Increasing Sequence Length Research Articles

Accuracy and power of bayes prediction of amino acid sites under positive selection.

Bayes prediction quantifies uncertainty by assigning posterior probabilities. It was used to identify amino acids in a protein under recurrent diversifying selection indicated by higher nonsynonymous (d(N)) than synonymous (d(S)) substitution rates or by omega = d(N)/d(S) > 1. Parameters were estimated by maximum likelihood under a codon substitution model that assumed several classes of sites with different omega ratios. The Bayes theorem was used to calculate the posterior probabilities of each site falling into these site classes. Here, we evaluate the performance of Bayes prediction of amino acids under positive selection by computer simulation. We measured the accuracy by the proportion of predicted sites that were truly under selection and the power by the proportion of true positively selected sites that were predicted by the method. The accuracy was slightly better for longer sequences, whereas the power was largely unaffected by the increase in sequence length. Both accuracy and power were higher for medium or highly diverged sequences than for similar sequences. We found that accuracy and power were unacceptably low when data contained only a few highly similar sequences. However, sampling a large number of lineages improved the performance substantially. Even for very similar sequences, accuracy and power can be high if over 100 taxa are used in the analysis. We make the following recommendations: (1) prediction of positive selection sites is not feasible for a few closely related sequences; (2) using a large number of lineages is the best way to improve the accuracy and power of the prediction; and (3) multiple models of heterogeneous selective pressures among sites should be applied in real data analysis.

Sequence analysis of poly(ethylene terephthalate)/poly(butylene terephthalate) copolymer prepared by ester‐interchange reactions

AbstractThe molecular structure of the copolyester formed through the interchange reaction in poly(ethylene terephthalate)/poly(butylene terephthalate) blends was investigated with 13C‐NMR spectroscopy. The molar fractions of heterolinkage triads in the copolyesters were lower than the values calculated by Bernoullian statistics; this indicates that the sequence of heterolinkages was far from a random distribution at the initial stage of the interchange reaction. However, the randomness increased and the number‐average sequence length decreased with reaction time. The solubility of the blend decreased with increasing sequence length, resulting from the formation of block copolymers with long sequence lengths at the initial stage of the interchange reaction. The solubility of the copolyester formed by a dibutyltin dilaurate (DBTDL)‐catalyzed reaction was higher than that of the copolyester formed by a titanium tetrabutoxide‐catalyzed reaction; this is related to the fact that alcoholysis prevailed in the DBTDL‐catalyzed reaction. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 82: 159–168, 2001

PHOTODEGRADATION OF St-MMA COPOLYMERS: CORRELATION OF DEGRADATION, STYRENE CONTENT, AND PHOTOPHYSICS

A series of styrene(St)-methyl methacrylate(MMA) copolymers with compositions ranging from 0 to 100% St were synthesized and exposed to UV light for various periods of time. The changes in yellowing (yellowness index—YI) and absorbance of exposed films were evaluated as a function of photolysis time and St content. Both the changes in YI and absorbance at 400 nm were found to increase dramatically for polymer films with styrene (St) content greater than about 50%. A direct correlation between increases in the YI and absorbance at 400 nm with mean styrene sequence length was found with a maximum change being obtained for copolymers with mean sequence length of approximately 5 St units or greater. A small absorbance shoulder at 270–290 nm was observed for copolymers with St content less than 30% after relatively short irradiation times (e. g. 2 hours). Excimer formation of copolymers in dilute solution was found to increase with an increase in St content and St sequence length; in films, a plateau in the relative excimer emission was attained with a St content of 60%, corresponding to a mean St sequence length of 2.

Appropriate Likelihood Ratio Tests and Marginal Distributions for Evolutionary Tree Models with Constraints on Parameters

We show how to make appropriate likelihood ratio tests for evolutionary tree models when parameters such as edge (internodes or branches) lengths have nonnegativity constraints. In such cases, under the null model of an edge length being zero, the marginal distribution of this parameter is proven to be a "half-normal", that is, 50% zero values and 50% the positive half of a normal distribution. Other constrained parameters, such as the proportion of invariant sites, give similar results. To make likelihood ratio tests between nested models, e.g., H(0): homogeneous site rates, and H(1): site rates follow a gamma distribution with variance 1/k, then asymptotically as sequence length increases, the distribution under H(0) becomes a mixture of chi distributions, in this case 50% chi(0), and 50% chi(1) (where the subscript denotes degrees of freedom, i.e. , not the usually assumed 100% chi(1); which leads to a conservative test). Such mixtures are sometimes called distributions. Simulations show that even with sequences as short as 125 sites, some parameters, including the proportion of invariant sites, fit asymptotic distributions closely.

