the Bayesian hierarchical model is the derivation of a novel finite difference method for solving the SIA partial differential equation (PDE). An additional novelty of this work is the correction of numerical errors induced through a numerical solution using a statistical model. This error correcting process models numerical errors that accumulate forward in time and spatial variation of numerical errors between the dome, interior, and margin of a glacier.

Noyes, Ben F. Mokaberi, Babak Mandoy, Ram Pate, Alex Huijgen, Ralph McBurney, Mike Chen, Owen

Reducing overlay error via an accurate APC feedback system is one of the main challenges in high volume production of the current and future nodes in the semiconductor industry. The overlay feedback system directly affects the number of dies meeting overlay specification and the number of layers requiring dedicated exposure tools through the fabrication flow. Increasing the former number and reducing the latter number is beneficial for the overall efficiency and yield of the fabrication process. An overlay feedback system requires accurate determination of the overlay error, or fingerprint, on exposed wafers in order to determine corrections to be automatically and dynamically applied to the exposure of future wafers. Since current and future nodes require correction per exposure (CPE), the resolution of the overlay fingerprint must be high enough to accommodate CPE in the overlay feedback system, or overlay control module (OCM). Determining a high resolution fingerprint from measured data requires extremely dense overlay sampling that takes a significant amount of measurement time. For static corrections this is acceptable, but in an automated dynamic correction system this method creates extreme bottlenecks for the throughput of said system as new lots have to wait until the previous lot is measured. One solution is using a less dense overlay sampling scheme and employing computationally up-sampled data to a dense fingerprint. That method uses a global fingerprint model over the entire wafer measured localized overlay errors are therefore not always represented in its up-sampled output. This paper will discuss a hybrid system shown in Fig. 1 that combines a computationally up-sampled fingerprint with the measured data to more accurately capture the actual fingerprint, including local overlay errors. Such a hybrid system is shown to result in reduced modelled residuals while determining the fingerprint, and better on-product overlay performance.

A highly accurate analytical solution is derived to the electromagnetic problem of a short vertical wire antenna located on a stratified ground. The derivation consists of three steps. First, the integration path of the integrals describing the fields of the dipole is deformed and wrapped around the pole singularities and the two vertical branch cuts of the integrands located in the upper half of the complex plane. This allows to decompose the radiated field into its three contributions, namely the above-surface ground wave, the lateral wave, and the trapped surface waves. Next, the square root terms responsible for the branch cuts are extracted from the integrands of the branch-cut integrals. Finally, the extracted square roots are replaced with their rational representations according to Newton's square root algorithm, and residue theorem is applied to give explicit expressions, in series form, for the fields. The rigorous integration procedure and the convergence of square root algorithm ensure that the obtained formulas converge to the exact solution . Numerical simulations are performed to show the validity and robustness of the developed formulation, as well as its advantages in terms of time cost over standard numerical integration procedures.

Joh, Hyungmok Lee, Seung-Wook Seong, Mingi Lee, Woo Seok Oh, Soong Ju

All-nanocrystal (NC)-based and all- solution -processed wearable resistance temperature detectors (RTDs) are introduced. The charge transport mechanisms of Ag NC thin films are engineered through various ligand treatments to design high performance RTDs. Highly conductive Ag NC thin films exhibiting metallic transport behavior with high positive temperature coefficients of resistance (TCRs) are achieved through tetrabutylammonium bromide treatment. Ag NC thin films showing hopping transport with high negative TCRs are created through organic ligand treatment. All- solution -based, one-step photolithography techniques that integrate two distinct opposite-sign TCR Ag NC thin films into an ultrathin single device are developed to decouple the mechanical effects such as human motion. The unconventional materials design and strategy enables highly accurate , sensitive, wearable and motion-free RTDs, demonstrated by experiments on moving or curved objects such as human skin, and simulation results based on charge transport analysis. This strategy provides a low cost and simple method to design wearable multifunctional sensors with high sensitivity which could be utilized in various fields such as biointegrated sensors or electronic skin. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Benner, Peter Dolgov, Sergey Khoromskaia, Venera Khoromskij, Boris N.

In this paper, we propose and study two approaches to approximate the solution of the Bethe-Salpeter equation (BSE) by using structured iterative eigenvalue solvers. Both approaches are based on the reduced basis method and low-rank factorizations of the generating matrices. We also propose to represent the static screen interaction part in the BSE matrix by a small active sub-block, with a size balancing the storage for rank-structured representations of other matrix blocks. We demonstrate by various numerical tests that the combination of the diagonal plus low-rank plus reduced-block approximation exhibits higher precision with low numerical cost, providing as well a distinct two-sided error estimate for the smallest eigenvalues of the Bethe-Salpeter operator. The complexity is reduced to O (Nb2) in the size of the atomic orbitals basis set, Nb, instead of the practically intractable O (Nb6) scaling for the direct diagonalization. In the second approach, we apply the quantized-TT (QTT) tensor representation to both, the long eigenvectors and the column vectors in the rank-structured BSE matrix blocks, and combine this with the ALS-type iteration in block QTT format. The QTT-rank of the matrix entities possesses almost the same magnitude as the number of occupied orbitals in the molecular systems, No approximation is estimated by O (log ⁡ (No)No2). We confirm numerically a considerable decrease in computational time for the presented iterative approaches applied to various compact and chain-type molecules, while supporting sufficient accuracy.

Louarroudi, E. Pintelon, R. Lataire, J.

Time-periodic (TP) phenomena occurring, for instance, in wind turbines, helicopters, anisotropic shaft-bearing systems, and cardiovascular/respiratory systems, are often not addressed when classical frequency response function (FRF) measurements are performed. As the traditional FRF concept is based on the linear time-invariant (LTI) system theory, it is only approximately valid for systems with varying dynamics. Accordingly, the quantification of any deviation from this ideal LTI framework is more than welcome. The “measure of deviation” allows us to define the notion of the best LTI (BLTI) approximation , which yields the best - in mean square sense - LTI description of a linear time-periodic LTP system. By taking into consideration the TP effects, it is shown in this paper that the variability of the BLTI measurement can be reduced significantly compared with that of classical FRF estimators. From a single experiment, the proposed identification methods can handle (non-)linear time-periodic [(N)LTP] systems in open-loop with a quantification of (i) the noise and/or the NL distortions, (ii) the TP distortions and (iii) the transient (leakage) errors. Besides, a geometrical interpretation of the BLTI approximation is provided, leading to a framework called vector FRF analysis. The theory presented is supported by numerical simulations as well as real measurements mimicking the well-known mechanical Mathieu oscillator.

