1
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O'Donnell T, Cazals F. Enhanced conformational exploration of protein loops using a global parameterization of the backbone geometry. J Comput Chem 2023; 44:1094-1104. [PMID: 36733189 DOI: 10.1002/jcc.27067] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2022] [Accepted: 12/22/2022] [Indexed: 02/04/2023]
Abstract
Flexible loops are paramount to protein functions, with action modes ranging from localized dynamics contributing to the free energy of the system, to large amplitude conformational changes accounting for the repositioning whole secondary structure elements or protein domains. However, generating diverse and low energy loops remains a difficult problem. This work introduces a novel paradigm to sample loop conformations, in the spirit of the hit-and-run (HAR) Markov chain Monte Carlo technique. The algorithm uses a decomposition of the loop into tripeptides, and a novel characterization of necessary conditions for Tripeptide Loop Closure to admit solutions. Denoting m the number of tripeptides, the algorithm works in an angular space of dimension 12 m. In this space, the hyper-surfaces associated with the aforementioned necessary conditions are used to run a HAR-like sampling technique. On classical loop cases up to 15 amino acids, our parameter free method compares favorably to previous work, generating more diverse conformational ensembles. We also report experiments on a 30 amino acids long loop, a size not processed in any previous work.
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Affiliation(s)
- Timothée O'Donnell
- Algorithms-Biology-Structure, Centre Inria at Université Côte d'Azur, Sophia Antipolis, France
| | - Frédéric Cazals
- Algorithms-Biology-Structure, Centre Inria at Université Côte d'Azur, Sophia Antipolis, France
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2
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Li Y, Mohanty S, Nilsson D, Hansson B, Mao K, Irbäck A. When a foreign gene meets its native counterpart: computational biophysics analysis of two PgiC loci in the grass Festuca ovina. Sci Rep 2020; 10:18752. [PMID: 33127989 PMCID: PMC7599235 DOI: 10.1038/s41598-020-75650-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2020] [Accepted: 10/16/2020] [Indexed: 11/14/2022] Open
Abstract
Duplicative horizontal gene transfer may bring two previously separated homologous genes together, which may raise questions about the interplay between the gene products. One such gene pair is the “native” PgiC1 and “foreign” PgiC2 in the perennial grass Festuca ovina. Both PgiC1 and PgiC2 encode cytosolic phosphoglucose isomerase, a dimeric enzyme whose proper binding is functionally essential. Here, we use biophysical simulations to explore the inter-monomer binding of the two homodimers and the heterodimer that can be produced by PgiC1 and PgiC2 in F. ovina. Using simulated native-state ensembles, we examine the structural properties and binding tightness of the dimers. In addition, we investigate their ability to withstand dissociation when pulled by a force. Our results suggest that the inter-monomer binding is tighter in the PgiC2 than the PgiC1 homodimer, which could explain the more frequent occurrence of the foreign PgiC2 homodimer in dry habitats. We further find that the PgiC1 and PgiC2 monomers are compatible with heterodimer formation; the computed binding tightness is comparable to that of the PgiC1 homodimer. Enhanced homodimer stability and capability of heterodimer formation with PgiC1 are properties of PgiC2 that may contribute to the retaining of the otherwise redundant PgiC2 gene.
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Affiliation(s)
- Yuan Li
- Computational Biology and Biological Physics, Department of Astronomy and Theoretical Physics, Lund University, 223 62, Lund, Sweden
| | - Sandipan Mohanty
- Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich, 52425, Jülich, Germany
| | - Daniel Nilsson
- Computational Biology and Biological Physics, Department of Astronomy and Theoretical Physics, Lund University, 223 62, Lund, Sweden
| | - Bengt Hansson
- Department of Biology, Lund University, 223 62, Lund, Sweden
| | - Kangshan Mao
- Key Laboratory of Bio-Resource and Eco-Environment of Ministry of Education, College of Life Sciences, State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu, 610065, China
| | - Anders Irbäck
- Computational Biology and Biological Physics, Department of Astronomy and Theoretical Physics, Lund University, 223 62, Lund, Sweden.
