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1.
Biophysical forcefields have contributed less than originally anticipated to recent progress in protein structure prediction. Here, we have investigated the selectivity of a recently developed all‐atom free‐energy forcefield for protein structure prediction and quality assessment (QA). Using a heuristic method, but excluding homology, we generated decoy‐sets for all targets of the CASP7 protein structure prediction assessment with <150 amino acids. The decoys in each set were then ranked by energy in short relaxation simulations and the best low‐energy cluster was submitted as a prediction. For four of nine template‐free targets, this approach generated high‐ranking predictions within the top 10 models submitted in CASP7 for the respective targets. For these targets, our de‐novo predictions had an average GDT_S score of 42.81, significantly above the average of all groups. The refinement protocol has difficulty for oligomeric targets and when no near‐native decoys are generated in the decoy library. For targets with high‐quality decoy sets the refinement approach was highly selective. Motivated by this observation, we rescored all server submissions up to 200 amino acids using a similar refinement protocol, but using no clustering, in a QA exercise. We found an excellent correlation between the best server models and those with the lowest energy in the forcefield. The free‐energy refinement protocol may thus be an efficient tool for relative QA and protein structure prediction. Proteins 2009. © 2009 Wiley‐Liss, Inc.  相似文献   

2.
The principal bottleneck in protein structure prediction is the refinement of models from lower accuracies to the resolution observed by experiment. We developed a novel constraints‐based refinement method that identifies a high number of accurate input constraints from initial models and rebuilds them using restrained torsion angle dynamics (rTAD). We previously created a Bayesian statistics‐based residue‐specific all‐atom probability discriminatory function (RAPDF) to discriminate native‐like models by measuring the probability of accuracy for atom type distances within a given model. Here, we exploit RAPDF to score (i.e., filter) constraints from initial predictions that may or may not be close to a native‐like state, obtain consensus of top scoring constraints amongst five initial models, and compile sets with no redundant residue pair constraints. We find that this method consistently produces a large and highly accurate set of distance constraints from which to build refinement models. We further optimize the balance between accuracy and coverage of constraints by producing multiple structure sets using different constraint distance cutoffs, and note that the cutoff governs spatially near versus distant effects in model generation. This complete procedure of deriving distance constraints for rTAD simulations improves the quality of initial predictions significantly in all cases evaluated by us. Our procedure represents a significant step in solving the protein structure prediction and refinement problem, by enabling the use of consensus constraints, RAPDF, and rTAD for protein structure modeling and refinement. Proteins 2009. © 2009 Wiley‐Liss, Inc.  相似文献   

3.
One of the major limitations of computational protein structure prediction is the deviation of predicted models from their experimentally derived true, native structures. The limitations often hinder the possibility of applying computational protein structure prediction methods in biochemical assignment and drug design that are very sensitive to structural details. Refinement of these low‐resolution predicted models to high‐resolution structures close to the native state, however, has proven to be extremely challenging. Thus, protein structure refinement remains a largely unsolved problem. Critical assessment of techniques for protein structure prediction (CASP) specifically indicated that most predictors participating in the refinement category still did not consistently improve model quality. Here, we propose a two‐step refinement protocol, called 3Drefine, to consistently bring the initial model closer to the native structure. The first step is based on optimization of hydrogen bonding (HB) network and the second step applies atomic‐level energy minimization on the optimized model using a composite physics and knowledge‐based force fields. The approach has been evaluated on the CASP benchmark data and it exhibits consistent improvement over the initial structure in both global and local structural quality measures. 3Drefine method is also computationally inexpensive, consuming only few minutes of CPU time to refine a protein of typical length (300 residues). 3Drefine web server is freely available at http://sysbio.rnet.missouri.edu/3Drefine/ . Proteins 2013. © 2012 Wiley Periodicals, Inc.  相似文献   

