Problem In Computational Structural Biology Research Articles

Computational structural biology in the era of deep learning.

By the time of the BPS conference, it will be almost three years since CASP14 results showed the AlphaFold2 method from DeepMind is able to model protein structures with an accuracy that in many cases is competitive with the best experiments. Since then, there has been an explosion of work applying deep learning and related methods to other problems in computational structural biology as well as further development of single protein approaches. In this talk I'll examine where the field has now advanced to, drawing primarily on the results of the most recent CASP (CASP15, results of which will be public at the end of 2022). In particular, what, if any, are the remaining limitations for high accuracy modeling of single protein structures? How close are protein complexes models to the accuracy achieved for single proteins? Have the methods been successively extended to modeling RNA structures? Are protein-organic ligand complexes treatable? How far have we progressed towards generating ensembles of conformations, not just single structures? How seriously should we take the estimated accuracy of models? I’ll also attempt to relate progress to the astonishing diversification of deep learning methods that has occurred and what the results tell us about how the methods work: is it all just dumb pattern recognition, or are principles of protein structure learned and applied?

Cotranscriptional Kinetic Folding of RNA Secondary Structures Including Pseudoknots.

Computational prediction of ribonucleic acid (RNA) structures is an important problem in computational structural biology. Studies of RNA structure formation often assume that the process starts from a fully synthesized sequence. Experimental evidence, however, has shown that RNA folds concurrently with its elongation. We investigate RNA secondary structure formation, including pseudoknots, that takes into account the cotranscriptional effects. We propose a single-nucleotide resolution kinetic model of the folding process of RNA molecules, where the polymerase-driven elongation of an RNA strand by a new nucleotide is included as a primitive operation, together with a stochastic simulation method that implements this folding concurrently with the transcriptional synthesis. Numerical case studies show that our cotranscriptional RNA folding model can predict the formation of conformations that are favored in actual biological systems. Our new computational tool can thus provide quantitative predictions and offer useful insights into the kinetics of RNA folding.

Efficient Sampling of Protein Loop Regions Using Conformational Hashing Complemented with Random Coordinate Descent.

De novo construction of loop regions is an important problem in computational structural biology. Compared to regions with well-defined secondary structure, loops tend to exhibit significant conformational heterogeneity. As a result, their structures are often ambiguous when determined using experimental data obtained by crystallography, cryo-EM, or NMR. Although structurally diverse models could provide a more relevant representation of proteins in their native states, obtaining large numbers of biophysically realistic and physiologically relevant loop conformations is a resource-consuming task. To address this need, we developed a novel loop construction algorithm, Hash/RCD, that combines knowledge-based conformational hashing with random coordinate descent (RCD). This hybrid approach achieved a closure rate of 100% on a benchmark set of 195 loops in 29 proteins that range from 3 to 31 residues. More importantly, the use of templates allows Hash/RCD to maintain the accuracy of state-of-the-art coordinate descent methods while reducing sampling time from over 400 to 141 ms. These results highlight how the integration of coordinate descent with knowledge-based sampling overcomes barriers inherent to either approach in isolation. This method may facilitate the identification of native-like loop conformations using experimental data or full-atom scoring functions by allowing rapid sampling of large numbers of loops. In this manuscript, we investigate and discuss the advantages, bottlenecks, and limitations of combining conformational hashing with RCD. By providing a detailed technical description of the Hash/RCD algorithm, we hope to facilitate its implementation by other researchers.

Prodconn - Protein Design using a Convolutional Neural Network

Designing protein sequences that fold to a given three-dimensional structure has long been a challenging problem in computational structural biology with significant theoretical and practical implications. Inverse folding problem (IFP) has been a challenging problem for several decades whose solutions will deepen our fundamental understanding of the sequence-structure relationship of proteins. A practical method for IFP will also have broad applications in the manufacturing and pharmaceutical industries.

ProDCoNN: Protein design using a convolutional neural network.

Designing protein sequences that fold to a given three-dimensional (3D) structure has long been a challenging problem in computational structural biology with significant theoretical and practical implications. In this study, we first formulated this problem as predicting the residue type given the 3D structural environment around the C α atom of a residue, which is repeated for each residue of a protein. We designed a nine-layer 3D deep convolutional neural network (CNN) that takes as input a gridded box with the atomic coordinates and types around a residue. Several CNN layers were designed to capture structure information at different scales, such as bond lengths, bond angles, torsion angles, and secondary structures. Trained on a very large number of protein structures, the method, called ProDCoNN (protein design with CNN), achieved state-of-the-art performance when tested on large numbers of test proteins and benchmark datasets.

