Similarity measures sequences

Sequence comparison is a technique for comparing two strings, sequences, or vectors for the purpose of determining the distance between them, and consequently their relationship. The items making up the sequence could be numbers, symbols, tones, letters, or words. We could, for example, compute a metric distance between the names William and Victor. Recognizing this, it is a simple extension to understand that assertions concerning the causes of firm performance are sequences of words, and that sequence comparison methodology can be used to compute similarity measures between these assertions. 

We have seen that, purely using techniques of sequence comparison, the function of about 40% of genes sequenced from genome projects can be inferred from sequence identity or similarity measures or by motif comparison using a variety of techniques. It is known that proteins exhibiting insignificant sequence similarity often adopt similar tertiary structures, which themselves have similar (or at least re-... 

Raychaudhury, C. and Nandy, A. (1999). Indexing Scheme and Similarity Measures for Macro-mlecular Sequences. J.Chem.Inf.Comput.ScL, 39,243-247. 

In the scientific context, the attempt is made to reduce the importance of diagnostic criteria to an absolute minimum. Fortunately, this is comparatively easy to do when dealing with chemical entities such as structural formulas, for their emotive impact is dearly very small. Moreover, similarity measures can be adopted that are algorithmic in nature, i.e. measures that involve no actual similarity calls. Tversky [20] has also investigated an asymmetry in similarity calls that can arise when the sequence of the presentation of objects is altered. This problem is typically encountei when one of the objects being compared is regarded as a prototype. In comparison of circles and ellipses, for instance, experimental observers consistently reported that ellipses were more similar to circles than drcles to ellipses. The rule here appears to be that a variant will... 

A simple comparison of these numerical sequences for two molecules provides a numerical similarity measure. One of the simplest of these measures for two different conformations K and K of a molecule is the number of element matches divided by the number of elements in the longer of the two vectors ... 

The shape-based similarities between various reaction mechanisms can be analysed and quantified by direct comparisons of their matrix sequences. A numerical similarity measure of reaction mechanisms is based on a measure of difference between the two matrix sequences the smaller the difference, the greater the similarity. The extreme case of shapewise equivalence of reaction mechanisms is represented by Eq. (47). 

Molecular Similarity and QSAR. - In a first contribution on the design of a practical, fast and reliable molecular similarity index Popelier107 proposed a measure operating in an abstract space spanned by properties evaluated at BCPs, called BCP space. Molecules are believed to be represented compactly and reliably in BCP space, as this space extracts the relevant information from the molecular ab initio wave functions. Typical problems of continuous quantum similarity measures are hereby avoided. The practical use of this novel method is adequately illustrated via the Hammett equation for para- and me/a-substituted benzoic acids. On the basis of the author s definition of distances between molecules in BCP space, the experimental sequence of acidities determined by the well-known a constant of a set of substituted congeners is reproduced. Moreover, the approach points out where the common reactive centre of the molecules is. The generality and feasibility of this method will enable predictions in medically related Quantitative Structure Activity Relationships (QSAR). This contribution combines the historically disparate fields of molecular similarity and QSAR. 

Certain rotational levels of triplet states are perturbed by the A Z state and emissions from these levels are seen by excitation of CO with a fourth positive emission lamp [Slanger and Black (900)]. The CO(a ri) state is produced by a weak absorption of 2062 A light [Harteck et al. (443)] or by the Hg( P ) sensitized reaction [Liuti et al., (644) Simonaitis and Heicklen (885)]. The reaction products of CO( ri) are COj and C3O2, which are probably formed by a similar reaction sequence proposed for the photolysis of CO by Xe and Kr lamps. Quenching rates of CO(a ri) by various gases have been measured [Taylor and Setser (963)]. The rate constant is on the order of 10" cm molec" sec. Various electronic states and their lifetimes are given in Table V-1. 

Biological sequences, which consist of a sequence of nucleotides, amino acids, or secondary-structure elements (SSEs), are different from the objects we have discussed in Section 5.1.1. Hence, the above similarity measures are not applicable to biological sequences. In recent decades, many approaches have been proposed for the similarity measurement of sequences, the common ones being the alignment-based measures. 

Sequence comparison, sometimes referred to as the edit distance (or Levenshtein distance) procedure (Levenshtein, 1966), is performed in order to determine the similarity by measuring the degree of agreement in the aligned positions of two sequences. The goal of sequence alignment is to complete the transformation with the minimum cost. In this context, the similarity measure between two sequences can be considered as an optimal alignment problem (Xu and Wunsch, 2005). 

---