HMMs will only be briefly treated, since their application to secondary structure has been relatively limited and unsucessful. In 1992, Stultz, et al. published a use of space state modeling to predict (among other properties) secondary structure. This approach relied on the use of a hand-built Markov Chain for each protein family to be studied. Beginning with the level of individual secondary structures, and using their knowledge of the spread of lengths, for example of alpha helices, and the relative frequencies of amino acids at each position in a helix the authors would generate a Markov Chain. These secondary structural elements were then peiced together to form Markov Models for an entire family (e.g. "a/b proteins with a central b sheet containing five, six, or seven b-strands." The authors generate 15 such models. For a given "unknown" protein (still a member of one of the authors' families in the examples they use) the maximally probable model is selected. The most probable alignment of the sequence with the model is then used to generate secondary structure assignments.

This approach is unsatisfactory for many reasons. First, the results, even on proteins which belong to families for which models have been built are significantly lower than those generated by other methods. Proteins from unknown or unmodeled families should score pathetically low. Second, the Markov models which are generated are not even optimized against representative members of their families, a seemingly obvious step. Unless one already knows the fold of one's protein of interest and is willing to generate a Markov model for it, this method will likely prove completely useless, and even if one does so, a significant chance exists that this will still be the case. The failure of this method does not rule out future advances using HMMs, but given the lack of ability to incorporate pairwise correlations in Markov Chains, they seem fundementally unsuited to the problem. For more information on HMMs, the reader is referred to a review by Krogh, et al. (1994) and an excellent tutorial by Rabiner (1989).