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Kneller DW, Gerlits O, Daemen LL, Pavlova A, Gumbart JC, Cheng Y, Kovalevsky A. Joint neutron/molecular dynamics vibrational spectroscopy reveals softening of HIV-1 protease upon binding of a tight inhibitor. Phys Chem Chem Phys 2022; 24:3586-3597. [PMID: 35089990 PMCID: PMC8940534 DOI: 10.1039/d1cp05487b] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
Biomacromolecules are inherently dynamic, and their dynamics are interwoven into function. The fast collective vibrational dynamics in proteins occurs in the low picosecond timescale corresponding to frequencies of ∼5-50 cm-1. This sub-to-low THz frequency regime covers the low-amplitude collective breathing motions of a whole protein and vibrations of the constituent secondary structure elements, such as α-helices, β-sheets and loops. We have used inelastic neutron scattering experiments in combination with molecular dynamics simulations to demonstrate the vibrational dynamics softening of HIV-1 protease, a target of HIV/AIDS antivirals, upon binding of a tight clinical inhibitor darunavir. Changes in the vibrational density of states of matching structural elements in the two monomers of the homodimeric protein are not identical, indicating asymmetric effects of darunavir on the vibrational dynamics. Three of the 11 major secondary structure elements contribute over 40% to the overall changes in the vibrational density of states upon darunavir binding. Molecular dynamics simulations informed by experiments allowed us to estimate that the altered vibrational dynamics of the protease would contribute -3.6 kcal mol-1 at 300 K, or 25%, to the free energy of darunavir binding. As HIV-1 protease drug resistance remains a concern, our results open a new avenue to help establish a direct quantitative link between protein vibrational dynamics and drug resistance.
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Affiliation(s)
- Daniel W. Kneller
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, U.S.A
| | - Oksana Gerlits
- Department of Natural Sciences, Tennessee Wesleyan University, Athens, TN 37303, U.S.A
| | - Luke L. Daemen
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, U.S.A
| | - Anna Pavlova
- School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, U.S.A
| | - James C. Gumbart
- School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, U.S.A
| | - Yongqiang Cheng
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA.
| | - Andrey Kovalevsky
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA.
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2
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Liao X, Purohit PK. Kinetics of self-assembly of inclusions due to lipid membrane thickness interactions. SOFT MATTER 2021; 17:2539-2556. [PMID: 33511382 DOI: 10.1039/d0sm01752c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Self-assembly of proteins on lipid membranes underlies many important processes in cell biology, such as, exo- and endo-cytosis, assembly of viruses, etc. An attractive force that can cause self-assembly is mediated by membrane thickness interactions between proteins. The free energy profile associated with this attractive force is a result of the overlap of thickness deformation fields around the proteins which can be calculated from the solution of a boundary value problem. Yet, the time scales over which two inclusions coalesce has not been explored, even though the evolution of particle concentrations on membranes has been modeled using phase-field approaches. In this paper we compute this time scale as a function of the initial distance between two inclusions by viewing their coalescence as a first passage time problem. The mean first passage time is computed using Langevin dynamics and a partial differential equation, and both methods are found to be in excellent agreement. Inclusions of three different shapes are studied and it is found that for two inclusions separated by about hundred nanometers the time to coalescence is hundreds of milliseconds irrespective of shape. An efficient computation of the interaction energy of inclusions is central to our work. We compute it using a finite difference technique and show that our results are in excellent agreement with those from a previously proposed semi-analytical method based on Fourier-Bessel series. The computational strategies described in this paper could potentially lead to efficient methods to explore the kinetics of self-assembly of proteins on lipid membranes.
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Affiliation(s)
- Xinyu Liao
- Graduate Group in Applied Mathematics and Computational Science, University of Pennsylvania, Philadelphia, PA 19104, USA.
| | - Prashant K Purohit
- Graduate Group in Applied Mathematics and Computational Science, University of Pennsylvania, Philadelphia, PA 19104, USA. and Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, USA
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3
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Stadtländer CTH. Biomembrane simulations: Computational studies of biological membranes. INFORMATICS IN MEDICINE UNLOCKED 2021. [DOI: 10.1016/j.imu.2021.100744] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/09/2023] Open
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Colla T, Bakhshandeh A, Levin Y. Osmotic stress and pore nucleation in charged biological nanoshells and capsids. SOFT MATTER 2020; 16:2390-2405. [PMID: 32067009 DOI: 10.1039/c9sm02532d] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
A model system is proposed to investigate the chemical equilibrium and mechanical stability of biological spherical-like nanoshells in contact with an aqueous solution with added dissociated electrolyte of a given concentration. The ionic chemical equilibrium across the permeable shell is investigated in the framework of an accurate Density Functional Theory (DFT) that incorporates electrostatic and hardcore correlations beyond the traditional mean-field (e.g., Poisson-Boltzmann) limit. The accuracy of the theory is tested by a direct comparison with Monte Carlo (MC) simulations. A simple analytical expression is then deduced which clearly highlights the entropic, electrostatic, and self-energy contributions to the osmotic stress over the shell in terms of the calculated ionic profiles. By invoking a continuum mean-field elastic approach to account for the shell surface stress upon osmotic stretching, the mechanical equilibrium properties of the shell under a wide variety of ionic strengths and surface charges are investigated. The model is further coupled to a continuum mechanical approach similar in structure to a Classical Nucleation Theory (CNT) to address the question of mechanical stability of the shells against a pore nucleation. This allows us to construct a phase diagram which delimits the mechanical stability of capsids for different ionic strengths and shell surface charges.