4.
Protein structure refinement is the challenging problem of operating on any protein structure prediction to improve its accuracy with respect to the native structure in a blind fashion. Although many approaches have been developed and tested during the last four CASP experiments, a majority of the methods continue to degrade models rather than improve them. Princeton_TIGRESS (Khoury et al., Proteins 2014;82:794–814) was developed previously and utilizes separate sampling and selection stages involving Monte Carlo and molecular dynamics simulations and classification using an SVM predictor. The initial implementation was shown to consistently refine protein structures 76% of the time in our own internal benchmarking on CASP 7‐10 targets. In this work, we improved the sampling and selection stages and tested the method in blind predictions during CASP11. We added a decomposition of physics‐based and hybrid energy functions, as well as a coordinate‐free representation of the protein structure through distance‐binning distances to capture fine‐grained movements. We performed parameter estimation to optimize the adjustable SVM parameters to maximize precision while balancing sensitivity and specificity across all cross‐validated data sets, finding enrichment in our ability to select models from the populations of similar decoys generated for targets in CASPs 7‐10. The MD stage was enhanced such that larger structures could be further refined. Among refinement methods that are currently implemented as web‐servers, Princeton_TIGRESS 2.0 demonstrated the most consistent and most substantial net refinement in blind predictions during CASP11. The enhanced refinement protocol Princeton_TIGRESS 2.0 is freely available as a web server at http://atlas.engr.tamu.edu/refinement/ . Proteins 2017; 85:1078–1098. © 2017 Wiley Periodicals, Inc.  相似文献   

5.
The determination of membrane protein (MP) structures has always trailed that of soluble proteins due to difficulties in their overexpression, reconstitution into membrane mimetics, and subsequent structure determination. The percentage of MP structures in the protein databank (PDB) has been at a constant 1–2% for the last decade. In contrast, over half of all drugs target MPs, only highlighting how little we understand about drug‐specific effects in the human body. To reduce this gap, researchers have attempted to predict structural features of MPs even before the first structure was experimentally elucidated. In this review, we present current computational methods to predict MP structure, starting with secondary structure prediction, prediction of trans‐membrane spans, and topology. Even though these methods generate reliable predictions, challenges such as predicting kinks or precise beginnings and ends of secondary structure elements are still waiting to be addressed. We describe recent developments in the prediction of 3D structures of both α‐helical MPs as well as β‐barrels using comparative modeling techniques, de novo methods, and molecular dynamics (MD) simulations. The increase of MP structures has (1) facilitated comparative modeling due to availability of more and better templates, and (2) improved the statistics for knowledge‐based scoring functions. Moreover, de novo methods have benefited from the use of correlated mutations as restraints. Finally, we outline current advances that will likely shape the field in the forthcoming decade. Proteins 2015; 83:1–24. © 2014 Wiley Periodicals, Inc.  相似文献   

6.
There have been steady improvements in protein structure prediction during the past 2 decades. However, current methods are still far from consistently predicting structural models accurately with computing power accessible to common users. Toward achieving more accurate and efficient structure prediction, we developed a number of novel methods and integrated them into a software package, MUFOLD. First, a systematic protocol was developed to identify useful templates and fragments from Protein Data Bank for a given target protein. Then, an efficient process was applied for iterative coarse‐grain model generation and evaluation at the Cα or backbone level. In this process, we construct models using interresidue spatial restraints derived from alignments by multidimensional scaling, evaluate and select models through clustering and static scoring functions, and iteratively improve the selected models by integrating spatial restraints and previous models. Finally, the full‐atom models were evaluated using molecular dynamics simulations based on structural changes under simulated heating. We have continuously improved the performance of MUFOLD by using a benchmark of 200 proteins from the Astral database, where no template with >25% sequence identity to any target protein is included. The average root‐mean‐square deviation of the best models from the native structures is 4.28 Å, which shows significant and systematic improvement over our previous methods. The computing time of MUFOLD is much shorter than many other tools, such as Rosetta. MUFOLD demonstrated some success in the 2008 community‐wide experiment for protein structure prediction CASP8. Proteins 2010. © 2009 Wiley‐Liss, Inc.  相似文献   