Trujillo Bueno, J. Fabiani Bendicho, P.

Iterative schemes based on Gauss-Seidel (G-S) and optimal successive over-relaxation (SOR) iteration are shown to provide a dramatic increase in the speed with which non-LTE radiation transfer (RT) problems can be solved. The convergence rates of these new RT methods are identical to those of upper triangular nonlocal approximate operator splitting techniques, but the computing time per iteration and the memory requirements are similar to those of a local operator splitting method. In addition to these properties, both methods are particularly suitable for multidimensional geometry, since they neither require the actual construction of nonlocal approximate operators nor the application of any matrix inversion procedure. Compared with the currently used Jacobi technique, which is based on the optimal local approximate operator (see Olson, Auer, & Buchler 1986), the G-S method presented here is faster by a factor 2. It gives excellent smoothing of the high-frequency error components, which makes it the iterative scheme of choice for multigrid radiative transfer. This G-S method can also be suitably combined with standard acceleration techniques to achieve even higher performance. Although the convergence rate of the optimal SOR scheme developed here for solving non-LTE RT problems is much higher than G-S, the computing time per iteration is also minimal, i.e., virtually identical to that of a local operator splitting method. While the conventional optimal local operator scheme provides the converged solution after a total CPU time (measured in arbitrary units) approximately equal to the number n of points per decade of optical depth, the time needed by this new method based on the optimal SOR iterations is only √n/2√2. This method is competitive with those that result from combining the above-mentioned Jacobi and G-S schemes with the best acceleration techniques. Contrary to what happens with the local operator splitting strategy currently in use, these novel

Greenwood, Jeremy R. Calkins, David Sullivan, Arron P. Shelley, John C.

Generating the appropriate protonation states of drug-like molecules in solution is important for success in both ligand- and structure-based virtual screening. Screening collections of millions of compounds requires a method for determining tautomers and their energies that is sufficiently rapid, accurate , and comprehensive. To maximise enrichment, the lowest energy tautomers must be determined from heterogeneous input, without over-enumerating unfavourable states. While computationally expensive, the density functional theory (DFT) method M06-2X/aug-cc-pVTZ(-f) [PB-SCRF] provides accurate energies for enumerated model tautomeric systems. The empirical Hammett-Taft methodology can very rapidly extrapolate substituent effects from model systems to drug-like molecules via the relationship between pKT and pKa. Combining the two complementary approaches transforms the tautomer problem from a scientific challenge to one of engineering scale-up, and avoids issues that arise due to the very limited number of measured pKT values, especially for the complicated heterocycles often favoured by medicinal chemists for their novelty and versatility. Several hundreds of pre-calculated tautomer energies and substituent pKa effects are tabulated in databases for use in structural adjustment by the program Epik, which treats tautomers as a subset of the larger problem of the protonation states in aqueous ensembles and their energy penalties. Accuracy and coverage is continually improved and expanded by parameterizing new systems of interest using DFT and experimental data. Recommendations are made for how to best incorporate tautomers in molecular design and virtual screening workflows.

Cioslowski, Jerzy Strasburger, Krzysztof

Electronic properties of several states of the five- and six-electron harmonium atoms are obtained from large-scale calculations employing explicitly correlated basis functions. The high accuracy of the computed energies (including their components), natural spinorbitals, and their occupation numbers makes them suitable for testing, calibration, and benchmarking of approximate formalisms of quantum chemistry and solid state physics. In the case of the five-electron species, the availability of the new data for a wide range of the confinement strengths ω allows for confirmation and generalization of the previously reached conclusions concerning the performance of the presently known approximations for the electron-electron repulsion energy in terms of the 1-matrix that are at heart of the density matrix functional theory (DMFT). On the other hand, the properties of the three low-lying states of the six-electron harmonium atom, computed at ω = 500 and ω = 1000, uncover deficiencies of the 1-matrix functionals not revealed by previous studies. In general, the previously published assessment of the present implementations of DMFT being of poor accuracy is found to hold. Extending the present work to harmonically confined systems with even more electrons is most likely counterproductive as the steep increase in computational cost required to maintain sufficient accuracy of the calculated properties is not expected to be matched by the benefits of additional information gathered from the resulting benchmarks.

Wen, Zhang Liu, Kai Chen, Xiaolian

In this study, non-Darcian flow to a partially penetrating well in a confined aquifer was investigated. The flow in the horizontal direction was assumed to be non-Darcian, while the flow in the vertical direction was assumed to be Darcian. The Izbash equation was employed to describe the non-Darcian flow in the horizontal direction of the aquifer. We used a linearization procedure to approximate the non-linear term in the governing equation enabling the mathematical model to be solved using a combination of Laplace and Fourier cosine transforms. Approximate analytical solutions for the drawdown were obtained and the impacts of different parameters on the drawdown were analyzed. The results indicated that a larger power index n in the Izbash equation leads to a larger drawdown at early times, while a larger n results in a smaller drawdown at late times. The drawdowns along the vertical direction z are symmetric if the well screen is located in the center of the aquifer, and the drawdown at the center of the aquifer is the largest along the vertical direction for this case. The length of the well screen w has little impact on the drawdown at early times, while a larger length of the well screen results in a smaller drawdown at late times. The drawdown increases with Kr at early times, while it decreases as Kr increases at late times, in which Kr is the apparent radial hydraulic conductivity. A sensitivity analysis of the parameters, i.e., the specific storage Ss, w, n and Kr, indicated that the drawdown is not sensitive to them at early times, while it is very sensitive to these parameters at late times especially to the power index n.

