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Tworek JW, Elcock AH. Orientationally Averaged Version of the Rotne-Prager-Yamakawa Tensor Provides a Fast but Still Accurate Treatment of Hydrodynamic Interactions in Brownian Dynamics Simulations of Biological Macromolecules. J Chem Theory Comput 2023; 19:5099-5111. [PMID: 37409946 PMCID: PMC10413861 DOI: 10.1021/acs.jctc.3c00476] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2023] [Indexed: 07/07/2023]
Abstract
The Brownian dynamics (BD) simulation technique is widely used to model the diffusive and conformational dynamics of complex systems comprising biological macromolecules. For the diffusive properties of macromolecules to be described correctly by BD simulations, it is necessary to include hydrodynamic interactions (HIs). When modeled at the Rotne-Prager-Yamakawa (RPY) level of theory, for example, the translational and rotational diffusion coefficients of isolated macromolecules can be accurately reproduced; when HIs are neglected, however, diffusion coefficients can be underestimated by an order of magnitude or more. The principal drawback to the inclusion of HIs in BD simulations is their computational expense, and several previous studies have sought to accelerate their modeling by developing fast approximations for the calculation of the correlated random displacements. Here, we explore the use of an alternative way to accelerate the calculation of HIs, i.e., by replacing the full RPY tensor with an orientationally averaged (OA) version which retains the distance dependence of the HIs but averages out their orientational dependence. We seek here to determine whether such an approximation can be justified in application to the modeling of typical proteins and RNAs. We show that the use of an OA-RPY tensor allows translational diffusion of macromolecules to be modeled with very high accuracy at the cost of rotational diffusion being underestimated by ∼25%. We show that this finding is independent of the type of macromolecule simulated and the level of structural resolution employed in the models. We also show, however, that these results are critically dependent on the inclusion of a non-zero term that describes the divergence of the diffusion tensor: when this term is omitted from simulations that use the OA-RPY model, unfolded macromolecules undergo rapid collapse. Our results indicate that the orientationally averaged RPY tensor is likely to be a useful, fast, approximate way of including HIs in BD simulations of intermediate-scale systems.
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Affiliation(s)
- John W. Tworek
- Department of Biochemistry
& Molecular Biology, University of Iowa, Iowa City, Iowa 52242, United States
| | - Adrian H. Elcock
- Department of Biochemistry
& Molecular Biology, University of Iowa, Iowa City, Iowa 52242, United States
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Fischer J, Radulescu A, Falus P, Richter D, Biehl R. Structure and Dynamics of Ribonuclease A during Thermal Unfolding: The Failure of the Zimm Model. J Phys Chem B 2021; 125:780-788. [PMID: 33470118 DOI: 10.1021/acs.jpcb.0c09476] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Disordered regions as found in intrinsically disordered proteins (IDP) or during protein folding define response time to stimuli and protein folding times. Neutron spin-echo spectroscopy is a powerful tool to directly access the collective motions of the unfolded chain to enlighten the physical origin of basic conformational relaxation. During the thermal unfolding of native ribonuclease A, we examine the structure and dynamics of the disordered state within a two-state transition model using polymer models, including internal friction, to describe the chain dynamics. The presence of four disulfide bonds alters the disordered configuration to a more compact configuration compared to a Gaussian chain that is defined by the additional links, as demonstrated by coarse-grained simulation. The dynamics of the disordered chain is described by Zimm dynamics with internal friction (ZIF) between neighboring amino acids. Relaxation times are dominated by mode-independent internal friction. Internal friction relaxation times show an Arrhenius-like behavior with an activation energy of 33 kJ/mol. The Zimm dynamics is dominated by internal friction and suggest that the characteristic motions correspond to overdamped elastic modes similar to the motions observed for folded proteins but within a pool of disordered configurations spanning the configurational space. For IDP, internal friction dominates while solvent friction and hydrodynamic interactions are smaller corrections.
