Hidden.Markov Models (HMMs) are applied t.0 the problems of statistical modeling, database searching and multiple sequence alignment of protein families and protein domains. These methods are demonstrated the on globin family, the protein kinase catalytic domain, and the EF-hand calcium binding motif. In each case the parameters of an HMM are estimated from a training set of unaligned sequences. After the HMM is built, it is used to obtain a multiple alignment of all the training sequences. It is also used to search the. SWISS-PROT 22 database for other sequences. that are members of the given protein family, or contain the given domain. The Hi " produces multiple alignments of good quality that agree closely with the alignments produced by programs that incorporate threedimensional structural information. When employed in discrimination tests (by examining how closely the sequences in a database fit the globin, kinase and EF-hand HMMs), the '\ HMM is able to distinguish members of these families from non-members with a high degree of accuracy. Both the HMM and PROFILESEARCH (a technique used to search for relationships between a protein sequence and multiply aligned sequences) perform better in these tests than PROSITE (a dictionary of sites and patterns in proteins). The HMM appecvs to have a slight advantage over PROFILESEARCH in terms of lower rates of false

A model based on intersections of stochastic context free grammars is presented to allow for the modeling of RNA pseudoknot structures. The model runs relatively fast, having the same order running time as stochastic context free grammar parsers. The model is shown to be able to perform database searches and find RNA sequences which resemble RNA pseudoknots which bind biotin. The problem domain of RNA biotin binders has significance in the support of the RNA world model of early life on earth.