Ikelle, Luc T. Osen, Are Amundsen, Lasse Shen, Yunqing

The classical linear solutions to the problem of multiple attenuation, like predictive deconvolution, τ-p filtering, or F-K filtering, are generally fast, stable, and robust compared to non-linear solutions , which are generally either iterative or in the form of a series with an infinite number of terms. These qualities have made the linear solutions more attractive to seismic data-processing practitioners. However, most linear solutions , including predictive deconvolution or F-K filtering, contain severe assumptions about the model of the subsurface and the class of free-surface multiples they can attenuate. These assumptions limit their usefulness. In a recent paper, we described an exception to this assertion for OBS data. We showed in that paper that a linear and non-iterative solution to the problem of attenuating free-surface multiples which is as accurate as iterative non-linear solutions can be constructed for OBS data. We here present a similar linear and non-iterative solution for attenuating free-surface multiples in towed-streamer data. For most practical purposes, this linear solution is as accurate as the non-linear ones.

An aquifer consisting of a skin zone and a formation zone is considered as a two-zone aquifer. Existing solutions for the problem of constant-flux pumping (CFP) in a two-zone confined aquifer involve laborious calculation. This study develops a new approximate solution for the problem based on a mathematical model including two steady-state flow equations with different hydraulic parameters for the skin and formation zones. A partially penetrating well may be treated as the Neumann condition with a known flux along the screened part and zero flux along the unscreened part. The aquifer domain is finite with an outer circle boundary treated as the Dirichlet condition. The steady-state drawdown solution of the model is derived by the finite Fourier cosine transform. Then, an approximate transient solution is developed by replacing the radius of the boundary in the steady-state solution with an analytical expression for a dimensionless time-dependent radius of influence. The approximate solution is capable of predicting good temporal drawdown distributions over the whole pumping period except at the early stage. A quantitative criterion for the validity of neglecting the vertical flow component due to a partially penetrating well is also provided. Conventional models considering radial flow without the vertical component for the CFP have good accuracy if satisfying the criterion.

An aquifer consisting of a skin zone and a formation zone is considered as a two-zone aquifer. Existing solutions for the problem of constant-flux pumping in a two-zone confined aquifer involve laborious calculation. This study develops a new approximate solution for the problem based on a mathematical model describing steady-state radial and vertical flows in a two-zone aquifer. Hydraulic parameters in these two zones can be different but are assumed homogeneous in each zone. A partially penetrating well may be treated as the Neumann condition with a known flux along the screened part and zero flux along the unscreened part. The aquifer domain is finite with an outer circle boundary treated as the Dirichlet condition. The steady-state drawdown solution of the model is derived by the finite Fourier cosine transform. Then, an approximate transient solution is developed by replacing the radius of the aquifer domain in the steady-state solution with an analytical expression for a dimensionless time-dependent radius of influence. The approximate solution is capable of predicting good temporal drawdown distributions over the whole pumping period except at the early stage. A quantitative criterion for the validity of neglecting the vertical flow due to a partially penetrating well is also provided. Conventional models considering radial flow without the vertical component for the constant-flux pumping have good accuracy if satisfying the criterion.

Schneider, André Lin, Zhongbing Sterckeman, Thibault Nguyen, Christophe

The dissociation of metal complexes in the soil solution can increase the availability of metals for root uptake. When it is accounted for in models of bioavailability of soil metals, the number of partial differential equations (PDEs) increases and the computation time to numerically solve these equations may be problematic when a large number of simulations are required, for example for sensitivity analyses or when considering root architecture. This work presents analytical solutions for the set of PDEs describing the bioavailability of soil metals including the kinetics of complexation for three scenarios where the metal complex in solution was fully inert, fully labile, or partially labile. The analytical solutions are only valid i) at steady-state when the PDEs become ordinary differential equations, the transient phase being not covered, ii) when diffusion is the major mechanism of transport and therefore, when convection is negligible, iii) when there is no between-root competition. The formulation of the analytical solutions is for cylindrical geometry but the solutions rely on the spread of the depletion profile around the root, which was modelled assuming a planar geometry. The analytical solutions were evaluated by comparison with the corresponding PDEs for cadmium in the case of the French agricultural soils. Provided that convection was much lower than diffusion (Péclet's number solutions were in very good agreement with those calculated from the PDEs, even in the case of a partially labile complex. The analytic solutions can be used instead of the PDEs to predict root uptake of metals. The analytic solutions were also used to build an indicator of the contribution of a complex to the uptake of the metal by roots, which can be helpful to predict the effect of soluble organic matter on the bioavailability of soil metals. Copyright © 2017 Elsevier B.V. All rights reserved.

Mazilu, I Mazilu, D A Melkerson, R E Hall-Mejia, E Beck, G J Nshimyumukiza, S da Fonseca, Carlos M

We present exact and approximate results for a class of cooperative sequential adsorption models using matrix theory, mean-field theory, and computer simulations. We validate our models with two customized experiments using ionically self-assembled nanoparticles on glass slides. We also address the limitations of our models and their range of applicability. The exact results obtained using matrix theory can be applied to a variety of two-state systems with cooperative effects.

Vidberg and Serene introduced a very useful technique for calculating the low temperature (T « T c) gap function of a superconductor which bypasses the real-frequency singular integral equations of Eliashberg. Blashke and Blocksdorf recognized and resolved a difficulty with the technique thereby extending it to higher temperatures. We present a much simpler method of doing essentially the same thing and, for a strong-coupling superconductor at a temperature near T c, compare the gap functions calculated using these methods with the accurate one computed directly from the real-frequency equations.

Results are presented from a linear Lagrangian entraining parcel model of an overshooting thunderstorm cloud top. The model, which is similar to that of Adler and Mack (1986), gives analytic exact solutions for vertical velocity and temperature by representing mixing with Rayleigh damping instead of nonlinearly. Model results are presented for various combinations of stratospheric lapse rate, drag intensity, and mixing strength. The results are compared to those of Adler and Mack.

Zheng, Youqi Choi, Sooyoung Lee, Deokjung

A new approach based on the method of characteristics (MOC) is proposed to solve the neutron transport equation. A new three-dimensional (3D) spatial discretization is applied to avoid the instability issue of the transverse leakage iteration of the traditional 2D/1D approach. In this new approach, the axial and radial variables are discretized in two different ways: the linear expansion is performed in the axial direction, then, the 3D solution of the angular flux is transformed to be the planar solution of 2D angular expansion moments, which are solved by the planar MOC sweeping. Based on the boundary and interface continuity conditions, the 2D expansion moment solution is equivalently transformed to be the solution of the axially averaged angular flux. Using the piecewise averaged angular flux at the top and bottom surfaces of 3D meshes, the planes are coupled to give the 3D angular flux distribution. The 3D CMFD linear system is established from the surface net current of every 3D pin-mesh to accelerate the convergence of power iteration. The STREAM code is extended to be capable of handling 3D problems based on the new approach. Several benchmarks are tested to verify its feasibility and accuracy, including the 3D homogeneous benchmarks and heterogeneous benchmarks. The computational sensitivity is discussed. The results show good accuracy in all tests. With the CMFD acceleration, the convergence is stable. In addition, a pin-cell problem with void gap is calculated. This shows the advantage compared to the traditional 2D/1D MOC methods.

