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Zaman AB, Inan TT, De Jong K, Shehu A. Adaptive Stochastic Optimization to Improve Protein Conformation Sampling. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2023; 20:2759-2771. [PMID: 34882562 DOI: 10.1109/tcbb.2021.3134103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We have long known that characterizing protein structures structure is key to understanding protein function. Computational approaches have largely addressed a narrow formulation of the problem, seeking to compute one native structure from an amino-acid sequence. Now AlphaFold2 is shown to be able to reveal a high-quality native structure for many proteins. However, researchers over the years have argued for broadening our view to account for the multiplicity of native structures. We now know that many protein molecules switch between different structures to regulate interactions with molecular partners in the cell. Elucidating such structures de novo is exceptionally difficult, as it requires exploration of possibly a very large structure space in search of competing, near-optimal structures. Here we report on a novel stochastic optimization method capable of revealing very different structures for a given protein from knowledge of its amino-acid sequence. The method leverages evolutionary search techniques and adapts its exploration of the search space to balance between exploration and exploitation in the presence of a computational budget. In addition to demonstrating the utility of this method for identifying multiple native structures, we additionally provide a benchmark dataset for researchers to continue work on this problem.
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2
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Zaman AB, Shehu A. Building maps of protein structure spaces in template-free protein structure prediction. J Bioinform Comput Biol 2020; 17:1940013. [DOI: 10.1142/s0219720019400134] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
An important goal in template-free protein structure prediction is how to control the quality of computed tertiary structures of a target amino-acid sequence. Despite great advances in algorithmic research, given the size, dimensionality, and inherent characteristics of the protein structure space, this task remains exceptionally challenging. It is current practice to aim to generate as many structures as can be afforded so as to increase the likelihood that some of them will reside near the sought but unknown biologically-active/native structure. When operating within a given computational budget, this is impractical and uninformed by any metrics of interest. In this paper, we propose instead to equip algorithms that generate tertiary structures, also known as decoy generation algorithms, with memory of the protein structure space that they explore. Specifically, we propose an evolving, granularity-controllable map of the protein structure space that makes use of low-dimensional representations of protein structures. Evaluations on diverse target sequences that include recent hard CASP targets show that drastic reductions in storage can be made without sacrificing decoy quality. The presented results make the case that integrating a map of the protein structure space is a promising mechanism to enhance decoy generation algorithms in template-free protein structure prediction.
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Affiliation(s)
- Ahmed Bin Zaman
- Department of Computer Science, George Mason University, Fairfax, VA 22030, USA
| | - Amarda Shehu
- Department of Computer Science, George Mason University, Fairfax, VA 22030, USA
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3
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Awosanya EO, Lapin J, Nevzorov AA. NMR "Crystallography" for Uniformly ( 13 C, 15 N)-Labeled Oriented Membrane Proteins. Angew Chem Int Ed Engl 2020; 59:3554-3557. [PMID: 31887238 DOI: 10.1002/anie.201915110] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2019] [Revised: 12/29/2019] [Indexed: 01/01/2023]
Abstract
In oriented-sample (OS) solid-state NMR of membrane proteins, the angular-dependent dipolar couplings and chemical shifts provide a direct input for structure calculations. However, so far only 1 H-15 N dipolar couplings and 15 N chemical shifts have been routinely assessed in oriented 15 N-labeled samples. The main obstacle for extending this technique to membrane proteins of arbitrary topology has remained in the lack of additional experimental restraints. We have developed a new experimental triple-resonance NMR technique, which was applied to uniformly doubly (15 N, 13 C)-labeled Pf1 coat protein in magnetically aligned DMPC/DHPC bicelles. The previously inaccessible 1 Hα -13 Cα dipolar couplings have been measured, which make it possible to determine the torsion angles between the peptide planes without assuming α-helical structure a priori. The fitting of three angular restraints per peptide plane and filtering by Rosetta scoring functions has yielded a consensus α-helical transmembrane structure for Pf1 protein.
