Pairwise sequence comparison

New domains and their boundaries have been defined manually from sequence alone for literally hundreds of protein domains. Finding regions of similarity between proteins allows detection of domains. However, defining the exact boundaries of the domain is often a more difficult problem. Certain rules can be used to find the maximum size of a domain from pairwise comparisons of proteins in a related family. 

In this context, each patient would be receiving each of the multiple treatments. In the cross-over trial with three treatments this would likely be a three-period, three-treatment design and patients would be randomised to one of the six sequences ABC, ACB, BAC, BCA, CAB or CBA. Although there are again ways of asking a simultaneous question relating to the equality of the three treatment means through an analysis of variance approach this is unlikely to be of particular relevance questions of real interest will concern pairwise comparisons. 

Comments as above for the between-patient designs apply also for the within-patient designs and in many cases the best approach will be to focus on a sequence of pairwise comparisons using the paired t-test. 

The Tar—Tar sequence as well as the A-form RNA and B-form DNA equivalents of Tar—Tar (see Fig. 20.3) do not contain palindromes. However, we have data from multiple independent simulations and the analysis of Ponomarev et al. can be repeated using data from pairs of simulations. The equivalent test is to compare the residue-resolved ion-contact distributions between replicate trajectories. Such comparisons are a stringent test if each simulation was separately initialized with randomized ion starting positions and velocities. The PCCs for the A-form RNA simulations are shown in Fig. 20.4. Error bars denote the standard errors across the six possible pairwise comparisons across four independent trajectories, each of... 

Pairwise comparison of two sequences is a fundamental process in sequence analysis. It defines the concepts of sequence identity, similarity, and homology as applied to two proteins, DNA or RNA sequences. Database interrogation can take the form of text queries or sequence similarity searches. Typically, the user employs a query sequence to conduct sequence similarity search so that the relationships between the query sequence (probe) and another sequence (target) can be quantified and their similarity assessed. 

The left-hand side of Table I summarizes the numbers of amino acid sequences and pairwise comparisons considered for each of the five pro-... 

Most methods of sequence alignment are designed for pairwise comparisons, although alignments among all taxa under study are necessary before phylogenetic analysis can begin. Many of the pairwise approaches... 

Phylogenetic analyses of sequences can be conducted by analyzing discrete characters (i.e., the nucleotides themselves) or by making pairwise comparisons of whole sequences (the distance approach). Deciding whether to use a distance-based or a character-based method depends on... 

Analysis of Variance (ANOVA) with treatment, subject (nested within sequence) and period as main factors were performed for Cmax and AUCo-inf. The 90% confidence intervals of the point estimates of the ratio of Cmax and AUCo-inf, and of the difference between treatments for tmax were determined. Pairwise comparisons to treatment A were made with treatment A versus treatment B being the primary comparison. 

PK data The PK parameters of ABC4321 in plasma were determined by individual PK analyses. The individual and mean concentrations of ABC4321 in plasma were tabulated and plotted. PK variables were listed and summarized by treatment with descriptive statistics. An analysis of variance (ANOVA) including sequence, subject nested within sequence, period, and treatment effects, was performed on the ln-transformed parameters (except tmax). The mean square error was used to construct the 90% confidence interval for treatment ratios. The point estimates were calculated as a ratio of the antilog of the least square means. Pairwise comparisons to treatment A were made. Whole blood concentrations of XYZ1234 were not used to perform PK analyses. 

Figure 6.5. Scoring pairwise alignments. Scoring schemes are comprised of a substitution matrix (S) and gap penalty. Here we consider a pairwise comparison of nucleotide sequences, and the matrix S scores +1 for a match and -1 for a mismatch (left). Three alignments of X and Y are shown, and each is scored using both a linear and an affine gap penalty. The score of each residue pair is shown beneath it, and these are summed to produce the alignment score. Note that the affine gap penalty scores neighboring gaps as -3 and -1 the ordering is not determined, but the end result is their sum -4.

Table 1. Pairwise comparison of the topology and primary sequence of members of the short spacer family. The alpha carbon atoms defining the zinc protease fold (orange segment. Fig. 3) have been used in the topological superposition [56]. The distances refer to the root mean square deviations of this fold between pairs of structures. The corresponding pairwise primary sequence homology is also shown.

Table 2. Pairwise comparison of the topology and sequence of members of the long spacer family. Primary sequences for human Angiotensin Converting Enzyme [57], Botulinum Neurotoxin A [58], human Neutral Endopeptidase [59] have been used in the pairwise sequence comparison. Legend as in Table 1.

When the lysin sequences of the first seven species were obtained, we were impressed at how much divergence had occurred between their primary structures (Figure 9 Table 1). We also discovered that amino acid replacement was mainly nonconservative regarding the class of residue replaced. Next, we made pairwise comparisons of the aligned cDNA sequences and scored the numbers of amino acid altering (nonsynonymous) and silent (synonymous) nucleotide changes in the 21 pairwise comparisons of the seven sequences. The data (Table 2) showed that the vast majority of codon differences between any two lysins are amino acid altering. For example, in the comparison of mature red and pinto abalone lysins of 136 codons, 25 of the codon differences are nonsynonymous and only one is silent (Lee and Vacquier, 1992). 

For many genes a database search will reveal a whole number of homologous sequences. One then wishes to learn about the evolution and the sequence conservation in such a group. This question surpasses what can reasonably be achieved by the sequence comparison methods described in Section 2.3. Pairwise comparisons do not readily show positions that are conserved among a whole set of sequences and tend to miss subtle similarities that become visible when observed simultaneously among many sequences. Thus, one wants to simultaneously compare several sequences. 

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