Vinyard, David J Zachary, Chase E Ananyev, Gennady Dismukes, G Charles

Forty-three years ago, Kok and coworkers introduced a phenomenological model describing period-four oscillations in O2 flash yields during photosynthetic water oxidation (WOC), which had been first reported by Joliot and coworkers. The original two-parameter Kok model was subsequently extended in its level of complexity to better simulate diverse data sets, including intact cells and isolated PSII-WOCs, but at the expense of introducing physically unrealistic assumptions necessary to enable numerical solutions . To date, analytical solutions have been found only for symmetric Kok models (inefficiencies are equally probable for all intermediates, called "S-states"). However, it is widely accepted that S-state reaction steps are not identical and some are not reversible (by thermodynamic restraints) thereby causing asymmetric cycles. We have developed a mathematically more rigorous foundation that eliminates unphysical assumptions known to be in conflict with experiments and adopts a new experimental constraint on solutions . This new algorithm termed STEAMM for S-state Transition Eigenvalues of Asymmetric Markov Models enables solutions to models having fewer adjustable parameters and uses automated fitting to experimental data sets, yielding higher accuracy and precision than the classic Kok or extended Kok models. This new tool provides a general mathematical framework for analyzing damped oscillations arising from any cycle period using any appropriate Markov model, regardless of symmetry. We illustrate applications of STEAMM that better describe the intrinsic inefficiencies for photon-to-charge conversion within PSII-WOCs that are responsible for damped period-four and period-two oscillations of flash O2 yields across diverse species, while using simpler Markov models free from unrealistic assumptions. Copyright © 2013 Elsevier B.V. All rights reserved.

We discuss the class of equations ∑i,j=0mAij(u)<∂iu>/<∂ti>∂+∑k,l=0nBkl(u)<∂ku>/<∂xk>∂=C(u) where Aij( u), Bkl( u) and C( u) are functions of u( x, t) as follows: (i) Aij, Bkl and C are polynomials of u or (ii) Aij, Bkl and C can be reduced to polynomials of u by means of Taylor series for small values of u. For these two cases the above-mentioned class of equations consists of nonlinear PDEs with polynomial nonlinearities. We show that the modified method of simplest equation is powerful tool for obtaining exact traveling-wave solution of this class of equations. The balance equations for the sub-class of traveling-wave solutions of the investigated class of equations are obtained. We illustrate the method by obtaining exact traveling-wave solutions (i) of the Swift-Hohenberg equation and (ii) of the generalized Rayleigh equation for the cases when the extended tanh-equation or the equations of Bernoulli and Riccati are used as simplest equations.

The propagation of photons in a medium with strongly anisotropic scattering is a problem with a considerable history. Like the propagation of electrons in metal foils, it may be solved in the small-angle scattering approximation by the use of Fourier-transform techniques. In certain limiting cases, one may even obtain analytic expressions. This paper presents some of these results in a model-independent form and also illustrates them by the use of four different phase-function models. Sample calculations are provided for comparison purposes

Maksimenko, V. V. Zagaynov, V. A. Semina, P. N. Zheltova, A. V. Maslenkova, E. V. Smolyanskiy, A. S.

The photon propagator describing the interaction of light with a monolayer of metal particles (island film) is calculated in the coherent potential approximation . It is shown that the shift in the frequency peak of a dipole surface plasmon for a monolayer particle relative to the analogous frequency of the plasma resonance for an isolated particle is not the only manifestation of the influence of neighboring particles. Neighboring particles also produce a bimodal structure in the spectrum line of the plasmon resonance. The possibility of fine structure in the plasmon resonance spectrum lines is predicted.

The three-dimensional boundary-layer equations in the limit as the normal coordinate tends to infinity are called the surface Euler equations. The present paper describes an accurate method for generating edge conditions for three-dimensional boundary-layer codes using these equations. The inviscid pressure distribution is first interpolated to the boundary-layer grid. The surface Euler equations are then solved with this pressure field and a prescribed set of initial and boundary conditions to yield the velocities along the two surface coordinate directions. Results for typical wing and fuselage geometries are presented. The smoothness and accuracy of the edge conditions obtained are found to be superior to the conventional interpolation procedures.

Mironova, Lidia A. Mironov, Sergej L.

Local Ca2+ signaling controls many neuronal functions, which is often achieved through spatial localization of Ca2+ signals. These nanodomains are formed due to combined effects of Ca2+ diffusion and binding to the cytoplasmic buffers. In this article we derived simple analytical expressions to describe Ca2+ diffusion in the presence of mobile and immobile buffers. A nonlinear character of the reaction-diffusion problem was circumvented by introducing a logarithmic approximation of the concentration term. The obtained formulas reproduce free Ca2+ levels up to 50 μM and their changes in the millisecond range. Derived equations can be useful to predict spatiotemporal profiles of large-amplitude [Ca2+] transients, which participate in various physiological processes. PMID:17872951

In this work, an exact scattering model for a system of clusters of spherical particles, based on the Rayleigh-Gans approximation , has been parameterized in such a way that it can be solved in inverse form using Thikhonov Regularization to obtain the morphological parameters of the clusters. That is to say, the average number of particles per cluster, the size of the primary spherical units that form the cluster, and the Discrete Distance Distribution Function from which the z-average square radius of gyration of the system of clusters is obtained. The methodology is validated through a series of simulated and experimental examples of x-ray and light scattering that show that the proposed methodology works satisfactorily in unideal situations such as: presence of error in the measurements, presence of error in the model, and several types of unideallities present in the experimental cases.

