## 5 Experimental Results
To this end, we employ the candidate patterns obtained from the previous experiments to test the presence of PROSITE signatures. We consider in detail again the first two families, \(Fa\) and \(Ni\), and the corresponding signatures. The other four families show similar results and are summarized in Table 4.  
We consider \(Ni_{2}\) and \(Fa_{2}\) directly as degenerate patterns, due to their low number of gaps, while we split signatures, \(Ni_{1}\) and \(Fa_{1}\), into two different patterns each and compute the statistics of these patterns accordingly. For both sets of patterns, \(\mathcal{M}\) and \(\mathcal{U}\), we compute the maximum similarity between each pattern in the set and the two signatures. The similarity between two patterns, \(m\) and \(m^{\prime}\), is the number of shared characters, including character classes, in the best alignment of \(m\)_versus_\(m^{\prime}\), without considering indels. Tables 5 and 6 summarize the maximum similarity, for different quorums, of \(\mathcal{M}\) and \(\mathcal{U}\), with each signature of the two protein families, \(Ni\) and \(Fa\). The second and third columns report the maximum similarity for the set of underlying patterns divided by the similarity of the original set. For example, in the first row of Table 5, the quorum is five. In this case, the maximum similarity of \(\mathcal{M}\) with the representative pattern, \(Ni_{1}\), is 26. The same value is obtained also for the corresponding set of underlying patterns, \(\mathcal{U}\), thus indicating that the pattern, \(Ni_{1}\), is retained with the same degree of accuracy. \begin{table}
\begin{tabular}{l c c c c} \hline  & \multicolumn{2}{c}{\(\mathbf{Ni_{1,2}}\)} & \multicolumn{2}{c}{\(\mathbf{Fa_{1,2}}\)} \\ \hline
**Binary Relation** & **Similarity** & **Rank** & **Similarity** & **Rank** \\ \hline Pattern priority & 151/157 & 2.78 & 247/264 & 5.34 \\ \(z\)-Score & 127/157 & 5.00 & 223/264 & 9.96 \\ Probability & 127/157 & 5.00 & 223/264 & 9.96 \\ Equal Probability & 127/157 & 5.00 & 223/264 & 9.96 \\ Frequency & 93/157 & 22.78 & 168/264 & 9.42 \\ Inverted frequency & 118/157 & 6.14 & 212/264 & 5.69 \\ Lexicographic order & 93/157 & 5.50 & 142/264 & 11.77 \\ \hline \end{tabular}
\end{table} 
Table 4: Comparison of performance between different binary relations applied to the underlying patterns: Pattern priority, \(z\)-score, probability with distribution based on the amino acid frequencies in \(s\), probability with no background (_i.e._, each amino acid scores \(1/20\)), frequency of patterns in \(s\), inverse frequency and the lexicographic order of occurrences. For each family, we summed up the maximum similarity with the two representative patterns for all quorums. Similarly, in the column rank, we show the average rank of the closest candidates to these patterns. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Quorum** & \
\begin{tabular}{c} **Max Similarity \(\mathbf{Ni_{1}}\)** \\ **(underlying/original)** \\ \end{tabular} &
\begin{tabular}{c} **Max Similarity \(\mathbf{Ni_{2}}\)** \\ **(underlying/original)** \\ \end{tabular} \\ \hline
5 & 26/26 & 9/12 \\
10 & 18/18 & 12/12 \\
15 & 11/11 & 9/12 \\
20 & 9/9 & 12/12 \\
22 & 9/9 & 12/12 \\
25 & 6/6 & 6/6 \\
30 & 6/6 & 6/6 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Normalized maximum similarity with the reference patterns of the family nickel-dependent hydrogenases, for different quorums. In principle, the binary relation of pattern priority can be replaced by any other traditional means of comparison. To this end, we compared the pattern priority rule with other standard ranking methods that were applied to the underlying filtering step. Table 4 reports the average scores for each measure for all six protein families, where a large maximum similarity with the two PROSITE signatures and a higher rank are preferable. In this context, we consider different ranking methods: The lexicographic order of patterns (Lexicographic), the number of occurrences (Frequency) and its inverse (Inverted Frequency).