Nucleotide Alphabet Research Articles

RNA folding and combinatory landscapes.

In this paper we view the folding of polynucleotide (RNA) sequences as a map that assigns to each sequence a minimum-free-energy pattern of base pairings, known as secondary structure. Considering only the free energy leads to an energy landscape over the sequence space. Taking into account structure generates a less visualizable nonscalar ``landscape,'' where a sequence space is mapped into a space of discrete ``shapes.'' We investigate the statistical features of both types of landscapes by computing autocorrelation functions, as well as distributions of energy and structure distances, as a function of distance in sequence space. RNA folding is characterized by very short structure correlation lengths compared to the diameter of the sequence space. The correlation lengths depend strongly on the size and the pairing rules of the underlying nucleotide alphabet. Our data suggest that almost every minimum-free-energy structure is found within a small neighborhood of any random sequence. The interest in such landscapes results from the fact that they govern natural and artificial processes of optimization by mutation and selection. Simple statistical model landscapes, like Kauffman and Levin's n-k model [J. Theor. Biol. 128, 11 (1987)], are often used as a proxy for understanding realistic landscapes, like those induced by RNA folding. We make a detailed comparison between the energy landscapes derived from RNA folding and those obtained from the n-k model. We derive autocorrelation functions for several variants of the n-k model, and briefly summarize work on its fine structure. The comparison leads to an estimate for k=7--8, independent of n, where n is the chain length. While the scaling behaviors agree, the fine structure is considerably different in the two cases. The reason is seen to be the extremely high frequency of neutral neighbors, that is, neighbors with identical energy (or structure), in the RNA case.

Effectiveness of measures requiring and not requiring prior sequence alignment for estimating the dissimilarity of natural sequences

Various measures of sequence dissimilarity have been evaluated by how well the additive least squares estimation of edges (branch lengths) of an unrooted evolutionary tree fit the observed pairwise dissimilarity measures and by how consistent the trees are for different data sets derived from the same set of sequences. This evaluation provided sensitive discrimination among dissimilarity measures and among possible trees. Dissimilarity measures not requiring prior sequence alignment did about as well as did the traditional mismatch counts requiring prior sequence alignment. Application of Jukes-Cantor correction to singlet mismatch counts worsened the results. Measures not requiring alignment had the advantage of being applicable to sequences too different to be critically alignable. Two different measures of pairwise dissimilarity not requiring alignment have been used: (1) multiplet distribution distance (MDD), the square of the Euclidean distance between vectors of the fractions of base signlets (or doublets, or triplets, or ...) in the respective sequences, and (2) complements of long words (CLW), the count of bases not occurring in significantly long common words. MDD was applicable to sequences more different than was CLW (noncoding), but the latter often gave better results where both measures were available (coding). MDD results were improved by using longer mutliplets and, if the sequences were coding, by using the larger amino acid and codon alphabets rather than the nucleotide alphabet. The additive least squares method could be used to provide a reasonable consensus of different trees for the same set of species (or related genes).

Genome structure described by formal languages.

Nucleic acid sequences may be looked upon as words over the alphabet of nucleotides. Naturally occurring DNAs and RNAs form subsets of the set of all possible words. The use of formal languages is proposed to describe the structure of these subsets. Regular languages defined by finite automata are introduced to demonstrate the application of the concept on RNA-phages of group I. This approach permits a concise characterization of grammatical patterns in genetic information.