Jin Emma Y, Qin Jing, Reidys Christian M
Center for Combinatorics, LMPC-TJKLC, Nankai University, Tianjin 300071, China.
Bull Math Biol. 2008 Jan;70(1):45-67. doi: 10.1007/s11538-007-9240-y. Epub 2007 Sep 26.
In this paper, we derive the generating function of RNA structures with pseudoknots. We enumerate all k-noncrossing RNA pseudoknot structures categorized by their maximal sets of mutually intersecting arcs. In addition, we enumerate pseudoknot structures over circular RNA. For 3-noncrossing RNA structures and RNA secondary structures we present a novel 4-term recursion formula and a 2-term recursion, respectively. Furthermore, we enumerate for arbitrary k all k-noncrossing, restricted RNA structures i.e. k-noncrossing RNA structures without 2-arcs i.e. arcs of the form (i,i+2), for 1< or =i< or =n-2.
在本文中，我们推导了具有假结的RNA结构的生成函数。我们枚举了所有按其相互交叉弧的最大集合分类的k - 非交叉RNA假结结构。此外，我们枚举了环状RNA上的假结结构。对于3 - 非交叉RNA结构和RNA二级结构，我们分别给出了一个新的四项递归公式和一个两项递归公式。此外，我们枚举了对于任意k的所有k - 非交叉受限RNA结构，即没有2 - 弧（即形式为(i, i + 2)的弧，其中1≤i≤n - 2）的k - 非交叉RNA结构。
