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Model-Free Inference for Characterizing Protein Mutations through a Coevolutionary Lens

Fan Yang, Zhao Ren, Wen Zhou, Kejue Jia, Robert Jernigan

TL;DR

This work reframes protein residue contact prediction as a statistical inference problem using a model-free partial correlation framework for multivariate categorical data derived from one-hot MSA encoding. By estimating interactions with a multivariate group Lasso and assessing direct coupling via a spectrum-based Wilks-type test on fitted residuals, the method yields edge-wise uncertainty quantification and supports FDR-controlled contact discovery. It further enables amino-acid-level inference to identify specific residue combinations driving contacts and introduces mutation-focused features derived from residual covariances to enhance downstream predictive models like ESM. Empirical results across multiple Pfam families show improved contact prediction performance and meaningful gains in mutation-effect prediction when augmenting existing embeddings with CATParc features, highlighting practical utility in coevolution and mutation analysis.

Abstract

Multiple sequence alignment (MSA) data play a crucial role in the study of protein mutations, with contact prediction being a notable application. Existing methods are often model-based or algorithmic and typically do not incorporate statistical inference to quantify the uncertainty of the prediction outcomes. To address this, we propose a novel framework that transforms the task of contact prediction into a statistical testing problem. Our approach is motivated by the partial correlation for continuous random variables. With one-hot encoding of MSA data, we are able to construct a partial correlation graph for multivariate categorical variables. In this framework, two connected nodes in the graph indicate that the corresponding positions on the protein form a contact. A new spectrum-based test statistic is introduced to test whether two positions are partially correlated. Moreover, the new framework enables the identification of amino acid combinations that contribute to the correlation within the identified contacts, an important but largely unexplored aspect of protein mutations. Numerical experiments demonstrate that our proposed method is valid in terms of controlling Type I errors and powerful in general. Real data applications on various protein families further validate the practical utility of our approach in coevolution and mutation analysis.

Model-Free Inference for Characterizing Protein Mutations through a Coevolutionary Lens

TL;DR

This work reframes protein residue contact prediction as a statistical inference problem using a model-free partial correlation framework for multivariate categorical data derived from one-hot MSA encoding. By estimating interactions with a multivariate group Lasso and assessing direct coupling via a spectrum-based Wilks-type test on fitted residuals, the method yields edge-wise uncertainty quantification and supports FDR-controlled contact discovery. It further enables amino-acid-level inference to identify specific residue combinations driving contacts and introduces mutation-focused features derived from residual covariances to enhance downstream predictive models like ESM. Empirical results across multiple Pfam families show improved contact prediction performance and meaningful gains in mutation-effect prediction when augmenting existing embeddings with CATParc features, highlighting practical utility in coevolution and mutation analysis.

Abstract

Multiple sequence alignment (MSA) data play a crucial role in the study of protein mutations, with contact prediction being a notable application. Existing methods are often model-based or algorithmic and typically do not incorporate statistical inference to quantify the uncertainty of the prediction outcomes. To address this, we propose a novel framework that transforms the task of contact prediction into a statistical testing problem. Our approach is motivated by the partial correlation for continuous random variables. With one-hot encoding of MSA data, we are able to construct a partial correlation graph for multivariate categorical variables. In this framework, two connected nodes in the graph indicate that the corresponding positions on the protein form a contact. A new spectrum-based test statistic is introduced to test whether two positions are partially correlated. Moreover, the new framework enables the identification of amino acid combinations that contribute to the correlation within the identified contacts, an important but largely unexplored aspect of protein mutations. Numerical experiments demonstrate that our proposed method is valid in terms of controlling Type I errors and powerful in general. Real data applications on various protein families further validate the practical utility of our approach in coevolution and mutation analysis.
Paper Structure (22 sections, 3 theorems, 12 equations, 4 figures, 2 tables, 1 algorithm)

This paper contains 22 sections, 3 theorems, 12 equations, 4 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Data format and related notations
  3. Partial correlations for multivariate categorical variable
  4. Statistical test for protein coevolutions
  5. Organization and more notations.
  6. Statistical framework for inferring protein coevolution
  7. Estimation procedure
  8. Testing framework for contact prediction
  9. Background on the CCA-related test
  10. Main results on the test statistic
  11. Comparison with other test statistics ($\ell_2$- and $\ell_{\infty}$-norm-based) and approaches (MI and PSICOV)
  12. Identifying amino acid combinations relevant to contacts and mutations
  13. Implementation
  14. Numerical Experiments
  15. Simulations based on the real data
  16. ...and 7 more sections

Key Result

Proposition 1

Under the null hypothesis $H_0: \mathbf{P}^{(1,2)}=0$, we have that where $W_{\ell'}\text{'s}\sim N(0,1)$ are independent, and $\Lambda_{\ell'}\text{'s}$ are the eigenvalues of $\mathop{\text{\normalfont{Cov}}}(\mathbf{Q})$ for $\ell'=1,\dots,d_1d_2$.

Figures (4)

  • Figure 1: (a) Protein sequences from the class A beta-lactamase family, with positions $21$-$45$ displaye. Positions $23$ and $30$ are spatially close and known to contact structurally. (b) Illustration of the Beta-lactamase TEM sequence (sequence in red in Plot (a), positions $21$-$32$), featuring Glutamic acid (E) at position $23$ and Lysine (K) at position $30$. The corresponding crystallization structure appears in Figure \ref{['fig:heatmap']}.
  • Figure 2: Demonstration of two different partial correlations.
  • Figure 3: ROC curves for Cases 5-8: $\square$, $\bigcirc$, $\bigtriangleup$, and $\lozenge$ represent our method (CATParc), L2, SUP, and PSICOV respectively. The red dashed line indicates a Type I error of $0.05$, and the solid colored symbols mark the empirical Type I error and power when the nominal level is $0.05$.
  • Figure 4: (a) Sankey diagram showcasing the correlation of amino acid groups between positions $23$ and $30$. The strength of the correlation is measured by the spectral norm of the associated submatrix of the self-normalized partial correlation matrix. (b) Residues $(23,30)$ highlighted in the crystallization structure of beta-lactamase TEM. (c) Self-normalized partial correlation map of amino acid pairs between positions $23$ and $30$.

Theorems & Definitions (4)

  • Proposition 1: Test statistic based on the oracle errors, muirhead1980asymptotic
  • Theorem 1
  • Remark 1
  • Proposition 2