When studying multi-body protein complexes, biochemists use computational tools that can suggest hundreds or thousands of their possible spatial configurations. However, it is not feasible to experimentally verify more than only a very small subset of them. In this paper, we propose a novel multiscale visual drilldown approach that was designed in tight collaboration with proteomic experts, enabling a systematic exploration of the configuration space. Our approach takes advantage of the hierarchical structure of the data -- from the whole ensemble of protein complex configurations to the individual configurations, their contact interfaces, and the interacting amino acids. Our new solution is based on interactively linked 2D and 3D views for individual hierarchy levels and at each level, we offer a set of selection and filtering operations enabling the user to narrow down the number of configurations that need to be manually scrutinized. Furthermore, we offer a dedicated filter interface, which provides the users with an overview of the applied filtering operations and enables them to examine their impact on the explored ensemble. This way, we maintain the history of the exploration process and thus enable the user to return to an earlier point of the exploration. We demonstrate the effectiveness of our approach on two case studies conducted by collaborating proteomic experts.
One of the first tools designed primarily for multi-body docking was CombDock @cite_10 . The algorithm works on a principle of hierarchical construction of the complex from smaller subunits and a greedy selection of the best-ranking subunits. The combinatorial step is followed by the reduction of solutions based on RMSD and a scoring function. Multi--LZerD @cite_24 uses a genetic algorithm to generate complexes from initial pairwise docks and applies an energy minimization structure refinement procedure for the ranking of the solutions. @cite_13 proposed an ant colony optimization approach to solve the combinatorial problem. DockStar @cite_33 formulates the task of detecting the spatial conformation of a protein complex as an Integer Linear Program. Unlike other methods, it also integrates experimental data from mass spectrometry into the scoring of the solutions. Another tool reusing pairwise docks in combination with experimental data is PRISM-EM @cite_14 . It uses density maps from cryo-electron microscopy for guiding the placement of subunits.
@cite_13 @cite_14 @cite_33 @cite_24 @cite_10
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The majority of proteins function when associated in multimolecular assemblies. Yet, prediction of the structures of multimolecular complexes has largely not been addressed, probably due to the magnitude of the combinatorial complexity of the problem. Docking applications have traditionally been used to predict pairwise interactions between molecules. We have developed an algorithm that extends the application of docking to multimolecular assemblies. We apply it to predict quaternary structures of both oligomers and multi-protein complexes. The algorithm predicted well a near-native arrangement of the input subunits for all cases in our data set, where the number of the subunits of the different target complexes varied from three to ten. In order to simulate a more realistic scenario, unbound cases were tested. In these cases the input conformations of the subunits are either unbound conformations of the subunits or a model obtained by a homology modeling technique. The successful predictions of the unbound cases, where the input conformations of the subunits are different from their conformations within the target complex, suggest that the algorithm is robust. We expect that this type of algorithm should be particularly useful to predict the structures of large macromolecular assemblies, which are difficult to solve by experimental structure determination. Many biological processes are governed by large assemblies of protein molecules. However, it is often very difficult to determine the three-dimensional structures of these assemblies using experimental biophysical techniques. Hence there is a need to develop computational approaches to fill this gap. This article presents an ant colony optimization approach to predict the structure of large multi-component protein complexes. Starting from pair-wise docking predictions, a multi-graph consisting of vertices representing the component proteins and edges representing candidate interactions is constructed. This allows the assembly problem to be expressed in terms of searching for a minimum weight spanning tree. However, because the problem remains highly combinatorial, the search space cannot be enumerated exhaustively and therefore heuristic optimisation techniques must be used. The utility of the ant colony based approach is demonstrated by re-assembling known protein complexes from the Protein Data Bank. The algorithm is able to identify near-native solutions for five of the six cases tested. This demonstrates that the ant colony approach provides a useful way to deal with the highly combinatorial multi-component protein assembly problem. The tertiary structures of protein complexes provide a crucial insight about the molecular mechanisms