What are Hidden Markov Models and how are they applied in bioinformatics?

Hidden Markov Models (HMMs) are probabilistic models for sequences where the underlying states are hidden but emit observable symbols. In bioinformatics, HMMs are used for: gene prediction (modeling exons, introns, and intergenic regions), protein family modeling (profile HMMs in HMMER and Pfam for domain detection), multiple sequence alignment construction, secondary structure prediction, and transmembrane topology prediction. Key algorithms include: Viterbi (find most probable state path), Forward-Backward (calculate state probabilities), and Baum-Welch (parameter training). Profile HMMs capture position-specific amino acid preferences and insertion/deletion probabilities for protein families.