ANDIS: an atomic angle- and distance-dependent statistical potential for protein structure quality assessment

Making Use of Averaging Methods in MODELLER for Protein Structure Prediction

Recent advances in protein structure prediction, driven by AlphaFold 2 and machine learning, demonstrate proficiency in static structures but encounter challenges in capturing essential dynamic features crucial for understanding biological function. In this context, homology-based modeling emerges as a cost-effective and computationally efficient alternative. The MODELLER (version 10.5, accessed on 30 November 2023) algorithm can be harnessed for this purpose since it computes intermediate models during simulated annealing, enabling the exploration of attainable configurational states and energies while minimizing its objective function. There have been a few attempts to date to improve the models generated by its algorithm, and in particular, there is no literature regarding the implementation of an averaging procedure involving the intermediate models in the MODELLER algorithm. In this study, we examined MODELLER's output using 225 target-template pairs, extracting the best representatives of intermediate models. Applying an averaging procedure to the selected intermediate structures based on statistical potentials, we aimed to determine: (1) whether averaging improves the quality of structural models during the building phase; (2) if ranking by statistical potentials reliably selects the best models, leading to improved final model quality; (3) whether using a single template versus multiple templates affects the averaging approach; (4) whether the "ensemble" nature of the MODELLER building phase can be harnessed to capture low-energy conformations in holo structures modeling. Our findings indicate that while improvements typically fall short of a few decimal points in the model evaluation metric, a notable fraction of configurations exhibit slightly higher similarity to the native structure than MODELLER's proposed final model. The averaging-building procedure proves particularly beneficial in (1) regions of low sequence identity between the target and template(s), the most challenging aspect of homology modeling; (2) holo protein conformations generation, an area in which MODELLER and related tools usually fall short of the expected performance.

RNAStat: An Integrated Tool for Statistical Analysis of RNA 3D Structures

The 3D architectures of RNAs are essential for understanding their cellular functions. While an accurate scoring function based on the statistics of known RNA structures is a key component for successful RNA structure prediction or evaluation, there are few tools or web servers that can be directly used to make comprehensive statistical analysis for RNA 3D structures. In this work, we developed RNAStat, an integrated tool for making statistics on RNA 3D structures. For given RNA structures, RNAStat automatically calculates RNA structural properties such as size and shape, and shows their distributions. Based on the RNA structure annotation from DSSR, RNAStat provides statistical information of RNA secondary structure motifs including canonical/non-canonical base pairs, stems, and various loops. In particular, the geometry of base-pairing/stacking can be calculated in RNAStat by constructing a local coordinate system for each base. In addition, RNAStat also supplies the distribution of distance between any atoms to the users to help build distance-based RNA statistical potentials. To test the usability of the tool, we established a non-redundant RNA 3D structure dataset, and based on the dataset, we made a comprehensive statistical analysis on RNA structures, which could have the guiding significance for RNA structure modeling. The python code of RNAStat, the dataset used in this work, and corresponding statistical data files are freely available at GitHub (https://github.com/RNA-folding-lab/RNAStat).

An information gain-based approach for evaluating protein structure models

For three decades now, knowledge-based scoring functions that operate through the "potential of mean force" (PMF) approach have continuously proven useful for studying protein structures. Although these statistical potentials are not to be confused with their physics-based counterparts of the same name-i.e. PMFs obtained by molecular dynamics simulations-their particular success in assessing the native-like character of protein structure predictions has lead authors to consider the computed scores as approximations of the free energy. However, this physical justification is a matter of controversy since the beginning. Alternative interpretations based on Bayes' theorem have been proposed, but the misleading formalism that invokes the inverse Boltzmann law remains recurrent in the literature. In this article, we present a conceptually new method for ranking protein structure models by quality, which is (i) independent of any physics-based explanation and (ii) relevant to statistics and to a general definition of information gain. The theoretical development described in this study provides new insights into how statistical PMFs work, in comparison with our approach. To prove the concept, we have built interatomic distance-dependent scoring functions, based on the former and new equations, and compared their performance on an independent benchmark of 60,000 protein structures. The results demonstrate that our new formalism outperforms statistical PMFs in evaluating the quality of protein structural decoys. Therefore, this original type of score offers a possibility to improve the success of statistical PMFs in the various fields of structural biology where they are applied. The open-source code is available for download at https://gitlab.rpbs.univ-paris-diderot.fr/src/ig-score.

Using Machine Learning in Accuracy Assessment of Knowledge-Based Energy and Frequency Base Likelihood in Protein Structures

Many aspects of the study of protein folding and dynamics have been affected by the accumulation of data about native protein structures and recent advances in machine learning. Computational methods for predicting protein structures from their sequences are now heavily based on machine learning tools and on approaches that extract knowledge and rules from data using probabilistic models. Many of these methods use scoring functions to determine which structure best fits a native protein sequence. Using computational approaches, we obtained two scoring functions: knowledge-based energy and likelihood of base frequency, and we compared their accuracy in measuring the sequence structure fit. We compared the machine learning models’ accuracy of predictions for knowledge-based energy and likelihood values to validate our results, showing that likelihood is a more accurate scoring function than knowledge-based energy.

Identification of native protein structures captured by principal interactions

Background

Evaluation of protein structure is based on trustworthy potential function. The total potential of a protein structure is approximated as the summation of all pair-wise interaction potentials. Knowledge-based potentials (KBP) are one type of potential functions derived by known experimentally determined protein structures. Although several KBP functions with different methods have been introduced, the key interactions that capture the total potential have not studied yet.

Results

In this study, we seek the interaction types that preserve as much of the total potential as possible. We employ a procedure based on the principal component analysis (PCA) to extract the significant and key interactions in native protein structures. We call these interactions as principal interactions and show that the results of the model that considers only these interactions are very close to the full interaction model that considers all interactions in protein fold recognition. In fact, the principal interactions maintain the discriminative power of the full interaction model. This method was evaluated on 3 KBPs with different contact definitions and thresholds of distance and revealed that their corresponding principal interactions are very similar and have a lot in common. Additionally, the principal interactions consisted of 20 % of the full interactions on average, and they are between residues, which are considered important in protein folding.

Conclusions

This work shows that all interaction types are not equally important in discrimination of native structure. The results of the reduced model based on principal interactions that were very close to the full interaction model suggest that a new strategy is needed to capture the role of remaining interactions (non-principal interactions) to improve the power of knowledge-based potential functions.

A simple neural network implementation of generalized solvation free energy for assessment of protein structural models

Rapid and accurate assessment of protein structural models is essential for protein structure prediction and design. Great progress has been made in this regard, especially by recent application of "knowledge-based" potentials. Various machine learning based protein structural model quality assessment methods are also quite successful. However, performance of traditional "physics-based" models has not been as effective. Based on our analysis of the fundamental computational limitation behind unsatisfactory performance of "physics-based" models, we propose a generalized solvation free energy (GSFE) framework, which is intrinsically flexible for multi-scale treatments and is amenable for machine learning implementation. Finally, we implemented a simple example of backbone-based residue level GSFE with neural network, which was found to have competitive performance when compared with highly complex latest "knowledge-based" atomic potentials in distinguishing native structures from decoys.