Selecting Near-Native Protein Structures from Predicted Decoy Sets Using Ordered Graphlet Degree Similarity.

Effective prediction of protein tertiary structure from sequence is an important and challenging problem in computational structural biology. Ab initio protein structure prediction is based on amino acid sequence alone, thus, it has a wide application area. With the ab initio method, a large number of candidate protein structures called decoy set can be predicted, however, it is a difficult problem to select a good near-native structure from the predicted decoy set. In this work we propose a new method for selecting the near-native structure from the decoy set based on both contact map overlap (CMO) and graphlets. By generalizing graphlets to ordered graphs, and using a dynamic programming to select the optimal alignment with an introduced gap penalty, a GR_score is defined for calculating the similarity between the three-dimensional (3D) decoy structures. The proposed method was applied to all 54 single-domain targets in CASP11 and all 43 targets in CASP10, and ensemble clustering was used to cluster the protein decoy structures based on the computed CR_scores. The most popular centroid structure was selected as the near-native structure. The experiments showed that compared to the SPICKER method, which is used in I-TASSER, the proposed method can usually select better near-native structures in terms of the similarity between the selected structure and the true native structure.

Data driven flexible backbone protein design.

Protein design remains an important problem in computational structural biology. Current computational protein design methods largely use physics-based methods, which make use of information from a single protein structure. This is despite the fact that multiple structures of many protein folds are now readily available in the PDB. While ensemble protein design methods can use multiple protein structures, they treat each structure independently. Here, we introduce a flexible backbone strategy, FlexiBaL-GP, which learns global protein backbone movements directly from multiple protein structures. FlexiBaL-GP uses the machine learning method of Gaussian Process Latent Variable Models to learn a lower dimensional representation of the protein coordinates that best represent backbone movements. These learned backbone movements are used to explore alternative protein backbones, while engineering a protein within a parallel tempered MCMC framework. Using the human ubiquitin–USP21 complex as a model we demonstrate that our design strategy outperforms current strategies for the interface design task of identifying tight binding ubiquitin variants for USP21.

Using Variable-Length Aligned Fragment Pairs and an Improved Transition Function for Flexible Protein Structure Alignment.

With the rapid growth of known protein 3D structures in number, how to efficiently compare protein structures becomes an essential and challenging problem in computational structural biology. At present, many protein structure alignment methods have been developed. Among all these methods, flexible structure alignment methods are shown to be superior to rigid structure alignment methods in identifying structure similarities between proteins, which have gone through conformational changes. It is also found that the methods based on aligned fragment pairs (AFPs) have a special advantage over other approaches in balancing global structure similarities and local structure similarities. Accordingly, we propose a new flexible protein structure alignment method based on variable-length AFPs. Compared with other methods, the proposed method possesses three main advantages. First, it is based on variable-length AFPs. The length of each AFP is separately determined to maximally represent a local similar structure fragment, which reduces the number of AFPs. Second, it uses local coordinate systems, which simplify the computation at each step of the expansion of AFPs during the AFP identification. Third, it decreases the number of twists by rewarding the situation where nonconsecutive AFPs share the same transformation in the alignment, which is realized by dynamic programming with an improved transition function. The experimental data show that compared with FlexProt, FATCAT, and FlexSnap, the proposed method can achieve comparable results by introducing fewer twists. Meanwhile, it can generate results similar to those of the FATCAT method in much less running time due to the reduced number of AFPs.

Evolutionary-inspired probabilistic search for enhancing sampling of local minima in the protein energy surface

BackgroundDespite computational challenges, elucidating conformations that a protein system assumes under physiologic conditions for the purpose of biological activity is a central problem in computational structural biology. While these conformations are associated with low energies in the energy surface that underlies the protein conformational space, few existing conformational search algorithms focus on explicitly sampling low-energy local minima in the protein energy surface.MethodsThis work proposes a novel probabilistic search framework, PLOW, that explicitly samples low-energy local minima in the protein energy surface. The framework combines algorithmic ingredients from evolutionary computation and computational structural biology to effectively explore the subspace of local minima. A greedy local search maps a conformation sampled in conformational space to a nearby local minimum. A perturbation move jumps out of a local minimum to obtain a new starting conformation for the greedy local search. The process repeats in an iterative fashion, resulting in a trajectory-based exploration of the subspace of local minima.Results and conclusionsThe analysis of PLOW's performance shows that, by navigating only the subspace of local minima, PLOW is able to sample conformations near a protein's native structure, either more effectively or as well as state-of-the-art methods that focus on reproducing the native structure for a protein system. Analysis of the actual subspace of local minima shows that PLOW samples this subspace more effectively that a naive sampling approach. Additional theoretical analysis reveals that the perturbation function employed by PLOW is key to its ability to sample a diverse set of low-energy conformations. This analysis also suggests directions for further research and novel applications for the proposed framework.

