SCUD: fast structure clustering of decoys using reference state to remove overall rotation

Unsupervised and Supervised Learning over theEnergy Landscape for Protein Decoy Selection

The energy landscape that organizes microstates of a molecular system and governs theunderlying molecular dynamics exposes the relationship between molecular form/structure, changesto form, and biological activity or function in the cell. However, several challenges stand in the wayof leveraging energy landscapes for relating structure and structural dynamics to function. Energylandscapes are high-dimensional, multi-modal, and often overly-rugged. Deep wells or basins inthem do not always correspond to stable structural states but are instead the result of inherentinaccuracies in semi-empirical molecular energy functions. Due to these challenges, energeticsis typically ignored in computational approaches addressing long-standing central questions incomputational biology, such as protein decoy selection. In the latter, the goal is to determine over apossibly large number of computationally-generated three-dimensional structures of a protein thosestructures that are biologically-active/native. In recent work, we have recast our attention on theprotein energy landscape and its role in helping us to advance decoy selection. Here, we summarizesome of our successes so far in this direction via unsupervised learning. More importantly, we furtheradvance the argument that the energy landscape holds valuable information to aid and advance thestate of protein decoy selection via novel machine learning methodologies that leverage supervisedlearning. Our focus in this article is on decoy selection for the purpose of a rigorous, quantitativeevaluation of how leveraging protein energy landscapes advances an important problem in proteinmodeling. However, the ideas and concepts presented here are generally useful to make discoveriesin studies aiming to relate molecular structure and structural dynamics to function.

From Extraction of Local Structures of Protein Energy Landscapes to Improved Decoy Selection in Template-Free Protein Structure Prediction

Due to the essential role that the three-dimensional conformation of a protein plays in regulating interactions with molecular partners, wet and dry laboratories seek biologically-active conformations of a protein to decode its function. Computational approaches are gaining prominence due to the labor and cost demands of wet laboratory investigations. Template-free methods can now compute thousands of conformations known as decoys, but selecting native conformations from the generated decoys remains challenging. Repeatedly, research has shown that the protein energy functions whose minima are sought in the generation of decoys are unreliable indicators of nativeness. The prevalent approach ignores energy altogether and clusters decoys by conformational similarity. Complementary recent efforts design protein-specific scoring functions or train machine learning models on labeled decoys. In this paper, we show that an informative consideration of energy can be carried out under the energy landscape view. Specifically, we leverage local structures known as basins in the energy landscape probed by a template-free method. We propose and compare various strategies of basin-based decoy selection that we demonstrate are superior to clustering-based strategies. The presented results point to further directions of research for improving decoy selection, including the ability to properly consider the multiplicity of native conformations of proteins.

Quality Assessment of Predicted Protein Models Using Energies Calculated by the Fragment Molecular Orbital Method

Protein structure prediction directly from sequences is a very challenging problem in computational biology. One of the most successful approaches employs stochastic conformational sampling to search an empirically derived energy function landscape for the global energy minimum state. Due to the errors in the empirically derived energy function, the lowest energy conformation may not be the best model. We have evaluated the use of energy calculated by the fragment molecular orbital method (FMO energy) to assess the quality of predicted models and its ability to identify the best model among an ensemble of predicted models. The fragment molecular orbital method implemented in GAMESS was used to calculate the FMO energy of predicted models. When tested on eight protein targets, we found that the model ranking based on FMO energies is better than that based on empirically derived energies when there is sufficient diversity among these models. This model diversity can be estimated prior to the FMO energy calculations. Our result demonstrates that the FMO energy calculated by the fragment molecular orbital method is a practical and promising measure for the assessment of protein model quality and the selection of the best protein model among many generated.

An improved method to detect correct protein folds using partial clustering

Background

Structure-based clustering is commonly used to identify correct protein folds among candidate folds (also called decoys) generated by protein structure prediction programs. However, traditional clustering methods exhibit a poor runtime performance on large decoy sets. We hypothesized that a more efficient “partial“ clustering approach in combination with an improved scoring scheme could significantly improve both the speed and performance of existing candidate selection methods.

Results

We propose a new scheme that performs rapid but incomplete clustering on protein decoys. Our method detects structurally similar decoys (measured using either C_α RMSD or GDT-TS score) and extracts representatives from them without assigning every decoy to a cluster. We integrated our new clustering strategy with several different scoring functions to assess both the performance and speed in identifying correct or near-correct folds. Experimental results on 35 Rosetta decoy sets and 40 I-TASSER decoy sets show that our method can improve the correct fold detection rate as assessed by two different quality criteria. This improvement is significantly better than two recently published clustering methods, Durandal and Calibur-lite. Speed and efficiency testing shows that our method can handle much larger decoy sets and is up to 22 times faster than Durandal and Calibur-lite.

