Increasing Sequence Length Research Articles

Increasing sequence length: process development and optimisation at the slab caster of Columbus Stainless

The present paper discusses the process development and optimisation conducted over a two-year period at the continuous caster at Columbus Stainless to allow an increased sequence length, thereby satisfying the continual drive for increased throughput, lower cost of production and higher quality. Increased sequence length results in longer exposure of refractory to steel or slag resulting in more erosion and chemical attack. The refractory system in use at Columbus Stainless was initially designed and optimised for 6 h of casting and the focus of the development was to increase this time to 14 h. This objective was achieved by modifications to tundish design and lining, optimisation of the tundish cover, modifications to stopper and SEN design, composition and operating practise. After these changes, the original objective of increasing the sequence length to 14 h was achieved with a concomitant saving in refractory cost per ton of up to 35%.

Improving Divergence Time Estimation in Phylogenetics: More Taxa vs. Longer Sequences

Maximum Likelihood (ML) is used as a standard method for estimating divergence times in phylogenetic trees. The method is consistent and hence the precision can be improved by analyzing longer sequences. In this paper we show that the precision can be improved also by including more taxa to the existing tree. It is a theoretical study, complemented with simulations, showing that the gain in precision is faster with increasing sequence length than with increasing number of taxa. We further compare the results of estimating divergence times using Maximum Likelihood with the much faster and less complex estimation method of Mean Path Length (MPL), which works with the evolution model of Jukes-Cantor (1969). It is shown that MPL is as good as ML in estimating divergence times of nodes that are located near the root in the tree, but ML is better in estimating the divergence times of nodes lower down.

Entropy Coding With Variable-Length Rewriting Systems

This paper describes a new set of block source codes well suited for data compression. These codes are defined by sets of productions rules of the form a.l->b, where a in A represents a value from the source alphabet A and l, b are -small- sequences of bits. These codes naturally encompass other Variable Length Codes (VLCs) such as Huffman codes. It is shown that these codes may have a similar or even a shorter mean description length than Huffman codes for the same encoding and decoding complexity. A first code design method allowing to preserve the lexicographic order in the bit domain is described. The corresponding codes have the same mean description length (mdl) as Huffman codes from which they are constructed. Therefore, they outperform from a compression point of view the Hu-Tucker codes designed to offer the lexicographic property in the bit domain. A second construction method allows to obtain codes such that the marginal bit probability converges to 0.5 as the sequence length increases and this is achieved even if the probability distribution function is not known by the encoder.

Sequence dependent charge transport through DNA molecules: The role of periodicity and long-range correlations

Understanding the intrinsic conduction properties in DNA plays a vital role in molecular electronic engineering. We use a tight-binding model to investigate the transmissivity, Lyapunov coefficient and localization length of DNA, including periodic poly(G)–poly(C), quasiperiodic Fibonacci polyGC and random sequences, as a function of sequence length and temperature. Our results show that the periodicity and long-range correlations in DNA can persist high transmittivity, and new transmission peaks can appear for whatever the sequence length or temperature increases, but the mean transmission coefficient decreases. Meanwhile, thermal enhancement of conductance is a generic feature in all these sequences and the asymptotic behaviors of localization length for random DNA are in good agreement with the mobility edge theory.

Entropy Coding With Variable-Length Rewriting Systems

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper describes a family of codes for entropy coding of memoryless sources. These codes are defined by sets of production rules of the form $a\bar{l} \rightarrow\bar{b}$ , where $a$ is a source symbol, and $\bar{l},\bar{b}$ are sequences of bits. The coding process can be modeled as a finite-state machine (FSM). A method to construct codes which preserve the lexicographic order in the binary-coded representation is described. For a given constraint on the number of states for the coding process, this method allows the construction of codes with a better compression efficiency than the HuTucker codes. A second method is proposed to construct codes such that the marginal bit probability of the compressed bitstream converges to 0.5 as the sequence length increases. This property is achieved even if the probability distribution function is not known by the encoder. </para>

Is There a Star Tree Paradox?