that regulate their functions and assembly. However, solving protein complex structures by experimental methods is often more difficult than single protein structures. Here, we have developed a novel computational multiple protein docking algorithm, Multi-LZerD, that builds models of multimeric complexes by effectively reusing pairwise docking predictions of component proteins. A genetic algorithm is applied to explore the conformational space followed by a structure refinement procedure. Benchmark on eleven hetero-multimeric complexes resulted in near native conformations for all but one of them (a root mean square deviation smaller than 2.5A). We also show that our method copes with unbound docking cases well, outperforming the methodology that can be directly compared to our approach. Multi-LZerD was able to predict near native structures for multimeric complexes of various topologies. Here we present a novel technique for the alignment of flexible proteins. The method does not require an a priori knowledge of the flexible hinge regions. The FlexProt algorithm simultaneously detects the hinge regions and aligns the rigid subparts of the molecules. Our technique is not sensitive to insertions and deletions. Numerous methods have been developed to solve rigid structural comparisons. Unlike FlexProt, all previously developed methods designed to solve the protein flexible alignment require an a priori knowledge of the hinge regions. The FlexProt method is based on 3-D pattern-matching algorithms combined with graph theoretic techniques. The algorithm is highly efficient. For example, it performs a structural comparison of a pair of proteins with 300 amino acids in about 7 s on a 400-MHz desktop PC. We provide experimental results obtained with this algorithm. First, we flexibly align pairs of proteins taken from the database of motions. These are extended by taking additional proteins from the same SCOP family. Next, we present some of the results obtained from exhaustive all-against-all flexible structural comparisons of 1329 SCOP family representatives. Our results include relatively high-scoring flexible structural alignments between the C-terminal merozoite surface protein vs. tissue factor; class II aminoacyl-tRNA synthase, histocompatibility antigen vs. neonatal FC receptor; tyrosine-protein kinase C-SRC vs. haematopoetic cell kinase (HCK); tyrosine-protein kinase C-SRC vs. titine protein (autoinhibited serine kinase domain); and tissue factor vs. hormone-binding protein. These are illustrated and discussed, showing the capabilities of this structural alignment algorithm, which allows un-predefined hinge-based motions. Proteins 2002;48:242–256. © 2002 Wiley-Liss, Inc. Background The development of accurate protein-protein docking programs is making this kind of simulations an effective tool to predict the 3D structure and the surface of interaction between the molecular partners in macromolecular complexes. However, correctly scoring multiple docking solutions is still an open problem. As a consequence, the accurate and tedious screening of many docking models is usually required in the analysis step. Motivation: During the past decade, the new focus on genomics has highlighted a particular challenge: to integrate the different views of the genome that are provided by various types of experimental data. Results: This paper describes a computational framework for integrating and drawing inferences from a collection of genome-wide measurements. Each dataset is represented via a kernel function, which defines generalized similarity relationships between pairs of entities, such as genes or proteins. The kernel representation is both flexible and efficient, and can be applied to many different types of data. Furthermore, kernel functions derived from different types of data can be combined in a straightforward fashion. Recent advances in the theory of kernel methods have provided efficient algorithms to perform such combinations in a way that minimizes a statistical loss function. These methods exploit semidefinite programming techniques to reduce the problem of finding optimizing kernel combinations to a convex optimization problem. Computational experiments performed using yeast genome-wide datasets, including amino acid sequences, hydropathy profiles, gene expression data and known protein--protein interactions, demonstrate the utility of this approach. A statistical learning algorithm trained from all of these data to recognize particular classes of proteins---membrane proteins and ribosomal proteins---performs significantly better than the same algorithm trained on any single type of data. Availability: Supplementary data at http: noble.gs.washington.edu proj sdp-svm Graphical abstractDisplay Omitted HighlightsGraded energy-model strategically mixes the 20×20 MJ potential matrix with 2×2 HP energy model.HP guided macro-mutation operator within GA provides efficient sampling.Proposed Algorithm outperformed other state-of-the-art approaches.Splits the energy function related complexities into two less complex functions through macro-mutation operator. Protein structure prediction is considered as one of the most challenging and computationally intractable combinatorial problem. Thus, the efficient modeling