Statistics of Random Protein Superpositions: p-Values for Pairwise Structure Alignment

Abstract

Quantification of statistical significance is essential for the interpretation of protein structural similarity. To address this, a random model for protein structure comparison was developed. Novelty of the model is threefold. First, a sample of random structure comparisons is restricted to molecules of the same size and shape as the superposition of interest. Second, careful selection of the sample and accurate modeling of shape allows approximation of the root mean square deviation (RMSD) distribution of random comparisons with a Nakagami probability density function. Third, through convolution, a second probability density function is obtained that describes the coordinate difference vector projections underlying the random distribution of RMSD. This last feature allows sampling random distributions of not only RMSD, but also any similarity score that depends on difference vector projections, such as GDT_TS score, TM score, and LiveBench 3D score. Probabilities estimated from the method correlate well with common measures of structural similarity, such as the Dali Z-score and the GDT_TS score. As a result, the p-value for a given superposition can be calculated using simple formulae depending on RMSD, radius of gyration, and thinnest molecular dimension. In addition to scoring structural similarity, p-values computed by this method can be applied to evaluation of homology modeling techniques, providing a statistically sound alternative to scores used in reference-independent evaluation of alignment quality.

Investigating Homology between Proteins using Energetic Profiles

“…In Null Model 2, the probability of chance occurrence at a particular level of structural or thermodynamic similarity was estimated from the frequency of observed length-matched gapless alignments between randomly selected pairs of non-homologous protein fragments. In this model, a minimum alpha-carbon RMSD structure superposition [34]–[36] of the fragment pair as well as the Pearson r -value between thermodynamic descriptors was computed. 30,000 pairs of fragments were chosen for each gapless alignment length L , where 10≤ L ≤100.…”

On the Role of Physics and Evolution in Dictating Protein Structure and Function

“…To ascertain whether a pair of proteins are structurally similar, a comparison metric is needed [14] . Such metrics include the root mean square deviation, RMSD, of the coordinates (generally of Cαs) and the GDT_TS score [15] .…”

Why not consider a spherical protein? Implications of backbone hydrogen bonding for protein structure and function

“…As indicated above, to ascertain whether a pair of proteins are structurally similar, a comparison metric is needed ( 23 ). There are a variety of such metrics including the root mean square deviation from native, RMSD, and the GDT_TS score ( 24 ); however, the statistical significance of these measures is length dependent ( 25 ).…”