Concerns have been raised that posterior probabilities on phylogenetic trees can be unreliable when the true tree is unresolved or has very short internal branches, because existing methods for Bayesian phylogenetic analysis do not explicitly evaluate unresolved trees. Two recent papers have proposed that evaluating only resolved trees results in a "star tree paradox": when the true tree is unresolved or close to it, posterior probabilities were predicted to become increasingly unpredictable as sequence length grows, resulting in inflated confidence in one resolved tree or another and an increasing risk of false-positive inferences. Here we show that this is not the case; existing Bayesian methods do not lead to an inflation of statistical confidence, provided the evolutionary model is correct and uninformative priors are assumed. Posterior probabilities do not become increasingly unpredictable with increasing sequence length, and they exhibit conservative type I error rates, leading to a low rate of false-positive inferences. With infinite data, posterior probabilities give equal support for all resolved trees, and the rate of false inferences falls to zero. We conclude that there is no star tree paradox caused by not sampling unresolved trees.

Progressive and Error-Resilient Transmission Strategies for VLC Encoded Signals over Noisy Channels

This paper addresses the issue of robust and progressive transmission of signals (e.g., images, video) encoded with variable length codes (VLCs) over error-prone channels. This paper first describes bitstream construction methods offering good properties in terms of error resilience and progressivity. In contrast with related algorithms described in the literature, all proposed methods have a linear complexity as the sequence length increases. The applicability of soft-input soft-output (SISO) and turbo decoding principles to resulting bitstream structures is investigated. In addition to error resilience, the amenability of the bitstream construction methods to progressive decoding is considered. The problem of code design for achieving good performance in terms of error resilience and progressive decoding with these transmission strategies is then addressed. The VLC code has to be such that the symbol energy is mainly concentrated on the first bits of the symbol representation (i.e., on the first transitions of the corresponding codetree). Simulation results reveal high performance in terms of symbol error rate (SER) and mean-square reconstruction error (MSE). These error-resilience and progressivity properties are obtained without any penalty in compression efficiency. Codes with such properties are of strong interest for the binarization of-ary sources in state-of-the-art image, and video coding systems making use of, for example, the EBCOT or CABAC algorithms. A prior statistical analysis of the signal allows the construction of the appropriate binarization code.

A computer simulation analysis of the accuracy of partial genome sequencing and restriction fragment analysis in the reconstruction of phylogenetic relationships

Partial genome sequencing (PGS) and restriction fragment analysis (RFA) are used frequently in molecular epidemiologic investigations. The relative accuracy of PGS and RFA in phylogenetic reconstruction has not been assessed. In this study, 32 model phylogenetic trees with 16 extant lineages were generated, for which DNA sequences were simulated under varying conditions of genome length, nucleotide substitution rate, and between-site substitution rate variation. Genotyping using PGS and RFA was simulated. The effect of tree structure (stemminess, imbalance, lineage variation) on the accuracy of phylogenetic reconstruction (topological and branch length similarity) was evaluated. Overall, PGS was more accurate than RFA. The accuracy of PGS increased with increasing sequence length. The accuracy of RFA increased with the number of restriction enzymes used. In fragment size comparison, the Dice and Nei–Li algorithms differed little, with both more accurate than the Fragment Size Distribution algorithm. For RFA, higher tree stemminess and longer genome length were associated with higher topological accuracy, whereas lower tree stemminess and lower substitution rates were associated with higher branch length accuracy. For PGS, lower tree imbalance was associated with higher topological accuracy, whereas lower tree stemminess, higher substitution rate, and lower between-site substitution rate variation were associated with higher branch length accuracy. RFA had higher topological accuracy than PGS only for the shortest sequence length (200 bps) at a low substitution rate, high tree stemminess, and long genome length. PGS had equal or higher accuracy in branch length reconstruction than RFA under all conditions investigated. Thus, partial genome sequencing is recommended over restriction fragment analysis for conditions within the parameter space examined.

