Optimisation of HMM topologies enhances DNA and protein sequence modelling

Hidden Markov models (HMMs) play a major role in applications to unravel biomolecular functionality. Though HMMs are technically mature and widely applied in computational biology, there is a potential of methodical optimisation concerning its modelling of biological data sources with varying sequence lengths. Single building blocks of these models, the states, are associated with a certain holding time, being the link to the length distribution of represented sequence motifs. An adaptation of regular HMM topologies to bell-shaped sequence lengths is achieved by a serial chain-linking of hidden states, while residing in the class of conventional hidden Markov models. The factor of the repetition of states (r) and the parameter for state-specific duration of stay (p) are determined by fitting the distribution of sequence lengths with the method of moments (MM) and maximum likelihood (ML). Performance evaluations of differently adjusted HMM topologies underline the impact of an optimisation for HMMs based on sequence lengths. Secondary structure prediction on internal transcribed spacer 2 sequences demonstrates exemplarily the general impact of topological optimisations. In summary, we propose a general methodology to improve the modelling behaviour of HMMs by topological optimisation with ML and a fast and easily implementable moment estimator.