Jiang, Pengfei Yue, Mufei Cong, Rihong Gao, Wenliang Yang, Tao

BiMnxFe3-xO6 (x = 1) represents a new type of oxide structure containing Bi3+ and competing magnetic super-exchanges. In literature, multiple magnetic states were realized at low temperatures in BiMnFe2O6, and the hypothetical parent compounds (BiMn3O6, BiFe3O6) were predicted to be different in magnetism. Herein, we performed a careful study on the syntheses of BiMnxFe3-xO6 at ambient pressure, and the solid solution range was determined to be 0.9 ≤ x ≤ 1.3 by Rietveld refinements on high-quality powder X-ray diffraction data. Due to the very similar cationic size of Mn3+ and Fe3+, and possibly the structural rigidity, there was no significant structure change in the whole range of solid solution . The magnetic behavior of BiMnxFe3-xO6 (x = 1.2, 1.22, 1.26, 1.28 and 1.3) was generally similar to BiMnFe2O6, while the relative higher concentration of Mn3+ led to the decreasing of the antiferromagnetic ordering temperature.

Ruas, Alexandre Simonin, Jean-Pierre Turq, Pierre Moisy, Philippe

This work is aimed at a description of the thermodynamic properties of actinide salt solutions at high concentration. The predictive capability of the binding mean spherical approximation (BIMSA) theory to describe the thermodynamic properties of electrolytes is assessed in the case of aqueous solutions of lanthanide(III) nitrate and chloride salts. Osmotic coefficients of cerium(III) nitrate and chloride were calculated from other lanthanide(III) salts properties. In parallel, concentrated binary solutions of cerium nitrate were prepared in order to measure experimentally its water activity and density as a function of concentration, at 25 degrees C. Water activities of several binary solutions of cerium chloride were also measured to check existing data on this salt. Then, the properties of cerium chloride and cerium nitrate solutions were compared within the BIMSA model. Osmotic coefficient values for promethium nitrate and promethium chloride given by this theory are proposed. Finally, water activity measurements were made to examine the fact that the ternary system Ce(NO3)3/HNO3/H2O and the quaternary system Ce(NO3)3/HNO3/N2H5NO3/H2O may be regarded as "simple solutions " (in the sense of Zdanovskii and Mikulin).

Samuha, Shmuel Mugnaioli, Enrico Grushko, Benjamin Kolb, Ute Meshi, Louisa

The crystal structure of the novel Al77Rh15Ru8 phase (which is an approximant of decagonal quasicrystals) was determined using modern direct methods (MDM) applied to automated electron diffraction tomography (ADT) data. The Al77Rh15Ru8 E-phase is orthorhombic [Pbma, a = 23.40 (5), b = 16.20 (4) and c = 20.00 (5) Å] and has one of the most complicated intermetallic structures solved solely by electron diffraction methods. Its structural model consists of 78 unique atomic positions in the unit cell (19 Rh/Ru and 59 Al). Precession electron diffraction (PED) patterns and high-resolution electron microscopy (HRTEM) images were used for the validation of the proposed atomic model. The structure of the E-phase is described using hierarchical packing of polyhedra and a single type of tiling in the form of a parallelogram. Based on this description, the structure of the E-phase is compared with that of the ε6-phase formed in Al-Rh-Ru at close compositions.

Gursoy, Gamze Terebus, Anna Youfang Cao Jie Liang

Stochasticity plays important roles in regulation of biochemical reaction networks when the copy numbers of molecular species are small. Studies based on Stochastic Simulation Algorithm (SSA) has shown that a basic reaction system can display stochastic focusing (SF) by increasing the sensitivity of the network as a result of the signal noise. Although SSA has been widely used to study stochastic networks, it is ineffective in examining rare events and this becomes a significant issue when the tails of probability distributions are relevant as is the case of SF. Here we use the ACME method to solve the exact solution of the discrete Chemical Master Equations and to study a network where SF was reported. We showed that the level of SF depends on the degree of the fluctuations of signal molecule. We discovered that signaling noise under certain conditions in the same reaction network can lead to a decrease in the system sensitivities, thus the network can experience stochastic defocusing. These results highlight the fundamental role of stochasticity in biological reaction networks and the need for exact computation of probability landscape of the molecules in the system.

Boundary approximation methods with partial solutions are presented for solving a complicated problem on an unbounded domain, with both a crack singularity and a corner singularity. Also an analysis of partial solutions near the singular points is provided. These methods are easy to apply, have good stability properties, and lead to highly accurate solutions . Hence, boundary approximation methods with partial solutions are recommended for the treatment of elliptic problems on unbounded domains provided that piecewise solution expansions, in particular, asymptotic solutions near the singularities and infinity, can be found.

DeChant, Lawrence Ray, Jaideep Lefantzi, Sophia .

The k-ε turbulence model has been described as perhaps “the most widely used complete turbulence model.” This family of heuristic Reynolds Averaged Navier-Stokes (RANS) turbulence closures is supported by a suite of model parameters that have been estimated by demanding the satisfaction of well-established canonical flows such as homogeneous shear flow, log-law behavior, etc. While this procedure does yield a set of so-called nominal parameters, it is abundantly clear that they do not provide a universally satisfactory turbulence model that is capable of simulating complex flows. Recent work on the Bayesian calibration of the k-ε model using jet-in-crossflow wind tunnelmore » data has yielded parameter estimates that are far more predictive than nominal parameter values. In this paper, we develop a self-similar asymptotic solution for axisymmetric jet-in-crossflow interactions and derive analytical estimates of the parameters that were inferred using Bayesian calibration. The self-similar method utilizes a near field approach to estimate the turbulence model parameters while retaining the classical far-field scaling to model flow field quantities. Our parameter values are seen to be far more predictive than the nominal values, as checked using RANS simulations and experimental measurements. They are also closer to the Bayesian estimates than the nominal parameters. A traditional simplified jet trajectory model is explicitly related to the turbulence model parameters and is shown to yield good agreement with measurement when utilizing the analytical derived turbulence model coefficients. Finally, the close agreement between the turbulence model coefficients obtained via Bayesian calibration and the analytically estimated coefficients derived in this paper is consistent with the contention that the Bayesian calibration approach is firmly rooted in the underlying physical description.« less

Xu, Chun-Long Zhang, Min-Cang

The arbitrary l-wave solutions to the Schrödinger equation for the deformed hyperbolic Manning-Rosen potential is investigated analytically by using the Nikiforov-Uvarov method, the centrifugal term is treated with an improved Greene and Aldrich's approximation scheme. The wavefunctions depend on the deformation parameter q, which is expressed in terms of the Jocobi polynomial or the hypergeometric function. The bound state energy is obtained, and the discrete spectrum is shown to be independent of the deformation parameter q.