Microdomain Scale Organization and Scattering Patterns of Associating Polymer Melts

A microscopic theory of the structure of compressible associating AB regular heteropolymer fluids is proposed based on polymer integral equation methods. The theory is employed to systematically explore, as a function of temperature, the influence of sticky group attractive energy, concentration, degree ofblockiness, and global architecture (telechelic, surfactant, multiblock) on self-assembly and microdomain formation as encoded in small-angle partial scattering structure factors. Characteristic apparent spinodal and order-disorder temperatures are estimated, and strong composition fluctuation effects are always present. The evolution of collective properties derived from scattering profiles such as microdomain period, intermultiplet coherence length, degree of Porodlike scattering, and modification of wide-angle intensity, with polymer structure and thermodynamic state are established. At fixed bare (chemical) driving force, end-functionalized architectures are found to form more ordered microphase-separated fluids than the multiblock analogues. Increasing sequence length also enhances self-assembly even at fixed global sticky group composition. Significant differences between telechelics composed of unimer sticky groups vs minitriblocks are found, with the former displaying many self-assembly features not in accord with classic block copolymer behavior. Semiquantitative comparisons with small-angle X-ray scattering experiments suggest the theory provides a realistic description of self-assembly in ionomer melts, and failure of incompressible random phase approximation approaches for many properties is documented. Predictions for the majority (nonpolar) monomer density fluctuations, and cross-correlations, are obtained. Subtle, but systematic structural changes are induced by the minority group self-assembly process which may be amenable to direct measurement using small-angle neutron scattering and are possibly of mechanical property relevance.

Performance analysis of correlation-based communication schemes utilizing chaos

Using chaotic signals in spread-spectrum communications has a few clear advantages over traditional approaches. Chaotic signals are nonperiodic, wideband, and more difficult to predict, reconstruct, and characterize than periodic carriers. These properties of chaotic signals make it more difficult to intercept and decode the information modulated upon them. However, many suggested chaos-based communication schemes do not provide processing gain, a feature highly desirable in spread-spectrum communication schemes. In this paper, we suggest two communication schemes that provide a processing gain. The performance of these and of the earlier proposed differential chaos shift keying is studied analytically and numerically for discrete time implementations. It is shown that, when performance is characterized by the dependence of bit error rate on E/sub b//N/sub 0/, the increase of the spreading sequence length beyond a certain point degrades the performance. For a given E/sub b//N/sub 0/, there is a length of the spreading sequence that minimizes the bit error rate.

Numerical investigation of light-wave localization in optical Fibonacci superlattices with symmetric internal structure

We study numerically the optical transmission of one-dimensional binary quasiperiodic dielectric multilayers, which are arranged in Fibonacci sequences along two opposite directions and possess a mirror symmetry. We find that the transmission coefficient is unity for all sequences studied at the central wavelength = 0, where 0 = 4nA (B)dA (B), with nA (B) and dA (B) being the index of refraction and thickness of two kinds of layer, respectively. As the number of layers in the sequence increases, more and more perfect transmission peaks appear. We observe a scaling of the transmission spectra with increasing sequence length. These phenomena will find applications in fabrication of multiwavelength narrow-band optical filters.

A few logs suffice to build (almost) all trees: Part II

Inferring evolutionary trees is an interesting and important problem in biology, but one that is computationally difficult as most associated optimization problems are NP-hard. Although many methods are provably statistically consistent (i.e. the probability of recovering the correct tree converges to 1 as the sequence length increases), the actual rate of convergence for different methods has not been well understood. In a recent paper we introduced a new method for reconstructing evolutionary trees called the dyadic closure method (DCM), and we showed that DCM has a very fast convergence rate. DCM runs in O(n5 log n) time, where n is the number of sequences, and so, although polynomial, the computational requirements are potentially too large to be of use in practice. In this paper we present another tree reconstruction method, the witness-antiwitness method (WAM). WAM is faster than DCM, especially on random trees, and converges to the true tree topology at the same rate as DCM. We also compare WAM to other methods used to reconstruct trees, including Neighbor Joining (possibly the most popular method among molecular biologists), and new methods introduced in the computer science literature.

