relation between rna sequences, structures, and shapes via variation networks

background: rna plays key role in many aspects of biological processes and its tertiary structure is critical for its biological function. rna secondary structure represents various significant portions of rna tertiary structure. since the biological function of rna is concluded indirectly from its primary structure, it would be important to analyze the relations between the rna sequences and their structures. one important tool to perform this kind of analysis is the neutral network which is a collection of rna sequences, all coding the same secondary structure, where each rna sequence is distinguished from the others by no more than a single base mutation. another high level and useful representation of an rna secondary structure is the rna shape, where it is holding the vicinity and nesting of structural components and reducing their lengths to one unit. this allows us to analyze the huge structural space corresponding to the larger rna sequences. objectives: in this study, a new concept, entitled variation network, over the set of all rna shapes is introduced. based on this concept, the potential relations between random and natural rna sequences, as well as their corresponding structures are analyzed. materials and methods: to explore the relations between random and natural rna sequences and their corresponding structures, different properties including frequency, normalized frequency, shape energy average, variation rate, normalized variation rate, neighborhood energy average, and stability were obtained and analyzed. results: the correlations among these properties of random and natural variation networks are presented.  base on the obtained correlations, all the employed datasets are highly correlated to each other from the frequency point of view, whereas they are not well correlated from the thermodynamic energy point of view. conclusions: since the thermodynamic energy value of an rna sequence over its secondary structure plays a key role in its function, this research conclude that the natural rna sequences are not generated randomly.