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1.
Most scoring functions for protein-protein docking algorithms are either atom-based or residue-based, with the former being able to produce higher quality structures and latter more tolerant to conformational changes upon binding. Earlier, we developed the ZRANK algorithm for reranking docking predictions, with a scoring function that contained only atom-based terms. Here we combine ZRANK's atom-based potentials with five residue-based potentials published by other labs, as well as an atom-based potential IFACE that we published after ZRANK. We simultaneously optimized the weights for selected combinations of terms in the scoring function, using decoys generated with the protein-protein docking algorithm ZDOCK. We performed rigorous cross validation of the combinations using 96 test cases from a docking benchmark. Judged by the integrative success rate of making 1000 predictions per complex, addition of IFACE and the best residue-based pair potential reduced the number of cases without a correct prediction by 38 and 27% relative to ZDOCK and ZRANK, respectively. Thus combination of residue-based and atom-based potentials into a scoring function can improve performance for protein-protein docking. The resulting scoring function is called IRAD (integration of residue- and atom-based potentials for docking) and is available at http://zlab.umassmed.edu.  相似文献   

2.
Protein-ligand docking: current status and future challenges   总被引:1,自引:0,他引:1  
Understanding the ruling principles whereby protein receptors recognize, interact, and associate with molecular substrates and inhibitors is of paramount importance in drug discovery efforts. Protein-ligand docking aims to predict and rank the structure(s) arising from the association between a given ligand and a target protein of known 3D structure. Despite the breathtaking advances in the field over the last decades and the widespread application of docking methods, several downsides still exist. In particular, protein flexibility-a critical aspect for a thorough understanding of the principles that guide ligand binding in proteins-is a major hurdle in current protein-ligand docking efforts that needs to be more efficiently accounted for. In this review the key concepts of protein-ligand docking methods are outlined, with major emphasis being given to the general strengths and weaknesses that presently characterize this methodology. Despite the size of the field, the principal types of search algorithms and scoring functions are reviewed and the most popular docking tools are briefly depicted. Recent advances that aim to address some of the traditional limitations associated with molecular docking are also described. A selection of hand-picked examples is used to illustrate these features.  相似文献   

3.
Treating flexibility in molecular docking is a major challenge in cell biology research. Here we describe the background and the principles of existing flexible protein-protein docking methods, focusing on the algorithms and their rational. We describe how protein flexibility is treated in different stages of the docking process: in the preprocessing stage, rigid and flexible parts are identified and their possible conformations are modeled. This preprocessing provides information for the subsequent docking and refinement stages. In the docking stage, an ensemble of pre-generated conformations or the identified rigid domains may be docked separately. In the refinement stage, small-scale movements of the backbone and side-chains are modeled and the binding orientation is improved by rigid-body adjustments. For clarity of presentation, we divide the different methods into categories. This should allow the reader to focus on the most suitable method for a particular docking problem.  相似文献   

4.
A major challenge in the field of protein-protein docking is to discriminate between the many wrong and few near-native conformations, i.e. scoring. Here, we introduce combinatorial complex-type-dependent scoring functions for different types of protein-protein complexes, protease/inhibitor, antibody/antigen, enzyme/inhibitor and others. The scoring functions incorporate both physical and knowledge-based potentials, i.e. atomic contact energy (ACE), the residue pair potential (RP), electrostatic and van der Waals' interactions. For different type complexes, the weights of the scoring functions were optimized by the multiple linear regression method, in which only top 300 structures with ligand root mean square deviation (L_RMSD) less than 20 A from the bound (co-crystallized) docking of 57 complexes were used to construct a training set. We employed the bound docking studies to examine the quality of the scoring function, and also extend to the unbound (separately crystallized) docking studies and extra 8 protein-protein complexes. In bound docking of the 57 cases, the first hits of protease/inhibitor cases are all ranked in the top 5. For the cases of antibody/antigen, enzyme/inhibitor and others, there are 17/19, 5/6 and 13/15 cases with the first hits ranked in the top 10, respectively. In unbound docking studies, the first hits of 9/17 protease/inhibitor, 6/19 antibody/antigen, 1/6 enzyme/inhibitor and 6/15 others' complexes are ranked in the top 10. Additionally, for the extra 8 cases, the first hits of the two protease/inhibitor cases are ranked in the top for the bound and unbound test. For the two enzyme/inhibitor cases, the first hits are ranked 1st for bound test, and the 119th and 17th for the unbound test. For the others, the ranks of the first hits are the 1st for the bound test and the 12th for the 1WQ1 unbound test. To some extent, the results validated our divide-and-conquer strategy in the docking study, which might hopefully shed light on the prediction of protein-protein interactions.  相似文献   