of convoluted search space, the clever use of energy functions, and more importantly, the use of effective sampling algorithms become crucial to address this problem. For protein structure modeling, an off-lattice model provides limited scopes to exercise and evaluate the algorithmic developments due to its astronomically large set of data-points. In contrast, an on-lattice model widens the scopes and permits studying the relatively larger proteins because of its finite set of data-points. In this work, we took the full advantage of an on-lattice model by using a face-centered-cube lattice that has the highest packing density with the maximum degree of freedom. We proposed a graded energy-strategically mixes the Miyazawa-Jernigan (MJ) energy with the hydrophobic-polar (HP) energy-based genetic algorithm (GA) for conformational search. In our application, we introduced a 2×2 HP energy guided macro-mutation operator within the GA to explore the best possible local changes exhaustively. Conversely, the 20×20 MJ energy model-the ultimate objective function of our GA that needs to be minimized-considers the impacts amongst the 20 different amino acids and allow searching the globally acceptable conformations. On a set of benchmark proteins, our proposed approach outperformed state-of-the-art approaches in terms of the free energy levels and the root-mean-square deviations. In-vitro methods for protein structure determination are time-consuming, cost-intensive, and failure-prone. Because of these expenses, alternative computer-based predictive methods have emerged. Predicting a protein’s 3-D structure from only its amino acid sequence—also known as ab initio protein structure prediction (PSP)—is computationally demanding because the search space is astronomically large and energy models are extremely complex. Some successes have been achieved in predictive methods but these are limited to small sized proteins (around 100 amino acids); thus, developing efficient algorithms, reducing the search space, and designing effective search guidance heuristics are necessary to study large sized proteins. An on-lattice model can be a better ground for rapidly developing and measuring the performance of a new algorithm, and hence we consider this model for larger proteins (>150 amino acids) to enhance the genetic algorithms (GAs) framework. In this paper, we formulate PSP as a combinatorial optimization problem that uses 3-D face-centered-cubic lattice coordinates to reduce the search space and hydrophobic-polar energy model to guide the search. The whole optimization process is controlled by an enhanced GA framework with four enhanced features: 1) an exhaustive generation approach to diversify the search; 2) a novel hydrophobic core-directed macro-mutation operator to intensify the search; 3) a per-generation duplication elimination strategy to prevent early convergence; and 4) a random-walk technique to recover from stagnation. On a set of standard benchmark proteins, our algorithm significantly outperforms state-of-the-art algorithms. We also experimentally show that our algorithm is robust enough to produce very similar results regardless of different parameter settings. We show that the maximization of the sum degrees-of-freedom for the static flat-fading multiple-input multiple-output (MIMO) interference channel is equivalent to a rank constrained rank minimization problem (RCRM), when the signal spaces span all available dimensions. The rank minimization corresponds to maximizing interference alignment (IA) so that interference spans the lowest dimensional subspace possible. The rank constraints account for the useful signal spaces spanning all available spatial dimensions. That way, we reformulate all IA requirements to requirements involving ranks. Then, we present a convex relaxation of the RCRM problem inspired by recent results in compressed sensing and low-rank matrix completion theory that rely on approximating rank with the nuclear norm. We show that the convex envelope of the sum of ranks of the interference matrices is the normalized sum of their corresponding nuclear norms and introduce tractable constraints that are asymptotically equivalent to the rank constraints for the initial problem. We also show that our heuristic relaxation can be tuned for the multi-cell interference channel. Furthermore, we experimentally show that in many cases the proposed algorithm attains perfect interference alignment and in some cases outperforms previous approaches for finding precoding and zero-forcing matrices for interference alignment. Abstract Two major components are required for a successful prediction of the three-dimensional structure of peptides and proteins: an efficient global optimization procedure which is capable of finding an appropriate local minimum for the strongly anisotropic function of hundreds of variables, and a set of free energy components for a protein molecule in solution which are computationally inexpensive enough to be used in the search procedure, yet sufficiently accurate to ensure the uniqueness of the native conformation. We here found an efficient way to make a random step in a Monte Carlo procedure given knowledge of the energy or statistical properties of conformational subspaces (e.g. φ-ψ zones or side-chain torsion angles). This biased probability Monte Carlo (BPMC) procedure randomly selects the subspace first, then makes a step to a new random position independent of the previous position, but according to the predefined continuous probability distribution. The random step is followed by a local minimization in torsion angle space. The positions, sizes and preferences for high-probability zones on φ-ψ maps and χ-angle maps were calculated for different residue types from the representative set of 191 and 161 protein 3D-structures, respectively. A fast and precise method to evaluate the electrostatic energy of a protein in solution is developed and combined with the BPMC procedure. The method is based on the modified spherical image charge approximation, efficiently projected onto a molecule of arbitrary shape. Comparison with the finite-difference solutions of the Poisson-Boltzmann equation shows high accuracy for our approach. The BPMC procedure is applied successfully to the structure prediction of 12- and 16-residue synthetic peptides and the determination of protein structure from NMR data, with the immunoglobulin binding domain of streptococcal protein G as an example. The BPMC runs display much better convergence properties than the non-biased simulations. The advantage of a true global optimization procedure for NMR structure determination is its ability to cope with local minima originating from data errors and ambiguities in NMR data. The results of basin-hopping global optimization simulations are presented for four small, α-helical proteins described by a coarse-grained potential. A step-taking scheme that incorporates the local conformational preferences extracted from a large number of high-resolution protein structures is compared with an unbiased scheme. In addition, the discrete path sampling method is used to investigate the folding of one of the proteins, namely, the villin headpiece subdomain. Folding times from kinetic Monte Carlo simulations and iterative calculations based on a Markovian first-step analysis for the resulting stationary-point database are in good mutual agreement, but differ significantly from the experimental values, probably because the native state is not the global free energy minimum for the potential employed. In the 0-extension problem, we are given a weighted graph with some nodes marked as terminals and a semimetric on the set of terminals. Our goal is to assign the rest of the nodes to terminals so as to minimize the sum, over all edges, of the product of the edge's weight and the distance between the terminals to which its endpoints are assigned. This problem generalizes the multiway cut problem of [SIAM J. Comput. , 23 (1994), pp. 864--894] and is closely related to the metric labeling problem introduced by Kleinberg and Tardos [Proceedings of the 40th IEEE Annual Symposium on Foundations of Computer Science, New York, 1999, pp. 14--23]. We present approximation algorithms for 0-Extension . In arbitrary graphs, we present a O(log k)-approximation algorithm, k being the number of terminals. We also give O(1)-approximation guarantees for weighted planar graphs. Our results are based on a natural metric relaxation of the problem previously considered by Karzanov [European J. Combin., 19 (1998), pp. 71--101]. It is similar in flavor to the linear programming relaxation of Garg, Vazirani, and Yannakakis [SIAM J. Comput. , 25 (1996), pp. 235--251] for the multicut problem, and similar to relaxations for other graph partitioning problems. We prove that the integrality ratio of the metric relaxation is at least @math for a positive c for infinitely many k. Our results improve some of the results of Kleinberg and Tardos, and they further our understanding on how to use metric relaxations. We have investigated an evolutionary algorithm for de novo all-atom folding of the bacterial ribosomal protein L20. We report results of two simulations that converge to near-native conformations of this 60-amino-acid, four-helix protein. We observe a steady increase of “native content” in both simulated ensembles and a large number of near-native conformations in their final populations. We argue that these structures represent a significant fraction of the low-energy metastable conformations, which characterize the folding funnel of this protein. These data validate our all-atom free-energy force field PFF01 for tertiary structure prediction of a previously inaccessible structural family of proteins. We also compare folding simulations of the evolutionary algorithm with the basin-hopping technique for the Trp-cage protein. We find that the evolutionary algorithm generates a dynamic memory in the simulated population, which leads to faster overall convergence. Motivation: Given protein–protein interaction (PPI) networks of a pair of species, a pairwise global alignment corresponds to a one-to-one mapping between their proteins. Based on the presupposition that such a mapping provides pairs of functionally orthologous proteins accurately, the results of the alignment may then be used in comparative systems biology problems such as function prediction verification or construction of evolutionary relationships. Results: We show that the problem is