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Affiliation(s)
- Thiago Colla
- Instituto de Física, Universidade Federal de Ouro Preto, CEP 35400-000, Ouro Preto, MG, Brazil.
| | - Amin Bakhshandeh
- Programa de Pós-Graduação em Física, Instituto de Física e Matemática, Universidade Federal de Pelotas, Caixa Postal 354, CEP 96010-900 Pelotas, RS, Brazil.
| | - Yan Levin
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970, Porto Alegre, RS, Brazil.
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Dharmavaram S, She SB, Lázaro G, Hagan MF, Bruinsma R. Gaussian curvature and the budding kinetics of enveloped viruses. PLoS Comput Biol 2019; 15:e1006602. [PMID: 31433804 PMCID: PMC6736314 DOI: 10.1371/journal.pcbi.1006602] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2018] [Revised: 09/10/2019] [Accepted: 06/20/2019] [Indexed: 02/07/2023] Open
Abstract
The formation of a membrane-enveloped virus starts with the assembly of a curved layer of capsid proteins lining the interior of the plasma membrane (PM) of the host cell. This layer develops into a spherical shell (capsid) enveloped by a lipid-rich membrane. In many cases, the budding process stalls prior to the release of the virus. Recently, Brownian dynamics simulations of a coarse-grained model system reproduced protracted pausing and stalling, which suggests that the origin of pausing/stalling is to be found in the physics of the budding process. Here, we propose that the pausing/stalling observed in the simulations can be understood as a purely kinetic phenomenon associated with the neck geometry. A geometrical potential energy barrier develops during the budding that must be overcome by capsid proteins diffusing along the membrane prior to incorporation into the capsid. The barrier is generated by a conflict between the positive Gauss curvature of the assembling capsid and the negative Gauss curvature of the neck region. A continuum theory description is proposed and is compared with the Brownian simulations of the budding of enveloped viruses. Despite intense study, the life-cycle of the HIV-1 virus continues to pose mysteries. One of these is the fact that the assembly of an HIV-1 virus along the plasma membrane (PM) of the host cell—the budding process—stalls prior to release of the virus. Many other important viral pathogens with a surrounding lipid membrane envelope display similar stalling. Combining numerical and analytical methods, we demonstrate that the neck-like shape of the membrane that forms prior to release of the virus creates a barrier that blocks the proteins required for the assembly process from reaching the budding virus. An improved understanding of the physics of the blocking process could enable new strategies to combat enveloped viruses.
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Affiliation(s)
- Sanjay Dharmavaram
- Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania, United States of America
| | - Selene Baochen She
- Department of Physics and Astronomy, University of California, Los Angeles, Los Angeles, California, United States of America
| | - Guillermo Lázaro
- Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts, United States of America
| | - Michael Francis Hagan
- Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts, United States of America
| | - Robijn Bruinsma
- Department of Physics and Astronomy, University of California, Los Angeles, Los Angeles, California, United States of America
- Department of Chemistry and Biochemistry, University of California, Los Angeles, Los Angeles, California, United States of America
- * E-mail:
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6
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Lázaro GR, Mukhopadhyay S, Hagan MF. Why Enveloped Viruses Need Cores-The Contribution of a Nucleocapsid Core to Viral Budding. Biophys J 2019; 114:619-630. [PMID: 29414708 DOI: 10.1016/j.bpj.2017.11.3782] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2017] [Revised: 11/11/2017] [Accepted: 11/27/2017] [Indexed: 11/17/2022] Open
Abstract
During the lifecycle of many enveloped viruses, a nucleocapsid core buds through the cell membrane to acquire an outer envelope of lipid membrane and viral glycoproteins. However, the presence of a nucleocapsid core is not required for assembly of infectious particles. To determine the role of the nucleocapsid core, we develop a coarse-grained computational model with which we investigate budding dynamics as a function of glycoprotein and nucleocapsid interactions, as well as budding in the absence of a nucleocapsid. We find that there is a transition between glycoprotein-directed budding and nucleocapsid-directed budding that occurs above a threshold strength of nucleocapsid interactions. The simulations predict that glycoprotein-directed budding leads to significantly increased size polydispersity and particle polymorphism. This polydispersity can be explained by a theoretical model accounting for the competition between bending energy of the membrane and the glycoprotein shell. The simulations also show that the geometry of a budding particle leads to a barrier to subunit diffusion, which can result in a stalled, partially budded state. We present a phase diagram for this and other morphologies of budded particles. Comparison of these structures against experiments could establish bounds on whether budding is directed by glycoprotein or nucleocapsid interactions. Although our model is motivated by alphaviruses, we discuss implications of our results for other enveloped viruses.