The ancestry of a sample of sequences subject to recombination.

In this article we discuss the ancestry of sequences sampled from the coalescent with recombination with constant population size 2N. We have studied a number of variables based on simulations of sample histories, and some analytical results are derived. Consider the leftmost nucleotide in the sequences. We show that the number of nucleotides sharing a most recent common ancestor (MRCA) with the leftmost nucleotide is approximately log(1 + 4N Lr)/4Nr when two sequences are compared, where L denotes sequence length in nucleotides, and r the recombination rate between any two neighboring nucleotides per generation. For larger samples, the number of nucleotides sharing MRCA with the leftmost nucleotide decreases and becomes almost independent of 4N Lr. Further, we show that a segment of the sequences sharing a MRCA consists in mean of 3/8Nr nucleotides, when two sequences are compared, and that this decreases toward 1/4Nr nucleotides when the whole population is sampled. A measure of the correlation between the genealogies of two nucleotides on two sequences is introduced. We show analytically that even when the nucleotides are separated by a large genetic distance, but share MRCA, the genealogies will show only little correlation. This is surprising, because the time until the two nucleotides shared MRCA is reciprocal to the genetic distance. Using simulations, the mean time until all positions in the sample have found a MRCA increases logarithmically with increasing sequence length and is considerably lower than a theoretically predicted upper bound. On the basis of simulations, it turns out that important properties of the coalescent with recombinations of the whole population are reflected in the properties of a sample of low size.

Chain flattening of spin-cast PMMMA on aluminum mirrors: Influence of polymer tacticity

Polymer tacticity has already been shown to be an influential parameter governing the behavior of polymer solutions and polymer blends, but not for polymer adsorption. However, using PMMA having a racemic fraction (ƒ r) ranging from 0.1 to 0.9, spin-cast on aluminum mirror surfaces, makes it possible to work out configuration differences in the adsorbed layer. Reflectance infra-red spectroscopy has been used to evaluate the fraction of surface bonded carbonyl groups (ƒ ab CO) and local conformations of both main and side chain. The ƒ ab CO value is 0.1 for highly syndiotactic PMMA and reaches 0.7 for mainly isotactic PMMA. This latter very high value of ƒ ab CO can only be explained by chain flattening resulting from a distortion from its Isotropic state. This distortion may be due to both strong interactions that may exist between PMMA and the aluminium substrate, and also to the spin-cast process that may lead to chain straightening and flattening. The assumption of conformational energy changes of both backbone and side chain is confirmed by changes in the FT-IR Av 2(1245 cm −1) Av 1(1265–1275 cm −1 ) ratio. Ellipsometric spectroscopy has provided information on the global conformation of adsorbed chains by precise thickness measurements. Thus, thickness ( h) increases for diluted solutions linearly from 10 to 70 A as the average syndiotactic sequence length ( n s ) increases. However, IR and ellipsometric results tend to prove that isotactic PMMA may adsorb on the aluminum surface in a more flattened way with longer chains than atactic and syndiotactic chains. This can be explained by the ability of chain segmental rearrangements ( meso tg state) that may allow isotactic PMMA to favor the establishment of interfacial acid-base bonds while the syndiotactic PMMA local stiffness of the tt state does not. The influence of the chain entropy in solution is also discussed as an important parameter.

The (mis)behavior of behavior analysis storage estimates

This paper investigates the dependence of estimates of reservoir storage capacity derived using behavior analysis on the length of inflow sequence used for overyear reservoir simulation. It has generally been assumed that simulation using behavior analysis, which incorporates a given probability of failure, will always give steady state estimates of the storage capacity (apart from the effects of the initial reservoir condition). The results reported here show that it may take sequence lengths as much as 1000 years or more for the mean of the distribution of storage capacity estimates to approach a stationary value. For some cases with high draft and high inflow variability, we show that a significant swing of the mean storage estimates from an initial downward bias into an upward bias occurs before their convergence to a stationary level. However, the median storage estimates always showed downward bias which sometimes decreased very slowly with increasing sequence length. We provide explanations for these observations and discuss some of the implications on the choice of inflow sequence length in determining reservoir storage capacities using behavior analysis.