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Affiliation(s)
- Emmanuel O Awosanya
- Department of Chemistry, North Carolina State University, 2620 Yarbrough Drive, Raleigh, NC, 27695-8204, USA
| | - Joel Lapin
- Department of Chemistry, North Carolina State University, 2620 Yarbrough Drive, Raleigh, NC, 27695-8204, USA
| | - Alexander A Nevzorov
- Department of Chemistry, North Carolina State University, 2620 Yarbrough Drive, Raleigh, NC, 27695-8204, USA
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4
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Awosanya EO, Lapin J, Nevzorov AA. NMR “Crystallography” for Uniformly (
13
C,
15
N)‐Labeled Oriented Membrane Proteins. Angew Chem Int Ed Engl 2020. [DOI: 10.1002/ange.201915110] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Affiliation(s)
- Emmanuel O. Awosanya
- Department of Chemistry North Carolina State University 2620 Yarbrough Drive Raleigh NC 27695-8204 USA
| | - Joel Lapin
- Department of Chemistry North Carolina State University 2620 Yarbrough Drive Raleigh NC 27695-8204 USA
| | - Alexander A. Nevzorov
- Department of Chemistry North Carolina State University 2620 Yarbrough Drive Raleigh NC 27695-8204 USA
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5
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Wang X, Huang SY. Integrating Bonded and Nonbonded Potentials in the Knowledge-Based Scoring Function for Protein Structure Prediction. J Chem Inf Model 2019; 59:3080-3090. [DOI: 10.1021/acs.jcim.9b00057] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Affiliation(s)
- Xinxiang Wang
- Institute of Biophysics, School of Physics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, P. R. China
| | - Sheng-You Huang
- Institute of Biophysics, School of Physics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, P. R. China
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Zaman AB, Shehu A. Balancing multiple objectives in conformation sampling to control decoy diversity in template-free protein structure prediction. BMC Bioinformatics 2019; 20:211. [PMID: 31023237 PMCID: PMC6485169 DOI: 10.1186/s12859-019-2794-5] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2019] [Accepted: 04/04/2019] [Indexed: 12/05/2022] Open
Abstract
Background Computational approaches for the determination of biologically-active/native three-dimensional structures of proteins with novel sequences have to handle several challenges. The (conformation) space of possible three-dimensional spatial arrangements of the chain of amino acids that constitute a protein molecule is vast and high-dimensional. Exploration of the conformation spaces is performed in a sampling-based manner and is biased by the internal energy that sums atomic interactions. Even state-of-the-art energy functions that quantify such interactions are inherently inaccurate and associate with protein conformation spaces overly rugged energy surfaces riddled with artifact local minima. The response to these challenges in template-free protein structure prediction is to generate large numbers of low-energy conformations (also referred to as decoys) as a way of increasing the likelihood of having a diverse decoy dataset that covers a sufficient number of local minima possibly housing near-native conformations. Results In this paper we pursue a complementary approach and propose to directly control the diversity of generated decoys. Inspired by hard optimization problems in high-dimensional and non-linear variable spaces, we propose that conformation sampling for decoy generation is more naturally framed as a multi-objective optimization problem. We demonstrate that mechanisms inherent to evolutionary search techniques facilitate such framing and allow balancing multiple objectives in protein conformation sampling. We showcase here an operationalization of this idea via a novel evolutionary algorithm that has high exploration capability and is also able to access lower-energy regions of the energy landscape of a given protein with similar or better proximity to the known native structure than several state-of-the-art decoy generation algorithms. Conclusions The presented results constitute a promising research direction in improving decoy generation for template-free protein structure prediction with regards to balancing of multiple conflicting objectives under an optimization framework. Future work will consider additional optimization objectives and variants of improvement and selection operators to apportion a fixed computational budget. Of particular interest are directions of research that attenuate dependence on protein energy models.
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Affiliation(s)
- Ahmed Bin Zaman
- Department of Computer Science, George Mason University, Fairfax, 22030, VA, USA
| | - Amarda Shehu
- Department of Computer Science, George Mason University, Fairfax, 22030, VA, USA.,Department of Bioengineering, George Mason University, Fairfax, 22030, VA, USA.,School of Systems Biology, George Mason University, Manassas, 20110, VA, USA
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Kandathil SM, Garza-Fabre M, Handl J, Lovell SC. Improved fragment-based protein structure prediction by redesign of search heuristics. Sci Rep 2018; 8:13694. [PMID: 30209258 PMCID: PMC6135816 DOI: 10.1038/s41598-018-31891-8] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2018] [Accepted: 08/22/2018] [Indexed: 11/09/2022] Open
Abstract
Difficulty in sampling large and complex conformational spaces remains a key limitation in fragment-based de novo prediction of protein structure. Our previous work has shown that even for small-to-medium-sized proteins, some current methods inadequately sample alternative structures. We have developed two new conformational sampling techniques, one employing a bilevel optimisation framework and the other employing iterated local search. We combine strategies of forced structural perturbation (where some fragment insertions are accepted regardless of their impact on scores) and greedy local optimisation, allowing greater exploration of the available conformational space. Comparisons against the Rosetta Abinitio method indicate that our protocols more frequently generate native-like predictions for many targets, even following the low-resolution phase, using a given set of fragment libraries. By contrasting results across two different fragment sets, we show that our methods are able to better take advantage of high-quality fragments. These improvements can also translate into more reliable identification of near-native structures in a simple clustering-based model selection procedure. We show that when fragment libraries are sufficiently well-constructed, improved breadth of exploration within runs improves prediction accuracy. Our results also suggest that in benchmarking scenarios, a total exclusion of fragments drawn from homologous templates can make performance differences between methods appear less pronounced.
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Affiliation(s)
- Shaun M Kandathil
- Division of Evolution and Genomic Sciences, School of Biological Sciences, Faculty of Biology, Medicine and Health, University of Manchester, Manchester, M13 9PL, United Kingdom. .,Department of Computer Science, University College London, Gower Street, London, WC1E 6BT, United Kingdom.
