Exploring protein energy landscapes with hierarchical clustering

Theory and Practice of Coarse-Grained Molecular Dynamics of Biologically Important Systems

Molecular dynamics with coarse-grained models is nowadays extensively used to simulate biomolecular systems at large time and size scales, compared to those accessible to all-atom molecular dynamics. In this review article, we describe the physical basis of coarse-grained molecular dynamics, the coarse-grained force fields, the equations of motion and the respective numerical integration algorithms, and selected practical applications of coarse-grained molecular dynamics. We demonstrate that the motion of coarse-grained sites is governed by the potential of mean force and the friction and stochastic forces, resulting from integrating out the secondary degrees of freedom. Consequently, Langevin dynamics is a natural means of describing the motion of a system at the coarse-grained level and the potential of mean force is the physical basis of the coarse-grained force fields. Moreover, the choice of coarse-grained variables and the fact that coarse-grained sites often do not have spherical symmetry implies a non-diagonal inertia tensor. We describe selected coarse-grained models used in molecular dynamics simulations, including the most popular MARTINI model developed by Marrink's group and the UNICORN model of biological macromolecules developed in our laboratory. We conclude by discussing examples of the application of coarse-grained molecular dynamics to study biologically important processes.

In Silico Structural Modeling and Analysis of Interactions of Tremellomycetes Cytochrome P450 Monooxygenases CYP51s with Substrates and Azoles

Cytochrome P450 monooxygenase CYP51 (sterol 14α-demethylase) is a well-known target of the azole drug fluconazole for treating cryptococcosis, a life-threatening fungal infection in immune-compromised patients in poor countries. Studies indicate that mutations in CYP51 confer fluconazole resistance on cryptococcal species. Despite the importance of CYP51 in these species, few studies on the structural analysis of CYP51 and its interactions with different azole drugs have been reported. We therefore performed in silico structural analysis of 11 CYP51s from cryptococcal species and other Tremellomycetes. Interactions of 11 CYP51s with nine ligands (three substrates and six azoles) performed by Rosetta docking using 10,000 combinations for each of the CYP51-ligand complex (11 CYP51s × 9 ligands = 99 complexes) and hierarchical agglomerative clustering were used for selecting the complexes. A web application for visualization of CYP51s' interactions with ligands was developed (http://bioshell.pl/azoledocking/). The study results indicated that Tremellomycetes CYP51s have a high preference for itraconazole, corroborating the in vitro effectiveness of itraconazole compared to fluconazole. Amino acids interacting with different ligands were found to be conserved across CYP51s, indicating that the procedure employed in this study is accurate and can be automated for studying P450-ligand interactions to cater for the growing number of P450s.

BioShell 3.0: Library for Processing Structural Biology Data

BioShell is an open-source package for processing biological data, particularly focused on structural applications. The package provides parsers, data structures and algorithms for handling and analyzing macromolecular sequences, structures and sequence profiles. The most frequently used routines are accessible by a set of easy-to-use command line utilities for a Linux environment. The full functionality of the package assumes knowledge of C++ or Python to assemble an application using this software library. Since the last publication that announced the version 2.0, the package has been greatly expanded and rewritten in C++ standard 11 (C++11) to improve its modularity and efficiency. A new testing platform has been implemented to continuously test the correctness and integrity of the package. More than two hundred test programs have been published to provide simple examples that can be used as templates. This makes BioShell an easy to use library that greatly speeds up development of bioinformatics applications and web services without compromising computational efficiency.