Conclusions

The new method, named HS-Forest, avoids the computationally expensive task of clustering every decoy, yet still allows superior correct-fold selection. Its improved speed, efficiency and decoy-selection performance should enable structure prediction researchers to work with larger decoy sets and significantly improve their ab initio structure prediction performance.

Fast algorithm for population-based protein structural model analysis

De novo protein structure prediction often generates a large population of candidates (models), and then selects near-native models through clustering. Existing structural model clustering methods are time consuming due to pairwise distance calculation between models. In this paper, we present a novel method for fast model clustering without losing the clustering accuracy. Instead of the commonly used pairwise root mean square deviation and TM-score values, we propose two new distance measures, Dscore1 and Dscore2, based on the comparison of the protein distance matrices for describing the difference and the similarity among models, respectively. The analysis indicates that both the correlation between Dscore1 and root mean square deviation and the correlation between Dscore2 and TM-score are high. Compared to the existing methods with calculation time quadratic to the number of models, our Dscore1-based clustering achieves a linearly time complexity while obtaining almost the same accuracy for near-native model selection. By using Dscore2 to select representatives of clusters, we can further improve the quality of the representatives with little increase in computing time. In addition, for large size (~500 k) models, we can give a fast data visualization based on the Dscore distribution in seconds to minutes. Our method has been implemented in a package named MUFOLD-CL, available at http://mufold.org/clustering.php.

Fast structure similarity searches among protein models: efficient clustering of protein fragments

BACKGROUND

For many predictive applications a large number of models is generated and later clustered in subsets based on structure similarity. In most clustering algorithms an all-vs-all root mean square deviation (RMSD) comparison is performed. Most of the time is typically spent on comparison of non-similar structures. For sets with more than, say, 10,000 models this procedure is very time-consuming and alternative faster algorithms, restricting comparisons only to most similar structures would be useful.

RESULTS

We exploit the inverse triangle inequality on the RMSD between two structures given the RMSDs with a third structure. The lower bound on RMSD may be used, when restricting the search of similarity to a reasonably low RMSD threshold value, to speed up similarity searches significantly. Tests are performed on large sets of decoys which are widely used as test cases for predictive methods, with a speed-up of up to 100 times with respect to all-vs-all comparison depending on the set and parameters used. Sample applications are shown.

CONCLUSIONS

The algorithm presented here allows fast comparison of large data sets of structures with limited memory requirements. As an example of application we present clustering of more than 100000 fragments of length 5 from the top500H dataset into few hundred representative fragments. A more realistic scenario is provided by the search of similarity within the very large decoy sets used for the tests. Other applications regard filtering nearly-indentical conformation in selected CASP9 datasets and clustering molecular dynamics snapshots.

AVAILABILITY

A linux executable and a Perl script with examples are given in the supplementary material (Additional file 1). The source code is available upon request from the authors.

Clustering 100,000 protein structure decoys in minutes

Ab initio protein structure prediction methods first generate large sets of structural conformations as candidates (called decoys), and then select the most representative decoys through clustering techniques. Classical clustering methods are inefficient due to the pairwise distance calculation, and thus become infeasible when the number of decoys is large. In addition, the existing clustering approaches suffer from the arbitrariness in determining a distance threshold for proteins within a cluster: a small distance threshold leads to many small clusters, while a large distance threshold results in the merging of several independent clusters into one cluster. In this paper, we propose an efficient clustering method through fast estimating cluster centroids and efficient pruning rotation spaces. The number of clusters is automatically detected by information distance criteria. A package named ONION, which can be downloaded freely, is implemented accordingly. Experimental results on benchmark data sets suggest that ONION is 14 times faster than existing tools, and ONION obtains better selections for 31 targets, and worse selection for 19 targets compared to SPICKER’s selections. On an average PC, ONION can cluster 100,000 decoys in around 12 minutes.

