Abstract
AbstractThe DNA sequences containing multifarious novel symmetrical structure frequently play crucial role in how genomes work. Here we present a new scheme for understanding the structural features and potential mathematical rules of symmetrical DNA sequences using a method containing stepwise classification and recursive computation. By defining the symmetry of DNA sequences, we classify all sequences and conclude a series of recursive equations for computing the quantity of all classes of sequences existing theoretically; moreover, the symmetries of the typical sequences at different levels are analyzed. The classification and quantitative relation demonstrate that DNA sequences have recursive and nested properties. The scheme may help us better discuss the formation and the growth mechanism of DNA sequences because it has a capability of educing the information about structure and quantity of longer sequences according to that of shorter sequences by some recursive rules. Our scheme may provide a new stepping stone to the theoretical characterization, as well as structural analysis, of DNA sequences.
Highlights
Advancement of DNA sequencing techniques accelerates the increase of DNA sequences data; one important challenge is to identify the biological significations of the huge amounts of DNA sequences
The study may be a new method for the study of the symmetry origin and the growth mechanism from part to whole of DNA symmetrical sequences, it offer a new thinking for the theoretical characterization and structural analysis of DNA sequences
The study is the first screen for the understanding of how symmetry plays key roles in DNA classification and theoretical computation and, as such, it serves as a guild for the future exploration of DNA growth mechanism and symmetry breaking principles
Summary
The multifarious repeat sequences containing novel structures account for a large portion of genomes. The sequences illustrated by edge 9-12 and edge 13-16 are defined as the second and the third kind of mirror conjugated sequences respectively, marked by MII and MIII In this way, edges and 13-16 illustrate four classes of different symmetries, respectively, and define four classes of symmetrical sequences. Based on the above principle of classification, we consider all cases concerning combination of different symmetries and have derived the formulas to calculate the quantities of all classes of asymmetry sequences. Where n denotes the single arm length, and Cni i!(n i)!
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