Table 1.
All cases are represented in terms of a gain function (G(θ, y)) and a probability distribution of sequence x in the input alignment A(px(θ|A)) which are components in the estimator (E2) (Figure 2)
| Algorithms |
G(θ, y) |
px(θ|A) |
Ref. | ||
|---|---|---|---|---|---|
| CentroidAlifold (new) | G3 |  |
P3 | Mixture of p(mcc)(θ|x)/p(contra)(θ|x) and p(alipffold)(θ|A)/p(pfold)(θ|A) | this work |
| CentroidAlifold (old) | G3 |  |
P2 | p(mcc)(θ|x) or p(contra)(θ|x) | (16) |
| McCaskill-MEA | G2 |  |
P2 | p(mcc)(θ|x) | (26) |
| PETfold | G2 |  |
P3 | Mixture of p(mcc)(θ|x) and p(pfold)(θ|A) | (37) |
| Pfold | G2 |  |
P1 | p(pfold)(θ|A) | (27) |
| Pfold-Centroid | G3 |  |
P1 | p(pfold)(θ|A) | (16,27) |
| RNAalifold | G1 | G(δ) | P1 | p(alipffold)(θ|A) | (2) |
| RNAalipffold-Centroid | G3 |  |
P1 | p(alipffold)(θ|A) | (2,16) |
| Algorithms | Disadvantages | S.I. |
|---|---|---|
| CentroidAlifold (old) | No use of the information of the input alignment A | Section A.5.1 |
| McCaskill-MEA | Use of  ; no use of the information of the input alignment A
|
Section A.5.7 |
| PETfold | Use of 
|
Section A.5.4 |
| Pfold | Use of 
|
Section A.5.5 |
| Pfold-Centroid | Use of the same distribution px(θ|A) for all x∈A | Section A.5.6 |
| RNAalifold | Use of Gδ (i.e. use of the ML estimator) | Section A.5.2 |
| RNAalipffold-Centroid | Use the same distribution px(θ|A) for all x∈A | Section A.5.3 |
, G(δ) and 
are the gain function used in the γ-centroid estimator (17), the delta function and the gain function used in CONTRAfold (19), respectively. p(mcc)(θ|x) and p(contra)(θ|x) are McCaskill model (18) and CONTRAfold model (19), respectively, each of which is a probability distribution of secondary structures of RNA sequence x. p(alipffold)(θ|A) and p(pfold)(θ|A) are RNAalipffold model (12) and Pfold model (14), respectively, each of which is a probability distribution of common secondary structures of the alignment A. G1-3 and P1-3 show the types of the gain function and the probability distribution, respectively, and G1, G2, P1 and P2 have drawbacks (see the main text). The disadvantages of each algorithm are shown in the bottom table. For comparison, the improved CentroidAlifold [denoted by ‘CentroidAlifold (new)’], which is introduced in this work, is also shown. The column ‘S.I.’ shows the section in the Supplementary Data.