7.
Protein structure refinement is an important but unsolved problem; it must be solved if we are to predict biological function that is very sensitive to structural details. Specifically, critical assessment of techniques for protein structure prediction (CASP) shows that the accuracy of predictions in the comparative modeling category is often worse than that of the template on which the homology model is based. Here we describe a refinement protocol that is able to consistently refine submitted predictions for all categories at CASP7. The protocol uses direct energy minimization of the knowledge‐based potential of mean force that is based on the interaction statistics of 167 atom types (Summa and Levitt, Proc Natl Acad Sci USA 2007; 104:3177–3182). Our protocol is thus computationally very efficient; it only takes a few minutes of CPU time to run typical protein models (300 residues). We observe an average structural improvement of 1% in GDT_TS, for predictions that have low and medium homology to known PDB structures (Global Distance Test score or GDT_TS between 50 and 80%). We also observe a marked improvement in the stereochemistry of the models. The level of improvement varies amongst the various participants at CASP, but we see large improvements (>10% increase in GDT_TS) even for models predicted by the best performing groups at CASP7. In addition, our protocol consistently improved the best predicted models in the refinement category at CASP7 and CASP8. These improvements in structure and stereochemistry prove the usefulness of our computationally inexpensive, powerful and automatic refinement protocol. Proteins 2010. © 2010 Wiley‐Liss, Inc.  相似文献   

8.
Comparative or homology modeling of a target protein based on sequence similarity to a protein with known structure is widely used to provide structural models of proteins. Depending on the target‐template similarity these model structures may contain regions of limited structural accuracy. In principle, molecular dynamics (MD) simulations can be used to refine protein model structures and also to model loop regions that connect structurally conserved regions but it is limited by the currently accessible simulation time scales. A recently developed biasing potential replica exchange (BP‐REMD) method was used to refine loops and complete decoy protein structures at atomic resolution including explicit solvent. In standard REMD simulations several replicas of a system are run in parallel at different temperatures allowing exchanges at preset time intervals. In a BP‐REMD simulation replicas are controlled by various levels of a biasing potential to reduce the energy barriers associated with peptide backbone dihedral transitions. The method requires much fewer replicas for efficient sampling compared with T‐REMD. Application of the approach to several protein loops indicated improved conformational sampling of backbone dihedral angle of loop residues compared to conventional MD simulations. BP‐REMD refinement simulations on several test cases starting from decoy structures deviating significantly from the native structure resulted in final structures in much closer agreement with experiment compared to conventional MD simulations. Proteins 2010. © 2010 Wiley‐Liss, Inc.  相似文献   

9.
Building reliable structural models of G protein‐coupled receptors (GPCRs) is a difficult task because of the paucity of suitable templates, low sequence identity, and the wide variety of ligand specificities within the superfamily. Template‐based modeling is known to be the most successful method for protein structure prediction. However, refinement of homology models within 1–3 Å Cα RMSD of the native structure remains a major challenge. Here, we address this problem by developing a novel protocol (foldGPCR) for modeling the transmembrane (TM) region of GPCRs in complex with a ligand, aimed to accurately model the structural divergence between the template and target in the TM helices. The protocol is based on predicted conserved inter‐residue contacts between the template and target, and exploits an all‐atom implicit membrane force field. The placement of the ligand in the binding pocket is guided by biochemical data. The foldGPCR protocol is implemented by a stepwise hierarchical approach, in which the TM helical bundle and the ligand are assembled by simulated annealing trials in the first step, and the receptor‐ligand complex is refined with replica exchange sampling in the second step. The protocol is applied to model the human β2‐adrenergic receptor (β2AR) bound to carazolol, using contacts derived from the template structure of bovine rhodopsin. Comparison with the X‐ray crystal structure of the β2AR shows that our protocol is particularly successful in accurately capturing helix backbone irregularities and helix‐helix packing interactions that distinguish rhodopsin from β2AR. Proteins 2010. © 2010 Wiley‐Liss, Inc.  相似文献   

10.
M. F. Thorpe  S. Banu Ozkan 《Proteins》2015,83(12):2279-2292
The most successful protein structure prediction methods to date have been template‐based modeling (TBM) or homology modeling, which predicts protein structure based on experimental structures. These high accuracy predictions sometimes retain structural errors due to incorrect templates or a lack of accurate templates in the case of low sequence similarity, making these structures inadequate in drug‐design studies or molecular dynamics simulations. We have developed a new physics based approach to the protein refinement problem by mimicking the mechanism of chaperons that rehabilitate misfolded proteins. The template structure is unfolded by selectively (targeted) pulling on different portions of the protein using the geometric based technique FRODA, and then refolded using hierarchically restrained replica exchange molecular dynamics simulations (hr‐REMD). FRODA unfolding is used to create a diverse set of topologies for surveying near native‐like structures from a template and to provide a set of persistent contacts to be employed during re‐folding. We have tested our approach on 13 previous CASP targets and observed that this method of folding an ensemble of partially unfolded structures, through the hierarchical addition of contact restraints (that is, first local and then nonlocal interactions), leads to a refolding of the structure along with refinement in most cases (12/13). Although this approach yields refined models through advancement in sampling, the task of blind selection of the best refined models still needs to be solved. Overall, the method can be useful for improved sampling for low resolution models where certain of the portions of the structure are incorrectly modeled. Proteins 2015; 83:2279–2292. © 2015 Wiley Periodicals, Inc.  相似文献   