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Affiliation(s)
- Guillermo R Lázaro
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts
| | | | - Michael F Hagan
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts.
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7
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Prestipino S, Munaò G, Costa D, Caccamo C. Self-assembly in a model colloidal mixture of dimers and spherical particles. J Chem Phys 2018; 146:084902. [PMID: 28249437 DOI: 10.1063/1.4976704] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Abstract
We investigate the structure of a dilute mixture of amphiphilic dimers and spherical particles, a model relevant to the problem of encapsulating globular "guest" molecules in a dispersion. Dimers and spheres are taken to be hard particles, with an additional attraction between spheres and the smaller monomers in a dimer. Using the Monte Carlo simulation, we document the low-temperature formation of aggregates of guests (clusters) held together by dimers, whose typical size and shape depend on the guest concentration χ. For low χ (less than 10%), most guests are isolated and coated with a layer of dimers. As χ progressively increases, clusters grow in size becoming more and more elongated and polydisperse; after reaching a shallow maximum for χ≈50%, the size of clusters again reduces upon increasing χ further. In one case only (χ=50% and moderately low temperature) the mixture relaxed to a fluid of lamellae, suggesting that in this case clusters are metastable with respect to crystal-vapor separation. On heating, clusters shrink until eventually the system becomes homogeneous on all scales. On the other hand, as the mixture is made denser and denser at low temperature, clusters get increasingly larger until a percolating network is formed.
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Affiliation(s)
- Santi Prestipino
- Dipartimento di Scienze Matematiche ed Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy
| | - Gianmarco Munaò
- Dipartimento di Scienze Matematiche ed Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy
| | - Dino Costa
- Dipartimento di Scienze Matematiche ed Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy
| | - Carlo Caccamo
- Dipartimento di Scienze Matematiche ed Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy
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8
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Michaels TCT, Bellaiche MMJ, Hagan MF, Knowles TPJ. Kinetic constraints on self-assembly into closed supramolecular structures. Sci Rep 2017; 7:12295. [PMID: 28947758 PMCID: PMC5613031 DOI: 10.1038/s41598-017-12528-8] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2017] [Accepted: 08/04/2017] [Indexed: 11/09/2022] Open
Abstract
Many biological and synthetic systems exploit self-assembly to generate highly intricate closed supramolecular architectures, ranging from self-assembling cages to viral capsids. The fundamental design principles that control the structural determinants of the resulting assemblies are increasingly well-understood, but much less is known about the kinetics of such assembly phenomena and it remains a key challenge to elucidate how these systems can be engineered to assemble in an efficient manner and avoid kinetic trapping. We show here that simple scaling laws emerge from a set of kinetic equations describing the self-assembly of identical building blocks into closed supramolecular structures and that this scaling behavior provides general rules that determine efficient assembly in these systems. Using this framework, we uncover the existence of a narrow range of parameter space that supports efficient self-assembly and reveal that nature capitalizes on this behavior to direct the reliable assembly of viral capsids on biologically relevant timescales.
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Affiliation(s)
- Thomas C T Michaels
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK.,Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
| | - Mathias M J Bellaiche
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK.,Laboratory of Chemical Physics, National Institute of Digestive and Diabetes and Kidney Diseases, National Institutes of Health, Bethesda, MD, 20892, USA
| | - Michael F Hagan
- Department of Physics, Brandeis University, Waltham, MA, 02454, USA
| | - Tuomas P J Knowles
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK. .,Cavendish Laboratory, Department of Physics, University of Cambridge, J J Thomson Avenue, Cambridge, CB3 1HE, United Kingdom.
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9
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Hagan MF, Zandi R. Recent advances in coarse-grained modeling of virus assembly. Curr Opin Virol 2016; 18:36-43. [PMID: 27016708 DOI: 10.1016/j.coviro.2016.02.012] [Citation(s) in RCA: 75] [Impact Index Per Article: 9.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2016] [Accepted: 02/29/2016] [Indexed: 01/08/2023]
Affiliation(s)
- Michael F Hagan
- Martin Fisher School of Physics, Brandeis University, Waltham, MA 02453, USA.
| | - Roya Zandi
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA.