NP-hard even for the case where the pair of networks are simply paths. We next provide a polynomial time heuristic algorithm, SPINAL, which consists of two main phases. In the first coarse-grained alignment phase, we construct all pairwise initial similarity scores based on pairwise local neighborhood matchings. Using the produced similarity scores, the fine-grained alignment phase produces the final one-to-one mapping by iteratively growing a locally improved solution subset. Both phases make use of the construction of neighborhood bipartite graphs and the contributors as a common primitive. We assess the performance of our algorithm on the PPI networks of yeast, fly, human and worm. We show that based on the accuracy measures used in relevant work, our method outperforms the state-of-the-art algorithms. Furthermore, our algorithm does not suffer from scalability issues, as such accurate results are achieved in reasonable running times as compared with the benchmark algorithms. Availability: Supplementary Document, open source codes, useful scripts, all the experimental data and the results are freely available at http: code.google.com p spinal . Contact: cesim@khas.edu.tr Supplementary information: Supplementary data are available at Bioinformatics online. Empirical scoring functions based on either molecular force fields or cheminformatics descriptors are widely used, in conjunction with molecular docking, during the early stages of drug discovery to predict potency and binding affinity of a drug-like molecule to a given target. These models require expert-level knowledge of physical chemistry and biology to be encoded as hand-tuned parameters or features rather than allowing the underlying model to select features in a data-driven procedure. Here, we develop a general 3-dimensional spatial convolution operation for learning atomic-level chemical interactions directly from atomic coordinates and demonstrate its application to structure-based bioactivity prediction. The atomic convolutional neural network is trained to predict the experimentally determined binding affinity of a protein-ligand complex by direct calculation of the energy associated with the complex, protein, and ligand given the crystal structure of the binding pose. Non-covalent interactions present in the complex that are absent in the protein-ligand sub-structures are identified and the model learns the interaction strength associated with these features. We test our model by predicting the binding free energy of a subset of protein-ligand complexes found in the PDBBind dataset and compare with state-of-the-art cheminformatics and machine learning-based approaches. We find that all methods achieve experimental accuracy and that atomic convolutional networks either outperform or perform competitively with the cheminformatics based methods. Unlike all previous protein-ligand prediction systems, atomic convolutional networks are end-to-end and fully-differentiable. They represent a new data-driven, physics-based deep learning model paradigm that offers a strong foundation for future improvements in structure-based bioactivity prediction. Motivation: Proteins usually fulfill their biological functions by interacting with other proteins. Although some methods have been developed to predict the binding sites of a monomer protein, these are not sufficient for prediction of the interaction between two monomer proteins. The correct prediction of interface residue pairs from two monomer proteins is still an open question and has great significance for practical experimental applications in the life sciences. We hope to build a method for the prediction of interface residue pairs that is suitable for those applications. Results: Here, we developed a novel deep network architecture called the multi-layered Long-Short Term Memory networks (LSTMs) approach for the prediction of protein interface residue pairs. Firstly, we created three new descriptions and used other six worked characterizations to describe an amino acid, then we employed these features to discriminate between interface residue pairs and non-interface residue pairs. Secondly, we used two thresholds to select residue pairs that are more likely to be interface residue pairs. Furthermore, this step increases the proportion of interface residue pairs and reduces the influence of imbalanced data. Thirdly, we built deep network architectures based on Long-Short Term Memory networks algorithm to organize and refine the prediction of interface residue pairs by employing features mentioned above. We trained the deep networks on dimers in the unbound state in the international Protein-protein Docking Benchmark version 3.0. The updated data sets in the versions 4.0 and 5.0 were used as the validation set and test set respectively. For our best model, the accuracy rate was over 62 when we chose the top 0.2 pairs of every dimer in the test set as predictions, which will be very helpful for the understanding of protein-protein interaction mechanisms and for guidance in biological experiments. Motivation: With the exponential growth of expression and protein–protein interaction (PPI) data, the frontier of research in systems biology shifts more and more to the integrated analysis of these large