Stacks in canonical RNA pseudoknot structures.
In this paper we study the distribution of stacks/loops in k-non-crossing, tau-canonical RNA pseudoknot structures (k,tau-structures). Here, an RNA structure is called k-non-crossing if it has no more than k-1 mutually crossing arcs and tau-canonical if each arc is contained in a stack of length at least tau. Based on the ordinary generating function of k,tau-structures [G. Ma, C.M. Reidys, Canonical RNA pseudoknot structures, J. Comput. Biol. 15 (10) (2008) 1257] we derive the bivariate generating function T(k, tau)(x, u) = Sigma(n>or=0)Sigma(0<or=t<or=n/2 T(k,tau)(n, t)u(t)x(n), where T(k,tau)(n, t) is the number of k,tau-structures having exactly t stacks and study its singularities. We show that for a specific parametrization of the variable u, T(k, tau)(x, u) exhibits a unique, dominant singularity. The particular shift of this singularity parametrized by u implies a central limit theorem for the distribution of stack-numbers. Our results are of importance for understanding the 'language' of minimum-free energy RNA pseudoknot structures, generated by computer folding algorithms.
Han
Hillary S W
HS
Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, PR China.
Reidys
Christian M
CM
D000465:Algorithms; D008958:Models, Molecular; D009690:Nucleic Acid Conformation; D012313:RNA / Q000737:chemistry*; D013816:Thermodynamics
D012313:RNA