Joint detection of a given number of reference fragments in a quasi-periodic sequence and its partition into segments containing series of identical fragments

The problem of joint a posteriori detection of reference fragments in a quasi-periodic sequence and its partition into segments containing series of recurring fragments from the reference tuple is solved. It is assumed that (i) an ordered reference tuple of sequences to be detected is given, (ii) the number of desired fragments is known, (iii) the index of the sequence term corresponding to the beginning of a fragment is a deterministic (not random) value, and (iv) a sequence distorted by an additive uncorrelated Gaussian noise is available for observation. It is established that the problem consists in testing a set of hypotheses about the mean of a random Gaussian vector. The cardinality of the set grows exponentially as the vector dimension (i.e., the sequence length) increases. An efficient a posteriori algorithm producing a maximum-likelihood optimal solution to the problem is substantiated. Time and space complexity bounds related to the parameters of the problem are derived. The results of numerical simulation are presented.

SiteFind: A software tool for introducing a restriction site as a marker for successful site-directed mutagenesis

BackgroundSite-directed mutagenesis is a widely-used technique for introducing mutations into a particular DNA sequence, often with the goal of creating a point mutation in the corresponding amino acid sequence but otherwise leaving the overall sequence undisturbed. However, this method provides no means for verifying its success other than sequencing the putative mutant construct: This can quickly become an expensive method for screening for successful mutations. An alternative to sequencing is to simultaneously introduce a restriction site near the point mutation in manner such that the restriction site has no effect on the translated amino acid sequence. Thus, the novel restriction site can be used as a marker for successful mutation which can be quickly and easily assessed. However, finding a restriction site that does not disturb the corresponding amino acid sequence is a time-consuming task even for experienced researchers. A fast and easy to use computer program is needed for this task.ResultsWe wrote a computer program, called SiteFind, to help us design a restriction site within the mutation primers without changing the peptide sequence. Because of the redundancy of genetic code, a given peptide can be encoded by many different DNA sequences. Since the list of possible restriction sites for a given DNA sequence is not always obvious, SiteFind automates this task. The number of possible sequences a computer program must search through increases exponentially as the sequence length increases. SiteFind uses a novel "moving window" algorithm to reduce the number of possible sequences to be searched to a manageable level. The user enters a nucleotide sequence, specifies what amino acid residues should be changed in the mutation, and SiteFind generates a list of possible restriction sites and what nucleotides must be changed to introduce that site. As a demonstration of its use, we successfully generated a single point mutation and a double point mutation in the wild-type sequence for Krüppel-like factor 4, an epithelium-specific transcription factor.ConclusionSiteFind is an intuitive, web-based program that enables the user to introduce a novel restriction site into the mutated nucleotide sequence for use as a marker of successful mutation. It is freely available from

How Much Data are Needed to Resolve a Difficult Phylogeny? Case Study in Lamiales

Reconstructing phylogeny is a crucial target of contemporary biology, now commonly approached through computerized analysis of genetic sequence data. In angiosperms, despite recent progress at the ordinal level, many relationships between families remain unclear. Here we take a case study from Lamiales, an angiosperm order in which interfamilial relationships have so far proved particularly problematic. We examine the effect of changing one factor-the quantity of sequence data analyzed-on phylogeny reconstruction in this group. We use simulation to estimate a priori the sequence data that would be needed to resolve an accurate, supported phylogeny of Lamiales. We investigate the effect of increasing the length of sequence data analyzed, the rate of substitution in the sequences used, and of combining gene partitions. This method could be a valuable technique for planning systematic investigations in other problematic groups. Our results suggest that increasing sequence length is a better way to improve support, resolution, and accuracy than employing sequences with a faster substitution rate. Indeed, the latter may in some cases have detrimental effects on phylogeny reconstruction. Further molecular sequencing-of at least 10,000 bp-should result in a fully resolved and supported phylogeny of Lamiales, but at present the problematic aspects of this tree model remain.

Biases in Phylogenetic Estimation Can Be Caused by Random Sequence Segments

We consider the effects of fully or partially random sequences on the estimation of four-taxon phylogenies. Fully or partially random sequences occur when whole subsets of sequences or some sites for subsets of sequences are independent of sequence data for the other taxa. Random sequences can be a consequence of misalignment or because sites evolve at very fast rates in some portions of a tree, a situation that occurs especially in analyses involving deep divergence times. One might reasonably speculate that random sites will only add noise to the estimation of a phylogeny. We show that in the case that a random sequence is added to a three-taxa alignment, it is more likely to be a neighbor of the sequence corresponding to the longest branch in the three-taxon tree. Surprisingly, when only about half of the sites show randomness, a long-branch-repels form of small sample bias occurs, and when a minority of sites show randomness this becomes a long-branch-attraction bias again. The most serious bias, one that does not vanish with increasing sequence length, occurs when more than one sequence is partially random. If there is a large amount of overlap in the random sites for two sequences, those two sequences will be attracted to each other; otherwise, they will repel each other. Random sequences or sites can, therefore, cause complicated biases in phylogenetic inference. We suggest performing analyses with and without potentially saturated sequences and/or misaligned sites, to check that these biases are not affecting the inferred branching pattern.

