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Bakker MJ, Gaffour A, Juhás M, Zapletal V, Stošek J, Bratholm LA, Pavlíková Přecechtělová J. Streamlining NMR Chemical Shift Predictions for Intrinsically Disordered Proteins: Design of Ensembles with Dimensionality Reduction and Clustering. J Chem Inf Model 2024; 64:6542-6556. [PMID: 39099394 DOI: 10.1021/acs.jcim.4c00809] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/06/2024]
Abstract
By merging advanced dimensionality reduction (DR) and clustering algorithm (CA) techniques, our study advances the sampling procedure for predicting NMR chemical shifts (CS) in intrinsically disordered proteins (IDPs), making a significant leap forward in the field of protein analysis/modeling. We enhance NMR CS sampling by generating clustered ensembles that accurately reflect the different properties and phenomena encapsulated by the IDP trajectories. This investigation critically assessed different rapid CS predictors, both neural network (e.g., Sparta+ and ShiftX2) and database-driven (ProCS-15), and highlighted the need for more advanced quantum calculations and the subsequent need for more tractable-sized conformational ensembles. Although neural network CS predictors outperformed ProCS-15 for all atoms, all tools showed poor agreement with HN CSs, and the neural network CS predictors were unable to capture the influence of phosphorylated residues, highly relevant for IDPs. This study also addressed the limitations of using direct clustering with collective variables, such as the widespread implementation of the GROMOS algorithm. Clustered ensembles (CEs) produced by this algorithm showed poor performance with chemical shifts compared to sequential ensembles (SEs) of similar size. Instead, we implement a multiscale DR and CA approach and explore the challenges and limitations of applying these algorithms to obtain more robust and tractable CEs. The novel feature of this investigation is the use of solvent-accessible surface area (SASA) as one of the fingerprints for DR alongside previously investigated α carbon distance/angles or ϕ/ψ dihedral angles. The ensembles produced with SASA tSNE DR produced CEs better aligned with the experimental CS of between 0.17 and 0.36 r2 (0.18-0.26 ppm) depending on the system and replicate. Furthermore, this technique produced CEs with better agreement than traditional SEs in 85.7% of all ensemble sizes. This study investigates the quality of ensembles produced based on different input features, comparing latent spaces produced by linear vs nonlinear DR techniques and a novel integrated silhouette score scanning protocol for tSNE DR.
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Affiliation(s)
- Michael J Bakker
- Faculty of Pharmacy in Hradec Králové, Charles University, Akademika Heyrovského 1203/8, 500 05 Hradec Králové, Czech Republic
| | - Amina Gaffour
- Faculty of Pharmacy in Hradec Králové, Charles University, Akademika Heyrovského 1203/8, 500 05 Hradec Králové, Czech Republic
| | - Martin Juhás
- Faculty of Pharmacy in Hradec Králové, Charles University, Akademika Heyrovského 1203/8, 500 05 Hradec Králové, Czech Republic
- Department of Chemistry, Faculty of Science, University of Hradec Králové, Rokitanského 62, 500 03 Hradec Králové, Czech Republic
| | - Vojtěch Zapletal
- Faculty of Pharmacy in Hradec Králové, Charles University, Akademika Heyrovského 1203/8, 500 05 Hradec Králové, Czech Republic
| | - Jakub Stošek
- Faculty of Pharmacy in Hradec Králové, Charles University, Akademika Heyrovského 1203/8, 500 05 Hradec Králové, Czech Republic
- Department of Chemistry, Faculty of Science, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic
| | - Lars A Bratholm
- School of Chemistry, University of Bristol, Cantock's Close, BS8 1TS Bristol, U.K
| | - Jana Pavlíková Přecechtělová
- Faculty of Pharmacy in Hradec Králové, Charles University, Akademika Heyrovského 1203/8, 500 05 Hradec Králové, Czech Republic
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2
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Puthenveetil R, Christenson ET, Vinogradova O. New Horizons in Structural Biology of Membrane Proteins: Experimental Evaluation of the Role of Conformational Dynamics and Intrinsic Flexibility. MEMBRANES 2022; 12:227. [PMID: 35207148 PMCID: PMC8877495 DOI: 10.3390/membranes12020227] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/01/2022] [Revised: 02/13/2022] [Accepted: 02/14/2022] [Indexed: 02/08/2023]
Abstract
A plethora of membrane proteins are found along the cell surface and on the convoluted labyrinth of membranes surrounding organelles. Since the advent of various structural biology techniques, a sub-population of these proteins has become accessible to investigation at near-atomic resolutions. The predominant bona fide methods for structure solution, X-ray crystallography and cryo-EM, provide high resolution in three-dimensional space at the cost of neglecting protein motions through time. Though structures provide various rigid snapshots, only an amorphous mechanistic understanding can be inferred from interpolations between these different static states. In this review, we discuss various techniques that have been utilized in observing dynamic conformational intermediaries that remain elusive from rigid structures. More specifically we discuss the application of structural techniques such as NMR, cryo-EM and X-ray crystallography in studying protein dynamics along with complementation by conformational trapping by specific binders such as antibodies. We finally showcase the strength of various biophysical techniques including FRET, EPR and computational approaches using a multitude of succinct examples from GPCRs, transporters and ion channels.
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Affiliation(s)
- Robbins Puthenveetil
- Section on Structural and Chemical Biology of Membrane Proteins, Neurosciences and Cellular and Structural Biology Division, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, 35A Convent Dr., Bethesda, MD 20892, USA
| | | | - Olga Vinogradova
- Department of Pharmaceutical Sciences, School of Pharmacy, University of Connecticut, Storrs, CT 06269, USA
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3
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Wang G, Zhai YJ, Xue ZZ, Xu YY. Improving Protein Subcellular Location Classification by Incorporating Three-Dimensional Structure Information. Biomolecules 2021; 11:1607. [PMID: 34827605 PMCID: PMC8615982 DOI: 10.3390/biom11111607] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2021] [Revised: 10/27/2021] [Accepted: 10/27/2021] [Indexed: 12/12/2022] Open
Abstract
The subcellular locations of proteins are closely related to their functions. In the past few decades, the application of machine learning algorithms to predict protein subcellular locations has been an important topic in proteomics. However, most studies in this field used only amino acid sequences as the data source. Only a few works focused on other protein data types. For example, three-dimensional structures, which contain far more functional protein information than sequences, remain to be explored. In this work, we extracted various handcrafted features to describe the protein structures from physical, chemical, and topological aspects, as well as the learned features obtained by deep neural networks. We then used these features to classify the protein subcellular locations. Our experimental results demonstrated that some of these structural features have a certain effect on the protein location classification, and can help improve the performance of sequence-based location predictors. Our method provides a new view for the analysis of protein spatial distribution, and is anticipated to be used in revealing the relationships between protein structures and functions.
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Affiliation(s)
- Ge Wang
- School of Biomedical Engineering, Southern Medical University, Guangzhou 510515, China; (G.W.); (Z.-Z.X.)
