1
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Su R, Wang S, McDargh Z, O'Shaughnessy B. Three membrane fusion pore families determine the pathway to pore dilation. Biophys J 2023; 122:3986-3998. [PMID: 37644721 PMCID: PMC10560699 DOI: 10.1016/j.bpj.2023.08.021] [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: 12/20/2022] [Revised: 06/19/2023] [Accepted: 08/25/2023] [Indexed: 08/31/2023] Open
Abstract
During exocytosis secretory vesicles fuse with a target membrane and release neurotransmitters, hormones, or other bioactive molecules through a membrane fusion pore. The initially small pore may subsequently dilate for full contents release, as commonly observed in amperometric traces. The size, shape, and evolution of the pore is critical to the course of contents release, but exact fusion pore solutions accounting for membrane tension and bending energy constraints have not been available. Here, we obtained exact solutions for fusion pores between two membranes. We find three families: a narrow pore, a wide pore, and an intermediate tether-like pore. For high tensions these are close to the catenoidal and tether solutions recently reported for freely hinged membrane boundaries. We suggest membrane fusion initially generates a stable narrow pore, and the dilation pathway is a transition to the stable wide pore family. The unstable intermediate pore is the transition state that sets the energy barrier for this dilation pathway. Pore dilation is mechanosensitive, as the energy barrier is lowered by increased membrane tension. Finally, we study fusion pores in nanodiscs, powerful systems for the study of individual pores. We show that nanodiscs stabilize fusion pores by locking them into the narrow pore family.
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Affiliation(s)
- Rui Su
- Department of Chemical Engineering, Columbia University, New York City, New York
| | - Shuyuan Wang
- Department of Chemical Engineering, Columbia University, New York City, New York; Department of Physics, Columbia University, New York City, New York
| | - Zachary McDargh
- Department of Chemical Engineering, Columbia University, New York City, New York
| | - Ben O'Shaughnessy
- Department of Chemical Engineering, Columbia University, New York City, New York.
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2
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Feng S, Park S, Choi YK, Im W. CHARMM-GUI Membrane Builder: Past, Current, and Future Developments and Applications. J Chem Theory Comput 2023; 19:2161-2185. [PMID: 37014931 PMCID: PMC10174225 DOI: 10.1021/acs.jctc.2c01246] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/06/2023]
Abstract
Molecular dynamics simulations of membranes and membrane proteins serve as computational microscopes, revealing coordinated events at the membrane interface. As G protein-coupled receptors, ion channels, transporters, and membrane-bound enzymes are important drug targets, understanding their drug binding and action mechanisms in a realistic membrane becomes critical. Advances in materials science and physical chemistry further demand an atomistic understanding of lipid domains and interactions between materials and membranes. Despite a wide range of membrane simulation studies, generating a complex membrane assembly remains challenging. Here, we review the capability of CHARMM-GUI Membrane Builder in the context of emerging research demands, as well as the application examples from the CHARMM-GUI user community, including membrane biophysics, membrane protein drug-binding and dynamics, protein-lipid interactions, and nano-bio interface. We also provide our perspective on future Membrane Builder development.
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Affiliation(s)
- Shasha Feng
- Departments of Biological Sciences and Chemistry, Lehigh University, Bethlehem, Pennsylvania 18015, United States
| | - Soohyung Park
- Departments of Biological Sciences and Chemistry, Lehigh University, Bethlehem, Pennsylvania 18015, United States
| | - Yeol Kyo Choi
- Departments of Biological Sciences and Chemistry, Lehigh University, Bethlehem, Pennsylvania 18015, United States
| | - Wonpil Im
- Departments of Biological Sciences and Chemistry, Lehigh University, Bethlehem, Pennsylvania 18015, United States
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3
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Bykhovskaia M. Molecular Dynamics Simulations of the Proteins Regulating Synaptic Vesicle Fusion. MEMBRANES 2023; 13:307. [PMID: 36984694 PMCID: PMC10058449 DOI: 10.3390/membranes13030307] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/23/2023] [Revised: 02/11/2023] [Accepted: 03/01/2023] [Indexed: 06/18/2023]
Abstract
Neuronal transmitters are packaged in synaptic vesicles (SVs) and released by the fusion of SVs with the presynaptic membrane (PM). An inflow of Ca2+ into the nerve terminal triggers fusion, and the SV-associated protein Synaptotagmin 1 (Syt1) serves as a Ca2+ sensor. In preparation for fusion, SVs become attached to the PM by the SNARE protein complex, a coiled-coil bundle that exerts the force overcoming SV-PM repulsion. A cytosolic protein Complexin (Cpx) attaches to the SNARE complex and differentially regulates the evoked and spontaneous release components. It is still debated how the dynamic interactions of Syt1, SNARE proteins and Cpx lead to fusion. This problem is confounded by heterogeneity in the conformational states of the prefusion protein-lipid complex and by the lack of tools to experimentally monitor the rapid conformational transitions of the complex, which occur at a sub-millisecond scale. However, these complications can be overcome employing molecular dynamics (MDs), a computational approach that enables simulating interactions and conformational transitions of proteins and lipids. This review discusses the use of molecular dynamics for the investigation of the pre-fusion protein-lipid complex. We discuss the dynamics of the SNARE complex between lipid bilayers, as well as the interactions of Syt1 with lipids and SNARE proteins, and Cpx regulating the assembly of the SNARE complex.