It is shown that the inverse analytical solutions , provided separately by Fymat and Box-McKellar, for reconstructing particle size distributions from remote spectral transmission measurements under the anomalous diffraction approximation can be derived using a cosine and a sine transform, respectively. Sufficient conditions of validity of the two formulas are established. Their comparison shows that the former solution is preferable to the latter in that it requires less a priori information (knowledge of the particle number density is not needed) and has wider applicability. For gamma-type distributions, and either a real or a complex refractive index, explicit expressions are provided for retrieving the distribution parameters such expressions are, interestingly, proportional to the geometric area of the polydispersion.

Deb, Kalyanmoy Sinha, Ankur

Bilevel optimization problems involve two optimization tasks (upper and lower level), in which every feasible upper level solution must correspond to an optimal solution to a lower level optimization problem. These problems commonly appear in many practical problem solving tasks including optimal control, process optimization, game-playing strategy developments, transportation problems, and others. However, they are commonly converted into a single level optimization problem by using an approximate solution procedure to replace the lower level optimization task. Although there exist a number of theoretical, numerical, and evolutionary optimization studies involving single-objective bilevel programming problems, not many studies look at the context of multiple conflicting objectives in each level of a bilevel programming problem. In this paper, we address certain intricate issues related to solving multi-objective bilevel programming problems, present challenging test problems, and propose a viable and hybrid evolutionary-cum-local-search based algorithm as a solution methodology. The hybrid approach performs better than a number of existing methodologies and scales well up to 40-variable difficult test problems used in this study. The population sizing and termination criteria are made self-adaptive, so that no additional parameters need to be supplied by the user. The study indicates a clear niche of evolutionary algorithms in solving such difficult problems of practical importance compared to their usual solution by a computationally expensive nested procedure. The study opens up many issues related to multi-objective bilevel programming and hopefully this study will motivate EMO and other researchers to pay more attention to this important and difficult problem solving activity.

The Michaelis-Menten rate equation can be found in most general biochemistry textbooks, where the time derivative of the substrate is a hyperbolic function of two kinetic parameters (the limiting rate V, and the Michaelis constant K(M) ) and the amount of substrate. However, fundamental concepts of enzyme kinetics can be difficult to understand fully, or can even be misunderstood, by students when based only on the differential form of the Michaelis-Menten equation, and the variety of methods available to calculate the kinetic constants from rate versus substrate concentration "textbook data." Consequently, enzyme kinetics can be confusing if an analytical solution of the Michaelis-Menten equation is not available. Therefore, the still rarely known exact solution to the Michaelis-Menten equation is presented here through the explicit closed-form equation in terms of the Lambert W(x) function. Unfortunately, as the W(x) is not available in standard curve-fitting computer programs, the practical use of this direct solution is limited for most life-science students. Thus, the purpose of this article is to provide analytical approximations to the equation for modeling Michaelis-Menten kinetics. The elementary and explicit nature of these approximations can provide students with direct and simple estimations of kinetic parameters from raw experimental time-course data. The Michaelis-Menten kinetics studied in the latter context can provide an ideal alternative to the 100-year-old problems of data transformation, graphical visualization, and data analysis of enzyme-catalyzed reactions. Hence, the content of the course presented here could gradually become an important component of the modern biochemistry curriculum in the 21st century. Copyright © 2011 Wiley Periodicals, Inc.

Weatherbee, Andrew Popov, Ivan Vitkin, Alex

The viscosity of turbid colloidal glucose solutions has been accurately determined from spectral domain optical coherence tomography (OCT) M-mode measurements and our recently developed OCT dynamic light scattering model. Results for various glucose concentrations, flow speeds, and flow angles are reported. The relative "combined standard uncertainty" uc(η) on the viscosity measurements was ±1% for the no-flow case and ±5% for the flow cases, a significant improvement in measurement robustness over previously published reports. The available literature data for the viscosity of pure water and our measurements differ by 1% (stagnant case) and 1.5% (flow cases), demonstrating good accuracy similar agreement is seen across the measured glucose concentration range when compared to interpolated literature values. The developed technique may contribute toward eventual noninvasive glucose measurements in medicine. (2017) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE).

Light transmission measurements through falling snow have produced results unexplainable by single scattering arguments. A two-stream approximation to radiative transfer is used to derive an analytical expression that describes the effects of multiple scattering as a function of the snow optical depth and the snow asymmetry parameter. The approximate solution is simple and it may be as accurate as the exact solution for describing the transmission measurements within the limits of experimental uncertainties.

Ekholm, T. Lanoix, P. Teerikorpi, P. Paturel, G. Fouqué, P.

A sample of 32 galaxies with accurate distance moduli from the Cepheid PL-relation (Lanoix cite) has been used to study the dynamical behaviour of the Local (Virgo) supercluster. We used analytical Tolman-Bondi (TB) solutions for a spherically symmetric density excess embedded in the Einstein-deSitter universe (q_0=0.5). Using 12 galaxies within Theta =30degr from the centre we found a mass estimate of 1.62M_virial for the Virgo cluster. This agrees with the finding of Teerikorpi et al. (cite) that TB-estimate may be larger than virial mass estimate from Tully & Shaya (cite). Our conclusions do not critically depend on our primary choice of the global H_0=57 km s-1 Mpc <-1>established from SNe Ia (Lanoix cite). The remaining galaxies outside Virgo region do not disagree with this value. Finally, we also found a TB- solution with the H_0 and q_0 cited yielding exactly one virial mass for the Virgo cluster.

The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations . Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.

The numerical approximation of solutions to linear functional differential equations are considered using the so called Legendre tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time differentiation. The approximate solution is then represented as a truncated Legendre series with time varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations . Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximations is made.