- Guangdong Provincial Key Laboratory of Medical Imaging Processing, Southern Medical University, Guangzhou 510515, China
- Guangdong Province Engineering Laboratory for Medical Imaging and Diagnostic Technology, Southern Medical University, Guangzhou 510515, China
| | - Yu-Jia Zhai
- Guangzhou Women and Children’s Medical Center, Department of Pharmacy, Guangzhou Medical University, Guangzhou 510623, China;
| | - Zhen-Zhen Xue
- School of Biomedical Engineering, Southern Medical University, Guangzhou 510515, China; (G.W.); (Z.-Z.X.)
- Guangdong Provincial Key Laboratory of Medical Imaging Processing, Southern Medical University, Guangzhou 510515, China
- Guangdong Province Engineering Laboratory for Medical Imaging and Diagnostic Technology, Southern Medical University, Guangzhou 510515, China
- Paul C. Lauterbur Research Center for Biomedical Imaging, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China
| | - Ying-Ying Xu
- School of Biomedical Engineering, Southern Medical University, Guangzhou 510515, China; (G.W.); (Z.-Z.X.)
- Guangdong Provincial Key Laboratory of Medical Imaging Processing, Southern Medical University, Guangzhou 510515, China
- Guangdong Province Engineering Laboratory for Medical Imaging and Diagnostic Technology, Southern Medical University, Guangzhou 510515, China
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4
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Molecular Dynamics Simulations of Human FOXO3 Reveal Intrinsically Disordered Regions Spread Spatially by Intramolecular Electrostatic Repulsion. Biomolecules 2021; 11:biom11060856. [PMID: 34201262 PMCID: PMC8228108 DOI: 10.3390/biom11060856] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2021] [Revised: 06/01/2021] [Accepted: 06/03/2021] [Indexed: 12/17/2022] Open
Abstract
The human transcription factor FOXO3 (a member of the 'forkhead' family of transcription factors) controls a variety of cellular functions that make it a highly relevant target for intervention in anti-cancer and anti-aging therapies. FOXO3 is a mostly intrinsically disordered protein (IDP). Absence of knowledge of its structural properties outside the DNA-binding domain constitutes a considerable obstacle to a better understanding of structure/function relationships. Here, I present extensive molecular dynamics (MD) simulation data based on implicit solvation models of the entire FOXO3/DNA complex, and accelerated MD simulations under explicit solvent conditions of a central region of particular structural interest (FOXO3120-530). A new graphical tool for studying and visualizing the structural diversity of IDPs, the Local Compaction Plot (LCP), is introduced. The simulations confirm the highly disordered nature of FOXO3 and distinguish various degrees of folding propensity. Unexpectedly, two 'linker' regions immediately adjacent to the DNA-binding domain are present in a highly extended conformation. This extended conformation is not due to their amino acid composition, but rather is caused by electrostatic repulsion of the domains connected by the linkers. FOXO3 is thus an IDP present in an unusually extended conformation to facilitate interaction with molecular interaction partners.
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5
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Nottebaum S, Weinzierl ROJ. Transcribing Genes the Hard Way: In Vitro Reconstitution of Nanoarchaeal RNA Polymerase Reveals Unusual Active Site Properties. Front Mol Biosci 2021; 8:669314. [PMID: 34141723 PMCID: PMC8204694 DOI: 10.3389/fmolb.2021.669314] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2021] [Accepted: 04/26/2021] [Indexed: 11/13/2022] Open
Abstract
Nanoarchaea represent a highly diverged archaeal phylum that displays many unusual biological features. The Nanoarchaeum equitans genome encodes a complete set of RNA polymerase (RNAP) subunits and basal factors. Several of the standard motifs in the active center contain radical substitutions that are normally expected to render the polymerase catalytically inactive. Here we show that, despite these unusual features, a RNAP reconstituted from recombinant Nanoarchaeum subunits is transcriptionally active. Using a sparse-matrix high-throughput screening method we identified an atypical stringent requirement for fluoride ions to maximize its activity under in vitro transcription conditions.
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Affiliation(s)
- Sven Nottebaum
- Department of Life Sciences, Imperial College London, London, United Kingdom
- Orthomol Pharmazeutische Vertriebs GmbH, Langenfeld, Germany
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6
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Cárdenas R, Martínez-Seoane J, Amero C. Combining Experimental Data and Computational Methods for the Non-Computer Specialist. Molecules 2020; 25:E4783. [PMID: 33081072 PMCID: PMC7594097 DOI: 10.3390/molecules25204783] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2020] [Revised: 08/25/2020] [Accepted: 08/28/2020] [Indexed: 01/01/2023] Open
Abstract
Experimental methods are indispensable for the study of the function of biological macromolecules, not just as static structures, but as dynamic systems that change conformation, bind partners, perform reactions, and respond to different stimulus. However, providing a detailed structural interpretation of the results is often a very challenging task. While experimental and computational methods are often considered as two different and separate approaches, the power and utility of combining both is undeniable. The integration of the experimental data with computational techniques can assist and enrich the interpretation, providing new detailed molecular understanding of the systems. Here, we briefly describe the basic principles of how experimental data can be combined with computational methods to obtain insights into the molecular mechanism and expand the interpretation through the generation of detailed models.
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Affiliation(s)
| | | | - Carlos Amero
- Laboratorio de Bioquímica y Resonancia Magnética Nuclear, Centro de Investigaciones Químicas, Instituto de Investigación en Ciencias Básicas y Aplicadas, Universidad Autónoma del Estado de Morelos, Cuernavaca, Morelos 62209, Mexico; (R.C.); (J.M.-S.)
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7
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Abstract
For evaluating the deepest evolutionary relationships among proteins, sequence similarity is too low for application of sequence-based homology search or phylogenetic methods. In such cases, comparison of protein structures, which are often better conserved than sequences, may provide an alternative means of uncovering deep evolutionary signal. Although major protein structure databases such as SCOP and CATH hierarchically group protein structures, they do not describe the specific evolutionary relationships within a hierarchical level. Structural phylogenies have the potential to fill this gap. However, it is difficult to assess evolutionary relationships derived from structural phylogenies without some means of assessing confidence in such trees. We therefore address two shortcomings in the application of structural data to deep phylogeny. First, we examine whether phylogenies derived from pairwise structural comparisons are sensitive to differences in protein length and shape. We find that structural phylogenetics is best employed where structures have very similar lengths, and that shape fluctuations generated during molecular dynamics simulations impact pairwise comparisons, but not so drastically as to eliminate evolutionary signal. Second, we address the absence of statistical support for structural phylogeny. We present a method for assessing confidence in a structural phylogeny using shape fluctuations generated via molecular dynamics or Monte Carlo simulations of proteins. Our approach will aid the evolutionary reconstruction of relationships across structurally defined protein superfamilies. With the Protein Data Bank now containing in excess of 158,000 entries (December 2019), we predict that structural phylogenetics will become a useful tool for ordering the protein universe.