5.
Docking is a computational technique that places a small molecule (ligand) in the binding site of its macromolecular target (receptor) and estimates its binding affinity. This review addresses methodological developments that have occurred in the docking field in 2009, with a particular focus on the more difficult, and sometimes controversial, aspects of this promising computational discipline. These developments aim to address the main challenges of docking: receptor representation (such aspects as structural waters, side chain protonation, and, most of all, flexibility (from side chain rotation to domain movement)), ligand representation (protonation, tautomerism and stereoisomerism, and the effect of input conformation), as well as accounting for solvation and entropy of binding. This review is strongly focused on docking advances in the context of drug design, specifically in virtual screening and fragment-based drug design.  相似文献   

6.
Huang SY  Zou X 《Proteins》2008,72(2):557-579
Using an efficient iterative method, we have developed a distance-dependent knowledge-based scoring function to predict protein-protein interactions. The function, referred to as ITScore-PP, was derived using the crystal structures of a training set of 851 protein-protein dimeric complexes containing true biological interfaces. The key idea of the iterative method for deriving ITScore-PP is to improve the interatomic pair potentials by iteration, until the pair potentials can distinguish true binding modes from decoy modes for the protein-protein complexes in the training set. The iterative method circumvents the challenging reference state problem in deriving knowledge-based potentials. The derived scoring function was used to evaluate the ligand orientations generated by ZDOCK 2.1 and the native ligand structures on a diverse set of 91 protein-protein complexes. For the bound test cases, ITScore-PP yielded a success rate of 98.9% if the top 10 ranked orientations were considered. For the more realistic unbound test cases, the corresponding success rate was 40.7%. Furthermore, for faster orientational sampling purpose, several residue-level knowledge-based scoring functions were also derived following the similar iterative procedure. Among them, the scoring function that uses the side-chain center of mass (SCM) to represent a residue, referred to as ITScore-PP(SCM), showed the best performance and yielded success rates of 71.4% and 30.8% for the bound and unbound cases, respectively, when the top 10 orientations were considered. ITScore-PP was further tested using two other published protein-protein docking decoy sets, the ZDOCK decoy set and the RosettaDock decoy set. In addition to binding mode prediction, the binding scores predicted by ITScore-PP also correlated well with the experimentally determined binding affinities, yielding a correlation coefficient of R = 0.71 on a test set of 74 protein-protein complexes with known affinities. ITScore-PP is computationally efficient. The average run time for ITScore-PP was about 0.03 second per orientation (including optimization) on a personal computer with 3.2 GHz Pentium IV CPU and 3.0 GB RAM. The computational speed of ITScore-PP(SCM) is about an order of magnitude faster than that of ITScore-PP. ITScore-PP and/or ITScore-PP(SCM) can be combined with efficient protein docking software to study protein-protein recognition.  相似文献   

7.
Critical Assessment of PRedicted Interactions (CAPRI) has proven to be a catalyst for the development of docking algorithms. An essential step in docking is the scoring of predicted binding modes in order to identify stable complexes. In 2005, CAPRI introduced the scoring experiment, where upon completion of a prediction round, a larger set of models predicted by different groups and comprising both correct and incorrect binding modes, is made available to all participants for testing new scoring functions independently from docking calculations. Here we present an expanded benchmark data set for testing scoring functions, which comprises the consolidated ensemble of predicted complexes made available in the CAPRI scoring experiment since its inception. This consolidated scoring benchmark contains predicted complexes for 15 published CAPRI targets. These targets were subjected to 23 CAPRI assessments, due to existence of multiple binding modes for some targets. The benchmark contains more than 19,000 protein complexes. About 10% of the complexes represent docking predictions of acceptable quality or better, the remainder represent incorrect solutions (decoys). The benchmark set contains models predicted by 47 different predictor groups including web servers, which use different docking and scoring procedures, and is arguably as diverse as one may expect, representing the state of the art in protein docking. The data set is publicly available at the following URL: http://cb.iri.univ‐lille1.fr/Users/lensink/Score_set . Proteins 2014; 82:3163–3169. © 2014 Wiley Periodicals, Inc.  相似文献   