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3
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Sorzano COS, Jiménez A, Mota J, Vilas JL, Maluenda D, Martínez M, Ramírez-Aportela E, Majtner T, Segura J, Sánchez-García R, Rancel Y, del Caño L, Conesa P, Melero R, Jonic S, Vargas J, Cazals F, Freyberg Z, Krieger J, Bahar I, Marabini R, Carazo JM. Survey of the analysis of continuous conformational variability of biological macromolecules by electron microscopy. Acta Crystallogr F Struct Biol Commun 2019; 75:19-32. [PMID: 30605122 PMCID: PMC6317454 DOI: 10.1107/s2053230x18015108] [Citation(s) in RCA: 38] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2018] [Accepted: 10/26/2018] [Indexed: 11/10/2022] Open
Abstract
Single-particle analysis by electron microscopy is a well established technique for analyzing the three-dimensional structures of biological macromolecules. Besides its ability to produce high-resolution structures, it also provides insights into the dynamic behavior of the structures by elucidating their conformational variability. Here, the different image-processing methods currently available to study continuous conformational changes are reviewed.
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Affiliation(s)
| | - A. Jiménez
- National Center of Biotechnology (CSIC), Spain
| | - J. Mota
- National Center of Biotechnology (CSIC), Spain
| | - J. L. Vilas
- National Center of Biotechnology (CSIC), Spain
| | - D. Maluenda
- National Center of Biotechnology (CSIC), Spain
| | - M. Martínez
- National Center of Biotechnology (CSIC), Spain
| | | | - T. Majtner
- National Center of Biotechnology (CSIC), Spain
| | - J. Segura
- National Center of Biotechnology (CSIC), Spain
| | | | - Y. Rancel
- National Center of Biotechnology (CSIC), Spain
| | - L. del Caño
- National Center of Biotechnology (CSIC), Spain
| | - P. Conesa
- National Center of Biotechnology (CSIC), Spain
| | - R. Melero
- National Center of Biotechnology (CSIC), Spain
| | - S. Jonic
- Sorbonne Université, UMR CNRS 7590, Muséum National d’Histoire Naturelle, IRD, Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, IMPMC, Paris, France
| | | | - F. Cazals
- Inria Sophia Antipolis – Méditerranée, France
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4
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Tubiana L, Jurásek M, Coluzza I. Implementing efficient concerted rotations using Mathematica and C code ⋆. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2018; 41:87. [PMID: 30022359 DOI: 10.1140/epje/i2018-11694-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2018] [Accepted: 06/28/2018] [Indexed: 06/08/2023]
Abstract
In this article we demonstrate a general and efficient metaprogramming implementation of concerted rotations using Mathematica. Concerted rotations allow the movement of a fixed portion of a polymer backbone with fixed bending angles, like a protein, while maintaining the correct geometry of the backbone and the initial and final points of the portion fixed. Our implementation uses Mathematica to generate a C code which is then wrapped in a library by a Python script. The user can modify the Mathematica notebook to generate a set of concerted rotations suited for a particular backbone geometry, without having to write the C code himself. The resulting code is highly optimized, performing on the order of thousands of operations per second.
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Affiliation(s)
- Luca Tubiana
- Computational Physics Department, University of Vienna, Sensengasse 8/10, 1090, Vienna, Austria.
