5 elements of CLESUM-hh and CLESUM-pp generally be- come larger in absolute values, and those of CLESUM-hp show the opposite tendency. The tendency is stronger for letters dominated by helices or sheets. bers in ASTRAL 40% compendium [47] and the total pair number is 21,039. In superfamily and fold, it is conve- nient to use SABmark [43] instead of using ASTRAL 40% because SABmark is systematically arranged and elabo- rately checked at both superfamily and fold level. The superfamily set contains 3,645 domains sorted into 426 subsets and the fold set (or be called twilight zone [48]) contains 1,740 domains sorted into 209 subsets, where each subsets contain between 3 to 25 structures. The superfamily set contains 18,724 structure pairs and the fold set contains 10,306. We apply MATT [45] to con- duct all-against-all pairwise alignment within each family or subset as our gold standard. Table IV shows that, hp-CL performs best while CL follows the second, both of them outperforms 10% to 100% than AA. For details, with the increase of TopK and length L , the accuracy of all coding systems grows better, while from family to fold level, the accuracy de- clines. It is surprising that at fold level, the accuracy of hp-CL outperforms AA more than 50% at the TopK SFP accuracy test and more than 100% at the TopK neighbor of AFP test, while in the latter, hp-CL got the average accuracy at about 71% given L = 18 from the Top-1 high- est neighbor of an AFP. Such feature may be applied to construct the Highest Similarity Fragment Block (HSFB) during the multiple structure alignment [23]. Given a seed structure and a certain position, if this position got many high score neighbors in other structures, may we say that this block (consisting the seed position and its neighbors) has a more probable chance in the final mul- tiple alignment. Moreover, we’ve shown the effectiveness of parameter self-adaptive strategy to create the SFP-list in [26]. At most cases self-adaptive strategy is compatible with fixed parameters , while the size of the SFP-list can be con- trolled empirically to about O(n $^{2}$/LEN H/6) with the LEN H=9 (Fig. 5). However, its hard to control the bal- ance between the size of the SFP-list and the threshold of SFP generated with fixed parameters strategy. Actually, the data of fixed length used in Table IV is considered all O(n $^{2}$) SFPs, then to select TopK; we’ve tested differ- ent SFP thresholds, if it is set too high there’ll lead to blank or few SFP-list while if it is set too loose then the SFP-list will be too much (data not shown). Finally, we may get the conclusion that, during struc- ture comparison, the only consideration of the TopK highest SFPs to built the initial alignment is feasible from family level to fold, so long as the coding system is specific enough. Also the employment of parameter self-adaptive strategy to generate SFPs is effective and economic. Note if the length of an AFP, say Len is longer than L , we’ll check each positions and the total number is Len − L + 1; if Len is shorter than L , we just skip this AFP. As a result, the TopK SFPs’ accuracy of a single pair of structures is a 0 or 1 measure, that is to say, within TopK we find a correct SFP or not. While the TopK neighbor of AFP’s accuracy is calculated by summing all correct positions found in any AFPs then dividing the total valid positions, the result is between 0.0 to 1.0. The benchmark we use is divided in three levels: fam- ily, superfamily and fold according to SCOP [46]. In fam- ily set, we use all SCOP families which have 2 to 25 mem- A coding system in protein structure is defined as an alphabet combined with its corresponding substitution matrix. Amino acids (AA) or all kinds of SAs can be treated as coding systems, so long as the alphabet has its substitution matrix. We’ll compare the performance of the following three ones, namely AA, CL and hp-CL, based on their TopK accuracy against a benchmark (Fig. 4). The difference between SFP and AFP is, we use SFPs to describe all local similar fragment pairs, while AFPs is a subset of SFPs that each of them should be in the final alignment [26]. FIG. 4: TopK accuracy check procedure. (A) Select a pair of struc- tures and aligned by MATT, resulting a series of AFPs. (B) Encode the pairwise structures, the coding system may be AA or SA. (C) Search for any SFPs with length L according to a certain coding system. (D) Sort these SFPs in descending order, the score is calculated by the corresponding substitution matrix. (E) Check whether there exists a correct SFP within TopK. (F) Search for any possible neighbor of a given AFP whose length is over L against the other string. (G) Sort these AFP’s neighbors. (H) Check their accuracy. TopK SFP’s Accuracy Check S R V L L S R V M M 6 ) 3L LMM / / 7 R S 7 R S 7 R S 7 R S 6 ) 3 / 6 ) 3 / 6 ) 3 / 6 ) 3 / 6 ) 3 / 6 ) 3 / 6 ) 3 / 6 ) 3 / 6 ) 3 / 6 ) 3O L V W 6 ) 3O L V WE\ V F R U H U D Q N 7 R S ( [ D F W 7 R S 3 D U W L D O 7 R S ( U U R U 7 R S ( [ D F W ' ( TopK AFP’s Neighbor Accuracy Check S R V S R V M M $ ) 3 / 7 R S 7 R S 7 R S 7 R S 6 ) 3 / 6 ) 3 / 6 ) 3 / $ ) 3 $ ) 3 $ ) 3 $ ) 3 6 ) 3 / 6 ) 3 / 6 ) 3 / 6 ) 3 / Aligned by  MATT $ ) 3 ’ V QH L J K E R U O L V W $ ) 3 ’ V QH L J K E R U O L V WE\ VF R U H U D Q N 7 R S ( [ D F W 7 R S ( U U R U 7 R S 3 D U W L D O 7 R S ( U U R U ) * + $ 6 ) 3 MM / % & 2. Performance 1. Overview B. Comparison between different coding systems