Adsorption of biomolecules and polymers to inorganic nanostructures plays a major role in the design of novel materials and therapeutics. The behavior of flexible molecules on solid surfaces at a scale of 1-1000 nm remains difficult and expensive to monitor using current laboratory techniques, while playing a critical role in energy conversion and composite materials as well as in understanding the origin of diseases. Approaches to implement key surface features and pH in molecular models of solids are explained, and distinct mechanisms of peptide recognition on metal nanostructures, silica and apatite surfaces in solution are described as illustrative examples. The influence of surface energies, specific surface features and protonation states on the structure of aqueous interfaces and selective biomolecular adsorption is found to be critical, comparable to the well-known influence of the charge state and pH of proteins and surfactants on their conformations and assembly. The representation of such details in molecular models according to experimental data and available chemical knowledge enables accurate simulations of unknown complex interfaces in atomic resolution in quantitative agreement with independent experimental measurements. In this context, the benefits of a uniform force field for all material classes and of a mineral surface structure database are discussed.

Bauschlicher, Charles W., Jr. Langhoff, Stephen R. Taylor, Peter R.

An important goal of quantum chemical calculations is to provide an understanding of chemical bonding and molecular electronic structure. A second goal, the prediction of energy differences to chemical accuracy, has been much harder to attain. First, the computational resources required to achieve such accuracy are very large, and second, it is not straightforward to demonstrate that an apparently accurate result, in terms of agreement with experiment, does not result from a cancellation of errors. Recent advances in electronic structure methodology, coupled with the power of vector supercomputers, have made it possible to solve a number of electronic structure problems exactly using the full configuration interaction (FCI) method within a subspace of the complete Hilbert space. These exact results can be used to benchmark approximate techniques that are applicable to a wider range of chemical and physical problems. The methodology of many-electron quantum chemistry is reviewed. Methods are considered in detail for performing FCI calculations. The application of FCI methods to several three-electron problems in molecular physics are discussed. A number of benchmark applications of FCI wave functions are described. Atomic basis sets and the development of improved methods for handling very large basis sets are discussed: these are then applied to a number of chemical and spectroscopic problems to transition metals and to problems involving potential energy surfaces. Although the experiences described give considerable grounds for optimism about the general ability to perform accurate calculations, there are several problems that have proved less tractable, at least with current computer resources, and these and possible solutions are discussed.

Vazquez-Leal, Hector Benhammouda, Brahim Filobello-Nino, Uriel Sarmiento-Reyes, Arturo Jimenez-Fernandez, Victor Manuel Garcia-Gervacio, Jose Luis Huerta-Chua, Jesus Morales-Mendoza, Luis Javier Gonzalez-Lee, Mario

This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant . 34L30.

We report the results of a series of calculations of state-to-state integral cross sections for collisions between O and nonvibrating H2O in the gas phase on a model nonreactive potential energy surface. The dynamical methods used include converged quantum mechanical scattering calculations, the j(z) conserving centrifugal sudden (j(z)-CCS) approximation , and quasi-classical trajectory (QCT) calculations. We consider three total energies 0.001, 0.002, and 0.005 E(h) and the nine initial states with rotational angular momentum less than or equal to 2 (h/2 pi). The j(z)-CCS approximation gives good results, while the QCT method can be quite unreliable for transitions to specific rotational sublevels. However, the QCT cross sections summed over final sublevels and averaged over initial sublevels are in better agreement with the quantum results.

Wei, G. W. Kouri, D. J. Hoffman, D. K.

A general procedure is proposed for constructing father and mother wavelets that have excellent time-frequency localization and can be used to generate entire wavelet families for use as wavelet transforms. One interesting feature of our father wavelets (scaling functions) is that they belong to a class of generalized delta sequences, which we refer to as distributed approximating functionals (DAFs). We indicate this by the notation wavelet-DAFs. Correspondingly, the mother wavelets generated from these wavelet-DAFs are appropriately called DAF-wavelets. Wavelet-DAFs can be regarded as providing a pointwise (localized) spectral method, which furnishes a bridge between the traditional global methods and local methods for solving partial differential equations. They are shown to provide extremely accurate numerical solutions for a number of nonlinear partial differential equations, including the Korteweg-de Vries (KdV) equation, for which a previous method has encountered difficulties (J. Comput. Phys. 132 (1997) 233).

Hu, Lianrui Chen, Kejuan Chen, Hui

Accurate modelings of reactions involving 3d transition metals (TMs) are very challenging to both ab initio and DFT approaches. To gain more knowledge in this field, we herein explored typical σ-bond activations of H-H, C-H, C-Cl, and C-C bonds promoted by nickel(0), a low-valent late 3d TM. For the key parameters of activation energy (ΔE ‡ ) and reaction energy (ΔE R ) for these reactions, various issues related to the computational accuracy were systematically investigated. From the scrutiny of convergence issue with one-electron basis set, augmented (A) basis functions are found to be important, and the CCSD(T)/CBS level with complete basis set (CBS) limit extrapolation based on augmented double-ζ and triple-ζ basis pair (ADZ and ATZ), which produces deviations below 1 kcal/mol from the reference, is recommended for larger systems. As an alternative, the explicitly correlated F12 method can accelerate the basis set convergence further, especially after its CBS extrapolations. Thus, the CCSD(T)-F12/CBS(ADZ-ATZ) level with computational cost comparable to the conventional CCSD(T)/CBS(ADZ-ATZ) level, is found to reach the accuracy of the conventional CCSD(T)/A5Z level, which produces deviations below 0.5 kcal/mol from the reference, and is also highly recommendable. Scalar relativistic effects and 3s3p core-valence correlation are non-negligible for achieving chemical accuracy of around 1 kcal/mol. From the scrutiny of convergence issue with the N-electron basis set, in comparison with the reference CCSDTQ result, CCSD(T) is found to be able to calculate ΔE ‡ quite accurately , which is not true for the ΔE R calculations. Using highest-level CCSD(T) results of ΔE ‡ in this work as references, we tested 18 DFT methods and found that PBE0 and CAM-B3LYP are among the three best performing functionals, irrespective of DFT empirical dispersion correction. With empirical dispersion correction included, ωB97XD is also recommendable due to its improved

