Drifting Markov models with polynomial drift and applications to DNA sequences

Area of Science:

• Computational Biology
• Bioinformatics
• Statistical Modeling

Background:

• Homogeneous Markov chains and hidden Markov models (HMMs) have limitations in capturing sequence heterogeneities.
• Modeling complex variations in DNA and protein sequences requires more flexible statistical frameworks.

Purpose of the Study:

• Introduce drifting Markov models (DMMs) as an advanced tool for modeling sequence heterogeneities.
• Demonstrate the reliability and flexibility of DMMs for analyzing DNA and protein sequences.
• Explore the application of DMMs in searching for rare words within DNA sequences.

Main Methods:

• Developed polynomial drifting Markov models where the transition matrix varies polynomially.
• Validated DMMs by comparing predicted nucleotide probability distributions with sliding window frequency analyses on DNA sequences.
• Integrated DMMs as states within a hidden Markov model framework for segment-based sequence analysis.

Main Results:

• High similarities observed between nucleotide distributions predicted by DMMs and empirical frequencies from sliding window analysis.
• DMMs demonstrate effectiveness in modeling sequence heterogeneities, outperforming traditional Markov models.
• DMMs prove to be a powerful tool for the search of rare words in DNA sequences.

Conclusions:

• Drifting Markov models provide a flexible and reliable method for analyzing sequence heterogeneities in biological data.
• DMMs can be effectively integrated with HMMs, enhancing their capability for complex sequence modeling.
• The developed DMMs offer a robust solution for identifying rare patterns in DNA sequences.