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Affiliation(s)
- Maria Bykhovskaia
- Neurology Department, Wayne State University, Detroit, MI 48202, USA
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4
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Warner JM, An D, Stratton BS, O'Shaughnessy B. A hemifused complex is the hub in a network of pathways to membrane fusion. Biophys J 2023; 122:374-385. [PMID: 36463406 PMCID: PMC9892611 DOI: 10.1016/j.bpj.2022.12.003] [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: 03/01/2022] [Revised: 06/25/2022] [Accepted: 11/30/2022] [Indexed: 12/12/2022] Open
Abstract
Membrane fusion is a critical step for many essential processes, from neurotransmission to fertilization. For over 40 years, protein-free fusion driven by calcium or other cationic species has provided a simplified model of biological fusion, but the mechanisms remain poorly understood. Cation-mediated membrane fusion and permeation are essential in their own right to drug delivery strategies based on cell-penetrating peptides or cation-bearing lipid nanoparticles. Experimental studies suggest calcium drives anionic membranes to a hemifused intermediate that constitutes a hub in a network of pathways, but the pathway selection mechanism is unknown. Here we develop a mathematical model that identifies the network hub as a highly dynamic hemifusion complex. Multivalent cations drive expansion of this high-tension hemifusion interface between interacting vesicles during a brief transient. The fate of this interface determines the outcome, either fusion, dead-end hemifusion, or vesicle lysis. The model reproduces the unexplained finding that calcium-driven fusion of vesicles with planar membranes typically stalls at hemifusion, and we show the equilibrated hemifused state is a novel lens-shaped complex. Thus, membrane fusion kinetics follow a stochastic trajectory within a network of pathways, with outcome weightings set by a hemifused complex intermediate.
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Affiliation(s)
- Jason M Warner
- Department of Chemical Engineering, Columbia University, New York, New York
| | - Dong An
- Department of Chemical Engineering, Columbia University, New York, New York
| | | | - Ben O'Shaughnessy
- Department of Chemical Engineering, Columbia University, New York, New York.
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5
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Rizo J, Sari L, Qi Y, Im W, Lin MM. All-atom molecular dynamics simulations of Synaptotagmin-SNARE-complexin complexes bridging a vesicle and a flat lipid bilayer. eLife 2022; 11:76356. [PMID: 35708237 PMCID: PMC9239685 DOI: 10.7554/elife.76356] [Citation(s) in RCA: 19] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2021] [Accepted: 06/15/2022] [Indexed: 12/14/2022] Open
Abstract
Synaptic vesicles are primed into a state that is ready for fast neurotransmitter release upon Ca2+-binding to Synaptotagmin-1. This state likely includes trans-SNARE complexes between the vesicle and plasma membranes that are bound to Synaptotagmin-1 and complexins. However, the nature of this state and the steps leading to membrane fusion are unclear, in part because of the difficulty of studying this dynamic process experimentally. To shed light into these questions, we performed all-atom molecular dynamics simulations of systems containing trans-SNARE complexes between two flat bilayers or a vesicle and a flat bilayer with or without fragments of Synaptotagmin-1 and/or complexin-1. Our results need to be interpreted with caution because of the limited simulation times and the absence of key components, but suggest mechanistic features that may control release and help visualize potential states of the primed Synaptotagmin-1-SNARE-complexin-1 complex. The simulations suggest that SNAREs alone induce formation of extended membrane-membrane contact interfaces that may fuse slowly, and that the primed state contains macromolecular assemblies of trans-SNARE complexes bound to the Synaptotagmin-1 C2B domain and complexin-1 in a spring-loaded configuration that prevents premature membrane merger and formation of extended interfaces, but keeps the system ready for fast fusion upon Ca2+ influx.