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Affiliation(s)
- Ashar J Malik
- Centre for Theoretical Chemistry and Physics, School of Natural and Computational Sciences, Massey University Auckland, Auckland, New Zealand.,Bioinformatics Institute, Agency for Science, Technology and Research, Singapore
| | - Anthony M Poole
- Bioinformatics Institute, School of Biological Sciences, University of Auckland, Auckland, New Zealand.,Digital Life Institute, University of Auckland, Auckland, New Zealand.,Biomolecular Interaction Centre, University of Canterbury, Christchurch, New Zealand
| | - Jane R Allison
- Bioinformatics Institute, School of Biological Sciences, University of Auckland, Auckland, New Zealand.,Digital Life Institute, University of Auckland, Auckland, New Zealand.,Biomolecular Interaction Centre, University of Canterbury, Christchurch, New Zealand.,Maurice Wilkins Centre for Molecular Biodiscovery, University of Auckland, Auckland, New Zealand
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8
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Jeffery HM, Weinzierl ROJ. Multivalent and Bidirectional Binding of Transcriptional Transactivation Domains to the MED25 Coactivator. Biomolecules 2020; 10:biom10091205. [PMID: 32825095 PMCID: PMC7564715 DOI: 10.3390/biom10091205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2020] [Revised: 08/14/2020] [Accepted: 08/17/2020] [Indexed: 11/16/2022] Open
Abstract
The human mediator subunit MED25 acts as a coactivator that binds the transcriptional activation domains (TADs) present in various cellular and viral gene-specific transcription factors. Previous studies, including on NMR measurements and site-directed mutagenesis, have only yielded low-resolution models that are difficult to refine further by experimental means. Here, we apply computational molecular dynamics simulations to study the interactions of two different TADs from the human transcription factor ETV5 (ERM) and herpes virus VP16-H1 with MED25. Like other well-studied coactivator-TAD complexes, the interactions of these intrinsically disordered domains with the coactivator surface are temporary and highly dynamic (‘fuzzy’). Due to the fact that the MED25 TAD-binding region is organized as an elongated cleft, we specifically asked whether these TADs are capable of binding in either orientation and how this could be achieved structurally and energetically. The binding of both the ETV5 and VP16-TADs in either orientation appears to be possible but occurs in a conformationally distinct manner and utilizes different sets of hydrophobic residues present in the TADs to drive the interactions. We propose that MED25 and at least a subset of human TADs specifically evolved a redundant set of molecular interaction patterns to allow binding to particular coactivators without major prior spatial constraints.
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Affiliation(s)
- Heather M. Jeffery
- Department of Life Sciences, Imperial College London, London SW7 2AZ, UK;
- Sir William Dunn School of Pathology, University of Oxford, Oxford OX1 3RE, UK
| | - Robert O. J. Weinzierl
- Department of Life Sciences, Imperial College London, London SW7 2AZ, UK;
- Correspondence:
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9
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Optimization of Molecular Dynamics Simulations of c-MYC 1-88-An Intrinsically Disordered System. Life (Basel) 2020; 10:life10070109. [PMID: 32664335 PMCID: PMC7400636 DOI: 10.3390/life10070109] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2020] [Revised: 07/06/2020] [Accepted: 07/07/2020] [Indexed: 11/28/2022] Open
Abstract
Many of the proteins involved in key cellular regulatory events contain extensive intrinsically disordered regions that are not readily amenable to conventional structure/function dissection. The oncoprotein c-MYC plays a key role in controlling cell proliferation and apoptosis and more than 70% of the primary sequence is disordered. Computational approaches that shed light on the range of secondary and tertiary structural conformations therefore provide the only realistic chance to study such proteins. Here, we describe the results of several tests of force fields and water models employed in molecular dynamics simulations for the N-terminal 88 amino acids of c-MYC. Comparisons of the simulation data with experimental secondary structure assignments obtained by NMR establish a particular implicit solvation approach as highly congruent. The results provide insights into the structural dynamics of c-MYC1-88, which will be useful for guiding future experimental approaches. The protocols for trajectory analysis described here will be applicable for the analysis of a variety of computational simulations of intrinsically disordered proteins.
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10
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Wang Y, Tian P, Boomsma W, Lindorff-Larsen K. Monte Carlo Sampling of Protein Folding by Combining an All-Atom Physics-Based Model with a Native State Bias. J Phys Chem B 2018; 122:11174-11185. [DOI: 10.1021/acs.jpcb.8b06335] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Yong Wang
- Structural Biology and NMR Laboratory, Linderstrøm-Lang Centre for Protein Science, Department of Biology, University of Copenhagen, Ole Maaløes Vej 5, DK-2200 Copenhagen N, Denmark
| | - Pengfei Tian
- Structural Biology and NMR Laboratory, Linderstrøm-Lang Centre for Protein Science, Department of Biology, University of Copenhagen, Ole Maaløes Vej 5, DK-2200 Copenhagen N, Denmark
- Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892, United States
| | - Wouter Boomsma
- Department of Computer Science, University of Copenhagen, 2100 Copenhagen Ø, Denmark
| | - Kresten Lindorff-Larsen
- Structural Biology and NMR Laboratory, Linderstrøm-Lang Centre for Protein Science, Department of Biology, University of Copenhagen, Ole Maaløes Vej 5, DK-2200 Copenhagen N, Denmark
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11
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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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12
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Devaurs D, Papanastasiou M, Antunes DA, Abella JR, Moll M, Ricklin D, Lambris JD, Kavraki LE. Native State of Complement Protein C3d Analysed via Hydrogen Exchange and Conformational Sampling. INTERNATIONAL JOURNAL OF COMPUTATIONAL BIOLOGY AND DRUG DESIGN 2018; 11:90-113. [PMID: 30700993 PMCID: PMC6349257 DOI: 10.1504/ijcbdd.2018.090834] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Hydrogen/deuterium exchange detected by mass spectrometry (HDXMS) provides valuable information on protein structure and dynamics. Although HDX-MS data is often interpreted using crystal structures, it was suggested that conformational ensembles produced by molecular dynamics simulations yield more accurate interpretations. In this paper, we analyse the complement protein C3d by performing an HDX-MS experiment, and evaluate several interpretation methodologies using an existing prediction model to derive HDX-MS data from protein structure. To interpret and refine C3d's HDX-MS data, we look for a conformation (or conformational ensemble) of C3d that allows computationally replicating this data. We confirm that crystal structures are not a good choice and suggest that conformational ensembles produced by molecular dynamics simulations might not always be satisfactory either. Finally, we show that coarse-grained conformational sampling of C3d produces a conformation from which its HDX-MS data can be replicated and refined.
