
HMMER-STRUCT

HMMER 10−4

pHMMAcc 10−4

pHMMOi 10−3 pHMM2D 10−3

pHMM3D 10−4

Paired two tailed t-test when comparing performance of each HMMERSTRUCT component with the combined model.

Table 3. HMMER-STRUCT paired t-test

## 4 Discussion

The accuracy of homology detection methods is essential for the problem of inferring the function of unknown-function proteins.

However, improving accuracy becomes hard when similarity between sequences is low. We proposed a method to improve pHMMs sensitivity by adding structural properties in the model building stage. We showed that the pHMMs trained according to this method are more sensitive than pHMMs trained from multiple sequence alignments, even if the alignment itself relied on structural properties. Our experiments demonstrated best performance for *pHMM2D*,
that used secondary structural properties, and for *pHMMOi*, that used packing density residues. Both pHMMs present similar performance. We believe that the good results obtained with the *pHMMoi* model can be attributed to the fact that tight packing is important for protein stability, and follow well-known results that indicate that amino-acids located in the core protein are more conserved than amino-acids located in other sites (Privalov, 2000). In the same way, the *pHMM2D* model achieve good performance as secondary structure elements are responsible for maintaining the form in homologue proteins. These elements form motifs and domains, which are related with protein function. Conserved sites may point to functionally and structurally important regions. These observations may explain the higher performance of models based on packing residues and on secondary structural properties.

The *pHMMAcc* models, based on amino-acid inaccessibility, and the *pHMM3D* models, based on three-dimensional coordinates, did not perform as well. The *pHMMAcc* models did not achieve statistical significance results, when they were compared with HMMER.

On the other hand, we observe that the inaccessibility property can be explained by hydrophobic effects, as are the amino-acids with hydrophobic side-chain that go toward the core protein by forming packages. Therefore hydrophobicity was represented in the *pHMMOi* model, that achieved good performance. Our results suggest the difference between models stems from the *pHMMOi* models to be more accurate and precise than what is used when building pHMMAcc.

However, we believe the inaccessibility property is already represented appropriately by *pHMMOi* model. Since amino-acids with high packing density already are inaccessible. Therefore, *pHMMOi* outperformed the *pHMMAcc*, as *pHMMoi* has more information than *pHMMAcc*.

The chief contribution of our method was achieved when all the models work together. The combined models performed significantly better than any single model. We believe that this results from the fact that each trained pHMMs represents a different structural property. Therefore, combining the models increases sensitivity by exploring the different structural properties.

Our method shows that structural information can be added during the training phase of pHMM to improve sensitivity, without much changes to the usage of pHMM methodology, and applied to recently discovered proteins for which there is little structural information.

## 5 Conclusion

The increasing number of studies involving pHMMs and the use of structural information has been quite remarkable (Hou *et al*., 2004; Alexandrov *et al*., 2004; Bystroff *et al*., 2000). Most of these approaches build structural models based on three-dimensional coordinates. In contrast, we present a novel methodology to train pHMMs based on structural alignment and other structural properties using a set of homologue protein sequences. Our method builds five models from an aligned homologue sequence set. Each model represents a different structural property, and the union of the models represent the structural context of aligned proteins. The properties used were primary, secondary and tertiary structures, accessibility and packing residue. Note that previous attempts have already used secondary and tertiary structural properties to train pHMM, though in quite a different way. However, accessibility and packing residue properties were used for the first time in pHMM training, with good results in the latter case.

In order, to build each model, we developed a novel sequenceweighting algorithm based on structural weights that are attributed for each amino-acid. Traditional weighting-algorithm works gives the same weight for every residue in the protein. Instead, we propose a method that gives a different weight to each aminoacid into a protein, according to structural properties that suggest it may be in a conserved region. Our results relied on prior work (Chakrabarti *et al*., 2004; Deane *et al*., 2003; Nishikawa *et al*.,
1986) that suggested interesting properties and estimated their weight.

Nowadays, the most popular approach to discovering the function of a newly found protein is through sequence similarity search. In fact, it is well known that structure is more conserved than sequence, and thus structural similarity can suggest function similarity. On the other hand, structural data is sparse and are usually not available for proteins with unknown function. Therefore, it is very important that methods that uses structural properties to build models will not need to rely on structural information for a new protein. Our method makes use of structural properties only at the model building stage, but not at scoring.

Our results show that the use of structural properties can improve the sensitivity of remote homology methods. Moreover, the combination of different model (one for each property) outperforms the use of individual properties. A number of future research directions present themselves. It will be interesting to include more models, such as that based on bond-hydrogen properties. Also, it will be interesting to apply our methodology to other remote homology tools, such as SAM (Hughey *et al*., 1996) and T-HMM Qian *et al*. (2004). Ultimately, we believe that our work is a step in the major challenge of finding the set of structural properties or features that represent precisely membership of a super family.