11.
Predicted protein residue–residue contacts can be used to build three‐dimensional models and consequently to predict protein folds from scratch. A considerable amount of effort is currently being spent to improve contact prediction accuracy, whereas few methods are available to construct protein tertiary structures from predicted contacts. Here, we present an ab initio protein folding method to build three‐dimensional models using predicted contacts and secondary structures. Our method first translates contacts and secondary structures into distance, dihedral angle, and hydrogen bond restraints according to a set of new conversion rules, and then provides these restraints as input for a distance geometry algorithm to build tertiary structure models. The initially reconstructed models are used to regenerate a set of physically realistic contact restraints and detect secondary structure patterns, which are then used to reconstruct final structural models. This unique two‐stage modeling approach of integrating contacts and secondary structures improves the quality and accuracy of structural models and in particular generates better β‐sheets than other algorithms. We validate our method on two standard benchmark datasets using true contacts and secondary structures. Our method improves TM‐score of reconstructed protein models by 45% and 42% over the existing method on the two datasets, respectively. On the dataset for benchmarking reconstructions methods with predicted contacts and secondary structures, the average TM‐score of best models reconstructed by our method is 0.59, 5.5% higher than the existing method. The CONFOLD web server is available at http://protein.rnet.missouri.edu/confold/ . Proteins 2015; 83:1436–1449. © 2015 Wiley Periodicals, Inc.  相似文献   

12.
A refinement protocol based on physics‐based techniques established for water soluble proteins is tested for membrane protein structures. Initial structures were generated by homology modeling and sampled via molecular dynamics simulations in explicit lipid bilayer and aqueous solvent systems. Snapshots from the simulations were selected based on scoring with either knowledge‐based or implicit membrane‐based scoring functions and averaged to obtain refined models. The protocol resulted in consistent and significant refinement of the membrane protein structures similar to the performance of refinement methods for soluble proteins. Refinement success was similar between sampling in the presence of lipid bilayers and aqueous solvent but the presence of lipid bilayers may benefit the improvement of lipid‐facing residues. Scoring with knowledge‐based functions (DFIRE and RWplus) was found to be as good as scoring using implicit membrane‐based scoring functions suggesting that differences in internal packing is more important than orientations relative to the membrane during the refinement of membrane protein homology models.  相似文献   

13.
The determination of G protein-coupled receptor (GPCR) structures at atomic resolution has improved understanding of cellular signaling and will accelerate the development of new drug candidates. However, experimental structures still remain unavailable for a majority of the GPCR family. GPCR structures and their interactions with ligands can also be modelled computationally, but such predictions have limited accuracy. In this work, we explored if molecular dynamics (MD) simulations could be used to refine the accuracy of in silico models of receptor-ligand complexes that were submitted to a community-wide assessment of GPCR structure prediction (GPCR Dock). Two simulation protocols were used to refine 30 models of the D3 dopamine receptor (D3R) in complex with an antagonist. Close to 60 μs of simulation time was generated and the resulting MD refined models were compared to a D3R crystal structure. In the MD simulations, the receptor models generally drifted further away from the crystal structure conformation. However, MD refinement was able to improve the accuracy of the ligand binding mode. The best refinement protocol improved agreement with the experimentally observed ligand binding mode for a majority of the models. Receptor structures with improved virtual screening performance, which was assessed by molecular docking of ligands and decoys, could also be identified among the MD refined models. Application of weak restraints to the transmembrane helixes in the MD simulations further improved predictions of the ligand binding mode and second extracellular loop. These results provide guidelines for application of MD refinement in prediction of GPCR-ligand complexes and directions for further method development.  相似文献   