NEW MDS AND CLUSTERING BASED ALGORITHMS FOR PROTEIN MODEL QUALITY ASSESSMENT AND SELECTION

In protein tertiary structure prediction, assessing the quality of predicted models is an essential task. Over the past years, many methods have been proposed for the protein model quality assessment (QA) and selection problem. Despite significant advances, the discerning power of current methods is still unsatisfactory. In this paper, we propose two new algorithms, CC-Select and MDS-QA, based on multidimensional scaling and k-means clustering. For the model selection problem, CC-Select combines consensus with clustering techniques to select the best models from a given pool. Given a set of predicted models, CC-Select first calculates a consensus score for each structure based on its average pairwise structural similarity to other models. Then, similar structures are grouped into clusters using multidimensional scaling and clustering algorithms. In each cluster, the one with the highest consensus score is selected as a candidate model. For the QA problem, MDS-QA combines single-model scoring functions with consensus to determine more accurate assessment score for every model in a given pool. Using extensive benchmark sets of a large collection of predicted models, we compare the two algorithms with existing state-of-the-art quality assessment methods and show significant improvement.

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.

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).

Improving a consensus approach for protein structure selection by removing redundancy

In protein tertiary structure prediction, a crucial step is to select near-native structures from a large number of predicted structural models. Over the years, extensive research has been conducted for the protein structure selection problem with most approaches focusing on developing more accurate energy or scoring functions. Despite significant advances in this area, the discerning power of current approaches is still unsatisfactory. In this paper, we propose a novel consensus-based algorithm for the selection of predicted protein structures. Given a set of predicted models, our method first removes redundant structures to derive a subset of reference models. Then, a structure is ranked based on its average pairwise similarity to the reference models. Using the CASP8 data set containing a large collection of predicted models for 122 targets, we compared our method with the best CASP8 quality assessment (QA) servers, which are all consensus based, and showed that our QA scores correlate better with the GDT-TSs than those of the CASP8 QA servers. We also compared our method with the state-of-the-art scoring functions and showed its improved performance for near-native model selection. The GDT-TSs of the top models picked by our method are on average more than 8 percent better than the ones selected by the best performing scoring function.

A multilayer evaluation approach for protein structure prediction and model quality assessment

Protein tertiary structures are essential for studying functions of proteins at molecular level. An indispensable approach for protein structure solution is computational prediction. Most protein structure prediction methods generate candidate models first and select the best candidates by model quality assessment (QA). In many cases, good models can be produced, but the QA tools fail to select the best ones from the candidate model pool. Because of incomplete understanding of protein folding, each QA method only reflects partial facets of a structure model and thus has limited discerning power with no one consistently outperforming others. In this article, we developed a set of new QA methods, including two QA methods for evaluating target/template alignments, a molecular dynamics (MD)-based QA method, and three consensus QA methods with selected references to reveal new facets of protein structures complementary to the existing methods. Moreover, the underlying relationship among different QA methods were analyzed and then integrated into a multilayer evaluation approach to guide the model generation and model selection in prediction. All methods are integrated and implemented into an innovative and improved prediction system hereafter referred to as MUFOLD. In CASP8 and CASP9, MUFOLD has demonstrated the proof of the principles in terms of both QA discerning power and structure prediction accuracy.

Study of a structurally similar kappa opioid receptor agonist and antagonist pair by molecular dynamics simulations

Among the structurally similar guanidinonaltrindole (GNTI) compounds, 5'-GNTI is an antagonist while 6'-GNTI is an agonist of the kappaOR opioid receptor. To explore how a subtle alteration of the ligand structure influences the receptor activity, we investigated two concurrent processes: the final steps of ligand binding at the receptor binding site and the initial steps of receptor activation. To trace these early activation steps, the membranous part of the receptor was built on an inactive receptor template while the extracellular loops were built using the ab initio CABS method. We used the simulated annealing procedure for ligand docking and all-atom molecular dynamics simulations to determine the immediate changes in the structure of the ligand-receptor complex. The binding of an agonist, in contrast to an antagonist, induced the breakage of the "3-7 lock" between helices TM3 and TM7. We also observed an action of the extended rotamer toggle switch which suggests that those two switches are interdependent.