Durandal: fast exact clustering of protein decoys

In protein folding, clustering is commonly used as one way to identify the best decoy produced. Initializing the pairwise distance matrix for a large decoy set is computationally expensive. We have proposed a fast method that works even on large decoy sets. This method is implemented in a software called Durandal. Durandal has been shown to be consistently faster than other software performing fast exact clustering. In some cases, Durandal can even outperform the speed of an approximate method. Durandal uses the triangular inequality to accelerate exact clustering, without compromising the distance function. Recently, we have further enhanced the performance of Durandal by incorporating a Quaternion-based characteristic polynomial method that has increased the speed of Durandal between 13% and 27% compared with the previous version. Durandal source code is available under the GNU General Public License at http://www.riken.jp/zhangiru/software/durandal_released_qcp.tgz. Alternatively, a compiled version of Durandal is also distributed with the nightly builds of the Phenix (http://www.phenix-online.org/) crystallographic software suite (Adams et al., Acta Crystallogr Sect D 2010, 66, 213).

Entropy-accelerated exact clustering of protein decoys

MOTIVATION

Clustering is commonly used to identify the best decoy among many generated in protein structure prediction when using energy alone is insufficient. Calculation of the pairwise distance matrix for a large decoy set is computationally expensive. Typically, only a reduced set of decoys using energy filtering is subjected to clustering analysis. A fast clustering method for a large decoy set would be beneficial to protein structure prediction and this still poses a challenge.

RESULTS

We propose a method using propagation of geometric constraints to accelerate exact clustering, without compromising the distance measure. Our method can be used with any metric distance. Metrics that are expensive to compute and have known cheap lower and upper bounds will benefit most from the method. We compared our method's accuracy against published results from the SPICKER clustering software on 40 large decoy sets from the I-TASSER protein folding engine. We also performed some additional speed comparisons on six targets from the 'semfold' decoy set. In our tests, our method chose a better decoy than the energy criterion in 25 out of 40 cases versus 20 for SPICKER. Our method also was shown to be consistently faster than another fast software performing exact clustering named Calibur. In some cases, our approach can even outperform the speed of an approximate method.

AVAILABILITY

Our C++ software is released under the GNU General Public License. It can be downloaded from http://www.riken.jp/zhangiru/software/durandal_released.tgz.

MUFOLD: A new solution for protein 3D structure prediction

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 Calpha 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 A, 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.

Calibur: a tool for clustering large numbers of protein decoys

BACKGROUND

Ab initio protein structure prediction methods generate numerous structural candidates, which are referred to as decoys. The decoy with the most number of neighbors of up to a threshold distance is typically identified as the most representative decoy. However, the clustering of decoys needed for this criterion involves computations with runtimes that are at best quadratic in the number of decoys. As a result currently there is no tool that is designed to exactly cluster very large numbers of decoys, thus creating a bottleneck in the analysis.

RESULTS

Using three strategies aimed at enhancing performance (proximate decoys organization, preliminary screening via lower and upper bounds, outliers filtering) we designed and implemented a software tool for clustering decoys called Calibur. We show empirical results indicating the effectiveness of each of the strategies employed. The strategies are further fine-tuned according to their effectiveness.Calibur demonstrated the ability to scale well with respect to increases in the number of decoys. For a sample size of approximately 30 thousand decoys, Calibur completed the analysis in one third of the time required when the strategies are not used.For practical use Calibur is able to automatically discover from the input decoys a suitable threshold distance for clustering. Several methods for this discovery are implemented in Calibur, where by default a very fast one is used. Using the default method Calibur reported relatively good decoys in our tests.

CONCLUSIONS

Calibur's ability to handle very large protein decoy sets makes it a useful tool for clustering decoys in ab initio protein structure prediction. As the number of decoys generated in these methods increases, we believe Calibur will come in important for progress in the field.

A model of local-minima distribution on conformational space and its application to protein structure prediction

A quantitative two-parameter model is developed to describe local energy minima distribution. On a conformational space measured by least-square-fitting root-mean-squared distance (RMSD), the number of local minima in a r RMSD region is proposed to be proportional to exp(-1/r). As part of the model derivations, the minimum RMSD of decoys from the largest cluster, the number of decoys in the largest cluster, and the RMSD distribution of the decoys have inner connections with each other. The model is successfully verified on a 49 helix-packing decoy set and a 30 loop-prediction decoy set, as well as both knowledge-based potential (DFIRE) and physical force-fields (OPLS and CHARMM). One of the model's applications is predicting behaviors of a large amount of decoys (e.g., minimum RMSD of 40,000 decoys) by generating only a small number of decoys (e.g., 500). It may be applied to structure predictions guided by any Lennard-Jones-like potential functions and can be extended to other sampling methods guided by simple energy terms.