Differential evaluation of the baroreceptor cardiac reflex effectiveness as a function of sequence length

Recently a new index of baroreceptor cardiac function has been proposed, the baroreflex effectiveness index (BEI). BEI was defined as the ratio between the number of systolic blood pressure (SBP) ramps (progressive beat-to-beat increases (“up”) or decreases (“down”)) followed by reflex changes in heart period and the total number of SBP ramps. In this study we tested BEI as a function of the length of cardiac sequences in which the reflex operates (3, 4, 5, and 6 beats) in human subjects in the laboratory. Results show an overall BEI of .65, with greater values for the “up” (.69) than for the “down” sequences (.62). These values are much higher than previously reported. When analyzed as a function of sequence length, BEI increases as sequence length decreases. This difference is more progressively observed in the “up” than in the “down” sequences. Both slope and overall blood pressure change of the SBP ramps increase as sequence length increases. Overall blood pressure change of the SBP ramps can predict BEI for the 4- ( r 2 ≈ .057) and 3-beat sequences ( r 2 ≈ .20). These results suggest the need to examine the effects of the setting/experimental manipulation on the average length of cardiac sequences, given that an observed change in BEI could be genuine or simply associated with a modification in the pattern of sequence length.

CALCULATION OF THE CROSSING TIME THROUGH THE FITNESS BARRIER IN A SYMMETRIC MULTIPLICATIVE LANDSCAPE

The crossing time through fitness barrier in a symmetric multiplicative landscape is systematically calculated for various mutation rates, fitness parameters, and sequence lengths by using a computer simulation. It is found that the crossing time scales as a power law in the mutation rate and the fitness parameter. It is also found that the crossing time increases exponentially as the sequence length increases. We have obtained the approximate formula, which decribes the asymptotic behavior of the crossing time in the long-crossing-time region, and the improved approximate formula with the correction factor, which nicely fit computer simulation results even below the long-crossing-time region. From the comparison between the approximate formula in the multiplicative landscape and the approximate formula in the sharply-peaked landscape, it is found that both landscapes have the same scaling effect of fitness parameter and mutation rate on the crossing time in the long-crossing-time region.

An Iterative Approach to Determining the Length of the Longest Common Subsequence of Two Strings

This paper concerns the longest common subsequence (LCS) shared by two sequences (or strings) of length N, whose elements are chosen at random from a finite alphabet. The exact distribution and the expected value of the length of the LCS, k say, between two random sequences is still an open problem in applied probability. While the expected value E(N) of the length of the LCS of two random strings is known to lie within certain limits, the exact value of E(N) and the exact distribution are unknown. In this paper, we calculate the length of the LCS for all possible pairs of binary sequences from N=1 to 14. The length of the LCS and the Hamming distance are represented in color on two all-against-all arrays. An iterative approach is then introduced in which we determine the pairs of sequences whose LCS lengths increased by one upon the addition of one letter to each sequence. The pairs whose score did increase are shown in black and white on an array, which has an interesting fractal-like structure. As the sequence length increases, R(N) (the proportion of sequences whose score increased) approaches the Chvatal–Sankoff constant a c (the proportionality constant for the linear growth of the expected length of the LCS with sequence length). We show that R(N) is converging more rapidly to a c than E(N)/N.