| | - Mario Garza-Fabre
- Decision and Cognitive Sciences Research Centre, University of Manchester, Manchester, M13 9PL, United Kingdom.,Center for Research and Advanced Studies of the National Polytechnic Institute (CINVESTAV-IPN), Km. 5.5 Carretera Cd. Victoria-Soto La Marina, Cd. Victoria, Tamaulipas, 87130, Mexico
| | - Julia Handl
- Decision and Cognitive Sciences Research Centre, University of Manchester, Manchester, M13 9PL, United Kingdom
| | - Simon C Lovell
- Division of Evolution and Genomic Sciences, School of Biological Sciences, Faculty of Biology, Medicine and Health, University of Manchester, Manchester, M13 9PL, United Kingdom
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8
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Gao S, Song S, Cheng J, Todo Y, Zhou M. Incorporation of Solvent Effect into Multi-Objective Evolutionary Algorithm for Improved Protein Structure Prediction. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2018; 15:1365-1378. [PMID: 28534784 DOI: 10.1109/tcbb.2017.2705094] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The problem of predicting the three-dimensional (3-D) structure of a protein from its one-dimensional sequence has been called the "holy grail of molecular biology", and it has become an important part of structural genomics projects. Despite the rapid developments in computer technology and computational intelligence, it remains challenging and fascinating. In this paper, to solve it we propose a multi-objective evolutionary algorithm. We decompose the protein energy function Chemistry at HARvard Macromolecular Mechanics force fields into bond and non-bond energies as the first and second objectives. Considering the effect of solvent, we innovatively adopt a solvent-accessible surface area as the third objective. We use 66 benchmark proteins to verify the proposed method and obtain better or competitive results in comparison with the existing methods. The results suggest the necessity to incorporate the effect of solvent into a multi-objective evolutionary algorithm to improve protein structure prediction in terms of accuracy and efficiency.
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9
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Wang X, Zhang D, Huang SY. New Knowledge-Based Scoring Function with Inclusion of Backbone Conformational Entropies from Protein Structures. J Chem Inf Model 2018; 58:724-732. [DOI: 10.1021/acs.jcim.7b00601] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Affiliation(s)
- Xinxiang Wang
- School of Physics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, P. R. China
| | - Di Zhang
- School of Physics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, P. R. China
| | - Sheng-You Huang
- School of Physics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, P. R. China
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10
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Yang B, Lin Z. Systematic search of conformations of five tetrapeptides and a divide and conquer strategy for the predictions of peptide structures. COMPUT THEOR CHEM 2017. [DOI: 10.1016/j.comptc.2017.03.014] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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11
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Topham CM, Barbe S, André I. An Atomistic Statistically Effective Energy Function for Computational Protein Design. J Chem Theory Comput 2016; 12:4146-68. [PMID: 27341125 DOI: 10.1021/acs.jctc.6b00090] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Shortcomings in the definition of effective free-energy surfaces of proteins are recognized to be a major contributory factor responsible for the low success rates of existing automated methods for computational protein design (CPD). The formulation of an atomistic statistically effective energy function (SEEF) suitable for a wide range of CPD applications and its derivation from structural data extracted from protein domains and protein-ligand complexes are described here. The proposed energy function comprises nonlocal atom-based and local residue-based SEEFs, which are coupled using a novel atom connectivity number factor to scale short-range, pairwise, nonbonded atomic interaction energies and a surface-area-dependent cavity energy term. This energy function was used to derive additional SEEFs describing the unfolded-state ensemble of any given residue sequence based on computed average energies for partially or fully solvent-exposed fragments in regions of irregular structure in native proteins. Relative thermal stabilities of 97 T4 bacteriophage lysozyme mutants were predicted from calculated energy differences for folded and unfolded states with an average unsigned error (AUE) of 0.84 kcal mol(-1) when compared to experiment. To demonstrate the utility of the energy function for CPD, further validation was carried out in tests of its capacity to recover cognate protein sequences and to discriminate native and near-native protein folds, loop conformers, and small-molecule ligand binding poses from non-native benchmark decoys. Experimental ligand binding free energies for a diverse set of 80 protein complexes could be predicted with an AUE of 2.4 kcal mol(-1) using an additional energy term to account for the loss in ligand configurational entropy upon binding. The atomistic SEEF is expected to improve the accuracy of residue-based coarse-grained SEEFs currently used in CPD and to extend the range of applications of extant atom-based protein statistical potentials.
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Affiliation(s)
- Christopher M Topham
- Université de Toulouse; INSA, UPS, INP; LISBP , 135 Avenue de Rangueil, F-31077 Toulouse, France.,CNRS, UMR5504 , F-31400 Toulouse, France.,INRA, UMR792 Ingénierie des Systèmes Biologiques et des Procédés , F-31400 Toulouse, France
| | - Sophie Barbe
- Université de Toulouse; INSA, UPS, INP; LISBP , 135 Avenue de Rangueil, F-31077 Toulouse, France.,CNRS, UMR5504 , F-31400 Toulouse, France.,INRA, UMR792 Ingénierie des Systèmes Biologiques et des Procédés , F-31400 Toulouse, France
| | - Isabelle André
- Université de Toulouse; INSA, UPS, INP; LISBP , 135 Avenue de Rangueil, F-31077 Toulouse, France.,CNRS, UMR5504 , F-31400 Toulouse, France.,INRA, UMR792 Ingénierie des Systèmes Biologiques et des Procédés , F-31400 Toulouse, France
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12
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Iacoangeli A, Marcatili P, Tramontano A. Exploiting Homology Information in Nontemplate Based Prediction of Protein Structures. J Chem Theory Comput 2015; 11:5045-51. [DOI: 10.1021/acs.jctc.5b00371] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Alfredo Iacoangeli
- Department
of Physics, Sapienza University of Rome, P.le A. Moro 4, 00185 Rome, Italy
| | - Paolo Marcatili
- Department
of Physics, Sapienza University of Rome, P.le A. Moro 4, 00185 Rome, Italy
| | - Anna Tramontano
- Department
of Physics, Sapienza University of Rome, P.le A. Moro 4, 00185 Rome, Italy
- Istituto
Pasteur Fondazione Cenci Bolognetti, Sapienza University of Rome, P.le
A. Moro 4, 00185 Rome, Italy
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13
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Shehu A. A Review of Evolutionary Algorithms for Computing Functional Conformations of Protein Molecules. METHODS IN PHARMACOLOGY AND TOXICOLOGY 2015. [DOI: 10.1007/7653_2015_47] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