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Affiliation(s)
- Didier Devaurs
- Department of Computer Science, Rice University, Houston, TX, USA
| | - Malvina Papanastasiou
- Department of Pathology and Laboratory Medicine, University of Pennsylvania, Philadelphia, PA, USA
- Broad Institute of MIT & Harvard, Cambridge, MA, USA
| | - Dinler A Antunes
- Department of Computer Science, Rice University, Houston, TX, USA
| | - Jayvee R Abella
- Department of Computer Science, Rice University, Houston, TX, USA
| | - Mark Moll
- Department of Computer Science, Rice University, Houston, TX, USA
| | - Daniel Ricklin
- Department of Pathology and Laboratory Medicine, University of Pennsylvania, Philadelphia, PA, USA
- Department of Pharmaceutical Sciences, University of Basel, Basel, Switzerland
| | - John D Lambris
- Department of Pathology and Laboratory Medicine, University of Pennsylvania, Philadelphia, PA, USA
| | - Lydia E Kavraki
- Department of Computer Science, Rice University, Houston, TX, USA
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13
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Kurut A, Fonseca R, Boomsma W. Driving Structural Transitions in Molecular Simulations Using the Nonequilibrium Candidate Monte Carlo. J Phys Chem B 2018; 122:1195-1204. [PMID: 29260565 DOI: 10.1021/acs.jpcb.7b11426] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Hybrid simulation procedures which combine molecular dynamics with Monte Carlo are attracting increasing attention as tools for improving the sampling efficiency in molecular simulations. In particular, encouraging results have been reported for nonequilibrium candidate protocols, in which a Monte Carlo move is applied gradually, and interleaved with a process that equilibrates the remaining degrees of freedom. Although initial studies have uncovered a substantial potential of the method, its practical applicability for sampling structural transitions in macromolecules remains incompletely understood. Here, we address this issue by systematically investigating the efficiency of the nonequilibrium candidate Monte Carlo on the sampling of rotameric distributions of two peptide systems at atomistic resolution both in vacuum and explicit solvent. The studied systems allow us to directly probe the efficiency with which a single or a few slow degrees of freedom can be driven between well-separated free-energy minima and to explore the sensitivity of the method toward the involved free parameters. In line with results on other systems, our study suggests that order-of-magnitude gains can be obtained in certain scenarios but also identifies challenges that arise when applying the procedure in explicit solvent.
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Affiliation(s)
- Anıl Kurut
- Department of Computer Science, University of Copenhagen , 2100 Copenhagen Ø, Denmark
| | - Rasmus Fonseca
- Department of Molecular and Cellular Physiology, Stanford University , Stanford, California 94305, United States
| | - Wouter Boomsma
- Department of Computer Science, University of Copenhagen , 2100 Copenhagen Ø, Denmark
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14
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In silico methods for design of biological therapeutics. Methods 2017; 131:33-65. [PMID: 28958951 DOI: 10.1016/j.ymeth.2017.09.008] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2017] [Revised: 09/21/2017] [Accepted: 09/23/2017] [Indexed: 12/18/2022] Open
Abstract
It has been twenty years since the first rationally designed small molecule drug was introduced into the market. Since then, we have progressed from designing small molecules to designing biotherapeutics. This class of therapeutics includes designed proteins, peptides and nucleic acids that could more effectively combat drug resistance and even act in cases where the disease is caused because of a molecular deficiency. Computational methods are crucial in this design exercise and this review discusses the various elements of designing biotherapeutic proteins and peptides. Many of the techniques discussed here, such as the deterministic and stochastic design methods, are generally used in protein design. We have devoted special attention to the design of antibodies and vaccines. In addition to the methods for designing these molecules, we have included a comprehensive list of all biotherapeutics approved for clinical use. Also included is an overview of methods that predict the binding affinity, cell penetration ability, half-life, solubility, immunogenicity and toxicity of the designed therapeutics. Biotherapeutics are only going to grow in clinical importance and are set to herald a new generation of disease management and cure.
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15
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Kassem MM, Wang Y, Boomsma W, Lindorff-Larsen K. Structure of the Bacterial Cytoskeleton Protein Bactofilin by NMR Chemical Shifts and Sequence Variation. Biophys J 2017; 110:2342-2348. [PMID: 27276252 DOI: 10.1016/j.bpj.2016.04.039] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2015] [Revised: 04/19/2016] [Accepted: 04/21/2016] [Indexed: 12/28/2022] Open
Abstract
Bactofilins constitute a recently discovered class of bacterial proteins that form cytoskeletal filaments. They share a highly conserved domain (DUF583) of which the structure remains unknown, in part due to the large size and noncrystalline nature of the filaments. Here, we describe the atomic structure of a bactofilin domain from Caulobacter crescentus. To determine the structure, we developed an approach that combines a biophysical model for proteins with recently obtained solid-state NMR spectroscopy data and amino acid contacts predicted from a detailed analysis of the evolutionary history of bactofilins. Our structure reveals a triangular β-helical (solenoid) conformation with conserved residues forming the tightly packed core and polar residues lining the surface. The repetitive structure explains the presence of internal repeats as well as strongly conserved positions, and is reminiscent of other fibrillar proteins. Our work provides a structural basis for future studies of bactofilin biology and for designing molecules that target them, as well as a starting point for determining the organization of the entire bactofilin filament. Finally, our approach presents new avenues for determining structures that are difficult to obtain by traditional means.
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Affiliation(s)
- Maher M Kassem
- Structural Biology and NMR Laboratory, Department of Biology, University of Copenhagen, Copenhagen, Denmark
| | - Yong Wang
- Structural Biology and NMR Laboratory, Department of Biology, University of Copenhagen, Copenhagen, Denmark
| | - Wouter Boomsma
- Structural Biology and NMR Laboratory, Department of Biology, University of Copenhagen, Copenhagen, Denmark
| | - Kresten Lindorff-Larsen
- Structural Biology and NMR Laboratory, Department of Biology, University of Copenhagen, Copenhagen, Denmark.
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16
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Devaurs D, Antunes DA, Papanastasiou M, Moll M, Ricklin D, Lambris JD, Kavraki LE. Coarse-Grained Conformational Sampling of Protein Structure Improves the Fit to Experimental Hydrogen-Exchange Data. Front Mol Biosci 2017; 4:13. [PMID: 28344973 PMCID: PMC5344923 DOI: 10.3389/fmolb.2017.00013] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2016] [Accepted: 02/24/2017] [Indexed: 11/13/2022] Open
Abstract
Monitoring hydrogen/deuterium exchange (HDX) undergone by a protein in solution produces experimental data that translates into valuable information about the protein's structure. Data produced by HDX experiments is often interpreted using a crystal structure of the protein, when available. However, it has been shown that the correspondence between experimental HDX data and crystal structures is often not satisfactory. This creates difficulties when trying to perform a structural analysis of the HDX data. In this paper, we evaluate several strategies to obtain a conformation providing a good fit to the experimental HDX data, which is a premise of an accurate structural analysis. We show that performing molecular dynamics simulations can be inadequate to obtain such conformations, and we propose a novel methodology involving a coarse-grained conformational sampling approach instead. By extensively exploring the intrinsic flexibility of a protein with this approach, we produce a conformational ensemble from which we extract a single conformation providing a good fit to the experimental HDX data. We successfully demonstrate the applicability of our method to four small and medium-sized proteins.