Development of PNA microarrays for gene diagnostics with TOF-SIMS

We have used time-of-flight secondary ion mass spectrometry (TOF-SIMS) to examine different immobilization processes of peptide nucleic acid (PNA) and their influence on the hybridization efficiency of unlabeled DNA fragments to complementary PNA. Two different approaches have been used to immobilize PNA onto Au surfaces. One method was to immobilize thiolated PNA in a single step reaction to the Au surface via an AuS bond. The other method was to crosslink the N-terminal end of the PNA to a preformed functionalized self-assembly monolayer (SAM). The influence of length and type of spacer molecules, which increase the distance between the biosensor surface and the PNA sequence, on the hybridization efficiency was also investigated. It was found that a greater spacer length leads to an increased hybridization efficiency. DNA could readily be identified by detecting PO 2 − and PO 3 − or other phosphate-containing molecules from the DNA backbone. Using TOF-SIMS a very good discrimination between complementary and non-complementary hybridized DNA sequences was achieved. It can be concluded that TOF-SIMS is a very useful technique for identifying unlabeled hybridized DNA on PNA biosensor chips. This method has the potential for providing a rapid method for DNA diagnostics and is also very suitable for studying the complexity of the immobilization and hybridization processes. Both the absence of a labeling procedure and the increase in the number of phosphate signals with increasing sequence length makes this technique especially useful for directly analyzing genomic DNA.

Splice variants: a homology modeling approach.

Splice variants play an important role within the cell in both increasing the proteome diversity and in cellular function. Splice variants are also associated with disease states and may play a role in their etiology. Information about splice variants has, until now, mostly been derived from the primary transcript or through cellular studies. In this study information from the transcript and other studies is combined with tertiary structure information derived from homology models. Through this method we have determined that it is possible to effectively model splice variants. Forty models of splice variants for fourteen proteins were produced. Analysis of the models shows that deletions produce superior model validation values. Additions to sequences where there is little homology become increasingly difficult to model with increasing sequence length. Many of the splicing events are associated with post-translational modification either in the N-terminal region by changing the signal peptide or by affecting the number or availability of glycosylation sites. Often the alternative exon combinations are associated with loss or gain of whole structural units, as opposed to just changing small loop regions. Losing part of the secondary structure may destabilize neighboring parts of the same secondary structure. Detailed analysis is given of four biomedically relevant proteins (Beta-site Amyloid Precursor Protein Cleaving enzyme (BACE), Interleukin-4, Frataxin and Hereditary hemochromatosis protein) and their associated splice variant models. The visualization of these possible structures provides new insights about their functionality and the possible etiology of associated diseases.

FOUNDATIONS AND EVIDENCE FOR AN INTERACTION‐BASED FLICT NEGOTIATION

This paper outlines 4 assumptions behind attempts to explain the sequential organization of communication behavior during conflict. These assumptions were supported by an analysis of behavioral sequences coded from 9 hostage negotiations and 20 divorce mediations. Analyses showed that negotiators use only a small proportion of available responses to other party's behavior, and that this proportion rapidly decreases as sequence length increases. Critical to this channeling in behavior was the triple‐interact (i.e., cue‐response‐cue‐response), which represents the maximum sequence length required to enable accurate prediction of negotiators' future behavior. More detailed analysis showed that the triple‐interact reduced uncertainty in behavior by over 70%, which compares to less than 1% from knowledge of negotiation context and approximately 10% from knowledge of individual differences.

Is sparse taxon sampling a problem for phylogenetic inference?

Rosenberg and Kumar (2001) addressed the importance of taxon sampling in phylogenetic analysis and concluded that phylogenetic error is “largely independent of taxon sample size” (2001:10756) and that their “results do not provide evidence in favor of adding taxa to problematic phylogenies” (2001:10756). In response to these conclusions, Zwickl and Hillis (2002) and Pollock et al. (2002) conducted additional simulations and reanalyzed the data presented by Rosenberg and Kumar (2001). Zwickl and Hillis and Pollock et al. showed that these conclusions of Rosenberg and Kumar could not be supported either by analyses of their original data or by new simulations that corrected a number of deficiencies in Rosenberg and Kumar’s original experimental design. Both Zwickl and Hillis and Pollock et al. found that increased taxon sampling resulted in greatly reduced phylogenetic estimation error, and Pollock et al. showed that the benefits of increased taxon sampling were similar to adding an equivalent amount of sequence length for the same taxa (in the ranges simulated by Rosenberg and Kumar). In their response, Rosenberg and Kumar (2002) focused on a slightly different conclusion from that in their original paper, which was that “longer sequences, rather than extensive sampling, will better improve the accuracy of phylogenetic inference” (2001:10751). In 2001, Rosenberg and Kumar argued that the beneficial effect of increasing taxa was 10-fold lower than the beneficial effect of increasing sequence length and that the effects of increased taxon sampling for the same genes were negligible (“largely independently” of phylogenetic error). Rosenberg and Kumar (2002) have now concluded that the beneficial effect of increasing taxon sample size is not small, but they suggested that the benefit comes simply from the overall increase in size of the data matrix (the total number of characters × taxa). Furthermore, they maintained that there is a greater benefit to increasing the total sequence length for few taxa than can be obtained by increasing taxon sampling for the same genes. Here, we discuss the two sets of conclusions reached by Rosenberg and Kumar (2001, 2002).