Influence of the sequence distribution on the crystalline structure of ethylene-dimethyl-aminoethylmethacrylate copolymers

The comonomer sequence distributions of a series of ethylene-dimethylaminoethymethacrylate copolymers (EDAM) were measured by quantitative high-resolution 13C n.m.r. spectroscopy. It was found that both the crystallinity and the lamellar thickness of EDAM samples increase linearly with the increase of the numerical average sequence length of ethylene run. It was further demonstrated that only ethylene longer than a critical length can participate in crystallization. Such a critical length was found to be independent of the molecular weight and composition of EDAM samples under the same crystallization condition.

Fluoromethylene Cyanate Ester Resins. Synthesis, Characterization, and Fluoromethylene Chain Length Effects

Fluoromethylene cyanate ester resins derived from the monomer series N⋮CO−CH2(CF2)nCH2−OC⋮N (where n = 3, 4, 6, 8, and 10) have been synthesized and characterized. Monomer melting points range from −8 to 181 °C, and characterization includes 1H, 13C, and 19F NMR and IR spectroscopy and DSC. Purification is a critical requirement for melt processing. The thermal curing reaction is a cyclotrimerization reaction of the cyanate functional group to the cyanurate heterocycle. Physical properties of resin castings and their variation with an increase in fluoromethylene sequence length from 3 to 10 CF2 units include density, 1.77−1.91 g/cm3; critical surface tension, 40−23 dyn/cm; refractive index, 1.447−1.382; dielectric constant, 2.7−2.3; 100 °C immersion water absorption, 1.67−0.68%; Tg, 84−101 °C; glass/rubber thermal expansion coefficient, (109/238−152/275 ppm/ °C; and gravimetric thermal stability, 0.0196−0.0064% weight loss/min at 300 °C). Compared with aromatic cyanate ester resins, the fluoromethylene cy...

Optimal sequencing strategies for surveying molecular genetic diversity.

Two commonly used measures of genetic diversity for intraspecies DNA sequence data are based, respectively, on the number of segregating sites, and on the average number of pairwise nucleotide differences. Expressions are derived for their variance in the presence of intragenic recombination for a panmictic population of fixed size that is at neutral equilibrium at the region sequenced. We show that, in contrast to the slow decrease in variance with increasing sample size, if the recombination rate is nonzero, the asymptotic rate of decrease of variance with increasing sequence length, for fixed sample size, is quite rapid. In particular, it is close to that which would be obtained by sequencing independent chromosome regions. The correlation between measures of diversity from linked regions is also examined. For a given total number of bases sequenced in a particular region, optimal sequencing strategies are derived. These typically involve sequencing relatively few (three to 10) long copies of the region. Under optimal strategies, the variances of the two measures are very similar for most parameter values considered. Results concerning optimal sequencing strategies will be sensitive to gross departures from the underlying assumptions, such as population bottlenecks, selective sweeps, and substantial population substructure.

A study of the interphase in styrene-methacrylic acid copolymer/glass bead composites

The influence of filler loading, size and surface treatment on the dynamic mechanical behaviour and thermal properties of styrene-methacrylic acid copolymer/glass bead composites is analysed. A theoretical approach to quantifying molecular mobility is proposed to explain the decrease in molecular motion due to strong matrix-filler linkages. The higher the filler content and the smaller the particle size, the greater the number of anchored bonds. This effect is enhanced for beads coated by silane or an elastomeric agent. In the latter case, the reduction in molecular motion is less evident owing to an increase in the mobile sequence length, which induces greater mobility.

Increasing sequence length favors alpha-helix over 3(10)-helix in alanine-based peptides: evidence for a length-dependent structural transition.

Ala-based peptides form marginally stable helices at low temperature and are conventionally considered as mixtures of alpha-helix and random coil. However, recent work with doubly spin-labeled peptides suggests that short 16-residue sequences contain a significant fraction of 3(10)-helix near the N-terminus (positions 4-8). Using the same double-label strategy, we report on the helix geometry of the peptides Ac-(AAAAK)nA-NH2 with n = 3 and n = 4. The 16-mer (n = 3) is now examined at a region near the C-terminus, and there is evidence for 3(10)-helix here as well. The 21-mer (n = 4) is examined in three regions of the sequence. In dramatic contrast to the 16-mer, the 21-mer exhibits the signature of alpha-helix at the N-terminus and on through the middle of the peptide. The 21-mer C-terminus, however, adopts the 3(10)-helix geometry as is often found for C-termini in protein alpha-helices. These data indicate that the proportion of alpha-helix and 3(10)-helix in Ala-based peptides depends upon the sequence length.

