A Composite Approach to Protein Tertiary Structure Prediction: Hidden Markov Model Based on Lattice

Bull Math Biol. 2019 Mar;81(3):899-918. doi: 10.1007/s11538-018-00542-4. Epub 2018 Dec 10.


The biological function of protein depends mainly on its tertiary structure which is determined by its amino acid sequence via the process of protein folding. Prediction of protein structure from its amino acid sequence is one of the most prominent problems in computational biology. Two basic methodologies on protein structure prediction are combined: ab initio method (3-D space lattice) and fold recognition method (hidden Markov model). The primary structure of proteins and 3-D coordinates of amino acid residues are put together in one hidden Markov model to learn the path of amino acid residues in 3-D space from the first atom to the last atom of each protein of each fold. Therefore, each model has the information of 3-D path of amino acids of each fold. The proposed method is compared to fold recognition methods which have hidden Markov model as a base of their algorithms having approaches on only amino acid sequence or secondary structure. To validate the proposed method, the models are assessed with three datasets. Results show that the proposed models outperform 7-HMM and 3-HMM in the same dataset. The face-centered cubic lattice which is the most compacted 3-D lattice reached the maximum classification accuracy in all experiments in comparison with the performance of the most effective version of optimized 3-HMM as well as the performance of the latest version of SAM 3.5. Results show that 3-D coordinates of atoms of amino acids in proteins have an important role in prediction. It also has great hidden information as compared to secondary structure of proteins in fold classification.

Keywords: Bravais lattice; Fold recognition; Hidden Markov model; Protein structure prediction; Tertiary structure.

MeSH terms

  • Algorithms
  • Amino Acid Sequence
  • Machine Learning
  • Markov Chains
  • Mathematical Concepts
  • Models, Molecular*
  • Protein Folding
  • Protein Structure, Secondary
  • Protein Structure, Tertiary*
  • Proteins / chemistry*


  • Proteins