Diversity of Sequences Folding to Highly and Poorly Designable Structures

Protein structures are evolutionarily more conserved than sequences, and sequences with very low sequence identity often share the same fold. This leads to the concept of protein designability. Elucidating the relationship between protein sequence and the three-dimensional structure that the sequence folds into is an important problem in computational structural biology.45 protein chains (40-mer) from the PDB were analyzed. Hydrophobic-polar sequences were generated and contact energies calculated by threading each sequence onto Cα coarse-grained protein structures. The minimum energy structure for each sequence was identified and the number of sequences folding to each fold (designability) was obtained. Highly designable structures obtained were found to be popular structural motifs.H/P mutational analysis of sequences folding to each conformation was performed. As designability increases, the total number of mutations was also found to increase. The sequences folding to the most designable structure (helix-turn-helix motif) were also analyzed. The degree of connectivity at each residue position correlates inversely with the degree of solvent exposure. The surface residues had fewer interactions compared to buried residues. Highly connected residues were also found to be more conserved than the other residue positions. i.e. the diversity of the sequences increases with designability; however, there are conserved positions.Using tripeptide percentages of the most and least designable sequences, ten-fold cross-validation was performed and designable sequences were found to be distinguishable (accuracies > 85%, AUC > 0.87). The same set of sequences was then used as a training set with a test set of real binary protein sequences. Designable sequences obtained mimic real protein sequences with accuracies of nearly 60%. Highly and poorly designable classes can be used to train machine learning algorithms to identify which real protein sequences are designable.

Exploration of the relationship between topology and designability of conformations

Protein structures are evolutionarily more conserved than sequences, and sequences with very low sequence identity frequently share the same fold. This leads to the concept of protein designability. Some folds are more designable and lots of sequences can assume that fold. Elucidating the relationship between protein sequence and the three-dimensional (3D) structure that the sequence folds into is an important problem in computational structural biology. Lattice models have been utilized in numerous studies to model protein folds and predict the designability of certain folds. In this study, all possible compact conformations within a set of two-dimensional and 3D lattice spaces are explored. Complementary interaction graphs are then generated for each conformation and are described using a set of graph features. The full HP sequence space for each lattice model is generated and contact energies are calculated by threading each sequence onto all the possible conformations. Unique conformation giving minimum energy is identified for each sequence and the number of sequences folding to each conformation (designability) is obtained. Machine learning algorithms are used to predict the designability of each conformation. We find that the highly designable structures can be distinguished from other non-designable conformations based on certain graphical geometric features of the interactions. This finding confirms the fact that the topology of a conformation is an important determinant of the extent of its designability and suggests that the interactions themselves are important for determining the designability.

I-TASSER server for protein 3D structure prediction

BackgroundPrediction of 3-dimensional protein structures from amino acid sequences represents one of the most important problems in computational structural biology. The community-wide Critical Assessment of Structure Prediction (CASP) experiments have been designed to obtain an objective assessment of the state-of-the-art of the field, where I-TASSER was ranked as the best method in the server section of the recent 7th CASP experiment. Our laboratory has since then received numerous requests about the public availability of the I-TASSER algorithm and the usage of the I-TASSER predictions.ResultsAn on-line version of I-TASSER is developed at the KU Center for Bioinformatics which has generated protein structure predictions for thousands of modeling requests from more than 35 countries. A scoring function (C-score) based on the relative clustering structural density and the consensus significance score of multiple threading templates is introduced to estimate the accuracy of the I-TASSER predictions. A large-scale benchmark test demonstrates a strong correlation between the C-score and the TM-score (a structural similarity measurement with values in [0, 1]) of the first models with a correlation coefficient of 0.91. Using a C-score cutoff > -1.5 for the models of correct topology, both false positive and false negative rates are below 0.1. Combining C-score and protein length, the accuracy of the I-TASSER models can be predicted with an average error of 0.08 for TM-score and 2 Å for RMSD.ConclusionThe I-TASSER server has been developed to generate automated full-length 3D protein structural predictions where the benchmarked scoring system helps users to obtain quantitative assessments of the I-TASSER models. The output of the I-TASSER server for each query includes up to five full-length models, the confidence score, the estimated TM-score and RMSD, and the standard deviation of the estimations. The I-TASSER server is freely available to the academic community at .