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Affiliation(s)
- Jennifer Fischer
- Jülich Centre for Neutron Science (JCNS-1) and Institute of Biological Information Processing (IBI-8), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
| | - Aurel Radulescu
- Jülich Centre for Neutron Science JCNS at Heinz Maier-Leibnitz Zentrum (MLZ), Forschungszentrum Jülich, 85748 Garching, Germany
| | - Peter Falus
- Institut Laue-Langevin (ILL), 71 rue des Martyrs, 38042 Grenoble, Cedex 9, France
| | - Dieter Richter
- Jülich Centre for Neutron Science (JCNS-1) and Institute of Biological Information Processing (IBI-8), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
| | - Ralf Biehl
- Jülich Centre for Neutron Science (JCNS-1) and Institute of Biological Information Processing (IBI-8), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
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García de la Torre J, Hernández Cifre J. Hydrodynamic Properties of Biomacromolecules and Macromolecular Complexes: Concepts and Methods. A Tutorial Mini-review. J Mol Biol 2020; 432:2930-2948. [DOI: 10.1016/j.jmb.2019.12.027] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2019] [Revised: 11/30/2019] [Accepted: 12/13/2019] [Indexed: 01/08/2023]
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Structural studies of RNA-protein complexes: A hybrid approach involving hydrodynamics, scattering, and computational methods. Methods 2016; 118-119:146-162. [PMID: 27939506 DOI: 10.1016/j.ymeth.2016.12.002] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2016] [Revised: 12/01/2016] [Accepted: 12/05/2016] [Indexed: 01/01/2023] Open
Abstract
The diverse functional cellular roles played by ribonucleic acids (RNA) have emphasized the need to develop rapid and accurate methodologies to elucidate the relationship between the structure and function of RNA. Structural biology tools such as X-ray crystallography and Nuclear Magnetic Resonance are highly useful methods to obtain atomic-level resolution models of macromolecules. However, both methods have sample, time, and technical limitations that prevent their application to a number of macromolecules of interest. An emerging alternative to high-resolution structural techniques is to employ a hybrid approach that combines low-resolution shape information about macromolecules and their complexes from experimental hydrodynamic (e.g. analytical ultracentrifugation) and solution scattering measurements (e.g., solution X-ray or neutron scattering), with computational modeling to obtain atomic-level models. While promising, scattering methods rely on aggregation-free, monodispersed preparations and therefore the careful development of a quality control pipeline is fundamental to an unbiased and reliable structural determination. This review article describes hydrodynamic techniques that are highly valuable for homogeneity studies, scattering techniques useful to study the low-resolution shape, and strategies for computational modeling to obtain high-resolution 3D structural models of RNAs, proteins, and RNA-protein complexes.
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Abstract
Understanding protein-inorganic surface interactions is central to the rational design of new tools in biomaterial sciences, nanobiotechnology and nanomedicine. Although a significant amount of experimental research on protein adsorption onto solid substrates has been reported, many aspects of the recognition and interaction mechanisms of biomolecules and inorganic surfaces are still unclear. Theoretical modeling and simulations provide complementary approaches for experimental studies, and they have been applied for exploring protein-surface binding mechanisms, the determinants of binding specificity towards different surfaces, as well as the thermodynamics and kinetics of adsorption. Although the general computational approaches employed to study the dynamics of proteins and materials are similar, the models and force-fields (FFs) used for describing the physical properties and interactions of material surfaces and biological molecules differ. In particular, FF and water models designed for use in biomolecular simulations are often not directly transferable to surface simulations and vice versa. The adsorption events span a wide range of time- and length-scales that vary from nanoseconds to days, and from nanometers to micrometers, respectively, rendering the use of multi-scale approaches unavoidable. Further, changes in the atomic structure of material surfaces that can lead to surface reconstruction, and in the structure of proteins that can result in complete denaturation of the adsorbed molecules, can create many intermediate structural and energetic states that complicate sampling. In this review, we address the challenges posed to theoretical and computational methods in achieving accurate descriptions of the physical, chemical and mechanical properties of protein-surface systems. In this context, we discuss the applicability of different modeling and simulation techniques ranging from quantum mechanics through all-atom molecular mechanics to coarse-grained approaches. We examine uses of different sampling methods, as well as free energy calculations. Furthermore, we review computational studies of protein-surface interactions and discuss the successes and limitations of current approaches.