Increased taxon sampling is advantageous for phylogenetic inference.

Until recently, it was believed that complex phylogenies might be extremely difficult to reconstruct due to the phenomenal rate of increase in the number of possible phylogenies as the number of taxa increases. However, Hillis (1996) showed through simulation that, for at least one complex phylogeny of angiosperms with 228 taxa, reconstruction was far more accurate than expected, even with relatively modest amounts of DNA sequence data. This led to a flurry of papers on the subject of taxon sampling and phylogenetic reconstruction, with focus quickly shifting from the question of whether complex phylogenies can be reconstructed to whether and how much an existing phylogeny can be improved through increased taxon sampling (Hillis, 1998; Kim, 1998; Poe, 1998; Poe and Swofford, 1999; Pollock and Bruno, 2000; Rannala et al., 1998; Yang, 1998). Although a statistician might intuitively believe that it is generally better (or at least no worse) to increase the amount of data to resolve a question in statistical inference, the benefits of taxon addition for phylogenetic inference remain controversial. Some researchers have argued that taxon addition can decrease accuracy (Kim, 1996,1998), while others believe that increased sampling improves accuracy (Graybeal, 1998; Hillis, 1996, 1998; Murphy et al., 2001; Poe, 1998; Pollock and Bruno, 2000; Pollock et al., 2000; Soltis et al., 1999). The reasons that different papers come to apparently contradictory conclusions deserve careful consideration. An often cited factor affecting the benefits of taxon addition is the phenomenon of long-branch attraction (LBA). Some phylogenetic methods have a bias toward preferential clustering of long branches, leading to erroneous results when those long branches do not actually represent a monophyletic assemblage (Felsenstein, 1978; Hendy and Penny, 1989). This phenomenon has been cited in favor of increased taxon sampling, since sampling can be designed to break up long branches (Hillis, 1998). However, increased sampling has also been implicated as a potential cause of LBA because addition of a new long branch may wrongly attract a pre-existing long branch that had previously been inferred correctly (Poe and Swofford, 1999; Rannala et al., 1998). LBA may also explain some simulations that have found problems in phylogeny estimation when sampling outside the taxonomic group of interest (but see Pollock and Bruno [2000] for an alternative explanation). Outside sampling in these simulations tended to add long branches, which tended to attract the longest unbroken branch in the group of interest (Hillis, 1998; Rannala et al., 1998). The degree to which LBA is a problem depends greatly on the method of analysis, and LBA is much less of a problem for maximum likelihood (ML) than for parsimony or distance methods (Bruno and Halpern, 1999). A recent paper on the subject of taxon addition (Rosenberg and Kumar, 2001) concludes that increased taxon sampling is of little benefit to phylogenetic inference when compared to increasing sequence length. We disagree with their interpretation and believe that their data support the importance of increased taxon sampling. In addition, some of their data were simulated under extreme conditions (i.e., substitution rates that were very high or low, or sequences that were unreasonably short). Large error values and nonlinear relationships at these extremes make it difficult to interpret effects for the majority of the range, and averaging across the entire range is inappropriate. Moreover, we do not believe that Rosenberg and Kumar (2001) used the most appropriate metric to measure the relative effect of taxon addition. Our reanalysis of their simulated data indicates that increased taxon sampling is highly beneficial for phylogenetic inference.