Modeling and prediction of mutation fitness on protein functionality with structural information using high-dimensional Potts model

2025-05-20

AI Summary

To address the high experimental cost and the limitations of existing Potts models—which ignore structural information and lack theoretical guarantees—in predicting functional effects of protein mutations, this paper proposes a high-dimensional Potts model incorporating three-dimensional structural information. Methodologically, it introduces node-wise polynomial regression to capture evolutionary dependencies, employs sparse group Lasso for parameter estimation, and pioneers a structure-aware pairwise site weighting regularization scheme. Theoretically, it establishes, for the first time, a tight ℓ₂ convergence rate bound for model parameters, matching the minimax lower bound under sparse group structures. Evaluated on high-throughput mutational data across 12 protein families, the proposed method significantly outperforms state-of-the-art baselines, achieving substantial improvements in mutation fitness prediction accuracy.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Evolutionary Learning
• Search and Optimization: Evolutionary Computation

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Quantifying the effects of amino acid mutations in proteins presents a significant challenge due to the vast combinations of residue sites and amino acid types, making experimental approaches costly and time-consuming. The Potts model has been used to address this challenge, with parameters capturing evolutionary dependency between residue sites within a protein family. However, existing methods often use the mean-field approximation to reduce computational demands, which lacks provable guarantees and overlooks critical structural information for assessing mutation effects. We propose a new framework for analyzing protein sequences using the Potts model with node-wise high-dimensional multinomial regression. Our method identifies key residue interactions and important amino acids, quantifying mutation effects through evolutionary energy derived from model parameters. It encourages sparsity in both site-wise and amino acid-wise dependencies through element-wise and group sparsity. We have established, for the first time to our knowledge, the $ell_2$ convergence rate for estimated parameters in the high-dimensional Potts model using sparse group Lasso, matching the existing minimax lower bound for high-dimensional linear models with a sparse group structure, up to a factor depending only on the multinomial nature of the Potts model. This theoretical guarantee enables accurate quantification of estimated energy changes. Additionally, we incorporate structural data into our model by applying penalty weights across site pairs. Our method outperforms others in predicting mutation fitness, as demonstrated by comparisons with high-throughput mutagenesis experiments across 12 protein families.

Problem

• Quantify mutation effects on proteins using Potts model
• Improve accuracy by incorporating structural information
• Establish theoretical guarantees for parameter estimation

Innovation

• Uses high-dimensional Potts model with sparse group Lasso
• Incorporates structural data via penalty weights
• Quantifies mutation effects through evolutionary energy