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10
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Ceratti DR, Obliger A, Jardat M, Rotenberg B, Dahirel V. Stochastic rotation dynamics simulation of electro-osmosis. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1037370] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Davide R. Ceratti
- Sorbonne Universités, UPMC Univ Paris 06, UMR PHENIX , Paris, France
- CNRS, UMR PHENIX , Paris, France
- Collège de France, UMR 7574, Chimie de la Matière Condensée de Paris
| | - Amaël Obliger
- Concrete Sustainability Hub, Department of Civil and Environmental Engineering, and MIT-CNRS Joint Laboratory, Massachusetts Institute of Technology , Cambridge, MA, United States
| | - Marie Jardat
- Sorbonne Universités, UPMC Univ Paris 06, UMR PHENIX , Paris, France
- CNRS, UMR PHENIX , Paris, France
| | - Benjamin Rotenberg
- Sorbonne Universités, UPMC Univ Paris 06, UMR PHENIX , Paris, France
- CNRS, UMR PHENIX , Paris, France
| | - Vincent Dahirel
- Sorbonne Universités, UPMC Univ Paris 06, UMR PHENIX , Paris, France
- CNRS, UMR PHENIX , Paris, France
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11
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Abstract
Viruses are nanoscale entities containing a nucleic acid genome encased in a protein shell called a capsid and in some cases are surrounded by a lipid bilayer membrane. This review summarizes the physics that govern the processes by which capsids assemble within their host cells and in vitro. We describe the thermodynamics and kinetics for the assembly of protein subunits into icosahedral capsid shells and how these are modified in cases in which the capsid assembles around a nucleic acid or on a lipid bilayer. We present experimental and theoretical techniques used to characterize capsid assembly, and we highlight aspects of virus assembly that are likely to receive significant attention in the near future.
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Affiliation(s)
- Jason D Perlmutter
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454;
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12
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Ruiz-Herrero T, Hagan MF. Simulations show that virus assembly and budding are facilitated by membrane microdomains. Biophys J 2015; 108:585-95. [PMID: 25650926 PMCID: PMC4317536 DOI: 10.1016/j.bpj.2014.12.017] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2014] [Revised: 11/25/2014] [Accepted: 12/05/2014] [Indexed: 01/01/2023] Open
Abstract
For many viruses, assembly and budding occur simultaneously during virion formation. Understanding the mechanisms underlying this process could promote biomedical efforts to block viral propagation and enable use of capsids in nanomaterials applications. To this end, we have performed molecular dynamics simulations on a coarse-grained model that describes virus assembly on a fluctuating lipid membrane. Our simulations show that the membrane can promote association of adsorbed subunits through dimensional reduction, but it also introduces thermodynamic and kinetic effects that can inhibit complete assembly. We find several mechanisms by which membrane microdomains, such as lipid rafts, reduce these effects, and thus, enhance assembly. We show how these predicted mechanisms can be experimentally tested. Furthermore, the simulations demonstrate that assembly and budding depend crucially on the system dynamics via multiple timescales related to membrane deformation, protein diffusion, association, and adsorption onto the membrane.
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Affiliation(s)
- Teresa Ruiz-Herrero
- Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, Madrid, España
| | - Michael F Hagan
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts.
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Zhang L, Lua LHL, Middelberg APJ, Sun Y, Connors NK. Biomolecular engineering of virus-like particles aided by computational chemistry methods. Chem Soc Rev 2015; 44:8608-18. [DOI: 10.1039/c5cs00526d] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
Multi-scale investigation of VLP self-assembly aided by computational methods is facilitating the design, redesign, and modification of functionalized VLPs.
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Affiliation(s)
- Lin Zhang
- Department of Biochemical Engineering and Key Laboratory of Systems Bioengineering of the Ministry of Education
- School of Chemical Engineering and Technology
- Tianjin University
- Tianjin 300072, People's Republic of China
| | - Linda H. L. Lua
- Protein Expression Facility
- The University of Queensland
- Brisbane, Australia
| | - Anton P. J. Middelberg
- Australian Institute for Bioengineering and Nanotechnology
- The University of Queensland
- Brisbane, Australia
| | - Yan Sun
- Department of Biochemical Engineering and Key Laboratory of Systems Bioengineering of the Ministry of Education
- School of Chemical Engineering and Technology
- Tianjin University
- Tianjin 300072, People's Republic of China
| | - Natalie K. Connors
- Australian Institute for Bioengineering and Nanotechnology
- The University of Queensland
- Brisbane, Australia
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