8.
Huang Z  Wong CF  Wheeler RA 《Proteins》2008,71(1):440-454
By docking flexible balanol to a rigid model of protein kinase A (PKA), we found that a new simulated annealing protocol termed disrupted velocity simulated annealing (DIVE-SA) outperformed the replica-exchange method and the traditional simulated annealing method in identifying the correct docking pose. In this protocol, the atomic velocities were reassigned periodically to encourage the system to sample a large conformational space. We also found that scaling potential energy surface to reduce structural transition barriers could further facilitate docking. The DIVE-SA method was then evaluated on its ability to perform flexible ligand-flexible protein docking of three ligands (balanol, a balanol analog, and ATP) to PKA. To reduce computational time and to avoid possible unphysical structural changes resulting from the use of nonoptimal force fields, a soft restrain was applied to keep the root-mean-square-deviation (RMSD) between instantaneous protein structures and a chosen reference structure small. Because the restrain was applied to the overall RMSD rather than to individual atoms, a protein could still experience relatively large conformational changes during docking. To examine the impact of applying such a restrain on docking, we constructed two semi-flexible protein models by choosing two different crystal structures as reference. Both the balanol analog and ATP were able to dock to either one of these semi-flexible protein models. On the other hand, balanol could only dock well to one of them. Further analysis indicated that the restrain on the glycine-rich loop was too strong, preventing it to adjust its structure to accommodate balanol in the binding pocket of PKA. Removing the restrain on the glycine-rich loop resulted in much better docking poses. This finding demonstrates the important role that the flexibility of the glycine-rich loop play in accepting different ligands and should profitably not be restrained in molecular docking so that more diverse ligands can be studied.  相似文献   

9.
GEMDOCK: a generic evolutionary method for molecular docking   总被引:1,自引:0,他引:1  
Yang JM  Chen CC 《Proteins》2004,55(2):288-304
We have developed an evolutionary approach for flexible ligand docking. This approval, GEMDOCK, uses a Generic Evolutionary Method for molecular DOCKing and an empirical scoring function. The former combines both discrete and continuous global search strategies with local search strategies to speed up convergence, whereas the latter results in rapid recognition of potential ligands. GEMDOCK was tested on a diverse data set of 100 protein-ligand complexes from the Protein Data Bank. In 79% of these complexes, the docked lowest energy ligand structures had root-mean-square derivations (RMSDs) below 2.0 A with respect to the corresponding crystal structures. The success rate increased to 85% if the structure water molecules were retained. We evaluated GEMDOCK on two cross-docking experiments in which each ligand of a protein ensemble was docked into each protein of the ensemble. Seventy-six percent of the docked structures had RMSDs below 2.0 A when the ligands were docked into foreign structures. We analyzed and validated GEMDOCK with respect to various search spaces and scoring functions, and found that if the scoring function was perfect, then the predicted accuracy was also essentially perfect. This study suggests that GEMDOCK is a useful tool for molecular recognition and may be used to systematically evaluate and thus improve scoring functions.  相似文献   

10.
Gorelik B  Goldblum A 《Proteins》2008,71(3):1373-1386
Multiple near-optimal conformations of protein-ligand complexes provide a better chance for accurate representation of biomolecular interactions, compared with a single structure. We present ISE-dock--a docking program which is based on the iterative stochastic elimination (ISE) algorithm. ISE eliminates values that consistently lead to the worst results, thus optimizing the search for docking poses. It constructs large sets of such poses with no additional computational cost compared with single poses. ISE-dock is validated using 81 protein-ligand complexes from the PDB and its performance was compared with those of Glide, GOLD, and AutoDock. ISE-dock has a better chance than the other three to find more than 60% top single poses under RMSD = 2.0 A and more than 80% under RMSD = 3.0 A from experimental. ISE alone produced at least one 3.0 A or better solutions among the top 20 poses in the entire test set. In 98% of the examined molecules, ISE produced solutions that are closer than 2.0 A from experimental. Paired t-tests (PTT) were used throughout to assess the significance of comparisons between the performances of the different programs. ISE-dock provides more than 100-fold docking solutions in a similar time frame as LGA in AutoDock. We demonstrate the usefulness of the large near optimal populations of ligand poses by showing a correlation between the docking results and experiments that support multiple binding modes in p38 MAP kinase (Pargellis et al., Nat Struct Biol 2002;9:268-272] and in Human Transthyretin (Hamilton, Benson, Cell Mol Life Sci 2001;58:1491-1521).  相似文献   

