Fuzzy measures and integrals in profile hidden Markov models for protein sequence analysis

The formulation of the classical profile HMMs is made under statistical independence assumption of the probability theory which is a limitation for modeling protein sequences because of a high degree of interdependency among homologous sequences of the same family. Fuzzy measure theory which is an extension of the additive theory, is developed by replacing the additive requirement of classical measures with weaker properties of continuity, monotonicity and semi-continuity. The strong interdependencies and the sequence preferences involved in the proteins make models based on fuzzy architecture better candidates for building profiles of a given family. In this paper, we investigate the characteristics and compare the performances of three different fuzzy profile HMMs based on possibility, λ and belief measures on globin and kinase families. The performances of the fuzzy models are also compared with profile HMMs. The results obtained in terms of Z-score plots, alignment analysis and ROC curves establish the superior performance of models based on fuzzy measures over classical models. It is shown that the possibility measure based fuzzy profile HMM has the best performance amongst all the models.