Statistical models for families of evolutionary related proteins have recently gained interest: in particular pairwise Potts models, as those inferred by the Direct-Coupling Analysis, have been able to extract information about the three-dimensional structure of folded proteins, and about the effect of amino-acid substitutions in proteins. These models are typically requested to reproduce the one- and two-point statistics of the amino-acid usage in these protein families,{\em i.e. ~ the so-called residue conservation and covariation statistics  . Pairwise Potts models are the maximum-entropy models achieving this. While being successful, these models depend on huge numbers of ad hoc {\em  introduced parameters, which have to be estimated from finite amount of data and whose biophysical interpretation remains unclear. Here we propose an approach to parameter reduction, which is based on collective-variable selection . It naturally leads to the formulation of statistical sequence models in terms of Hopfield-Potts models , with the Hopfield patterns being the collective variables . These models can be accurately inferred using a mapping to restricted Boltzmann machines and persistent contrastive divergence. We show that, when applied to protein data, even 20-40 patterns are sufficient to obtain statistically generative models. The Hopfield patterns are interpretable in terms of sequence motifs and may be used to clusterize amino-acid sequences into functional sub-families. However, the distributed collective nature of these motifs intrinsically limits the ability of Hopfield-Potts models in predicting contact maps, showing the necessity of developing models going beyond the Hopfield-Potts models discussed here.
Statistical models for families of evolutionary related proteins have recently gained interest: in particular pairwise Potts models, as those inferred by the Direct-Coupling Analysis, have been able to extract information about the three-dimensional structure of folded proteins, and about the effect of amino-acid substitutions in proteins. These models are typically requested to reproduce the one- and two-point statistics of the amino-acid usage in a protein family,{\em i.e. ~to capture the so-called residue conservation and covariation statistics of proteins of common evolutionary origin . Pairwise Potts models are the maximum-entropy models achieving this. While being successful, these models depend on huge numbers of {\em ad hoc introduced parameters, which have to be estimated from finite amount of data and whose biophysical interpretation remains unclear. Here we propose an approach to parameter reduction, which is based on selecting collective sequence motifs . It naturally leads to the formulation of statistical sequence models in terms of Hopfield-Potts models . These models can be accurately inferred using a mapping to restricted Boltzmann machines and persistent contrastive divergence. We show that, when applied to protein data, even 20-40 patterns are sufficient to obtain statistically close-to-generative models. The Hopfield patterns form interpretable sequence motifs and may be used to clusterize amino-acid sequences into functional sub-families. However, the distributed collective nature of these motifs intrinsically limits the ability of Hopfield-Potts models in predicting contact maps, showing the necessity of developing models going beyond the Hopfield-Potts models discussed here.
R
these protein families,
a protein family,
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~
~to capture
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of proteins of common evolutionary origin
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ad hoc
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ad hoc
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collective-variable selection
selecting collective sequence motifs
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, with the Hopfield patterns being the collective variables
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generative
close-to-generative
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are interpretable in terms of
form interpretable