11.
Park MS  Gao C  Stern HA 《Proteins》2011,79(1):304-314
To investigate the effects of multiple protonation states on protein-ligand recognition, we generated alternative protonation states for selected titratable groups of ligands and receptors. The selection of states was based on the predicted pK(a) of the unbound receptor and ligand and the proximity of titratable groups of the receptor to the binding site. Various ligand tautomer states were also considered. An independent docking calculation was run for each state. Several protocols were examined: using an ensemble of all generated states of ligand and receptor, using only the most probable state of the unbound ligand/receptor, and using only the state giving the most favorable docking score. The accuracies of these approaches were compared, using a set of 176 protein-ligand complexes (15 receptors) for which crystal structures and measured binding affinities are available. The best agreement with experiment was obtained when ligand poses from experimental crystal structures were used. For 9 of 15 receptors, using an ensemble of all generated protonation states of the ligand and receptor gave the best correlation between calculated and measured affinities.  相似文献   

12.
Król M  Tournier AL  Bates PA 《Proteins》2007,68(1):159-169
Molecular Dynamics (MD) simulations have been performed on a set of rigid-body docking poses, carried out over 25 protein-protein complexes. The results show that fully flexible relaxation increases the fraction of native contacts (NC) by up to 70% for certain docking poses. The largest increase in the fraction of NC is observed for docking poses where anchor residues are able to sample their bound conformation. For each MD simulation, structural snap-shots were clustered and the centre of each cluster used as the MD-relaxed docking pose. A comparison between two energy-based scoring schemes, the first calculated for the MD-relaxed poses, the second for energy minimized poses, shows that the former are better in ranking complexes with large hydrophobic interfaces. Furthermore, complexes with large interfaces are generally ranked well, regardless of the type of relaxation method chosen, whereas complexes with small hydrophobic interfaces remain difficult to rank. In general, the results indicate that current force-fields are able to correctly describe direct intermolecular interactions between receptor and ligand molecules. However, these force-fields still fail in cases where protein-protein complexes are stabilized by subtle energy contributions.  相似文献   

13.
Docking programs can generate subsets of a compound collection with an increased percentage of actives against a target (enrichment) by predicting their binding mode (pose) and affinity (score), and retrieving those with the highest scores. Using the QXP and GOLD programs, we compared the ability of six single scoring functions (PLP, Ligscore, Ludi, Jain, ChemScore, PMF) and four composite scoring models (Mean Rank: MR, Rank-by-Vote: Vt, Bayesian Statistics: BS and PLS Discriminant Analysis: DA) to separate compounds that are active against CDK2 from inactives. We determined the enrichment for the entire set of actives (IC50 < 10 microM) and for three activity subsets. In all cases, the enrichment for each subset was lower than for the entire set of actives. QXP outperformed GOLD at pose prediction, but yielded only moderately better enrichments. Five to six scoring functions yielded good enrichments with GOLD poses, while typically only two worked well with QXP poses. For each program, two scoring functions generally performed better than the others (Ligscore2 and Ludi for GOLD; QXP and Jain for QXP). Composite scoring functions yielded better results than single scoring functions. The consensus approaches MR and Vt worked best when separating micromolar inhibitors from inactives. The statistical approaches BS and DA, which require training data, performed best when distinguishing between low and high nanomolar inhibitors. The key observation that all hit rate profiles for all four activity intervals for all scoring schemes for both programs are significantly better than random, is evidence that docking can be successfully applied to enrich compound collections.  相似文献   

