## 5 Experimental Results  
In this section, we discuss the ability of underlying patterns to efficiently capture meaningful biological information. A general problem in genome and proteome research is the identification of signals represented by means of degenerate patterns. In this sense, some modern degenerate pattern discovery tools proved to be useful in biological sequence analysis, as we have discussed at the beginning of the paper. Here, we first collect the degenerate patterns in the output from one of these tools, say a set of patterns, \(\mathcal{M}\), and then, present some preliminary experimental results in order to support the theoretical properties shown in the above sections. More generally, there are two types of scenarios where the notion of underlying patterns could be useful. The first case is when a region of interest has already been identified, so that it is possible to analyze and select only those patterns that are underlying with respect to that particular region, without considering the whole set of patterns. Another possible application is the case where we just want to filter all patterns in \(\mathcal{M}\), looking at the whole sequence. In this context, we present some results for the latter scenario. We take as input, \(\mathcal{M}\), the set of patterns extracted by Varun [12,25], a tool for _de novo_ pattern discovery. The dataset consists of six protein families for which [PERSON] successfully extracts the representative patterns contained in the PROSITE signatures (release 20.85) [12]. For each signature, we select all sequences in the Swiss-Prot database that share that signature. In summary, our dataset is the following. 1. Nickel-Dependent hydrogenases (id PS00508; in short, _Ni_). These are enzymes that catalyze the reversible activation of hydrogen and are further involved in the binding of nickel. The family is composed by 22 sequences of about 12,300 amino acids in total. This family contains two representative signatures, \(Ni_{1}=\)_RG[FILMV]E...........[EM PQS][KR].C[GR][ILMV]C_ and \(Ni_{2}=\)_[FY]D[IP][CU][AILMV][AGS]C_. 2. Coagulation factors 5/8 type C domain (FA58C) (id PS01286; in short, _Fa_). This family is composed by 40 sequences of about 46,500 amino acids in total. They share two signatures: \(Fa_{1}=\)_[FWY][ILV].[AFILV][DEGNST]....[FILV].[IV]. [ILTV][KMQT]G_ and \(Fa_{2}=\)_[LM]R.[EG][ILPV].GC_. 3. Formate and nitrite transporters (id PS01005; in short, _Form_). The signature _[LVMA][LYVM].G[GSTA][DES][FI][TN][GS]_ is present in 17 sequences of a total length of 5300 amino acids. 4. Ubiquitin-Activating enzyme (id PS00865; in short, _Ubi_). The active site _P[LVMG]CT[LYM][KRHA]. [FTNM]P_ appears in 36 proteins of about 25,200 amino acids in total. 5. RNA polymerases M/15 Kd subunits (id PS01030; in short, _Poly_). The representative signature _[FY]C.[DEKSTG]C[GNK][DNSA][LYMHG][LYM]_ occurs in 29 sequences of about 4000 amino acids. 6. Dbl homology domain (id PS00741; in short, _Dbl_). The signature _[LM]..[LIVMFYWGS][LI]..[PEQ][LIVMRF]..[LIVM].[KRS].[LT].[LIVM].[DEQN][LIVM]... [STM]_ appears in 65 sequences of a total length of 18,750 amino acids. To prove that the information captured by the underlying patterns is relevant with respect to the protein families under examination, we devised two kinds of tests. In the first test, we compare the original set of patterns in the input, \(\mathcal{M}\), with the set of underlying patterns in the output, \(\mathcal{U}\), using global measures. In the second, we investigate the ability to filter a list of meaningful patterns and retain the representative ones, perhaps with a higher rank. In the first set of experiments, we use Varun to extract patterns from the above families of protein sequences for different quorums, \(q\). For each family, we concatenate the sequences and extract patterns from the concatenation; thus, in all the experiments, the quorum refers to the number of occurrences in the concatenation of all sequences of a certain family.