The total conformational energy is assumed to consist of pairwise interaction energies between atoms or residues, each of which is expressed as a product of a conformation-dependent function (an element of a contact matrix, C-matrix) and a sequence-dependent energy parameter (an element of a contact energy matrix, E-matrix). Such pairwise interactions in proteins force native C-matrices to be in a relationship as if the interactions are a Go-like potential [N. Go, Annu. Rev. Biophys. Bioeng. 12. 183 (1983)] for the native C-matrix, because the lowest bound of the total energy function is equal to the total energy of the native conformation interacting in a Go-like pairwise potential. This relationship between C- and E-matrices corresponds to (a) a parallel relationship between the eigenvectors of the C- and E-matrices and a linear relationship between their eigenvalues, and (b) a parallel relationship between a contact number vector and the principal eigenvectors of the C- and E-matrices; the E-matrix is expanded in a series of eigenspaces with an additional constant term, which corresponds to a threshold of contact energy that approximately separates native contacts from non-native ones. These relationships are confirmed in 182 representatives from each family of the SCOP database by examining inner products between the principal eigenvector of the C-matrix, that of the E-matrix evaluated with a statistical contact potential, and a contact number vector. In addition, the spectral representation of C- and E-matrices reveals that pairwise residue-residue interactions, which depends only on the types of interacting amino acids but not on other residues in a protein, are insufficient and other interactions including residue connectivities and steric hindrance are needed to make native structures the unique lowest energy conformations.
PIPER: An FFT-based Protein Docking Program with Pairwise Potentials
快速傅立叶变换（FFT）相关方法用于蛋白质-蛋白质对接可以评估网格上数十亿对接构象的能量，如果能量以相关函数的形式描述。在这里，这种限制被删除，该方法是有效地使用成对的相互作用潜力，大大提高对接结果。其基本思想是用对应于几个主要特征值的特征向量来近似相互作用矩阵，从而得到一个写为几个相关函数之和的能量表达式，并通过重复的FFT计算来解决问题。除了描述该方法是如何实现的，我们提出了一类新的结构为基础的成对分子间的潜力。从蛋白质-蛋白质复合物的结构中提取DARS（Decoys As the Reference State）势，并使用大量对接构象作为诱饵来推导参考状态中的原子对分布。目前版本的DARS潜力很好地适用于酶抑制剂复合物。与新的FFT为基础的程序，DARS提供了更好的对接结果比早期的方法，在许多情况下，产生50%以上的近天然对接构象。尽管对于抗体-抗原对的潜力远不是最佳的，但是结果仍然比早期的FFT方法给出的结果稍好。对接程序PIPER可免费用于非商业应用。
Native contacts between residues could be predicted from the amino acid sequence of proteins, and the predicted contact information could assist the de novo protein structure prediction. Here, we present a novel pipeline of a residue contact predictor AmoebaContact and a contact-assisted folder GDFold for rapid protein structure prediction. Unlike mainstream contact predictors that utilize human-designed neural networks, AmoebaContact adopts a set of network architectures that are found as optimal for contact prediction through automatic searching and predicts the residue contacts at a series …
Given native 2D contact map, protein 3D structure could be reconstructed with accuracy of 2A or better, and such reconstruction is a feasible computational approach for protein folding problem. The prediction accuracy from traditional methods is generally too poor to useful, but the recent deep learning model has significantly improved the accuracy. In this study, we proposed a neural network model comprising a bi-directional recurrent neural network and artificial neural network. Over the non-redundant database of all available protein 3D structures in Protein Data Bank, this deep learning mo…
The analysis of coevolution of residues in homologous proteins is a powerful tool to predict their native conformation. The standard framework in which coevolutionary analysis is usually worked out is that of equilibrium Potts models, assuming that proteins have evolved for enough time to reach thermodynamic equilibrium in sequence space. Here we propose a model to describe correlations in sequences based on an explicit description of the evolutionary kinetics of proteins. We show that this procedure improves the correct prediction of native contacts with respect to equilibrium--based models.