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Affiliation(s)
- Didier Devaurs
- Department of Computer Science, Rice UniversityHouston, TX, USA
| | | | - Malvina Papanastasiou
- Department of Pathology and Laboratory Medicine, University of PennsylvaniaPhiladelphia, PA, USA
- Broad Institute of MIT & HarvardCambridge, MA, USA
| | - Mark Moll
- Department of Computer Science, Rice UniversityHouston, TX, USA
| | - Daniel Ricklin
- Department of Pathology and Laboratory Medicine, University of PennsylvaniaPhiladelphia, PA, USA
- Department of Pharmaceutical Sciences, University of BaselBasel, Switzerland
| | - John D. Lambris
- Department of Pathology and Laboratory Medicine, University of PennsylvaniaPhiladelphia, PA, USA
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17
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Antonov LD, Olsson S, Boomsma W, Hamelryck T. Bayesian inference of protein ensembles from SAXS data. Phys Chem Chem Phys 2017; 18:5832-8. [PMID: 26548662 DOI: 10.1039/c5cp04886a] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
The inherent flexibility of intrinsically disordered proteins (IDPs) and multi-domain proteins with intrinsically disordered regions (IDRs) presents challenges to structural analysis. These macromolecules need to be represented by an ensemble of conformations, rather than a single structure. Small-angle X-ray scattering (SAXS) experiments capture ensemble-averaged data for the set of conformations. We present a Bayesian approach to ensemble inference from SAXS data, called Bayesian ensemble SAXS (BE-SAXS). We address two issues with existing methods: the use of a finite ensemble of structures to represent the underlying distribution, and the selection of that ensemble as a subset of an initial pool of structures. This is achieved through the formulation of a Bayesian posterior of the conformational space. BE-SAXS modifies a structural prior distribution in accordance with the experimental data. It uses multi-step expectation maximization, with alternating rounds of Markov-chain Monte Carlo simulation and empirical Bayes optimization. We demonstrate the method by employing it to obtain a conformational ensemble of the antitoxin PaaA2 and comparing the results to a published ensemble.
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Affiliation(s)
- L D Antonov
- Bioinformatics Centre, Department of Biology, University of Copenhagen, Ole Maaloes Vej 5, DK-2200 Copenhagen N, Denmark.
| | - S Olsson
- Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, ETH-Hönggerberg, Vladimir-Prelog-Weg 2, CH-8093 Zürich, Switzerland and Institute for Research in Biomedicine, Università della Svizzera Italiana, Via Vincenzo Vela 6, CH-6500 Bellinzona, Switzerland
| | - W Boomsma
- Structural Biology and NMR Laboratory, Department of Biology, University of Copenhagen, Ole Maaloes Vej 5, DK-2200 Copenhagen N, Denmark
| | - T Hamelryck
- Bioinformatics Centre, Department of Biology, University of Copenhagen, Ole Maaloes Vej 5, DK-2200 Copenhagen N, Denmark.
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18
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Bratholm LA, Jensen JH. Protein structure refinement using a quantum mechanics-based chemical shielding predictor. Chem Sci 2016; 8:2061-2072. [PMID: 28451325 PMCID: PMC5399634 DOI: 10.1039/c6sc04344e] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2016] [Accepted: 11/15/2016] [Indexed: 11/21/2022] Open
Abstract
We show that a QM-based predictor of a protein backbone and CB chemical shifts is of comparable accuracy to empirical chemical shift predictors after chemical shift-based structural refinement that removes small structural errors (errors in chemical shifts shown in red).
The accurate prediction of protein chemical shifts using a quantum mechanics (QM)-based method has been the subject of intense research for more than 20 years but so far empirical methods for chemical shift prediction have proven more accurate. In this paper we show that a QM-based predictor of a protein backbone and CB chemical shifts (ProCS15, PeerJ, 2016, 3, e1344) is of comparable accuracy to empirical chemical shift predictors after chemical shift-based structural refinement that removes small structural errors. We present a method by which quantum chemistry based predictions of isotropic chemical shielding values (ProCS15) can be used to refine protein structures using Markov Chain Monte Carlo (MCMC) simulations, relating the chemical shielding values to the experimental chemical shifts probabilistically. Two kinds of MCMC structural refinement simulations were performed using force field geometry optimized X-ray structures as starting points: simulated annealing of the starting structure and constant temperature MCMC simulation followed by simulated annealing of a representative ensemble structure. Annealing of the CHARMM structure changes the CA-RMSD by an average of 0.4 Å but lowers the chemical shift RMSD by 1.0 and 0.7 ppm for CA and N. Conformational averaging has a relatively small effect (0.1–0.2 ppm) on the overall agreement with carbon chemical shifts but lowers the error for nitrogen chemical shifts by 0.4 ppm. If an amino acid specific offset is included the ProCS15 predicted chemical shifts have RMSD values relative to experiments that are comparable to popular empirical chemical shift predictors. The annealed representative ensemble structures differ in CA-RMSD relative to the initial structures by an average of 2.0 Å, with >2.0 Å difference for six proteins. In four of the cases, the largest structural differences arise in structurally flexible regions of the protein as determined by NMR, and in the remaining two cases, the large structural change may be due to force field deficiencies. The overall accuracy of the empirical methods are slightly improved by annealing the CHARMM structure with ProCS15, which may suggest that the minor structural changes introduced by ProCS15-based annealing improves the accuracy of the protein structures. Having established that QM-based chemical shift prediction can deliver the same accuracy as empirical shift predictors we hope this can help increase the accuracy of related approaches such as QM/MM or linear scaling approaches or interpreting protein structural dynamics from QM-derived chemical shift.
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Affiliation(s)
- Lars A Bratholm
- Department of Chemistry , University of Copenhagen , Copenhagen , Denmark . ; ; http://www.twitter.com/janhjensen
| | - Jan H Jensen
- Department of Chemistry , University of Copenhagen , Copenhagen , Denmark . ; ; http://www.twitter.com/janhjensen
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19
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Li L, Li J, Xiao W, Li Y, Qin Y, Zhou S, Yang H. Prediction the Substrate Specificities of Membrane Transport Proteins Based on Support Vector Machine and Hybrid Features. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2016; 13:947-953. [PMID: 26571537 DOI: 10.1109/tcbb.2015.2495140] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
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20
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Vestergaard B. Analysis of biostructural changes, dynamics, and interactions – Small-angle X-ray scattering to the rescue. Arch Biochem Biophys 2016; 602:69-79. [DOI: 10.1016/j.abb.2016.02.029] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2016] [Revised: 02/17/2016] [Accepted: 02/26/2016] [Indexed: 12/27/2022]
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21
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Lamiable A, Thevenet P, Tufféry P. A critical assessment of hidden markov model sub-optimal sampling strategies applied to the generation of peptide 3D models. J Comput Chem 2016; 37:2006-16. [PMID: 27317417 DOI: 10.1002/jcc.24422] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2016] [Revised: 05/03/2016] [Accepted: 05/17/2016] [Indexed: 12/23/2022]
Abstract
Hidden Markov Model derived structural alphabets are a probabilistic framework in which the complete conformational space of a peptidic chain is described in terms of probability distributions that can be sampled to identify conformations of largest probabilities. Here, we assess how three strategies to sample sub-optimal conformations-Viterbi k-best, forward backtrack and a taboo sampling approach-can lead to the efficient generation of peptide conformations. We show that the diversity of sampling is essential to compensate biases introduced in the estimates of the probabilities, and we find that only the forward backtrack and a taboo sampling strategies can efficiently generate native or near-native models. Finally, we also find such approaches are as efficient as former protocols, while being one order of magnitude faster, opening the door to the large scale de novo modeling of peptides and mini-proteins. © 2016 Wiley Periodicals, Inc.
