Hidden Markov models (HMMs) are probabilistic statistical models which are useful in bioinformatics - particularly analysing protein and nucleotide sequences. The Markov component means that the identity of the system's following state depends only on the transition probabilities of the current state of the system. The hidden component means that the identity and nature of the state cannot be directly observed - instead, each state has a set of emitted states, which are observed, each with their own emission probability. In a biological context, states are sequence positions, match states (M) are alignment positions, and emissions are residues. Also applicable to biological sequences are special states for deletion (D) and insertion (I) states, which allow the HMM to be robust to mutations to some extent.
HMMs are built from a multiple sequence alignment - that is, aligned sequences of emitted states. Computers can infer the underlying HMM by interpretation of the observed sequences, and bioinformaticians can use the HMM to classify a novel protein as being part of the group or not. Profile HMMs are built from alignments of related sequences - novel protein sequences which score highly in the HMM indicate homology between the novel protein and the proteins whose sequences built the HMM. Thus, HMMs are useful tools for identifying protein domains in sequence, and are actually used by online bioinformatic tools such as Pfam and SMART, not to mention HMMER itself.
It stands to reason that, if HMMs can identify protein domains, then they can also identify polypeptide and genomic features. Examples of simple HMMs which identify Gln-rich peptide sequences and alternating AT-rich and GC-rich nucleotide sequences are illustrated.
The fact that Pfam, SMART, and HMMER work is evidence enough that HMMs are good enough. However, they are not the holy grail: as is common with Markov models, HMMs have no memory effect. Due to the next state only depending on the current state, long-range secondary and tertiary structure interactions are completely ignored. Only the primary sequence is taken into account. Bioinformaticians turn to co-variance and co-evolutionary methods to study these effects. Second, the model assumes that all amino acid emission probabilities are independent of what has just been emitted, again, due to no memory effect. This is not a good assumption in biology, as, for example, hydrophobic residues usually occur together in the primary sequence so as to clump together and exclude water. Thus, a better model would increase the probability of the occurrence of a hydrophobic residue following a previous hydrophobic, even in the I states.
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