Cotranslational folding depends on the folding speed and stability of the nascent protein. It remains difficult, however, to predict which proteins cotranslationally fold. Here, we simulate evolution of model proteins to investigate how native structure influences evolution of cotranslational folding. We developed a model that connects protein folding during and after translation to cellular fitness. Model proteins evolved improved folding speed and stability, with proteins adopting one of two strategies for folding quickly. Low contact order proteins evolve to fold cotranslationally. Such pro…
Potential function of simplified protein models for discriminating native proteins from decoys: Combining contact interaction and local sequence-dependent geometry
Studying evolutionary correlations in alignments of homologous sequences by means of an inverse Potts model has proven useful to obtain residue-residue contact energies and to predict contacts in proteins. The quality of the results depend much on several choices of the detailed model and on the algorithms used. We built, in a very controlled way, synthetic alignments with statistical properties similar to those of real proteins, and used them to assess the performance of different inversion algorithms and of their variants. Realistic synthetic alignments display typical features of low--tempe…
Global coevolutionary models of homologous protein families, as constructed by direct coupling analysis (DCA), have recently gained popularity in particular due to their capacity to accurately predict residue-residue contacts from sequence information alone, and thereby to facilitate tertiary and quaternary protein structure prediction. More recently, they have also been used to predict fitness effects of amino-acid substitutions in proteins, and to predict evolutionary conserved protein-protein interactions. These models are based on two currently unjustified hypotheses: (a) correlations in t…
Compound-protein pairs dominate FDA-approved drug-target pairs and the prediction of compound-protein affinity and contact (CPAC) could help accelerate drug discovery. In this study we consider proteins as multi-modal data including 1D amino-acid sequences and (sequence-predicted) 2D residue-pair contact maps. We empirically evaluate the embeddings of the two single modalities in their accuracy and generalizability of CPAC prediction (i.e. structure-free interpretable compound-protein affinity prediction). And we rationalize their performances in both challenges of embedding individual modalit…
Hydrostatic pressure is a common perturbation to probe the conformations of proteins. There are two common forms of pressure dependent potentials of mean force (PMFs) derived from hydrophobic molecules available for the coarse grained molecular simulations of protein folding and unfolding under hydrostatic pressure. Although both PMF includes a desolvation barrier separating the well of a direct contact and the well of a solvent mediated contact, how these features vary with hydrostatic pressure is still debated. There is a need of a systematic comparison of these two PMFs on a protein. We inv…
Predicting Secondary Structures, Contact Numbers, and Residue-wise Contact Orders of Native Protein Structure from Amino Acid Sequence by Critical Random Networks
The mechanisms by which a protein's 3D structure can be determined based on its amino acid sequence have long been one of the key mysteries of biophysics. Often simplistic models, such as those derived from geometric constraints, capture bulk real-world 3D protein-protein properties well. One approach is using protein contact maps to better understand proteins' properties. Here, we investigate the emergent behaviour of contact maps for different geometrically constrained models and real-world protein systems. We derive an analytical approximation for the distribution of model amino acid distan…
Coronaviruses are a class of virus responsible of the recent outbreak of Human Severe Acute Respiratory Syndrome. The molecular machinery behind the viral entry and thus infectivity is based on the formation of the complex of virus spike protein with the angiotensin-converting enzyme 2 (ACE2). The detection of putative allosteric sites on the viral spike protein can trace the path to develop allosteric drugs to weaken the strength of the spike-ACE2 interface and, thus, reduce the viral infectivity. In this work we present results of the application of the Protein Contact Network (PCN) paradigm…
Computational methods for predicting the interface contacts between proteins come highly sought after for drug discovery as they can significantly advance the accuracy of alternative approaches, such as protein-protein docking, protein function analysis tools, and other computational methods for protein bioinformatics. In this work, we present the Geometric Transformer, a novel geometry-evolving graph transformer for rotation and translation-invariant protein interface contact prediction, packaged within DeepInteract, an end-to-end prediction pipeline. DeepInteract predicts partner-specific pr…
Contact-assisted protein folding has made very good progress, but two challenges remain. One is accurate contact prediction for proteins lack of many sequence homologs and the other is that time-consuming folding simulation is often needed to predict good 3D models from predicted contacts. We show that protein distance matrix can be predicted well by deep learning and then directly used to construct 3D models without folding simulation at all. Using distance geometry to construct 3D models from our predicted distance matrices, we successfully folded 21 of the 37 CASP12 hard targets with a medi…
Learning language of protein sequences, which captures non-local interactions between amino acids close in the spatial structure, is a long-standing bioinformatics challenge, which requires at least context-free grammars. However, complex character of protein interactions impedes unsupervised learning of context-free grammars. Using structural information to constrain the syntactic trees proved effective in learning probabilistic natural and RNA languages. In this work, we establish a framework for learning probabilistic context-free grammars for protein sequences from syntactic trees partiall…
Department of Electrical；Computer Engineering, Texas A\&M University, College Station, TX 77843, United States；Department of Computer Science；Engineering, Texas A\&M University, College Station, TX 77843, United States
Predicting compound-protein affinity is critical for accelerating drug discovery. Recent progress made by machine learning focuses on accuracy but leaves much to be desired for interpretability. Through molecular contacts underlying affinities, our large-scale interpretability assessment finds commonly-used attention mechanisms inadequate. We thus formulate a hierarchical multi-objective learning problem whose predicted contacts form the basis for predicted affinities. We further design a physics-inspired deep relational network, DeepRelations, with intrinsically explainable architecture. Spec…
Predicting three dimensional residue-residue contacts from evolutionary information in protein sequences was attempted already in the early 1990s. However, contact prediction accuracies of methods evaluated in CASP experiments before CASP11 remained quite low, typically with $<20$% true positives. Recently, contact prediction has been significantly improved to the level that an accurate three dimensional model of a large protein can be generated on the basis of predicted contacts. This improvement was attained by disentangling direct from indirect correlations in amino acid covariations or cos…