| | - Miroslav Jurásek
- Faculty of Science, Masaryk University, Kotlářská 2, 602 00, Brno, Czech Republic
- CEITEC - Central European Institute of Technology, Kamenice 5, 625 00, Brno, Czech Republic
| | - Ivan Coluzza
- CIC biomaGUNE Parque Cientfico y Tecnolgico de Gipuzkoa, Paseo Miramn 182, 20014, Donostia / San Sebastin, Gipuzkoa, Spain
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5
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Denarie L, Al-Bluwi I, Vaisset M, Siméon T, Cortés J. Segmenting Proteins into Tripeptides to Enhance Conformational Sampling with Monte Carlo Methods. Molecules 2018; 23:molecules23020373. [PMID: 29425162 PMCID: PMC6017905 DOI: 10.3390/molecules23020373] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2017] [Accepted: 02/01/2018] [Indexed: 12/02/2022] Open
Abstract
This paper presents an approach to enhance conformational sampling of proteins employing stochastic algorithms such as Monte Carlo (MC) methods. The approach is based on a mechanistic representation of proteins and on the application of methods originating from robotics. We outline the general ideas of our approach and detail how it can be applied to construct several MC move classes, all operating on a shared representation of the molecule and using a single mathematical solver. We showcase these sampling techniques on several types of proteins. Results show that combining several move classes, which can be easily implemented thanks to the proposed approach, significantly improves sampling efficiency.
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Affiliation(s)
- Laurent Denarie
- LAAS-CNRS, Université de Toulouse, CNRS, 31400 Toulouse, France.
| | - Ibrahim Al-Bluwi
- LAAS-CNRS, Université de Toulouse, CNRS, 31400 Toulouse, France.
| | - Marc Vaisset
- LAAS-CNRS, Université de Toulouse, CNRS, 31400 Toulouse, France.
| | - Thierry Siméon
- LAAS-CNRS, Université de Toulouse, CNRS, 31400 Toulouse, France.
| | - Juan Cortés
- LAAS-CNRS, Université de Toulouse, CNRS, 31400 Toulouse, France.
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6
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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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7
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Olsson S, Noé F. Mechanistic Models of Chemical Exchange Induced Relaxation in Protein NMR. J Am Chem Soc 2016; 139:200-210. [DOI: 10.1021/jacs.6b09460] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Affiliation(s)
- Simon Olsson
- Computational Molecular
Biology,
FB Mathematik und Informatik, Freie Universität Berlin, Berlin 14195, Germany
| | - Frank Noé
- Computational Molecular
Biology,
FB Mathematik und Informatik, Freie Universität Berlin, Berlin 14195, Germany
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8
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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: 6] [Impact Index Per Article: 0.8] [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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9
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Abstract
Loops undergoing thermal fluctuations are prevalent in nature. Ringlike or cross-linked polymers, cyclic macromolecules, and protein-mediated DNA loops all belong to this category. Stability of these molecules are generally described in terms of free energy, an average quantity, but it may also be impacted by local fluctuating forces acting within these systems. The full distribution of these forces can thus give us insights into mechanochemistry beyond the predictive capability of thermodynamics. In this paper, we study the force exerted by an inextensible semiflexible polymer constrained in a looped state. By using a simulation method termed "phase-space sampling," we generate the equilibrium distribution of chain conformations in both position and momentum space. We compute the constraint forces between the two ends of the loop in this chain ensemble using Lagrangian mechanics, and show that the mean of these forces is equal to the thermodynamic force. By analyzing kinetic and potential contributions to the forces, we find that the mean force acts in the direction of increasing extension not because of bending stress, but in spite of it. Furthermore, we obtain a distribution of constraint forces as a function of chain length, extension, and stiffness. Notably, increasing contour length decreases the average force, but the additional freedom allows fluctuations in the constraint force to increase. The force distribution is asymmetric and falls off less sharply than a Gaussian distribution. Our work exemplifies a system where large-amplitude fluctuations occur in a way unforeseen by a purely thermodynamic framework, and offers computational tools useful for efficient, unbiased simulation of a constrained system.