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14
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Saleh S, Olson B, Shehu A. A population-based evolutionary search approach to the multiple minima problem in de novo protein structure prediction. BMC STRUCTURAL BIOLOGY 2013; 13 Suppl 1:S4. [PMID: 24565020 PMCID: PMC3953177 DOI: 10.1186/1472-6807-13-s1-s4] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
Background Elucidating the native structure of a protein molecule from its sequence of amino acids, a problem known as de novo structure prediction, is a long standing challenge in computational structural biology. Difficulties in silico arise due to the high dimensionality of the protein conformational space and the ruggedness of the associated energy surface. The issue of multiple minima is a particularly troublesome hallmark of energy surfaces probed with current energy functions. In contrast to the true energy surface, these surfaces are weakly-funneled and rich in comparably deep minima populated by non-native structures. For this reason, many algorithms seek to be inclusive and obtain a broad view of the low-energy regions through an ensemble of low-energy (decoy) conformations. Conformational diversity in this ensemble is key to increasing the likelihood that the native structure has been captured. Methods We propose an evolutionary search approach to address the multiple-minima problem in decoy sampling for de novo structure prediction. Two population-based evolutionary search algorithms are presented that follow the basic approach of treating conformations as individuals in an evolving population. Coarse graining and molecular fragment replacement are used to efficiently obtain protein-like child conformations from parents. Potential energy is used both to bias parent selection and determine which subset of parents and children will be retained in the evolving population. The effect on the decoy ensemble of sampling minima directly is measured by additionally mapping a conformation to its nearest local minimum before considering it for retainment. The resulting memetic algorithm thus evolves not just a population of conformations but a population of local minima. Results and conclusions Results show that both algorithms are effective in terms of sampling conformations in proximity of the known native structure. The additional minimization is shown to be key to enhancing sampling capability and obtaining a diverse ensemble of decoy conformations, circumventing premature convergence to sub-optimal regions in the conformational space, and approaching the native structure with proximity that is comparable to state-of-the-art decoy sampling methods. The results are shown to be robust and valid when using two representative state-of-the-art coarse-grained energy functions.
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15
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Molloy K, Saleh S, Shehu A. Probabilistic search and energy guidance for biased decoy sampling in ab initio protein structure prediction. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2013; 10:1162-1175. [PMID: 24384705 DOI: 10.1109/tcbb.2013.29] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Adequate sampling of the conformational space is a central challenge in ab initio protein structure prediction. In the absence of a template structure, a conformational search procedure guided by an energy function explores the conformational space, gathering an ensemble of low-energy decoy conformations. If the sampling is inadequate, the native structure may be missed altogether. Even if reproduced, a subsequent stage that selects a subset of decoys for further structural detail and energetic refinement may discard near-native decoys if they are high energy or insufficiently represented in the ensemble. Sampling should produce a decoy ensemble that facilitates the subsequent selection of near-native decoys. In this paper, we investigate a robotics-inspired framework that allows directly measuring the role of energy in guiding sampling. Testing demonstrates that a soft energy bias steers sampling toward a diverse decoy ensemble less prone to exploiting energetic artifacts and thus more likely to facilitate retainment of near-native conformations by selection techniques. We employ two different energy functions, the associative memory Hamiltonian with water and Rosetta. Results show that enhanced sampling provides a rigorous testing of energy functions and exposes different deficiencies in them, thus promising to guide development of more accurate representations and energy functions.
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Abstract
Coarse-grained models for protein folding and aggregation are used to explore large dimension scales and timescales that are inaccessible to all-atom models in explicit aqueous solution. Combined with enhanced configuration search methods, these simplified models with various levels of granularity offer the possibility to determine equilibrium structures, compare folding kinetics and thermodynamics with experiments for single proteins and understand the dynamic assembly of amyloid proteins leading to neurodegenerative diseases. I shall describe recent progress in developing such models, and discuss their potentials and limitations in probing the folding and misfolding of proteins with computer simulations.
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17
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Wu X, Hodoscek M, Brooks BR. Replica exchanging self-guided Langevin dynamics for efficient and accurate conformational sampling. J Chem Phys 2012; 137:044106. [PMID: 22852596 DOI: 10.1063/1.4737094] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This work presents a replica exchanging self-guided Langevin dynamics (RXSGLD) simulation method for efficient conformational searching and sampling. Unlike temperature-based replica exchanging simulations, which use high temperatures to accelerate conformational motion, this method uses self-guided Langevin dynamics (SGLD) to enhance conformational searching without the need to elevate temperatures. A RXSGLD simulation includes a series of SGLD simulations, with simulation conditions differing in the guiding effect and/or temperature. These simulation conditions are called stages and the base stage is one with no guiding effect. Replicas of a simulation system are simulated at the stages and are exchanged according to the replica exchanging probability derived from the SGLD partition function. Because SGLD causes less perturbation on conformational distribution than high temperatures, exchanges between SGLD stages have much higher probabilities than those between different temperatures. Therefore, RXSGLD simulations have higher conformational searching ability than temperature based replica exchange simulations. Through three example systems, we demonstrate that RXSGLD can generate target canonical ensemble distribution at the base stage and achieve accelerated conformational searching. Especially for large systems, RXSGLD has remarkable advantages in terms of replica exchange efficiency, conformational searching ability, and system size extensiveness.