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Affiliation(s)
- Josep Rizo
- Department of Biophysics, The University of Texas Southwestern Medical Center, Dallas, United States.,Department of Biochemistry, University of Texas Southwestern Medical Center, Dallas, United States.,Department of Pharmacology, University of Texas Southwestern Medical Center, Dallas, United States
| | - Levent Sari
- Department of Biophysics, The University of Texas Southwestern Medical Center, Dallas, United States.,Green Center for Systems Biology, The University of Texas Southwestern Medical Center, Dallas, United States
| | - Yife Qi
- Department of Medicinal Chemistry, School of Pharmacy, Fudan University, Shanghai, China
| | - Wonpil Im
- Department of Biological Sciences, Lehigh University, Bethlehem, United States.,Department of Chemistry, Lehigh University, Bethlehem, United States.,Department of Bioengineering, Lehigh University, Bethlehem, United States.,Department of Computer Science and Engineering, Lehigh University, Bethlehem, United States
| | - Milo M Lin
- Department of Biophysics, The University of Texas Southwestern Medical Center, Dallas, United States.,Green Center for Systems Biology, The University of Texas Southwestern Medical Center, Dallas, United States
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6
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Urbina FL, Gupton SL. SNARE-Mediated Exocytosis in Neuronal Development. Front Mol Neurosci 2020; 13:133. [PMID: 32848598 PMCID: PMC7427632 DOI: 10.3389/fnmol.2020.00133] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2020] [Accepted: 07/02/2020] [Indexed: 12/15/2022] Open
Abstract
The formation of the nervous system involves establishing complex networks of synaptic connections between proper partners. This developmental undertaking requires the rapid expansion of the plasma membrane surface area as neurons grow and polarize, extending axons through the extracellular environment. Critical to the expansion of the plasma membrane and addition of plasma membrane material is exocytic vesicle fusion, a regulated mechanism driven by soluble N-ethylmaleimide-sensitive factor attachment proteins receptors (SNAREs). Since their discovery, SNAREs have been implicated in several critical neuronal functions involving exocytic fusion in addition to synaptic transmission, including neurite initiation and outgrowth, axon specification, axon extension, and synaptogenesis. Decades of research have uncovered a rich variety of SNARE expression and function. The basis of SNARE-mediated fusion, the opening of a fusion pore, remains an enigmatic event, despite an incredible amount of research, as fusion is not only heterogeneous but also spatially small and temporally fast. Multiple modes of exocytosis have been proposed, with full-vesicle fusion (FFV) and kiss-and-run (KNR) being the best described. Whereas most in vitro work has reconstituted fusion using VAMP-2, SNAP-25, and syntaxin-1; there is much to learn regarding the behaviors of distinct SNARE complexes. In the past few years, robust heterogeneity in the kinetics and fate of the fusion pore that varies by cell type have been uncovered, suggesting a paradigm shift in how the modes of exocytosis are viewed is warranted. Here, we explore both classic and recent work uncovering the variety of SNAREs and their importance in the development of neurons, as well as historical and newly proposed modes of exocytosis, their regulation, and proteins involved in the regulation of fusion kinetics.
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Affiliation(s)
- Fabio L. Urbina
- Department of Cell Biology and Physiology, University of North Carolina at Chapel Hill, Chapel Hill, NC, United States
| | - Stephanie L. Gupton
- Department of Cell Biology and Physiology, University of North Carolina at Chapel Hill, Chapel Hill, NC, United States
- UNC Neuroscience Center, Chapel Hill, NC, United States
- UNC Lineberger Comprehensive Cancer Center, Chapel Hill, NC, United States
- Carolina Institute for Developmental Disabilities, University of North Carolina at Chapel Hill, Chapel Hill, NC, United States
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7
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Chen L, Wu Z, Wu X, Liao Y, Dai X, Shi X. The Application of Coarse-Grained Molecular Dynamics to the Evaluation of Liposome Physical Stability. AAPS PharmSciTech 2020; 21:138. [PMID: 32419093 DOI: 10.1208/s12249-020-01680-6] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2019] [Accepted: 04/09/2020] [Indexed: 12/16/2022] Open
Abstract
Physical stability is one of critical characteristics of liposome, especially to its clinical application. Vesicle fusion was one of the common physical stability phenomena that occurred during the long storage period. Because vesicle fusion could be easily checked by the change of vesicle size, it was widely applied in the evaluation of liposome physical stability. However, since the method requires the liposome to be placed under certain conditions for long-term observation, a liposome physical stability test usually takes several weeks, which greatly hinders the research efficiency. In this study, to speed up the research efficiency, coarse-grained molecular dynamics was first applied in the study of liposome physical stability. By analyzing the microprocess of vesicle fusion, two parameters including diffusion constant and the total time of the vesicle morphology transition process were employed to study the liposome physical stability. Then, in order to verify the applicability of two parameters, the physical stability of elastic liposomes and conventional liposomes was compared at 3 different temperatures. It was found that the fusion probability and speed of elastic liposomes were higher than those of conventional liposomes. Thus, elastic liposomes showed a worse physical stability compared with that of conventional liposomes, which was consistent with former research. Through this research, a new efficient method based on coarse-grained molecular dynamics was proposed for the study of liposome physical stability.