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Ramakrishnan SK, Zhu J, Gergely C. Organic-inorganic interface simulation for new material discoveries. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2016. [DOI: 10.1002/wcms.1277] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Sathish Kumar Ramakrishnan
- Nanobiology Institute; Yale University; West Haven CT USA
- Laboratoire Charles Coulomb (L2C); UMR 5221 CNRS-Université de Montpellier; Montpellier France
| | - Jie Zhu
- Nanobiology Institute; Yale University; West Haven CT USA
| | - Csilla Gergely
- Laboratoire Charles Coulomb (L2C); UMR 5221 CNRS-Université de Montpellier; Montpellier France
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Benítez AA, Hernández Cifre JG, Díaz Baños FG, de la Torre JG. Prediction of solution properties and dynamics of RNAs by means of Brownian dynamics simulation of coarse-grained models: Ribosomal 5S RNA and phenylalanine transfer RNA. BMC BIOPHYSICS 2015; 8:11. [PMID: 26629336 PMCID: PMC4666080 DOI: 10.1186/s13628-015-0025-7] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/22/2015] [Accepted: 11/18/2015] [Indexed: 12/02/2022]
Abstract
Background The possibility of validating biological macromolecules with locally disordered domains like RNA against solution properties is helpful to understand their function. In this work, we present a computational scheme for predicting global properties and mimicking the internal dynamics of RNA molecules in solution. A simple coarse-grained model with one bead per nucleotide and two types of intra-molecular interactions (elastic interactions and excluded volume interactions) is used to represent the RNA chain. The elastic interactions are modeled by a set of Hooke springs that form a minimalist elastic network. The Brownian dynamics technique is employed to simulate the time evolution of the RNA conformations. Results That scheme is applied to the 5S ribosomal RNA of E. Coli and the yeast phenylalanine transfer RNA. From the Brownian trajectory, several solution properties (radius of gyration, translational diffusion coefficient, and a rotational relaxation time) are calculated. For the case of yeast phenylalanine transfer RNA, the time evolution and the probability distribution of the inter-arm angle is also computed. Conclusions The general good agreement between our results and some experimental data indicates that the model is able to capture the tertiary structure of RNA in solution. Our simulation results also compare quite well with other numerical data. An advantage of the scheme described here is the possibility of visualizing the real time macromolecular dynamics. Electronic supplementary material The online version of this article (doi:10.1186/s13628-015-0025-7) contains supplementary material, which is available to authorized users.
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Abstract
The hydrodynamic parameters measured in an AUC experiment, s(20,w) and D(t)(20,w)(0), can be used to gain information on the solution structure of (bio)macromolecules and their assemblies. This entails comparing the measured parameters with those that can be computed from usually "dry" structures by "hydrodynamic modeling." In this chapter, we will first briefly put hydrodynamic modeling in perspective and present the basic physics behind it as implemented in the most commonly used methods. The important "hydration" issue is also touched upon, and the distinction between rigid bodies versus those for which flexibility must be considered in the modeling process is then made. The available hydrodynamic modeling/computation programs, HYDROPRO, BEST, SoMo, AtoB, and Zeno, the latter four all implemented within the US-SOMO suite, are described and their performance evaluated. Finally, some literature examples are presented to illustrate the potential applications of hydrodynamics in the expanding field of multiresolution modeling.
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Affiliation(s)
- Mattia Rocco
- Biopolimeri e Proteomica, IRCCS AOU San Martino-IST, Istituto Nazionale per la Ricerca sul Cancro, Genova, Italy.
| | - Olwyn Byron
- School of Life Sciences, College of Medical, Veterinary and Life Sciences, University of Glasgow, Glasgow, G12 8QQ, Scotland, United Kingdom.
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Długosz M, Antosiewicz JM. Toward an Accurate Modeling of Hydrodynamic Effects on the Translational and Rotational Dynamics of Biomolecules in Many-Body Systems. J Phys Chem B 2015; 119:8425-39. [PMID: 26068580 DOI: 10.1021/acs.jpcb.5b04675] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Proper treatment of hydrodynamic interactions is of importance in evaluation of rigid-body mobility tensors of biomolecules in Stokes flow and in simulations of their folding and solution conformation, as well as in simulations of the translational and rotational dynamics of either flexible or rigid molecules in biological systems at low Reynolds numbers. With macromolecules conveniently modeled in calculations or in dynamic simulations as ensembles of spherical frictional elements, various approximations to hydrodynamic interactions, such as the two-body, far-field Rotne-Prager approach, are commonly used, either without concern or as a compromise between the accuracy and the numerical complexity. Strikingly, even though the analytical Rotne-Prager approach fails to describe (both in the qualitative and quantitative sense) mobilities in the simplest system consisting of two spheres, when the distance between their surfaces is of the order of their size, it is commonly applied to model hydrodynamic effects in macromolecular systems. Here, we closely investigate hydrodynamic effects in two and three-body systems, consisting of bead-shell molecular models, using either the analytical Rotne-Prager approach, or an accurate numerical scheme that correctly accounts for the many-body character of hydrodynamic interactions and their short-range behavior. We analyze mobilities, and translational and rotational velocities of bodies resulting from direct forces acting on them. We show, that with the sufficient number of frictional elements in hydrodynamic models of interacting bodies, the far-field approximation is able to provide a description of hydrodynamic effects that is in a reasonable qualitative as well as quantitative agreement with the description resulting from the application of the virtually exact numerical scheme, even for small separations between bodies.