14.
The DOcking decoy‐based Optimized Potential (DOOP) energy function for protein structure prediction is based on empirical distance‐dependent atom‐pair interactions. To optimize the atom‐pair interactions, native protein structures are decomposed into polypeptide chain segments that correspond to structural motives involving complete secondary structure elements. They constitute near native ligand–receptor systems (or just pairs). Thus, a total of 8609 ligand–receptor systems were prepared from 954 selected proteins. For each of these hypothetical ligand–receptor systems, 1000 evenly sampled docking decoys with 0–10 Å interface root‐mean‐square‐deviation (iRMSD) were generated with a method used before for protein–protein docking. A neural network‐based optimization method was applied to derive the optimized energy parameters using these decoys so that the energy function mimics the funnel‐like energy landscape for the interaction between these hypothetical ligand–receptor systems. Thus, our method hierarchically models the overall funnel‐like energy landscape of native protein structures. The resulting energy function was tested on several commonly used decoy sets for native protein structure recognition and compared with other statistical potentials. In combination with a torsion potential term which describes the local conformational preference, the atom‐pair‐based potential outperforms other reported statistical energy functions in correct ranking of native protein structures for a variety of decoy sets. This is especially the case for the most challenging ROSETTA decoy set, although it does not take into account side chain orientation‐dependence explicitly. The DOOP energy function for protein structure prediction, the underlying database of protein structures with hypothetical ligand–receptor systems and their decoys are freely available at http://agknapp.chemie.fu‐berlin.de/doop/ . Proteins 2015; 83:881–890. © 2015 Wiley Periodicals, Inc.  相似文献   

15.
Pauling's mastery of peptide stereochemistry—based on small molecule crystal structures and the theory of chemical bonding—led to his realization that the peptide unit is planar and then to the Pauling–Corey–Branson model of the α‐helix. Similarly, contemporary protein structure refinement is based on experimentally determined diffraction data together with stereochemical restraints. However, even an X‐ray structure at ultra‐high resolution is still an under‐determined model in which the linkage among refinement parameters is complex. Consequently, restrictions imposed on any given parameter can affect the entire structure. Here, we examine recent studies of high resolution protein X‐ray structures, where substantial distortions of the peptide plane are found to be commonplace. Planarity is assessed by the ω‐angle, a dihedral angle determined by the peptide bond (C? N) and its flanking covalent neighbors; for an ideally planar trans peptide, ω = 180°. By using a freely available refinement package, Phenix [Afonine et al. (2012) Acta Cryst. D, 68:352–367], we demonstrate that tightening default restrictions on the ω‐angle can significantly reduce apparent deviations from peptide unit planarity without consequent reduction in reported evaluation metrics (e.g., R‐factors). To be clear, our result does not show that substantial non‐planarity is absent, only that an equivalent alternative model is possible. Resolving this disparity will ultimately require improved understanding of the deformation energy. Meanwhile, we urge inclusion of ω‐angle statistics in new structure reports in order to focus critical attention on the usual practice of assigning default values to ω‐angle constraints during structure refinement. Proteins 2015; 83:1687–1692. © 2015 Wiley Periodicals, Inc.  相似文献   

16.
Yunqi Li  Yang Zhang 《Proteins》2009,76(3):665-676
Protein structure prediction approaches usually perform modeling simulations based on reduced representation of protein structures. For biological utilizations, it is an important step to construct full atomic models from the reduced structure decoys. Most of the current full atomic model reconstruction procedures have defects which either could not completely remove the steric clashes among backbone atoms or generate final atomic models with worse topology similarity relative to the native structures than the reduced models. In this work, we develop a new protocol, called REMO, to generate full atomic protein models by optimizing the hydrogen‐bonding network with basic fragments matched from a newly constructed backbone isomer library of solved protein structures. The algorithm is benchmarked on 230 nonhomologous proteins with reduced structure decoys generated by I‐TASSER simulations. The results show that REMO has a significant ability to remove steric clashes, and meanwhile retains good topology of the reduced model. The hydrogen‐bonding network of the final models is dramatically improved during the procedure. The REMO algorithm has been exploited in the recent CASP8 experiment which demonstrated significant improvements of the I‐TASSER models in both atomic‐level structural refinement and hydrogen‐bonding network construction. Proteins 2009. © 2009 Wiley‐Liss, Inc.  相似文献   