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Affiliation(s)
- Xiongwu Wu
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute (NHLBI), National Institutes of Health (NIH), Bethesda, Maryland 20892, USA.
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18
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Chitsaz M, Mayo SL. GRID: a high-resolution protein structure refinement algorithm. J Comput Chem 2012; 34:445-50. [PMID: 23065773 DOI: 10.1002/jcc.23151] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2012] [Revised: 07/31/2012] [Accepted: 08/27/2012] [Indexed: 12/27/2022]
Abstract
The energy-based refinement of protein structures generated by fold prediction algorithms to atomic-level accuracy remains a major challenge in structural biology. Energy-based refinement is mainly dependent on two components: (1) sufficiently accurate force fields, and (2) efficient conformational space search algorithms. Focusing on the latter, we developed a high-resolution refinement algorithm called GRID. It takes a three-dimensional protein structure as input and, using an all-atom force field, attempts to improve the energy of the structure by systematically perturbing backbone dihedrals and side-chain rotamer conformations. We compare GRID to Backrub, a stochastic algorithm that has been shown to predict a significant fraction of the conformational changes that occur with point mutations. We applied GRID and Backrub to 10 high-resolution (≤ 2.8 Å) crystal structures from the Protein Data Bank and measured the energy improvements obtained and the computation times required to achieve them. GRID resulted in energy improvements that were significantly better than those attained by Backrub while expending about the same amount of computational resources. GRID resulted in relaxed structures that had slightly higher backbone RMSDs compared to Backrub relative to the starting crystal structures. The average RMSD was 0.25 ± 0.02 Å for GRID versus 0.14 ± 0.04 Å for Backrub. These relatively minor deviations indicate that both algorithms generate structures that retain their original topologies, as expected given the nature of the algorithms.
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Affiliation(s)
- Mohsen Chitsaz
- Biochemistry and Molecular Biophysics Option, California Institute of Technology, Pasadena, California 91125, USA
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19
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Lü Q, Xia XY, Chen R, Miao DJ, Chen SS, Quan LJ, Li HO. When the lowest energy does not induce native structures: parallel minimization of multi-energy values by hybridizing searching intelligences. PLoS One 2012; 7:e44967. [PMID: 23028708 PMCID: PMC3460973 DOI: 10.1371/journal.pone.0044967] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2012] [Accepted: 08/16/2012] [Indexed: 12/03/2022] Open
Abstract
Background Protein structure prediction (PSP), which is usually modeled as a computational optimization problem, remains one of the biggest challenges in computational biology. PSP encounters two difficult obstacles: the inaccurate energy function problem and the searching problem. Even if the lowest energy has been luckily found by the searching procedure, the correct protein structures are not guaranteed to obtain. Results A general parallel metaheuristic approach is presented to tackle the above two problems. Multi-energy functions are employed to simultaneously guide the parallel searching threads. Searching trajectories are in fact controlled by the parameters of heuristic algorithms. The parallel approach allows the parameters to be perturbed during the searching threads are running in parallel, while each thread is searching the lowest energy value determined by an individual energy function. By hybridizing the intelligences of parallel ant colonies and Monte Carlo Metropolis search, this paper demonstrates an implementation of our parallel approach for PSP. 16 classical instances were tested to show that the parallel approach is competitive for solving PSP problem. Conclusions This parallel approach combines various sources of both searching intelligences and energy functions, and thus predicts protein conformations with good quality jointly determined by all the parallel searching threads and energy functions. It provides a framework to combine different searching intelligence embedded in heuristic algorithms. It also constructs a container to hybridize different not-so-accurate objective functions which are usually derived from the domain expertise.
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Affiliation(s)
- Qiang Lü
- School of Computer Science and Technology, Soochow University, Suzhou, China.
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20
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Simoncini D, Berenger F, Shrestha R, Zhang KYJ. A probabilistic fragment-based protein structure prediction algorithm. PLoS One 2012; 7:e38799. [PMID: 22829868 PMCID: PMC3400640 DOI: 10.1371/journal.pone.0038799] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2012] [Accepted: 05/10/2012] [Indexed: 11/23/2022] Open
Abstract
Conformational sampling is one of the bottlenecks in fragment-based protein structure prediction approaches. They generally start with a coarse-grained optimization where mainchain atoms and centroids of side chains are considered, followed by a fine-grained optimization with an all-atom representation of proteins. It is during this coarse-grained phase that fragment-based methods sample intensely the conformational space. If the native-like region is sampled more, the accuracy of the final all-atom predictions may be improved accordingly. In this work we present EdaFold, a new method for fragment-based protein structure prediction based on an Estimation of Distribution Algorithm. Fragment-based approaches build protein models by assembling short fragments from known protein structures. Whereas the probability mass functions over the fragment libraries are uniform in the usual case, we propose an algorithm that learns from previously generated decoys and steers the search toward native-like regions. A comparison with Rosetta AbInitio protocol shows that EdaFold is able to generate models with lower energies and to enhance the percentage of near-native coarse-grained decoys on a benchmark of proteins. The best coarse-grained models produced by both methods were refined into all-atom models and used in molecular replacement. All atom decoys produced out of EdaFold’s decoy set reach high enough accuracy to solve the crystallographic phase problem by molecular replacement for some test proteins. EdaFold showed a higher success rate in molecular replacement when compared to Rosetta. Our study suggests that improving low resolution coarse-grained decoys allows computational methods to avoid subsequent sampling issues during all-atom refinement and to produce better all-atom models. EdaFold can be downloaded from http://www.riken.jp/zhangiru/software/.