Understanding protein folding: small proteins in silico

Recent improvements in methodology and increased computer power now allow atomistic computer simulations of protein folding. We briefly review several advanced Monte Carlo algorithms that have contributed to this development. Details of folding simulations of three designed mini proteins are shown. Adding global translations and rotations has allowed us to handle multiple chains and to simulate the aggregation of six beta-amyloid fragments. In a different line of research we have developed several algorithms to predict local features from sequence. In an outlook we sketch how such biasing could extend the application spectrum of Monte Carlo simulations to structure prediction of larger proteins.

Towards the high-resolution protein structure prediction. Fast refinement of reduced models with all-atom force field

Background

Although experimental methods for determining protein structure are providing high resolution structures, they cannot keep the pace at which amino acid sequences are resolved on the scale of entire genomes. For a considerable fraction of proteins whose structures will not be determined experimentally, computational methods can provide valuable information. The value of structural models in biological research depends critically on their quality. Development of high-accuracy computational methods that reliably generate near-experimental quality structural models is an important, unsolved problem in the protein structure modeling.

Results

Large sets of structural decoys have been generated using reduced conformational space protein modeling tool CABS. Subsequently, the reduced models were subject to all-atom reconstruction. Then, the resulting detailed models were energy-minimized using state-of-the-art all-atom force field, assuming fixed positions of the alpha carbons. It has been shown that a very short minimization leads to the proper ranking of the quality of the models (distance from the native structure), when the all-atom energy is used as the ranking criterion. Additionally, we performed test on medium and low accuracy decoys built via classical methods of comparative modeling. The test placed our model evaluation procedure among the state-of-the-art protein model assessment methods.

Conclusion

These test computations show that a large scale high resolution protein structure prediction is possible, not only for small but also for large protein domains, and that it should be based on a hierarchical approach to the modeling protocol. We employed Molecular Mechanics with fixed alpha carbons to rank-order the all-atom models built on the scaffolds of the reduced models. Our tests show that a physic-based approach, usually considered computationally too demanding for large-scale applications, can be effectively used in such studies.

Modification and optimization of the united-residue (UNRES) potential energy function for canonical simulations. I. Temperature dependence of the effective energy function and tests of the optimization method with single training proteins

We report the modification and parametrization of the united-residue (UNRES) force field for energy-based protein structure prediction and protein folding simulations. We tested the approach on three training proteins separately: 1E0L (beta), 1GAB (alpha), and 1E0G (alpha + beta). Heretofore, the UNRES force field had been designed and parametrized to locate native-like structures of proteins as global minima of their effective potential energy surfaces, which largely neglected the conformational entropy because decoys composed of only lowest-energy conformations were used to optimize the force field. Recently, we developed a mesoscopic dynamics procedure for UNRES and applied it with success to simulate protein folding pathways. However, the force field turned out to be largely biased toward -helical structures in canonical simulations because the conformational entropy had been neglected in the parametrization. We applied the hierarchical optimization method, developed in our earlier work, to optimize the force field; in this method, the conformational space of a training protein is divided into levels, each corresponding to a certain degree of native-likeness. The levels are ordered according to increasing native-likeness; level 0 corresponds to structures with no native-like elements, and the highest level corresponds to the fully native-like structures. The aim of optimization is to achieve the order of the free energies of levels, decreasing as their native-likeness increases. The procedure is iterative, and decoys of the training protein(s) generated with the energy function parameters of the preceding iteration are used to optimize the force field in a current iteration. We applied the multiplexing replica-exchange molecular dynamics (MREMD) method, recently implemented in UNRES, to generate decoys; with this modification, conformational entropy is taken into account. Moreover, we optimized the free-energy gaps between levels at temperatures corresponding to a predominance of folded or unfolded structures, as well as to structures at the putative folding-transition temperature, changing the sign of the gaps at the transition temperature. This enabled us to obtain force fields characterized by a single peak in the heat capacity at the transition temperature. Furthermore, we introduced temperature dependence to the UNRES force field; this is consistent with the fact that it is a free-energy and not a potential energy function. beta