datasets. Of particular interest is the identification of functional modules in PPI networks, sharing common cellular function beyond the scope of classical pathways, by means of detecting differentially expressed regions in PPI networks. This requires on the one hand an adequate scoring of the nodes in the network to be identified and on the other hand the availability of an effective algorithm to find the maximally scoring network regions. Various heuristic approaches have been proposed in the literature. Results: Here we present the first exact solution for this problem, which is based on integer-linear programming and its connection to the well-known prize-collecting Steiner tree problem from Operations Research. Despite the NP-hardness of the underlying combinatorial problem, our method typically computes provably optimal subnetworks in large PPI networks in a few minutes. An essential ingredient of our approach is a scoring function defined on network nodes. We propose a new additive score with two desirable properties: (i) it is scalable by a statistically interpretable parameter and (ii) it allows a smooth integration of data from various sources. We apply our method to a well-established lymphoma microarray dataset in combination with associated survival data and the large interaction network of HPRD to identify functional modules by computing optimal-scoring subnetworks. In particular, we find a functional interaction module associated with proliferation over-expressed in the aggressive ABC subtype as well as modules derived from non-malignant by-stander cells. Availability: Our software is available freely for non-commercial purposes at http: www.planet-lisa.net. Contact: tobias.mueller@biozentrum.uni-wuerzburg.de The search for efficient and predictive methods to describe the protein folding process at the all-atom level remains an important grand-computational challenge. The development of multi-teraflop architectures, such as the IBM BlueGene used in this study, has been motivated in part by the large computational requirements of such studies. Here we report the predictive all-atom folding of the forty-amino acid HIV accessory protein using an evolutionary stochastic optimization technique. We implemented the optimization method as a master-client model on an IBM BlueGene, where the algorithm scales near perfectly from 64 to 4096 processors in virtual processor mode. Starting from a completely extended conformation, we optimize a population of 64 conformations of the protein in our all-atom free-energy model PFF01. Using 2048 processors the algorithm predictively folds the protein to a near-native conformation with an RMS deviation of 3.43 A in <24 h. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2007 Here, we present MultiProt, a fully automated highly efficient technique to detect mul- tiple structural alignments of protein structures. MultiProt finds the common geometrical cores be- tween input molecules. To date, most methods for multiple alignment start from the pairwise align- ment solutions. This may lead to a small overall alignment. In contrast, our method derives multiple alignments from simultaneous superpositions of in- put molecules. Further, our method does not re- quire that all input molecules participate in the alignment. Actually, it efficiently detects high scor- ing partial multiple alignments for all possible num- ber of molecules in the input. To demonstrate the power of MultiProt, we provide a number of case studies. First, we demonstrate known multiple align- ments of protein structures to illustrate the perfor- mance of MultiProt. Next, we present various biologi- cal applications. These include: (1) a partial alignment of hinge-bent domains; (2) identification of functional groups of G-proteins; (3) analysis of binding sites; and (4) protein-protein interface align- ment. Some applications preserve the sequence or- der of the residues in the alignment, whereas others are order-independent. It is their residue sequence order-independence that allows application of MultiProt to derive multiple alignments of binding sites and of protein-protein interfaces, making Mul- tiProt an extremely useful structural tool. Proteins In this paper we investigate the problem of Simultaneous Localization and Mapping (SLAM) for a multi robot system. Relaxing some assumptions that characterize related work we propose an application of Rao-Blackwellized Particle Filters (RBPF) for the purpose of cooperatively estimating SLAM posterior. We consider a realistic setup in which the robots start from unknown initial poses (relative locations are unknown too), and travel in the environment in order to build a shared representation of the latter. The robots are required to exchange a small amount of information only when a rendezvous event occurs and to measure relative poses during the meeting. As a consequence the approach also applies when using an unreliable wireless channel or short range communication technologies (bluetooth, RFId, etc.). Moreover it allows to take into account the uncertainty in relative pose measurements. The proposed technique, which constitutes a distributed solution to the multi robot SLAM problem, is further validated through simulations and experimental tests.