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Affiliation(s)
- David Simoncini
- Zhang Initiative Research Unit, Advanced Science Institute, RIKEN, Wako, Saitama, Japan
| | - Francois Berenger
- Zhang Initiative Research Unit, Advanced Science Institute, RIKEN, Wako, Saitama, Japan
| | - Rojan Shrestha
- Zhang Initiative Research Unit, Advanced Science Institute, RIKEN, Wako, Saitama, Japan
- Department of Computational Biology, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Chiba, Japan
| | - Kam Y. J. Zhang
- Zhang Initiative Research Unit, Advanced Science Institute, RIKEN, Wako, Saitama, Japan
- Department of Computational Biology, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Chiba, Japan
- * E-mail:
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21
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Dal Palú A, Spyrakis F, Cozzini P. A new approach for investigating protein flexibility based on Constraint Logic Programming. The first application in the case of the estrogen receptor. Eur J Med Chem 2012; 49:127-40. [PMID: 22277571 DOI: 10.1016/j.ejmech.2012.01.003] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2011] [Revised: 01/05/2012] [Accepted: 01/05/2012] [Indexed: 12/01/2022]
Abstract
We describe the potential of a novel method, based on Constraint Logic Programming (CLP), developed for an exhaustive sampling of protein conformational space. The CLP framework proposed here has been tested and applied to the estrogen receptor, whose activity and function is strictly related to its intrinsic, and well known, dynamics. We have investigated in particular the flexibility of H12, focusing on the pathways followed by the helix when moving from one stable crystallographic conformation to the others. Millions of geometrically feasible conformations were generated, selected and the traces connecting the different forms were determined by using a shortest path algorithm. The preliminary analyses showed a marked agreement between the crystallographic agonist-like, antagonist-like and hypothetical apo forms, and the corresponding conformations identified by the CLP framework. These promising results, together with the short computational time required to perform the analyses, make this constraint-based approach a valuable tool for the study of protein folding prediction. The CLP framework enables one to consider various structural and energetic scenarious, without changing the core algorithm. To show the feasibility of the method, we intentionally choose a pure geometric setting, neglecting the energetic evaluation of the poses, in order to be independent from a specific force field and to provide the possibility of comparing different behaviours associated with various energy models.
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Handl J, Knowles J, Vernon R, Baker D, Lovell SC. The dual role of fragments in fragment-assembly methods for de novo protein structure prediction. Proteins 2011; 80:490-504. [PMID: 22095594 DOI: 10.1002/prot.23215] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2011] [Revised: 08/17/2011] [Accepted: 09/14/2011] [Indexed: 11/07/2022]
Abstract
In fragment-assembly techniques for protein structure prediction, models of protein structure are assembled from fragments of known protein structures. This process is typically guided by a knowledge-based energy function and uses a heuristic optimization method. The fragments play two important roles in this process: they define the set of structural parameters available, and they also assume the role of the main variation operators that are used by the optimiser. Previous analysis has typically focused on the first of these roles. In particular, the relationship between local amino acid sequence and local protein structure has been studied by a range of authors. The correlation between the two has been shown to vary with the window length considered, and the results of these analyses have informed directly the choice of fragment length in state-of-the-art prediction techniques. Here, we focus on the second role of fragments and aim to determine the effect of fragment length from an optimization perspective. We use theoretical analyses to reveal how the size and structure of the search space changes as a function of insertion length. Furthermore, empirical analyses are used to explore additional ways in which the size of the fragment insertion influences the search both in a simulation model and for the fragment-assembly technique, Rosetta.
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Affiliation(s)
- Julia Handl
- Manchester Business School, The University of Manchester, United Kingdom.
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23
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Huang SY, Zou X. Statistical mechanics-based method to extract atomic distance-dependent potentials from protein structures. Proteins 2011; 79:2648-61. [PMID: 21732421 PMCID: PMC11108592 DOI: 10.1002/prot.23086] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2011] [Revised: 04/21/2011] [Accepted: 05/09/2011] [Indexed: 12/25/2022]
Abstract
In this study, we have developed a statistical mechanics-based iterative method to extract statistical atomic interaction potentials from known, nonredundant protein structures. Our method circumvents the long-standing reference state problem in deriving traditional knowledge-based scoring functions, by using rapid iterations through a physical, global convergence function. The rapid convergence of this physics-based method, unlike other parameter optimization methods, warrants the feasibility of deriving distance-dependent, all-atom statistical potentials to keep the scoring accuracy. The derived potentials, referred to as ITScore/Pro, have been validated using three diverse benchmarks: the high-resolution decoy set, the AMBER benchmark decoy set, and the CASP8 decoy set. Significant improvement in performance has been achieved. Finally, comparisons between the potentials of our model and potentials of a knowledge-based scoring function with a randomized reference state have revealed the reason for the better performance of our scoring function, which could provide useful insight into the development of other physical scoring functions. The potentials developed in this study are generally applicable for structural selection in protein structure prediction.