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8
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Benhaim MA, Lee KK. New Biophysical Approaches Reveal the Dynamics and Mechanics of Type I Viral Fusion Machinery and Their Interplay with Membranes. Viruses 2020; 12:E413. [PMID: 32276357 PMCID: PMC7232462 DOI: 10.3390/v12040413] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2020] [Revised: 04/04/2020] [Accepted: 04/04/2020] [Indexed: 12/27/2022] Open
Abstract
Protein-mediated membrane fusion is a highly regulated biological process essential for cellular and organismal functions and infection by enveloped viruses. During viral entry the membrane fusion reaction is catalyzed by specialized protein machinery on the viral surface. These viral fusion proteins undergo a series of dramatic structural changes during membrane fusion where they engage, remodel, and ultimately fuse with the host membrane. The structural and dynamic nature of these conformational changes and their impact on the membranes have long-eluded characterization. Recent advances in structural and biophysical methodologies have enabled researchers to directly observe viral fusion proteins as they carry out their functions during membrane fusion. Here we review the structure and function of type I viral fusion proteins and mechanisms of protein-mediated membrane fusion. We highlight how recent technological advances and new biophysical approaches are providing unprecedented new insight into the membrane fusion reaction.
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Affiliation(s)
- Mark A. Benhaim
- Department of Medicinal Chemistry, University of Washington, Seattle, WA 98195-7610, USA;
| | - Kelly K. Lee
- Department of Medicinal Chemistry, University of Washington, Seattle, WA 98195-7610, USA;
- Biological Physics Structure and Design Program, University of Washington, Seattle, WA 98195-7610, USA
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9
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Crone NS, Kros A, Boyle AL. Modulation of Coiled-Coil Binding Strength and Fusogenicity through Peptide Stapling. Bioconjug Chem 2020; 31:834-843. [PMID: 32058706 PMCID: PMC7086394 DOI: 10.1021/acs.bioconjchem.0c00009] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2020] [Revised: 02/13/2020] [Indexed: 12/20/2022]
Abstract
Peptide stapling is a technique which has been widely employed to constrain the conformation of peptides. One of the effects of such a constraint can be to modulate the interaction of the peptide with a binding partner. Here, a cysteine bis-alkylation stapling technique was applied to generate structurally isomeric peptide variants of a heterodimeric coiled-coil forming peptide. These stapled variants differed in the position and size of the formed macrocycle. C-terminal stapling showed the most significant changes in peptide structure and stability, with calorimetric binding analysis showing a significant reduction of binding entropy for stapled variants. This entropy reduction was dependent on cross-linker size and was accompanied by a change in binding enthalpy, illustrating the effects of preorganization. The stapled peptide, along with its binding partner, were subsequently employed as fusogens in a liposome model system. An increase in both lipid- and content-mixing was observed for one of the stapled peptide variants: this increased fusogenicity was attributed to increased coiled-coil binding but not to membrane affinity, an interaction theorized to be a primary driving force in this fusion system.
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Affiliation(s)
- Niek S.