14.
We report on the synthesis, activity testing, docking, and quantum mechanical scoring of novel imidazo[1,2‐c]pyrimidin‐5(6H)‐one scaffold for cyclin‐dependent kinase 2 (CDK2) inhibition. A series of 26 compounds substituted with aromatic moieties at position 8 has been tested in in vitro enzyme assays and shown to inhibit CDK2. 2D structure‐activity relationships have ascertained that small substituents at position 8 (up to the size of naphtyl or methoxyphenyl) generally lead to single‐digit micromolar IC50 values, whereas bigger substituents (substituted biphenyls) decreased the compounds' activities. The binding modes of the compounds obtained using Glide docking have exhibited up to 2 hinge‐region hydrogen bonds to CDK2 and differed in the orientation of the inhibitor core and the placement of the 8‐substituents. Semiempirical quantum mechanics‐based scoring identified probable favourable binding modes, which will serve for future structure‐based design and synthetic optimization of substituents of the heterocyclic core. In summary, we have identified a novel core for CDK2 inhibition and will explore it further to increase the potencies of the compounds and also monitor selectivities against other protein kinases.  相似文献   

15.
This article describes the implementation of a new docking approach. The method uses a Tabu search methodology to dock flexibly ligand molecules into rigid receptor structures. It uses an empirical objective function with a small number of physically based terms derived from fitting experimental binding affinities for crystallographic complexes. This means that docking energies produced by the searching algorithm provide direct estimates of the binding affinities of the ligands. The method has been tested on 50 ligand-receptor complexes for which the experimental binding affinity and binding geometry are known. All water molecules are removed from the structures and ligand molecules are minimized in vacuo before docking. The lowest energy geometry produced by the docking protocol is within 1.5 Å root-mean square of the experimental binding mode for 86% of the complexes. The lowest energies produced by the docking are in fair agreement with the known free energies of binding for the ligands. Proteins 33:367–382, 1998. © 1998 Wiley-Liss, Inc.  相似文献   

16.
Huang SY  Zou X 《Proteins》2007,66(2):399-421
One approach to incorporate protein flexibility in molecular docking is the use of an ensemble consisting of multiple protein structures. Sequentially docking each ligand into a large number of protein structures is computationally too expensive to allow large-scale database screening. It is challenging to achieve a good balance between docking accuracy and computational efficiency. In this work, we have developed a fast, novel docking algorithm utilizing multiple protein structures, referred to as ensemble docking, to account for protein structural variations. The algorithm can simultaneously dock a ligand into an ensemble of protein structures and automatically select an optimal protein structure that best fits the ligand by optimizing both ligand coordinates and the conformational variable m, where m represents the m-th structure in the protein ensemble. The docking algorithm was validated on 10 protein ensembles containing 105 crystal structures and 87 ligands in terms of binding mode and energy score predictions. A success rate of 93% was obtained with the criterion of root-mean-square deviation <2.5 A if the top five orientations for each ligand were considered, comparable to that of sequential docking in which scores for individual docking are merged into one list by re-ranking, and significantly better than that of single rigid-receptor docking (75% on average). Similar trends were also observed in binding score predictions and enrichment tests of virtual database screening. The ensemble docking algorithm is computationally efficient, with a computational time comparable to that for docking a ligand into a single protein structure. In contrast, the computational time for the sequential docking method increases linearly with the number of protein structures in the ensemble. The algorithm was further evaluated using a more realistic ensemble in which the corresponding bound protein structures of inhibitors were excluded. The results show that ensemble docking successfully predicts the binding modes of the inhibitors, and discriminates the inhibitors from a set of noninhibitors with similar chemical properties. Although multiple experimental structures were used in the present work, our algorithm can be easily applied to multiple protein conformations generated by computational methods, and helps improve the efficiency of other existing multiple protein structure(MPS)-based methods to accommodate protein flexibility.  相似文献   

17.
Murphy J  Gatchell DW  Prasad JC  Vajda S 《Proteins》2003,53(4):840-854
Two structure-based potentials are used for both filtering (i.e., selecting a subset of conformations generated by rigid-body docking), and rescoring and ranking the selected conformations. ACP (atomic contact potential) is an atom-level extension of the Miyazawa-Jernigan potential parameterized on protein structures, whereas RPScore (residue pair potential score) is a residue-level potential, based on interactions in protein-protein complexes. These potentials are combined with other energy terms and applied to 13 sets of protein decoys, as well as to the results of docking 10 pairs of unbound proteins. For both potentials, the ability to discriminate between near-native and non-native docked structures is substantially improved by refining the structures and by adding a van der Waals energy term. It is observed that ACP and RPScore complement each other in a number of ways (e.g., although RPScore yields more hits than ACP, mainly as a result of its better performance for charged complexes, ACP usually ranks the near-native complexes better). As a general solution to the protein-docking problem, we have found that the best discrimination strategies combine either an RPScore filter with an ACP-based scoring function, or an ACP-based filter with an RPScore-based scoring function. Thus, ACP and RPScore capture complementary structural information, and combining them in a multistage postprocessing protocol provides substantially better discrimination than the use of the same potential for both filtering and ranking the docked conformations.  相似文献   