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Affiliation(s)
- Sheng-You Huang
- Department of Physics and Astronomy, Department of Biochemistry, Dalton Cardiovascular Research Center, and Informatics Institute, University of Missouri, Columbia, MO 65211
| | - Xiaoqin Zou
- Department of Physics and Astronomy, Department of Biochemistry, Dalton Cardiovascular Research Center, and Informatics Institute, University of Missouri, Columbia, MO 65211
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van Dijk ADJ, Morabito G, Fiers M, van Ham RCHJ, Angenent GC, Immink RGH. Sequence motifs in MADS transcription factors responsible for specificity and diversification of protein-protein interaction. PLoS Comput Biol 2010; 6:e1001017. [PMID: 21124869 PMCID: PMC2991254 DOI: 10.1371/journal.pcbi.1001017] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2010] [Accepted: 10/27/2010] [Indexed: 11/18/2022] Open
Abstract
Protein sequences encompass tertiary structures and contain information about specific molecular interactions, which in turn determine biological functions of proteins. Knowledge about how protein sequences define interaction specificity is largely missing, in particular for paralogous protein families with high sequence similarity, such as the plant MADS domain transcription factor family. In comparison to the situation in mammalian species, this important family of transcription regulators has expanded enormously in plant species and contains over 100 members in the model plant species Arabidopsis thaliana. Here, we provide insight into the mechanisms that determine protein-protein interaction specificity for the Arabidopsis MADS domain transcription factor family, using an integrated computational and experimental approach. Plant MADS proteins have highly similar amino acid sequences, but their dimerization patterns vary substantially. Our computational analysis uncovered small sequence regions that explain observed differences in dimerization patterns with reasonable accuracy. Furthermore, we show the usefulness of the method for prediction of MADS domain transcription factor interaction networks in other plant species. Introduction of mutations in the predicted interaction motifs demonstrated that single amino acid mutations can have a large effect and lead to loss or gain of specific interactions. In addition, various performed bioinformatics analyses shed light on the way evolution has shaped MADS domain transcription factor interaction specificity. Identified protein-protein interaction motifs appeared to be strongly conserved among orthologs, indicating their evolutionary importance. We also provide evidence that mutations in these motifs can be a source for sub- or neo-functionalization. The analyses presented here take us a step forward in understanding protein-protein interactions and the interplay between protein sequences and network evolution.
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Affiliation(s)
| | | | - Martijn Fiers
- Plant Research International, Bioscience, Wageningen, The Netherlands
| | | | - Gerco C. Angenent
- Plant Research International, Bioscience, Wageningen, The Netherlands
- Centre for BioSystems Genomics (CBSG), Wageningen, The Netherlands
| | - Richard G. H. Immink
- Plant Research International, Bioscience, Wageningen, The Netherlands
- Centre for BioSystems Genomics (CBSG), Wageningen, The Netherlands
- * E-mail:
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25
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Hamelryck T, Borg M, Paluszewski M, Paulsen J, Frellsen J, Andreetta C, Boomsma W, Bottaro S, Ferkinghoff-Borg J. Potentials of mean force for protein structure prediction vindicated, formalized and generalized. PLoS One 2010; 5:e13714. [PMID: 21103041 PMCID: PMC2978081 DOI: 10.1371/journal.pone.0013714] [Citation(s) in RCA: 54] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2010] [Accepted: 10/04/2010] [Indexed: 11/26/2022] Open
Abstract
Understanding protein structure is of crucial importance in science, medicine and biotechnology. For about two decades, knowledge-based potentials based on pairwise distances – so-called “potentials of mean force” (PMFs) – have been center stage in the prediction and design of protein structure and the simulation of protein folding. However, the validity, scope and limitations of these potentials are still vigorously debated and disputed, and the optimal choice of the reference state – a necessary component of these potentials – is an unsolved problem. PMFs are loosely justified by analogy to the reversible work theorem in statistical physics, or by a statistical argument based on a likelihood function. Both justifications are insightful but leave many questions unanswered. Here, we show for the first time that PMFs can be seen as approximations to quantities that do have a rigorous probabilistic justification: they naturally arise when probability distributions over different features of proteins need to be combined. We call these quantities “reference ratio distributions” deriving from the application of the “reference ratio method.” This new view is not only of theoretical relevance but leads to many insights that are of direct practical use: the reference state is uniquely defined and does not require external physical insights; the approach can be generalized beyond pairwise distances to arbitrary features of protein structure; and it becomes clear for which purposes the use of these quantities is justified. We illustrate these insights with two applications, involving the radius of gyration and hydrogen bonding. In the latter case, we also show how the reference ratio method can be iteratively applied to sculpt an energy funnel. Our results considerably increase the understanding and scope of energy functions derived from known biomolecular structures.
