RNAdualPF: software to compute the dual partition function with sample applications in molecular evolution theory

BMC Bioinformatics

Table 1 Base pair dual partition function table. Given the target structure with sequence constraints depicted in Fig. 2, RNAdualPF computes and stores all the partial dual partition function values for the substructures enclosed by each base pair

Index	i	j	Type	AU	CG	GC	UA	GU	UG	Z ^∗(i,j)
1	18	23	Tetraloop	0.000	0.000	0.364	0.000	0.000	0.000	0.364
2	17	24	Stack	10.977	17.859	76.923	10.977	10.977	3.525	131.238
3	16	26	R. bulge	11.690	70.834	184.603	12.771	13.347	3.915	297.160
4	6	10	Triloop	0.004	0.010	0.010	0.004	0.004	0.004	0.038
5	5	11	Stack	0.750	3.022	5.234	0.899	0.960	0.256	11.120
6	3	13	Int. loop	109.842	256.875	424.976	108.653	117.851	108.132	1126.330
7	2	14	Stack	10853.104	86208.448	170643.321	12575.544	13285.398	3647.077	297212.891
8	1	27	Multiloop	1558.575	7895.583	7895.583	1558.575	1558.575	1558.575	22025.464
9	1	28	S ₀	–	–	–	–	–	–	88101.856

The first column indicates the base pair index which dictates the order in which the dual partition function is computed for different loops closed by the base pair (i,j), where we the index of base pair (i,j) is defined to be the rank of (i,j) in the total ordering defined in Eq. (10). Columns i and j indicate the opening and closing positions of each base pair. Type indicates the type of element in the secondary structure closed by each base pair, where R. bulge stands for right bulge, Stack for stacking base pair, and Int. loop for interior loop. The dual partition function Z ^∗(i,j) of the substructure closed by base pair (i,j) appears in the rightmost column, while the partition function Z ^∗(i,j,X,Y) for each of the six canonical base pairs is given in columns 5-10. Note that for base pair 1, sequence constraints depicted in Fig. 2 force i and j to be instantiated respectively to G and C, hence the dual partition function Z ^∗(i,j;X,Y) is zero for any base pair different than GC. The last column of the last row of the table shows the total dual partition function Z ^∗(s ₀) for the target structure s ₀

ISSN: 1471-2105