18.
A new approach to predicting the ligand-binding sites of proteins was developed, using protein-ligand docking computation. In this method, many compounds in a random library are docked onto the whole protein surface. We assumed that the true ligand-binding site would exhibit stronger affinity to the compounds in the random library than the other sites, even if the random library did not include the ligand corresponding to the true binding site. We also assumed that the affinity of the true ligand-binding site would be correlated to the docking scores of the compounds in the random library, if the ligand-binding site was correctly predicted. We call this method the molecular-docking binding-site finding (MolSite) method. The MolSite method was applied to 89 known protein-ligand complex structures extracted from the Protein Data Bank, and it predicted the correct binding sites with about 80-99% accuracy, when only the single top-ranked site was adopted. In addition, the average docking score was weakly correlated to the experimental protein-ligand binding free energy, with a correlation coefficient of 0.44.  相似文献   

19.
Wu MY  Dai DQ  Yan H 《Proteins》2012,80(9):2137-2153
Protein-ligand docking is widely applied to structure-based virtual screening for drug discovery. This article presents a novel docking technique, PRL-Dock, based on hydrogen bond matching and probabilistic relaxation labeling. It deals with multiple hydrogen bonds and can match many acceptors and donors simultaneously. In the matching process, the initial probability of matching an acceptor with a donor is estimated by an efficient scoring function and the compatibility coefficients are assigned according to the coexisting condition of two hydrogen bonds. After hydrogen bond matching, the geometric complementarity of the interacting donor and acceptor sites is taken into account for displacement of the ligand. It is reduced to an optimization problem to calculate the optimal translation and rotation matrixes that minimize the root mean square deviation between two sets of points, which can be solved using the Kabsch algorithm. In addition to the van der Waals interaction, the contribution of intermolecular hydrogen bonds in a complex is included in the scoring function to evaluate the docking quality. A modified Lennard-Jones 12-6 dispersion-repulsion term is used to estimate the van der Waals interaction to make the scoring function fairly "soft" so that ligands are not heavily penalized for small errors in the binding geometry. The calculation of this scoring function is very convenient. The evaluation is carried out on 278 rigid complexes and 93 flexible ones where there is at least one intermolecular hydrogen bond. The experiment results of docking accuracy and prediction of binding affinity demonstrate that the proposed method is highly effective.  相似文献   

20.
Yue Cao  Yang Shen 《Proteins》2020,88(8):1091-1099
Structural information about protein-protein interactions, often missing at the interactome scale, is important for mechanistic understanding of cells and rational discovery of therapeutics. Protein docking provides a computational alternative for such information. However, ranking near-native docked models high among a large number of candidates, often known as the scoring problem, remains a critical challenge. Moreover, estimating model quality, also known as the quality assessment problem, is rarely addressed in protein docking. In this study, the two challenging problems in protein docking are regarded as relative and absolute scoring, respectively, and addressed in one physics-inspired deep learning framework. We represent protein and complex structures as intra- and inter-molecular residue contact graphs with atom-resolution node and edge features. And we propose a novel graph convolutional kernel that aggregates interacting nodes’ features through edges so that generalized interaction energies can be learned directly from 3D data. The resulting energy-based graph convolutional networks (EGCN) with multihead attention are trained to predict intra- and inter-molecular energies, binding affinities, and quality measures (interface RMSD) for encounter complexes. Compared to a state-of-the-art scoring function for model ranking, EGCN significantly improves ranking for a critical assessment of predicted interactions (CAPRI) test set involving homology docking; and is comparable or slightly better for Score_set, a CAPRI benchmark set generated by diverse community-wide docking protocols not known to training data. For Score_set quality assessment, EGCN shows about 27% improvement to our previous efforts. Directly learning from 3D structure data in graph representation, EGCN represents the first successful development of graph convolutional networks for protein docking.  相似文献   

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