Gonis, Antonios Zhang, Xiaoguang

This is a comment on the paper by Aftab Alam, Brian G. Wilson, and D. D. Johnson [1], proposing the solution of the near-field corrections (NFC s) problem for the Poisson equation for extended, e.g., space filling, charge densities. We point out that the problem considered by the authors can be simply avoided by means of performing certain integrals in a particular order, while their method does not address the genuine problem of NFC s that arises when the solution of the Poisson equation is attempted within multiple scattering theory. We also point out a flaw in their line ofmore » reasoning leading to the expression for the potential inside the bounding sphere of a cell that makes it inapplicable to certain geometries.« less

This is a Comment on the paper by Alam, Wilson, and Johnson [Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.84.205106 84, 205106 (2011)], proposing the solution of the near-field corrections (NFCs) problem for the Poisson equation for extended, e.g., space-filling charge densities. We point out that the problem considered by the authors can be simply avoided by means of performing certain integrals in a particular order, whereas, their method does not address the genuine problem of NFCs that arises when the solution of the Poisson equation is attempted within multiple-scattering theory. We also point out a flaw in their line of reasoning, leading to the expression for the potential inside the bounding sphere of a cell that makes it inapplicable for certain geometries.

Broeckhoven, Ken Desmet, Gert

Using a combination of both analytical and numerical techniques, approximate analytical expressions have been established for the transient and long time limit band broadening, originating from the presence of a thin disturbed sidewall layer in liquid chromatography columns, including packed, monolithic as well as microfabricated columns. The established expressions can be used to compare the importance of a thin disturbed sidewall layer with that of other radial heterogeneity effects (such as transcolumn packing density variations due to the relief of packing stresses). The expressions are independent of the actual velocity profile inside the layer as long as the disturbed sidewall layer occupies less than 2.5% of the column width.

Van Vlaenderen, Ilse Van Bellinghen, Laure-Anne Meier, Genevieve Nautrup, Barbara Poulsen

Indirect herd effect from vaccination of children offers potential for improving the effectiveness of influenza prevention in the remaining unvaccinated population. Static models used in cost-effectiveness analyses cannot dynamically capture herd effects. The objective of this study was to develop a methodology to allow herd effect associated with vaccinating children against seasonal influenza to be incorporated into static models evaluating the cost-effectiveness of influenza vaccination. Two previously published linear equations for approximation of herd effects in general were compared with the results of a structured literature review undertaken using PubMed searches to identify data on herd effects specific to influenza vaccination. A linear function was fitted to point estimates from the literature using the sum of squared residuals. The literature review identified 21 publications on 20 studies for inclusion. Six studies provided data on a mathematical relationship between effective vaccine coverage in subgroups and reduction of influenza infection in a larger unvaccinated population. These supported a linear relationship when effective vaccine coverage in a subgroup population was between 20% and 80%. Three studies evaluating herd effect at a community level, specifically induced by vaccinating children, provided point estimates for fitting linear equations. The fitted linear equation for herd protection in the target population for vaccination (children) was slightly less conservative than a previously published equation for herd effects in general. The fitted linear equation for herd protection in the non-target population was considerably less conservative than the previously published equation. This method of approximating herd effect requires simple adjustments to the annual baseline risk of influenza in static models: (1) for the age group targeted by the childhood vaccination strategy (i.e. children) and (2) for other age groups not targeted (e

Background Indirect herd effect from vaccination of children offers potential for improving the effectiveness of influenza prevention in the remaining unvaccinated population. Static models used in cost-effectiveness analyses cannot dynamically capture herd effects. The objective of this study was to develop a methodology to allow herd effect associated with vaccinating children against seasonal influenza to be incorporated into static models evaluating the cost-effectiveness of influenza vaccination. Methods Two previously published linear equations for approximation of herd effects in general were compared with the results of a structured literature review undertaken using PubMed searches to identify data on herd effects specific to influenza vaccination. A linear function was fitted to point estimates from the literature using the sum of squared residuals. Results The literature review identified 21 publications on 20 studies for inclusion. Six studies provided data on a mathematical relationship between effective vaccine coverage in subgroups and reduction of influenza infection in a larger unvaccinated population. These supported a linear relationship when effective vaccine coverage in a subgroup population was between 20% and 80%. Three studies evaluating herd effect at a community level, specifically induced by vaccinating children, provided point estimates for fitting linear equations. The fitted linear equation for herd protection in the target population for vaccination (children) was slightly less conservative than a previously published equation for herd effects in general. The fitted linear equation for herd protection in the non-target population was considerably less conservative than the previously published equation. Conclusions This method of approximating herd effect requires simple adjustments to the annual baseline risk of influenza in static models: (1) for the age group targeted by the childhood vaccination strategy (i.e. children) and (2

M'halla, Jalel M'halla, Sondes Wipff, Georges

Calorimetric measurements of heats of dilution: QDC→0 =- nsφL,sexp, of aqueous solutions of NaBPh 4 are determined at 25 °C in the concentration range: 0 solute-solute attraction due to the specific hydration of the BPh 4- ion in presence of Na +. In order to present a deeper physico-chemical analysis of the dilution process of NaBPh 4, we used Molecular Dynamics Simulations of different mixtures of ns NaBPh 4 ( 0⩽ ns⩽64 ) and nw TIP3P water molecules ( 2473⩽ nw⩽4024 ). φL,sMD are calculated directly in terms of apparent molar energies or indirectly in terms of partial molar energies. MD results show that the sign of the slope: d φMDL,s/d C is very sensitive to the charge distribution on the BPh 4- ion. On the other hand, according to our analysis this slope depend on a specific contribution ΦSpe,s defined by: m dΦ Spe, s/ dm≈- nh[e hw-(e w) b] , m is the molecularity and nh is the hydration number. The condition d Φse,s/d m≫0, implies that the molecular energy of hydration molecules: ehw is more negative than the molecular energy ( ew) b of water molecules in the bulk solution . This condition is satisfied in the case of strong ion-solvent interaction or in the case of hydrophobic hydration. MD results concerning the separation of ehw in terms of ehiw and ehww energies, show that the H bonds of water molecules around BPh 4- ions are partially broken: contrarily to the Na + ion, the BPh 4- ion cannot orient completely the water dipoles in the direction of its local field. However, it seems that the TIP3P model cannot explain completely the enhancement of the H bonds of water molecules in the second shell around the BPh 4- ion, by comparison to the H bonds in bulk solution . This analysis is important from the fact that, the hydrophobic interaction is governed by the potential


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