A. Crone
- Supramolecular and Biomaterials
Chemistry, Leiden Institute of Chemistry, Leiden University, Einsteinweg 55, 2333 CC Leiden, The Netherlands
| | - Alexander Kros
- Supramolecular and Biomaterials
Chemistry, Leiden Institute of Chemistry, Leiden University, Einsteinweg 55, 2333 CC Leiden, The Netherlands
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10
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Karatekin E, Rothman JE. FEBS Letters Special Issue on Exocytosis and Endocytosis. FEBS Lett 2019; 592:3477-3479. [PMID: 30417372 DOI: 10.1002/1873-3468.13274] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- Erdem Karatekin
- Department of Cellular and Molecular Physiology, Yale University School of Medicine, New Haven, CT, USA.,Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, CT, USA.,Nanobiology Institute, Yale University, West Haven, CT, USA.,Centre National de la Recherche Scientifique (CNRS), Paris, France
| | - James E Rothman
- Nanobiology Institute, Yale University, West Haven, CT, USA.,Department of Cell Biology, Yale University School of Medicine, New Haven, CT, USA.,Department of Clinical and Experimental Epilepsy, Institute of Neurology, University College London, UK
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11
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Lu T, Guo H. How the Membranes Fuse: From Spontaneous to Induced. ADVANCED THEORY AND SIMULATIONS 2019. [DOI: 10.1002/adts.201900032] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Teng Lu
- Beijing National Laboratory for Molecular SciencesJoint Laboratory of Polymer Sciences and MaterialsState Key Laboratory of Polymer Physics and ChemistryInstitute of Chemistry, Chinese Academy of Sciences Beijing 100190 China
| | - Hongxia Guo
- Beijing National Laboratory for Molecular SciencesJoint Laboratory of Polymer Sciences and MaterialsState Key Laboratory of Polymer Physics and ChemistryInstitute of Chemistry, Chinese Academy of Sciences Beijing 100190 China
- Division of Polymer Science and MaterialsSchool of Chemical SciencesUniversity of Chinese Academy of Sciences Beijing 100049 China
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12
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Manca F, Pincet F, Truskinovsky L, Rothman JE, Foret L, Caruel M. SNARE machinery is optimized for ultrafast fusion. Proc Natl Acad Sci U S A 2019; 116:2435-2442. [PMID: 30700546 PMCID: PMC6377469 DOI: 10.1073/pnas.1820394116] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022] Open
Abstract
SNARE proteins zipper to form complexes (SNAREpins) that power vesicle fusion with target membranes in a variety of biological processes. A single SNAREpin takes about 1 s to fuse two bilayers, yet a handful can ensure release of neurotransmitters from synaptic vesicles much faster: in a 10th of a millisecond. We propose that, similar to the case of muscle myosins, the ultrafast fusion results from cooperative action of many SNAREpins. The coupling originates from mechanical interactions induced by confining scaffolds. Each SNAREpin is known to have enough energy to overcome the fusion barrier of 25-[Formula: see text]; however, the fusion barrier only becomes relevant when the SNAREpins are nearly completely zippered, and from this state, each SNAREpin can deliver only a small fraction of this energy as mechanical work. Therefore, they have to act cooperatively, and we show that at least three of them are needed to ensure fusion in less than a millisecond. However, to reach the prefusion state collectively, starting from the experimentally observed half-zippered metastable state, the SNAREpins have to mechanically synchronize, which takes more time as the number of SNAREpins increases. Incorporating this somewhat counterintuitive idea in a simple coarse-grained model results in the prediction that there should be an optimum number of SNAREpins for submillisecond fusion: three to six over a wide range of parameters. Interestingly, in situ cryoelectron microscope tomography has very recently shown that exactly six SNAREpins participate in the fusion of each synaptic vesicle. This number is in the range predicted by our theory.
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Affiliation(s)
- Fabio Manca
- Laboratoire de Physique de l'Ecole Normale Supérieure (LPENS), CNRS, Ecole Normale Supérieure, 75005 Paris, France
- LPENS, Sorbonne Université, 75005 Paris, France
- LPENS, Université Paris-Diderot, 75005 Paris, France
- LPENS, Université PSL, 75005 Paris, France
| | - Frederic Pincet
- Laboratoire de Physique de l'Ecole Normale Supérieure (LPENS), CNRS, Ecole Normale Supérieure, 75005 Paris, France
- LPENS, Sorbonne Université, 75005 Paris, France
- LPENS, Université Paris-Diderot, 75005 Paris, France
- LPENS, Université PSL, 75005 Paris, France
| | - Lev Truskinovsky
- Physique et Mécanique des Milieux Hétérogènes, CNRS, Ecole Supérieure de Physique et de Chimie Industrielles, Université PSL, 75231 Paris Cedex 05, France
| | - James E Rothman
- Department of Cell Biology, Yale University, New Haven, CT 06520;
- Department of Experimental Epilepsy, Institute of Neurology, University College London, London WC1E 6BT, United Kingdom
| | - Lionel Foret
- Laboratoire de Physique de l'Ecole Normale Supérieure (LPENS), CNRS, Ecole Normale Supérieure, 75005 Paris, France
- LPENS, Sorbonne Université, 75005 Paris, France
- LPENS, Université Paris-Diderot, 75005 Paris, France
- LPENS, Université PSL, 75005 Paris, France
| | - Matthieu Caruel
- Modélisation et Simulation Multi-Echelle, CNRS, Université Paris-Est Créteil, 94010 Créteil Cedex, France
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