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Affiliation(s)
- A Lamiable
- INSERM UMR-S 973, Université Paris Diderot, Sorbonne Paris Cité
| | - P Thevenet
- INSERM UMR-S 973, Université Paris Diderot, Sorbonne Paris Cité
| | - P Tufféry
- INSERM UMR-S 973, Université Paris Diderot, Sorbonne Paris Cité
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22
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Tian P, Lindorff-Larsen K, Boomsma W, Jensen MH, Otzen DE. A Monte Carlo Study of the Early Steps of Functional Amyloid Formation. PLoS One 2016; 11:e0146096. [PMID: 26745180 PMCID: PMC4706413 DOI: 10.1371/journal.pone.0146096] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2015] [Accepted: 12/14/2015] [Indexed: 11/18/2022] Open
Abstract
In addition to their well-known roles in neurodegenerative diseases and amyloidoses, amyloid structures also assume important functional roles in the cell. Although functional amyloid shares many physiochemical properties with its pathogenic counterpart, it is evolutionarily optimized to avoid cytotoxicity. This makes it an interesting study case for aggregation phenomenon in general. One of the most well-known examples of a functional amyloid, E. coli curli, is an essential component in the formation of bacterial biofilm, and is primarily formed by aggregates of the protein CsgA. Previous studies have shown that the minor sequence variations observed in the five different subrepeats (R1-R5), which comprise the CsgA primary sequence, have a substantial influence on their individual aggregation propensities. Using a recently described diffusion-optimized enhanced sampling approach for Monte Carlo simulations, we here investigate the equilibrium properties of the monomeric and dimeric states of these subrepeats, to probe whether structural properties observed in these early stage oligomers are decisive for the characteristics of the resulting aggregate. We show that the dimerization propensities of these peptides have strong correlations with their propensity for amyloid formation, and provide structural insights into the inter- and intramolecular contacts that appear to be essential in this process.
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Affiliation(s)
- Pengfei Tian
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100, Copenhagen, Denmark.,Linderstrøm-Lang Centre for Protein Science and Structural Biology and NMR Laboratory, Department of Biology, University of Copenhagen, Ole Maaløes Vej 5, DK-2200, Copenhagen N, Denmark
| | - Kresten Lindorff-Larsen
- Linderstrøm-Lang Centre for Protein Science and Structural Biology and NMR Laboratory, Department of Biology, University of Copenhagen, Ole Maaløes Vej 5, DK-2200, Copenhagen N, Denmark
| | - Wouter Boomsma
- Linderstrøm-Lang Centre for Protein Science and Structural Biology and NMR Laboratory, Department of Biology, University of Copenhagen, Ole Maaløes Vej 5, DK-2200, Copenhagen N, Denmark
| | - Mogens Høgh Jensen
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100, Copenhagen, Denmark
| | - Daniel Erik Otzen
- Interdisciplinary Nanoscience Center (iNANO), Centre for Insoluble Protein Structures (inSPIN), Department of Molecular Biology, Aarhus University, Gustav Wieds Vej 10, 8000, Aarhus C, Denmark
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23
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Larsen AS, Bratholm LA, Christensen AS, Channir M, Jensen JH. ProCS15: a DFT-based chemical shift predictor for backbone and Cβ atoms in proteins. PeerJ 2015; 3:e1344. [PMID: 26623185 PMCID: PMC4662583 DOI: 10.7717/peerj.1344] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2015] [Accepted: 10/01/2015] [Indexed: 12/16/2022] Open
Abstract
We present ProCS15: a program that computes the isotropic chemical shielding values of backbone and Cβ atoms given a protein structure in less than a second. ProCS15 is based on around 2.35 million OPBE/6-31G(d,p)//PM6 calculations on tripeptides and small structural models of hydrogen-bonding. The ProCS15-predicted chemical shielding values are compared to experimentally measured chemical shifts for Ubiquitin and the third IgG-binding domain of Protein G through linear regression and yield RMSD values of up to 2.2, 0.7, and 4.8 ppm for carbon, hydrogen, and nitrogen atoms. These RMSD values are very similar to corresponding RMSD values computed using OPBE/6-31G(d,p) for the entire structure for each proteins. These maximum RMSD values can be reduced by using NMR-derived structural ensembles of Ubiquitin. For example, for the largest ensemble the largest RMSD values are 1.7, 0.5, and 3.5 ppm for carbon, hydrogen, and nitrogen. The corresponding RMSD values predicted by several empirical chemical shift predictors range between 0.7–1.1, 0.2–0.4, and 1.8–2.8 ppm for carbon, hydrogen, and nitrogen atoms, respectively.
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Affiliation(s)
- Anders S Larsen
- Department of Pharmacy, University of Copenhagen , Copenhagen , Denmark
| | - Lars A Bratholm
- Department of Chemistry, University of Copenhagen , Copenhagen , Denmark
| | | | - Maher Channir
- Department of Chemistry, University of Copenhagen , Copenhagen , Denmark
| | - Jan H Jensen
- Department of Chemistry, University of Copenhagen , Copenhagen , Denmark
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24
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Olsson S, Ekonomiuk D, Sgrignani J, Cavalli A. Molecular Dynamics of Biomolecules through Direct Analysis of Dipolar Couplings. J Am Chem Soc 2015; 137:6270-8. [PMID: 25895902 DOI: 10.1021/jacs.5b01289] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Residual dipolar couplings (RDCs) are important probes in structural biology, but their analysis is often complicated by the determination of an alignment tensor or its associated assumptions. We here apply the maximum entropy principle to derive a tensor-free formalism which allows for direct, dynamic analysis of RDCs and holds the classic tensor formalism as a special case. Specifically, the framework enables us to robustly analyze data regardless of whether a clear separation of internal and overall dynamics is possible. Such a separation is often difficult in the core subjects of current structural biology, which include multidomain and intrinsically disordered proteins as well as nucleic acids. We demonstrate the method is tractable and self-consistent and generalizes to data sets comprised of observations from multiple different alignment conditions.
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Affiliation(s)
- Simon Olsson
- †Institute for Research in Biomedicine, Via Vincenzo Vela 6, CH-6500 Bellinzona, Switzerland.,‡Laboratory of Physical Chemistry, Eidgenössische Technische Hochschule Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Dariusz Ekonomiuk
- †Institute for Research in Biomedicine, Via Vincenzo Vela 6, CH-6500 Bellinzona, Switzerland
| | - Jacopo Sgrignani
- †Institute for Research in Biomedicine, Via Vincenzo Vela 6, CH-6500 Bellinzona, Switzerland
| | - Andrea Cavalli
- †Institute for Research in Biomedicine, Via Vincenzo Vela 6, CH-6500 Bellinzona, Switzerland.,§Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW United Kingdom
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25
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An efficient algorithm to perform local concerted movements of a chain molecule. PLoS One 2015; 10:e0118342. [PMID: 25825903 PMCID: PMC4380501 DOI: 10.1371/journal.pone.0118342] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2014] [Accepted: 01/14/2015] [Indexed: 11/19/2022] Open
Abstract
The devising of efficient concerted rotation moves that modify only selected local portions of chain molecules is a long studied problem. Possible applications range from speeding the uncorrelated sampling of polymeric dense systems to loop reconstruction and structure refinement in protein modeling. Here, we propose and validate, on a few pedagogical examples, a novel numerical strategy that generalizes the notion of concerted rotation. The usage of the Denavit-Hartenberg parameters for chain description allows all possible choices for the subset of degrees of freedom to be modified in the move. They can be arbitrarily distributed along the chain and can be distanced between consecutive monomers as well. The efficiency of the methodology capitalizes on the inherent geometrical structure of the manifold defined by all chain configurations compatible with the fixed degrees of freedom. The chain portion to be moved is first opened along a direction chosen in the tangent space to the manifold, and then closed in the orthogonal space. As a consequence, in Monte Carlo simulations detailed balance is easily enforced without the need of using Jacobian reweighting. Moreover, the relative fluctuations of the degrees of freedom involved in the move can be easily tuned. We show different applications: the manifold of possible configurations is explored in a very efficient way for a protein fragment and for a cyclic molecule; the "local backbone volume", related to the volume spanned by the manifold, reproduces the mobility profile of all-α helical proteins; the refinement of small protein fragments with different secondary structures is addressed. The presented results suggest our methodology as a valuable exploration and sampling tool in the context of bio-molecular simulations.