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Affiliation(s)
- Maciej Długosz
- †Centre of New Technologies, University of Warsaw, Stefana Banacha 2c, Warsaw 02-097, Poland
| | - Jan M Antosiewicz
- ‡Department of Biophysics, Faculty of Physics, University of Warsaw, Zwirki i Wigury 93, Warsaw 02-089, Poland
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Ionic strength effect in polyelectrolyte dilute solutions within the Debye–Hückel approximation: Monte Carlo and Brownian dynamics simulations. Polym Bull (Berl) 2014. [DOI: 10.1007/s00289-014-1186-2] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Amorós D, Ortega A, García de la Torre J. Prediction of Hydrodynamic and Other Solution Properties of Partially Disordered Proteins with a Simple, Coarse-Grained Model. J Chem Theory Comput 2013; 9:1678-85. [DOI: 10.1021/ct300948u] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- D. Amorós
- Departamento de Química Física,
Facultad
de Química, Universidad de Murcia, 30071 Murcia, Spain
| | - A. Ortega
- Departamento de Química Física,
Facultad
de Química, Universidad de Murcia, 30071 Murcia, Spain
| | - J. García de la Torre
- Departamento de Química Física,
Facultad
de Química, Universidad de Murcia, 30071 Murcia, Spain
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12
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Długosz M, Zieliński P, Trylska J. Brownian dynamics simulations on CPU and GPU with BD_BOX. J Comput Chem 2011; 32:2734-44. [PMID: 21638295 DOI: 10.1002/jcc.21847] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2011] [Revised: 04/27/2011] [Accepted: 04/30/2011] [Indexed: 11/07/2022]
Abstract
There has been growing interest in simulating biological processes under in vivo conditions due to recent advances in experimental techniques dedicated to study single particle behavior in crowded environments. We have developed a software package, BD_BOX, for multiscale Brownian dynamics simulations. BD_BOX can simulate either single molecules or multicomponent systems of diverse, interacting molecular species using flexible, coarse-grained bead models. BD_BOX is written in C and employs modern computer architectures and technologies; these include MPI for distributed-memory architectures, OpenMP for shared-memory platforms, NVIDIA CUDA framework for GPGPU, and SSE vectorization for CPU.
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Affiliation(s)
- Maciej Długosz
- Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw, Warsaw, Poland.
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Mereghetti P, Kokh D, McCammon JA, Wade RC. Diffusion and association processes in biological systems: theory, computation and experiment. BMC BIOPHYSICS 2011; 4:2. [PMID: 21595997 PMCID: PMC3093674 DOI: 10.1186/2046-1682-4-2] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 02/17/2011] [Accepted: 03/02/2011] [Indexed: 12/17/2022]
Abstract
Macromolecular diffusion plays a fundamental role in biological processes. Here, we give an overview of recent methodological advances and some of the challenges for understanding how molecular diffusional properties influence biological function that were highlighted at a recent workshop, BDBDB2, the second Biological Diffusion and Brownian Dynamics Brainstorm.
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Affiliation(s)
- Paolo Mereghetti
- Heidelberg Institute for Theoretical Studies (HITS) gGmbH, Schloss-Wolfsbrunnenweg 35, 69118 Heidelberg, Germany.
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Brookes E, Demeler B, Rocco M. Developments in the US-SOMO bead modeling suite: new features in the direct residue-to-bead method, improved grid routines, and influence of accessible surface area screening. Macromol Biosci 2010; 10:746-53. [PMID: 20480513 DOI: 10.1002/mabi.200900474] [Citation(s) in RCA: 46] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
The US-SOMO suite provides a flexible interface for accurately computing solution parameters from 3D structures of biomacromolecules through bead-modeling approaches. We present an extended analysis of the influence of accessible surface area screening, overlap reduction routines, and approximations for non-coded residues and missing atoms on the computed parameters for models built by the residue-to-bead direct correspondence and the cubic grid methods. Importantly, by taking the theoretical hydration into account at the atomic level, the performance of the grid-type models becomes comparable or exceeds that of the corresponding hydrated residue-to-bead models.
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Affiliation(s)
- Emre Brookes
- Department of Biochemistry, The University of Texas Health Science Center at San Antonio, San Antonio, Texas, TX 78229, USA
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de la Torre JG, Ortega Á, Amorós D, Schmidt RR, Cifre JGH. Methods and Tools for the Prediction of Hydrodynamic Coefficients and Other Solution Properties of Flexible Macromolecules in Solution. A Tutorial Minireview. Macromol Biosci 2010; 10:721-30. [DOI: 10.1002/mabi.200900464] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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