Topological Properties of RNA Variation Networks over the Space of RNA Shapes

The function of an RNA sequence is related to its tertiary structure. Since dealing with RNA tertiary structure is very complicated, the RNA secondary structure is used instead. RNA secondary structure denotes various considerable aspects of RNA tertiary structure, and the biological function of an RNA sequence is assumed to be related to its secondary structure. Another useful illustration of an RNA secondary structure is the RNA shape, where it is holding the vicinity and nesting of structural components and shrinking their lengths to one. It would be significant to analyze the relations between the RNA sequences and their structures. One of the useful methods to perform these kinds of analysis is the neutral network. A neutral network can be considered as a graph whose vertex set is a collection of RNA sequences, all coding the same secondary structure, in which two RNA sequences are connected if one of them can be obtained from the other by a single base mutation. In this paper, a novel concept, entitled variation network, over the set of all RNA shapes is proposed to analyze the relation between the RNA sequences and their shapes, as well as to discover different topological properties of the RNA shapes. Based on the variation network, several topological properties, such as clustering coefficient, topological coefficient, average shortest path distribution, and centrality are calculated for natural RNA sequences. Also, the correlations between power-law function and some distributions over the variation network are obtained. These correlations indicate that the variation network is a kind of complex biological network, having scale-free structure and small world property. MATCH