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26
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Bratholm LA, Christensen AS, Hamelryck T, Jensen JH. Bayesian inference of protein structure from chemical shift data. PeerJ 2015; 3:e861. [PMID: 25825683 PMCID: PMC4375973 DOI: 10.7717/peerj.861] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2014] [Accepted: 03/06/2015] [Indexed: 12/15/2022] Open
Abstract
Protein chemical shifts are routinely used to augment molecular mechanics force fields in protein structure simulations, with weights of the chemical shift restraints determined empirically. These weights, however, might not be an optimal descriptor of a given protein structure and predictive model, and a bias is introduced which might result in incorrect structures. In the inferential structure determination framework, both the unknown structure and the disagreement between experimental and back-calculated data are formulated as a joint probability distribution, thus utilizing the full information content of the data. Here, we present the formulation of such a probability distribution where the error in chemical shift prediction is described by either a Gaussian or Cauchy distribution. The methodology is demonstrated and compared to a set of empirically weighted potentials through Markov chain Monte Carlo simulations of three small proteins (ENHD, Protein G and the SMN Tudor Domain) using the PROFASI force field and the chemical shift predictor CamShift. Using a clustering-criterion for identifying the best structure, together with the addition of a solvent exposure scoring term, the simulations suggests that sampling both the structure and the uncertainties in chemical shift prediction leads more accurate structures compared to conventional methods using empirical determined weights. The Cauchy distribution, using either sampled uncertainties or predetermined weights, did, however, result in overall better convergence to the native fold, suggesting that both types of distribution might be useful in different aspects of the protein structure prediction.
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Affiliation(s)
- Lars A. Bratholm
- Department of Chemistry, University of Copenhagen, Copenhagen, Denmark
| | | | - Thomas Hamelryck
- Department of Biology, University of Copenhagen, Copenhagen, Denmark
| | - Jan H. Jensen
- Department of Chemistry, University of Copenhagen, Copenhagen, Denmark
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27
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Picchini U, Forman JL. Accelerating inference for diffusions observed with measurement error and large sample sizes using approximate Bayesian computation. J STAT COMPUT SIM 2015. [DOI: 10.1080/00949655.2014.1002101] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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28
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Equilibrium simulations of proteins using molecular fragment replacement and NMR chemical shifts. Proc Natl Acad Sci U S A 2014; 111:13852-7. [PMID: 25192938 DOI: 10.1073/pnas.1404948111] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
Abstract
Methods of protein structure determination based on NMR chemical shifts are becoming increasingly common. The most widely used approaches adopt the molecular fragment replacement strategy, in which structural fragments are repeatedly reassembled into different complete conformations in molecular simulations. Although these approaches are effective in generating individual structures consistent with the chemical shift data, they do not enable the sampling of the conformational space of proteins with correct statistical weights. Here, we present a method of molecular fragment replacement that makes it possible to perform equilibrium simulations of proteins, and hence to determine their free energy landscapes. This strategy is based on the encoding of the chemical shift information in a probabilistic model in Markov chain Monte Carlo simulations. First, we demonstrate that with this approach it is possible to fold proteins to their native states starting from extended structures. Second, we show that the method satisfies the detailed balance condition and hence it can be used to carry out an equilibrium sampling from the Boltzmann distribution corresponding to the force field used in the simulations. Third, by comparing the results of simulations carried out with and without chemical shift restraints we describe quantitatively the effects that these restraints have on the free energy landscapes of proteins. Taken together, these results demonstrate that the molecular fragment replacement strategy can be used in combination with chemical shift information to characterize not only the native structures of proteins but also their conformational fluctuations.
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29
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Olsson S, Vögeli BR, Cavalli A, Boomsma W, Ferkinghoff-Borg J, Lindorff-Larsen K, Hamelryck T. Probabilistic Determination of Native State Ensembles of Proteins. J Chem Theory Comput 2014; 10:3484-91. [DOI: 10.1021/ct5001236] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Simon Olsson
- Bioinformatics
Centre, Department of Biology, Faculty of Science, University of Copenhagen, Copenhagen, Denmark
- Institute for Research in Biomedicine, CH-6500 Bellinzona, Switzerland
| | - Beat Rolf Vögeli
- Laboratory
of Physical Chemistry, Eidgenössische Technische Hochschule Zürich, 8093 Zürich, Switzerland
| | - Andrea Cavalli
- Institute for Research in Biomedicine, CH-6500 Bellinzona, Switzerland
| | - Wouter Boomsma
- Structural
Biology and NMR Laboratory, Department of Biology, Faculty of Science, University of Copenhagen, Copenhagen, Denmark
| | - Jesper Ferkinghoff-Borg
- Cellular
Signal Integration Group, Center for Biological Sequence Analysis, Technical University of Denmark, Lyngby, Denmark
| | - Kresten Lindorff-Larsen
- Structural
Biology and NMR Laboratory, Department of Biology, Faculty of Science, University of Copenhagen, Copenhagen, Denmark
| | - Thomas Hamelryck
- Bioinformatics
Centre, Department of Biology, Faculty of Science, University of Copenhagen, Copenhagen, Denmark
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30
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Forman JL, Sørensen M. A transformation approach to modelling multi-modal diffusions. J Stat Plan Inference 2014. [DOI: 10.1016/j.jspi.2013.09.013] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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31
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Wüstner D, Sklenar H. Atomistic Monte Carlo simulation of lipid membranes. Int J Mol Sci 2014; 15:1767-803. [PMID: 24469314 PMCID: PMC3958820 DOI: 10.3390/ijms15021767] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2013] [Revised: 12/06/2013] [Accepted: 01/09/2014] [Indexed: 02/07/2023] Open
Abstract
Biological membranes are complex assemblies of many different molecules of which analysis demands a variety of experimental and computational approaches. In this article, we explain challenges and advantages of atomistic Monte Carlo (MC) simulation of lipid membranes. We provide an introduction into the various move sets that are implemented in current MC methods for efficient conformational sampling of lipids and other molecules. In the second part, we demonstrate for a concrete example, how an atomistic local-move set can be implemented for MC simulations of phospholipid monomers and bilayer patches. We use our recently devised chain breakage/closure (CBC) local move set in the bond-/torsion angle space with the constant-bond-length approximation (CBLA) for the phospholipid dipalmitoylphosphatidylcholine (DPPC). We demonstrate rapid conformational equilibration for a single DPPC molecule, as assessed by calculation of molecular energies and entropies. We also show transition from a crystalline-like to a fluid DPPC bilayer by the CBC local-move MC method, as indicated by the electron density profile, head group orientation, area per lipid, and whole-lipid displacements. We discuss the potential of local-move MC methods in combination with molecular dynamics simulations, for example, for studying multi-component lipid membranes containing cholesterol.
