Investigating Statistical Conditions of Coevolutionary Signals that Enable Algorithmic Predictions of Protein Partners

This study examines the statistical conditions of coevolutionary signals that allow algorithmic predictions of protein partners based on amino acid sequences rather than 3D structures. It introduces a Markov stochastic model that predicts the number of correct protein partners based on coevolutionary information. The model defines state probabilities using a Poisson mixture of normal distributions, with key parameters including the total number of protein sequences <i>M</i>, the coevolutionary information gap α, and variance σ₀². The model suggests that algorithmic approaches that maximize coevolutionary information cannot effectively resolve partners in protein families with a large number of sequences <i>M</i> ≥ 100. The model shows that true-positive (TP) rates can be enhanced by disregarding mismatches among similar sequences. This approach allows a distinction, in terms of {α, σ₀²}, between optimized solutions with trivial errors and other degenerate solutions. Our findings enable the a priori classification of protein families where partners can be reliably predicted by ignoring trivial errors between similar sequences, advancing the understanding of coevolutionary models for large protein data sets.