Encoded Walks and Correlations in Sequence Data

Abstract

Abstract The statistical analysis of sequence data has generated ongoing interest. The statistical properties of nucleic acid and protein sequences (see Doolittle, 1990; Volkenstein, 1994) provides important information on both the evolution and thermodynamic stability of biomacromolecules. In addition to conventional statistical approaches (for reviews, see, Karlin et al. (1991) and White (1994), fractal analyses of DNA and protein sequences have: given new insight into sequence correlations (Peng et al., 1992; Voss, 1992; Buldyrev et al., 1993; Dewey, 1993; Pande et al., 1994; Balafas and Dewey, 1995). In this chapter, we consider such analyses. They represent a problem in discrete dynamics very different from those discussed in the previous chapter. Lattice walks can be constructed from sequence information in a variety of ways. These encoded walks result from assigning a specific numerical value and spatial direction to the members in the sequence. For instance, in DNA problems it is common to give purines a+ 1 step on a one-dimensional lattice and pyrimidines a—1 step (Peng et al., 1992; Voss, 1992; Buldyrev et al., 1993). Similar walks have been studied in protein sequences and have been based on a specific chemical or physical property of the monomeric unit (Pande et al., 1994). The resulting trajectories of these encoded walks can be analyzed as diffusion problems. Deviation of the encoded walk from random behavior provides evidence for long-range correlations.