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Affiliation(s)
- Daniel Wüstner
- Department of Biochemistry and Molecular Biology, University of Southern Denmark, Odense M DK-5230, Denmark.
| | - Heinz Sklenar
- Theoretical Biophysics Group, Max Delbrück Center for Molecular Medicine, Robert-Rössle-Str. 10, Berlin D-13125, Germany.
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32
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Christensen AS, Linnet TE, Borg M, Boomsma W, Lindorff-Larsen K, Hamelryck T, Jensen JH. Protein structure validation and refinement using amide proton chemical shifts derived from quantum mechanics. PLoS One 2013; 8:e84123. [PMID: 24391900 PMCID: PMC3877219 DOI: 10.1371/journal.pone.0084123] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2013] [Accepted: 11/11/2013] [Indexed: 11/18/2022] Open
Abstract
We present the ProCS method for the rapid and accurate prediction of protein backbone amide proton chemical shifts--sensitive probes of the geometry of key hydrogen bonds that determine protein structure. ProCS is parameterized against quantum mechanical (QM) calculations and reproduces high level QM results obtained for a small protein with an RMSD of 0.25 ppm (r = 0.94). ProCS is interfaced with the PHAISTOS protein simulation program and is used to infer statistical protein ensembles that reflect experimentally measured amide proton chemical shift values. Such chemical shift-based structural refinements, starting from high-resolution X-ray structures of Protein G, ubiquitin, and SMN Tudor Domain, result in average chemical shifts, hydrogen bond geometries, and trans-hydrogen bond ((h3)J(NC')) spin-spin coupling constants that are in excellent agreement with experiment. We show that the structural sensitivity of the QM-based amide proton chemical shift predictions is needed to obtain this agreement. The ProCS method thus offers a powerful new tool for refining the structures of hydrogen bonding networks to high accuracy with many potential applications such as protein flexibility in ligand binding.
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Affiliation(s)
| | - Troels E. Linnet
- Structural Biology and NMR Laboratory, Department of Biology, University of Copenhagen, Copenhagen, Denmark
| | - Mikael Borg
- Structural Bioinformatics Group, Section for Computational and RNA Biology, Department of Biology, University of Copenhagen, Copenhagen, Denmark
| | - Wouter Boomsma
- Structural Biology and NMR Laboratory, Department of Biology, University of Copenhagen, Copenhagen, Denmark
| | - Kresten Lindorff-Larsen
- Structural Biology and NMR Laboratory, Department of Biology, University of Copenhagen, Copenhagen, Denmark
| | - Thomas Hamelryck
- Structural Bioinformatics Group, Section for Computational and RNA Biology, Department of Biology, University of Copenhagen, Copenhagen, Denmark
| | - Jan H. Jensen
- Department of Chemistry, University of Copenhagen, Copenhagen, Denmark
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33
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Olsson S, Frellsen J, Boomsma W, Mardia KV, Hamelryck T. Inference of structure ensembles of flexible biomolecules from sparse, averaged data. PLoS One 2013; 8:e79439. [PMID: 24244505 PMCID: PMC3820694 DOI: 10.1371/journal.pone.0079439] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2013] [Accepted: 09/24/2013] [Indexed: 11/21/2022] Open
Abstract
We present the theoretical foundations of a general principle to infer structure ensembles of flexible biomolecules from spatially and temporally averaged data obtained in biophysical experiments. The central idea is to compute the Kullback-Leibler optimal modification of a given prior distribution with respect to the experimental data and its uncertainty. This principle generalizes the successful inferential structure determination method and recently proposed maximum entropy methods. Tractability of the protocol is demonstrated through the analysis of simulated nuclear magnetic resonance spectroscopy data of a small peptide.
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Affiliation(s)
- Simon Olsson
- Bioinformatics Centre, Department of Biology, Faculty of Science, University of Copenhagen, Copenhagen, Denmark
- * E-mail: (SO); (TH)
| | - Jes Frellsen
- Bioinformatics Centre, Department of Biology, Faculty of Science, University of Copenhagen, Copenhagen, Denmark
| | - Wouter Boomsma
- Structural Biology and NMR Laboratory, Department of Biology, Faculty of Science, University of Copenhagen, Copenhagen, Denmark
| | - Kanti V. Mardia
- Department of Statistics, School of Mathematics, University of Leeds, Leeds, United Kingdom
| | - Thomas Hamelryck
- Bioinformatics Centre, Department of Biology, Faculty of Science, University of Copenhagen, Copenhagen, Denmark
- * E-mail: (SO); (TH)
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Valentin JB, Andreetta C, Boomsma W, Bottaro S, Ferkinghoff-Borg J, Frellsen J, Mardia KV, Tian P, Hamelryck T. Formulation of probabilistic models of protein structure in atomic detail using the reference ratio method. Proteins 2013; 82:288-99. [PMID: 23934827 DOI: 10.1002/prot.24386] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2013] [Revised: 07/02/2013] [Accepted: 07/18/2013] [Indexed: 01/10/2023]
Abstract
We propose a method to formulate probabilistic models of protein structure in atomic detail, for a given amino acid sequence, based on Bayesian principles, while retaining a close link to physics. We start from two previously developed probabilistic models of protein structure on a local length scale, which concern the dihedral angles in main chain and side chains, respectively. Conceptually, this constitutes a probabilistic and continuous alternative to the use of discrete fragment and rotamer libraries. The local model is combined with a nonlocal model that involves a small number of energy terms according to a physical force field, and some information on the overall secondary structure content. In this initial study we focus on the formulation of the joint model and the evaluation of the use of an energy vector as a descriptor of a protein's nonlocal structure; hence, we derive the parameters of the nonlocal model from the native structure without loss of generality. The local and nonlocal models are combined using the reference ratio method, which is a well-justified probabilistic construction. For evaluation, we use the resulting joint models to predict the structure of four proteins. The results indicate that the proposed method and the probabilistic models show considerable promise for probabilistic protein structure prediction and related applications.
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Affiliation(s)
- Jan B Valentin
- The Bioinformatics Centre, Department of Biology, University of Copenhagen, Copenhagen, Denmark
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35
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Johansson KE, Hamelryck T. A simple probabilistic model of multibody interactions in proteins. Proteins 2013; 81:1340-50. [DOI: 10.1002/prot.24277] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2012] [Revised: 01/31/2013] [Accepted: 02/18/2013] [Indexed: 11/10/2022]
Affiliation(s)
- Kristoffer Enøe Johansson
- Section for Biomolecular Sciences; Department of Biology, University of Copenhagen; Ole Maal⊘es Vej 5, DK-2200 Copenhagen N Denmark
| | - Thomas Hamelryck
- Section for Computational and RNA biology; Department of Biology, University of Copenhagen; Room 1.2.22, Ole Maal⊘es Vej 5 DK-2200 Copenhagen N Denmark
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