How Pairwise Coevolutionary Models Capture the Collective Residue Variability in Proteins?

Area of Science:

• Computational Biology
• Structural Bioinformatics
• Evolutionary Biology

Background:

• Global coevolutionary models, like direct coupling analysis (DCA), are popular for predicting protein structure and interactions from sequence data.
• Current DCA models rely on the unproven hypotheses that amino acid correlations arise from direct couplings and that pairwise couplings are sufficient.

Purpose of the Study:

• To systematically address the hypotheses underlying DCA models using a precise Boltzmann-machine learning inference scheme.
• To investigate the collective nature of correlations and the sufficiency of pairwise couplings in capturing protein residue variability.

Main Methods:

• Development and application of a Boltzmann-machine learning inference scheme.
• Analysis of correlation structures, including three-residue correlations and protein family clustering in sequence space.

Main Results:

• Correlations in homologous proteins are built collectively through numerous coupling paths informed by 3D structure.
• Pairwise coevolutionary models accurately capture collective residue variability, even for properties not explicitly included in the inference process.
• The models successfully predict three-residue correlations and the clustered structure of protein families.

Conclusions:

• The findings strongly support the sufficiency of pairwise coevolutionary models for accurately capturing residue variability in homologous protein families.
• This validates the widespread application of DCA in predicting protein structure, interactions, and fitness effects.