The Expected Order of Saturated RNA Secondary Structures

2011/07/15 by Emma Yu Jin, Jin, Emma Yu, Markus E. Nebel +1
Computer Science · Mathematics · #05A16 #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #cs.IT #math.CO #math.IT #msc:05A16

paper · pdf · doi:10.48550/arxiv.1107.3033

2 figures

arxiv created 2011/07/15 · arxiv updated 2011/07/18

Abstract

We show the expected order of RNA saturated secondary structures of size n is log₄n(1+O((log₂n)/(n))), if we select the saturated secondary structure uniformly at random. Furthermore, the order of saturated secondary structures is sharply concentrated around its mean. As a consequence saturated structures and structures in the traditional model behave the same with respect to the expected order. Thus we may conclude that the traditional model has already drawn the right picture and conclusions inferred from it with respect to the order (the overall shape) of a structure remain valid even if enforcing saturation (at least in expectation).

Related

• A Remark on Deriving Precise Upper Bounds of the Number of the RNA Secondary Structures
• Analytical description of finite size effects for RNA secondary structures
• RNA secondary structures having a compatible sequence of certain nucleotide ratios
• Expected degree for RNA secondary structure networks
• Predicting RNA Secondary Structures with Arbitrary Pseudoknots by Maximizing the Number of Stacking Pairs