Comparison study on k-word statistical measures for protein: from sequence to 'sequence space'

Abstract

Background: Many proposed statistical measures can efficiently compare protein sequence to further infer protein structure, function and evolutionary information. They share the same idea of using k-word frequencies of protein sequences. Given a protein sequence, the information on its related protein sequences hasn't been used for protein sequence comparison until now. This paper proposed a scheme to construct protein 'sequence space' which was associated with protein sequences related to the given protein, and the performances of statistical measures were compared when they explored the information on protein 'sequence space' or not. This paper also presented two statistical measures for protein: gre.k (generalized relative entropy) and gsm.k (gapped similarity measure).

Results: We tested statistical measures based on protein 'sequence space' or not with three data sets. This not only offers the systematic and quantitative experimental assessment of these statistical measures, but also naturally complements the available comparison of statistical measures based on protein sequence. Moreover, we compared our statistical measures with alignment-based measures and the existing statistical measures. The experiments were grouped into two sets. The first one, performed via ROC (Receiver Operating Curve) analysis, aims at assessing the intrinsic ability of the statistical measures to discriminate and classify protein sequences. The second set of the experiments aims at assessing how well our measure does in phylogenetic analysis. Based on the experiments, several conclusions can be drawn and, from them, novel valuable guidelines for the use of protein 'sequence space' and statistical measures were obtained.

Conclusion: Alignment-based measures have a clear advantage when the data is high redundant. The more efficient statistical measure is the novel gsm.k introduced by this article, the cos.k followed. When the data becomes less redundant, gre.k proposed by us achieves a better performance, but all the other measures perform poorly on classification tasks. Almost all the statistical measures achieve improvement by exploring the information on 'sequence space' as word's length increases, especially for less redundant data. The reasonable results of phylogenetic analysis confirm that Gdis.k based on 'sequence space' is a reliable measure for phylogenetic analysis. In summary, our quantitative analysis verifies that exploring the information on 'sequence space' is a promising way to improve the abilities of statistical measures for protein comparison.

Figure 1

ROC curves for data CK. ROC (a) for our measures, alignment-based measures and other statistical measures, all the statistical measures are based on k-word frequencies of protein sequence, with the parameter values as suffix. ROC (b) for our measures, alignment-based measures and other statistical measures, all the statistical measures are based on k-word frequencies of protein 'sequence space', with the parameter values as suffix. All the abbreviations of (dis)similarity measures are illustrated in the "List of abbreviations" section. A random classifier would generate equal proportions of FP and TP classifications, which corresponds to the ROC diagonal (dashed line).

Figure 2

ROC curves for data RS. ROC (a) for our measures, alignment-based measures and other statistical measures, all the statistical measures are based on k-word frequencies of protein sequence, with the parameter values as suffix. ROC (b) for our measures, alignment-based measures and other statistical measures, all the statistical measures are based on k-word frequencies of protein 'sequence space', with the parameter values as suffix. All the abbreviations of (dis)similarity measures are illustrated in the "List of abbreviations" section. A random classifier would generate equal proportions of FP and TP classifications, which corresponds to the ROC diagonal (dashed line).

Figure 3

ROC curves for data SP. ROC (a) for our measures, alignment-based measures and other statistical measures, all the statistical measures are based on k-word frequencies of protein sequence, with the parameter values as suffix. ROC (b) for our measures, alignment-based measures and other statistical measures, all the statistical measures are based on k-word frequencies of protein 'sequence space', with the parameter values as suffix. All the abbreviations of (dis)similarity measures are illustrated in the "List of abbreviations" section. A random classifier would generate equal proportions of FP and TP classifications, which corresponds to the ROC diagonal (dashed line).

Figure 4

DAUC values for data CK. The DAUC values of seven statistical measures for data CK. All statistical measures based on k-word frequencies of protein 'sequence space' run with k from 1 to 4, where protein 'sequence space' is constructed according to ten score matrices. One graph presents each word length (from 1 to 4).

Figure 5

DAUC values for data RS. The DAUC values of seven statistical measures for data RS. All statistical measures based on k-word frequencies of protein 'sequence space' run with k from 1 to 4, where protein 'sequence space' is constructed according to ten score matrices. One graph presents each word length (from 1 to 4).

Figure 6

DAUC values for data SP. The DAUC values of seven statistical measures for data SP. All statistical measures based on k-word frequencies of protein 'sequence space' run with k from 1 to 4, where protein 'sequence space' is constructed according to ten score matrices. One graph presents each word length (from 1 to 4).

Figure 7

MAUC values for data sets CK, RS and SP. The MAUC values for the data CK, RS and SP, one for each data. All the statistical measures are based on k-word frequencies of protein 'sequence space', with ten score matrices to build protein 'sequence space'.

Figure 8

The diagram of phylogenetic relationships. Phylogenetic relationships are obtained by neighbor-joining program based on our statistical distance measure Gdis.k using all six SMC subfamilies, as well as the related MukB and Rad50. Bootstraps are based on 100 replications, and bootstrap values, lower than 50, are hidden.

Figure 9

Representation of a star set. a: the diagram of star set, S is similar to A, T and N in BLOSUM62 substitution matrix, and S is the midpoint; b: the star set consists of the midpoint S and vertices A, T and N.