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Affiliation(s)
- Thomas Hamelryck
- Bioinformatics Center, Department of Biology, University of Copenhagen, Copenhagen, Denmark
- * E-mail: (TH); (JFB)
| | - Mikael Borg
- Bioinformatics Center, Department of Biology, University of Copenhagen, Copenhagen, Denmark
| | - Martin Paluszewski
- Bioinformatics Center, Department of Biology, University of Copenhagen, Copenhagen, Denmark
| | - Jonas Paulsen
- Bioinformatics Center, Department of Biology, University of Copenhagen, Copenhagen, Denmark
| | - Jes Frellsen
- Bioinformatics Center, Department of Biology, University of Copenhagen, Copenhagen, Denmark
| | - Christian Andreetta
- Bioinformatics Center, Department of Biology, University of Copenhagen, Copenhagen, Denmark
| | - Wouter Boomsma
- Biomedical Engineering, Technical University of Denmark (DTU) Elektro, Technical University of Denmark, Lyngby, Denmark
- Department of Chemistry, University of Cambridge, Cambridge, United Kingdom
| | - Sandro Bottaro
- Biomedical Engineering, Technical University of Denmark (DTU) Elektro, Technical University of Denmark, Lyngby, Denmark
| | - Jesper Ferkinghoff-Borg
- Biomedical Engineering, Technical University of Denmark (DTU) Elektro, Technical University of Denmark, Lyngby, Denmark
- * E-mail: (TH); (JFB)
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Multiscale coarse-graining of the protein energy landscape. PLoS Comput Biol 2010; 6:e1000827. [PMID: 20585614 PMCID: PMC2891700 DOI: 10.1371/journal.pcbi.1000827] [Citation(s) in RCA: 103] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2010] [Accepted: 05/21/2010] [Indexed: 12/05/2022] Open
Abstract
A variety of coarse-grained (CG) models exists for simulation of proteins. An outstanding problem is the construction of a CG model with physically accurate conformational energetics rivaling all-atom force fields. In the present work, atomistic simulations of peptide folding and aggregation equilibria are force-matched using multiscale coarse-graining to develop and test a CG interaction potential of general utility for the simulation of proteins of arbitrary sequence. The reduced representation relies on multiple interaction sites to maintain the anisotropic packing and polarity of individual sidechains. CG energy landscapes computed from replica exchange simulations of the folding of Trpzip, Trp-cage and adenylate kinase resemble those of other reduced representations; non-native structures are observed with energies similar to those of the native state. The artifactual stabilization of misfolded states implies that non-native interactions play a deciding role in deviations from ideal funnel-like cooperative folding. The role of surface tension, backbone hydrogen bonding and the smooth pairwise CG landscape is discussed. Ab initio folding aside, the improved treatment of sidechain rotamers results in stability of the native state in constant temperature simulations of Trpzip, Trp-cage, and the open to closed conformational transition of adenylate kinase, illustrating the potential value of the CG force field for simulating protein complexes and transitions between well-defined structural states. Biological function originates from the dynamical motions of proteins in response to cellular stimuli. Protein dynamics arise from physical interactions that are well-predicted by detailed atomistic simulations. In order to examine large protein complexes on long timescales of biological importance, however, coarse-grained simulation approaches are needed to complement experiment. Previous coarse-grained models have proved successful for investigations involving a given protein's native structure, including protein folding and structure prediction. We construct a model capable of simulating proteins regardless of their sequence or structure. The present coarse-grained model was, however, developed rigorously from the underlying atomistic forces as opposed to knowledge-based or ad hoc parameterizations. Examination of the model predictions on various accessible timescales reveals successes and limitations of the model. While functionally relevant conformational transitions can be studied, the coarse-grained representation has some difficulty with the ab initio folding of the peptide chain into its proper structure. Our observations highlight the complex molecular nature of a protein's underlying energy landscape, offering rigorous insight into the information missing in reduced representations of the peptide chain. With these caveats in mind, the physical interaction–based, coarse-grained model will find application in simulations of a wide variety of proteins and continue to guide future coarse-graining efforts.
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Tian P. Computational protein design, from single domain soluble proteins to membrane proteins. Chem Soc Rev 2010; 39:2071-82. [DOI: 10.1039/b810924a] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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28
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Lappe M, Bagler G, Filippis I, Stehr H, Duarte JM, Sathyapriya R. Designing evolvable libraries using multi-body potentials. Curr Opin Biotechnol 2009; 20:437-46. [DOI: 10.1016/j.copbio.2009.07.008] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2009] [Revised: 07/15/2009] [Accepted: 07/25/2009] [Indexed: 01/13/2023]
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Bowman GR, Pande VS. The roles of entropy and kinetics in structure prediction. PLoS One 2009; 4:e5840. [PMID: 19513117 PMCID: PMC2688754 DOI: 10.1371/journal.pone.0005840] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2009] [Accepted: 05/11/2009] [Indexed: 12/02/2022] Open
Abstract
Background Here we continue our efforts to use methods developed in the folding mechanism community to both better understand and improve structure prediction. Our previous work demonstrated that Rosetta's coarse-grained potentials may actually impede accurate structure prediction at full-atom resolution. Based on this work we postulated that it may be time to work completely at full-atom resolution but that doing so may require more careful attention to the kinetics of convergence. Methodology/Principal Findings To explore the possibility of working entirely at full-atom resolution, we apply enhanced sampling algorithms and the free energy theory developed in the folding mechanism community to full-atom protein structure prediction with the prominent Rosetta package. We find that Rosetta's full-atom scoring function is indeed able to recognize diverse protein native states and that there is a strong correlation between score and Cα RMSD to the native state. However, we also show that there is a huge entropic barrier to folding under this potential and the kinetics of folding are extremely slow. We then exploit this new understanding to suggest ways to improve structure prediction. Conclusions/Significance Based on this work we hypothesize that structure prediction may be improved by taking a more physical approach, i.e. considering the nature of the model thermodynamics and kinetics which result from structure prediction simulations.
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Affiliation(s)
- Gregory R. Bowman
- Biophysics Program, Stanford University, Stanford, California, United States of America
| | - Vijay S. Pande
- Department of Chemistry, Stanford University, Stanford, California, United States of America
- * E-mail:
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