Effect of phenyltriethoxysilane as external donor on the microstructure of ethylene-propylene copolymers

The effect of an external electron donor, namely, phenyltriethoxysilane (PES) on the compositional heterogeneity and the microstructure of ethylene-propylene copolymers prepared using a titanium-magnesium catalyst has been investigated. Addition of PES causes an increase in the average sequence length of ethylene and propylene. The products of reactivity ratios of ethylene and propylene indicate that the copolymer is blocky in nature. The external donor produces a propylene sequence in the copolymer which is richer in mmmm pentads.

Application of entropy measures derived from the ergodic theory of dynamical systems to rat locomotor behavior.

Measures of complexity derived from ergodic theory of dynamical systems were developed and applied to an exemplary data set describing locomotor movements of rats in a bounded space. A symbolic dynamical system was obtained by partitioning the event space into equally probable partition elements, using a k-dimensional tree. The measures calculated from the symbolic sequences included the topological entropy (ht)--i.e., the rate of increase of all possible sequences with increasing sequence length--and the metric entropy (hm)--i.e., the rate of increase of all likely sequences with increasing sequence length. These measures were used to assess changes in rat locomotor behavior as recorded in the behavioral pattern monitor (BPM) that were induced by amphetamine (0.25, 0.50, 1.0, or 2.0 mg/kg) and 3,4-methylenedioxymethamphetamine (MDMA; 1.25, 2.5, 5.0, or 10.0 mg/kg). Amphetamine increased the mean activity, ht, and hm. MDMA resulted in a monotonic dose-response curve for activity but exhibited a biphasic dose response in ht and hm. In particular, some animals in the higher dose groups showed a ht in the range of the saline controls, whereas other animals exhibited a significantly reduced ht and a greater decrease in hm, suggesting that two different behavioral reactions coexist within the same higher dose range of MDMA. An important implication of our method is that, in applied ergodic measure-theoretic approaches, the partition that determines the elements of the symbolic dynamical system should not be specified a priori on abstract mathematical grounds but should be chosen relative to its significance with respect to the data set in question. Here, the animal constructs its own spatiotemporal partition in behavioral phase space.

The organization of rapid movement sequences as a function of sequence length

An experiment was performed to test the predictions made by the subprogram retrieval model (Sternberg et al. 1978) for the production of rapid movement sequences, and to search for the maximum number of elements that can be planned in advance of sequence execution. Subjects performed rapid sequences of 1 to 8 finger taps under both simple and choice RT conditions. Increasing sequence length had no effect on choice RT, but caused simple RT to increase nonlinearly, with the greatest effect between 1 and 3 taps. Intertap intervals did not increase as a function of sequence length. The sequences' timing and force patterns suggested that sequences up to 8 taps were organized as single performance units. The results indicate a fundamental difference between activating a plan for a single tap and a sequence plan in which several elements must be coordinated and timed. Increasing the number of elements beyond 3 does not necessarily add processing steps in the selection and activation of the sequence plan, at least for sequences involving the repetition of a simple element.

Acetylene-cyclopentene copolymers

Cyclopentene (CP) and 7,8-bis(trifluoromethyl)tricyclo-[4,2,2,02,5]-deca-3,7,9-triene (p-A) were copolymerized. The copolymers were thermally converted to acetylene-cyclopentene copolymers ACP-13, ACP-11, and ACP-31 containing 60.3%, 48.3% and 39.4% of CP, respectively. Infrared spectroscopy showed the copolymers to have increasing sequence length of conjugated double bonds with increasing acetylene contents. The copolymers have only small amounts of unpaired spins which are only one-tenth to one-hundredth of that found in normal trans-poly(acetylene). The copolymers absorb large quantities of iodine, which on the basis of sp 2-carbon atoms are comparable to iodine doped poly(acetylene). Doped ACP-copolymers acquire some increase of conductivity up to 10−4 (Ω cm)−1 for ACP-31 copolymer and evacuation returned the materials to their insulating states even though the samples retained a few mole % of I3 −. The results are attributed to low carrier concentration and mobility.