Shape-dependent designability studies of lattice proteins

One important problem in computational structural biology is protein designability, that is,why protein sequences are not random strings of amino acids but instead showregular patterns that encode protein structures. Many previous studies that haveattempted to solve the problem have relied upon reduced models of proteins. Inparticular, the 2D square and the 3D cubic lattices together with reduced amino acidalphabet models have been examined extensively and have led to interesting resultsthat shed some light on the evolutionary relationship among proteins. Here weperform designability studies on the 2D square lattice and explore the effects ofvariable overall shapes on protein designability using a binary hydrophobic–polar(HP) amino acid alphabet. Because we rely on a simple energy function thatcounts the total number of H–H interactions between non-sequential residues, werestrict our studies to protein shapes that have the same number of residues andalso a constant number of non-bonded contacts. We have found that there is amarked difference in the designability between various protein shapes, with some ofthem accounting for a significantly larger share of the total foldable sequences.

Ab initio modeling of small proteins by iterative TASSER simulations

BackgroundPredicting 3-dimensional protein structures from amino-acid sequences is an important unsolved problem in computational structural biology. The problem becomes relatively easier if close homologous proteins have been solved, as high-resolution models can be built by aligning target sequences to the solved homologous structures. However, for sequences without similar folds in the Protein Data Bank (PDB) library, the models have to be predicted from scratch. Progress in the ab initio structure modeling is slow. The aim of this study was to extend the TASSER (threading/assembly/refinement) method for the ab initio modeling and examine systemically its ability to fold small single-domain proteins.ResultsWe developed I-TASSER by iteratively implementing the TASSER method, which is used in the folding test of three benchmarks of small proteins. First, data on 16 small proteins (< 90 residues) were used to generate I-TASSER models, which had an average Cα-root mean square deviation (RMSD) of 3.8Å, with 6 of them having a Cα-RMSD < 2.5Å. The overall result was comparable with the all-atomic ROSETTA simulation, but the central processing unit (CPU) time by I-TASSER was much shorter (150 CPU days vs. 5 CPU hours). Second, data on 20 small proteins (< 120 residues) were used. I-TASSER folded four of them with a Cα-RMSD < 2.5Å. The average Cα-RMSD of the I-TASSER models was 3.9Å, whereas it was 5.9Å using TOUCHSTONE-II software. Finally, 20 non-homologous small proteins (< 120 residues) were taken from the PDB library. An average Cα-RMSD of 3.9Å was obtained for the third benchmark, with seven cases having a Cα-RMSD < 2.5Å.ConclusionOur simulation results show that I-TASSER can consistently predict the correct folds and sometimes high-resolution models for small single-domain proteins. Compared with other ab initio modeling methods such as ROSETTA and TOUCHSTONE II, the average performance of I-TASSER is either much better or is similar within a lower computational time. These data, together with the significant performance of automated I-TASSER server (the Zhang-Server) in the 'free modeling' section of the recent Critical Assessment of Structure Prediction (CASP)7 experiment, demonstrate new progresses in automated ab initio model generation. The I-TASSER server is freely available for academic users .

SDU: A Semidefinite Programming-Based Underestimation Method for Stochastic Global Optimization in Protein Docking

This paper introduces a new stochastic global optimization method targeting protein-protein docking problems, an important class of problems in computational structural biology. The method is based on finding general convex quadratic underestimators to the binding energy function that is funnel-like. Finding the optimum underestimator requires solving a semidefinite programming problem, hence the name semidefinite programming-based underestimation (SDU). The underestimator is used to bias sampling in the search region. It is established that under appropriate conditions SDU locates the global energy minimum with probability approaching one as the sample size grows. A detailed comparison of SDU with a related method of convex global underestimator (CGU), and computational results for protein-protein docking problems are provided.

Statistical and Bayesian approaches to RNA secondary structure prediction

Prediction of RNA secondary structure is a fundamental problem in computational structural biology. For several decades, free energy minimization has been the most popular method for prediction from a single sequence. In recent years, the McCaskill algorithm for computation of partition function and base-pair probabilities has become increasingly appreciated. This paradigm-shifting work has inspired the developments of extended partition function algorithms, statistical sampling and clustering, and application of Bayesian statistical inference. The performance of thermodynamics-based methods is limited by thermodynamic rules and parameters. However, further improvements may come from statistical estimates derived from structural databases for thermodynamics parameters with weak or little experimental data. The Bayesian inference approach appears to be promising in this context.