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Affiliation(s)
- James T Waters
- School of Physics, Georgia Institute of Technology, 837 State Street, Atlanta, Georgia 30332-0430, USA
| | - Harold D Kim
- School of Physics, Georgia Institute of Technology, 837 State Street, Atlanta, Georgia 30332-0430, USA
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10
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Perez A, MacCallum JL, Coutsias EA, Dill KA. Constraint methods that accelerate free-energy simulations of biomolecules. J Chem Phys 2015; 143:243143. [PMID: 26723628 PMCID: PMC4684272 DOI: 10.1063/1.4936911] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2015] [Accepted: 11/18/2015] [Indexed: 01/07/2023] Open
Abstract
Atomistic molecular dynamics simulations of biomolecules are critical for generating narratives about biological mechanisms. The power of atomistic simulations is that these are physics-based methods that satisfy Boltzmann's law, so they can be used to compute populations, dynamics, and mechanisms. But physical simulations are computationally intensive and do not scale well to the sizes of many important biomolecules. One way to speed up physical simulations is by coarse-graining the potential function. Another way is to harness structural knowledge, often by imposing spring-like restraints. But harnessing external knowledge in physical simulations is problematic because knowledge, data, or hunches have errors, noise, and combinatoric uncertainties. Here, we review recent principled methods for imposing restraints to speed up physics-based molecular simulations that promise to scale to larger biomolecules and motions.
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Affiliation(s)
- Alberto Perez
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York 11794, USA
| | - Justin L MacCallum
- Department of Chemistry, University of Calgary, Calgary, Alberta T2N 1N4, Canada
| | - Evangelos A Coutsias
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York 11794, USA
| | - Ken A Dill
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York 11794, USA
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11
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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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12
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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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13
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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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14
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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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15
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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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16
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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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17
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Irbäck A, Mohanty S. All-Atom Monte Carlo Simulations of Protein Folding and Aggregation. COMPUTATIONAL METHODS TO STUDY THE STRUCTURE AND DYNAMICS OF BIOMOLECULES AND BIOMOLECULAR PROCESSES 2014. [DOI: 10.1007/978-3-642-28554-7_13] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
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18
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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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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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20
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Boomsma W, Frellsen J, Harder T, Bottaro S, Johansson KE, Tian P, Stovgaard K, Andreetta C, Olsson S, Valentin JB, Antonov LD, Christensen AS, Borg M, Jensen JH, Lindorff-Larsen K, Ferkinghoff-Borg J, Hamelryck T. PHAISTOS: a framework for Markov chain Monte Carlo simulation and inference of protein structure. J Comput Chem 2013; 34:1697-705. [PMID: 23619610 DOI: 10.1002/jcc.23292] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2012] [Revised: 03/14/2013] [Accepted: 03/20/2013] [Indexed: 11/10/2022]
Abstract
We present a new software framework for Markov chain Monte Carlo sampling for simulation, prediction, and inference of protein structure. The software package contains implementations of recent advances in Monte Carlo methodology, such as efficient local updates and sampling from probabilistic models of local protein structure. These models form a probabilistic alternative to the widely used fragment and rotamer libraries. Combined with an easily extendible software architecture, this makes PHAISTOS well suited for Bayesian inference of protein structure from sequence and/or experimental data. Currently, two force-fields are available within the framework: PROFASI and OPLS-AA/L, the latter including the generalized Born surface area solvent model. A flexible command-line and configuration-file interface allows users quickly to set up simulations with the desired configuration. PHAISTOS is released under the GNU General Public License v3.0. Source code and documentation are freely available from http://phaistos.sourceforge.net. The software is implemented in C++ and has been tested on Linux and OSX platforms.
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Affiliation(s)
- Wouter Boomsma
- Department of Biology, University of Copenhagen, Copenhagen, 2200, Denmark
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21
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Harder T, Borg M, Bottaro S, Boomsma W, Olsson S, Ferkinghoff-Borg J, Hamelryck T. An Efficient Null Model for Conformational Fluctuations in Proteins. Structure 2012; 20:1028-39. [DOI: 10.1016/j.str.2012.03.020] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2011] [Revised: 03/08/2012] [Accepted: 03/12/2012] [Indexed: 10/28/2022]
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