17.
Protein structure refinement aims to perform a set of operations given a predicted structure to improve model quality and accuracy with respect to the native in a blind fashion. Despite the numerous computational approaches to the protein refinement problem reported in the previous three CASPs, an overwhelming majority of methods degrade models rather than improve them. We initially developed a method tested using blind predictions during CASP10 which was officially ranked in 5th place among all methods in the refinement category. Here, we present Princeton_TIGRESS, which when benchmarked on all CASP 7,8,9, and 10 refinement targets, simultaneously increased GDT_TS 76% of the time with an average improvement of 0.83 GDT_TS points per structure. The method was additionally benchmarked on models produced by top performing three‐dimensional structure prediction servers during CASP10. The robustness of the Princeton_TIGRESS protocol was also tested for different random seeds. We make the Princeton_TIGRESS refinement protocol freely available as a web server at http://atlas.princeton.edu/refinement . Using this protocol, one can consistently refine a prediction to help bridge the gap between a predicted structure and the actual native structure. Proteins 2014; 82:794–814. © 2013 Wiley Periodicals, Inc.  相似文献   

18.
Misura KM  Baker D 《Proteins》2005,59(1):15-29
Achieving atomic level accuracy in de novo structure prediction presents a formidable challenge even in the context of protein models with correct topologies. High-resolution refinement is a fundamental test of force field accuracy and sampling methodology, and its limited success in both comparative modeling and de novo prediction contexts highlights the limitations of current approaches. We constructed four tests to identify bottlenecks in our current approach and to guide progress in this challenging area. The first three tests showed that idealized native structures are stable under our refinement simulation conditions and that the refinement protocol can significantly decrease the root mean square deviation (RMSD) of perturbed native structures. In the fourth test we applied the refinement protocol to de novo models and showed that accurate models could be identified based on their energies, and in several cases many of the buried side chains adopted native-like conformations. We also showed that the differences in backbone and side-chain conformations between the refined de novo models and the native structures are largely localized to loop regions and regions where the native structure has unusual features such as rare rotamers or atypical hydrogen bonding between beta-strands. The refined de novo models typically have higher energies than refined idealized native structures, indicating that sampling of local backbone conformations and side-chain packing arrangements in a condensed state is a primary obstacle.  相似文献   

19.
Many proteins need to form oligomers to be functional, so oligomer structures provide important clues to biological roles of proteins. Prediction of oligomer structures therefore can be a useful tool in the absence of experimentally resolved structures. In this article, we describe the server and human methods that we used to predict oligomer structures in the CASP13 experiment. Performances of the methods on the 42 CASP13 oligomer targets consisting of 30 homo-oligomers and 12 hetero-oligomers are discussed. Our server method, Seok-assembly, generated models with interface contact similarity measure greater than 0.2 as model 1 for 11 homo-oligomer targets when proper templates existed in the database. Model refinement methods such as loop modeling and molecular dynamics (MD)-based overall refinement failed to improve model qualities when target proteins have domains not covered by templates or when chains have very small interfaces. In human predictions, additional experimental data such as low-resolution electron microscopy (EM) map were utilized. EM data could assist oligomer structure prediction by providing a global shape of the complex structure.  相似文献   

20.
Raval A  Piana S  Eastwood MP  Dror RO  Shaw DE 《Proteins》2012,80(8):2071-2079
Accurate computational prediction of protein structure represents a longstanding challenge in molecular biology and structure-based drug design. Although homology modeling techniques are widely used to produce low-resolution models, refining these models to high resolution has proven difficult. With long enough simulations and sufficiently accurate force fields, molecular dynamics (MD) simulations should in principle allow such refinement, but efforts to refine homology models using MD have for the most part yielded disappointing results. It has thus far been unclear whether MD-based refinement is limited primarily by accessible simulation timescales, force field accuracy, or both. Here, we examine MD as a technique for homology model refinement using all-atom simulations, each at least 100 μs long-more than 100 times longer than previous refinement simulations-and a physics-based force field that was recently shown to successfully fold a structurally diverse set of fast-folding proteins. In MD simulations of 24 proteins chosen from the refinement category of recent Critical Assessment of Structure Prediction (CASP) experiments, we find that in most cases, simulations initiated from homology models drift away from the native structure. Comparison with simulations initiated from the native structure suggests that force field accuracy is the primary factor limiting MD-based refinement. This problem can be mitigated to some extent by restricting sampling to the neighborhood of the initial model, leading to structural improvement that, while limited, is roughly comparable to the leading alternative methods.  相似文献   

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