1
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Kidder KM, Noid WG. Analysis of mapping atomic models to coarse-grained resolution. J Chem Phys 2024; 161:134113. [PMID: 39365018 DOI: 10.1063/5.0220989] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2024] [Accepted: 09/10/2024] [Indexed: 10/05/2024] Open
Abstract
Low-resolution coarse-grained (CG) models provide significant computational and conceptual advantages for simulating soft materials. However, the properties of CG models depend quite sensitively upon the mapping, M, that maps each atomic configuration, r, to a CG configuration, R. In particular, M determines how the configurational information of the atomic model is partitioned between the mapped ensemble of CG configurations and the lost ensemble of atomic configurations that map to each R. In this work, we investigate how the mapping partitions the atomic configuration space into CG and intra-site components. We demonstrate that the corresponding coordinate transformation introduces a nontrivial Jacobian factor. This Jacobian factor defines a labeling entropy that corresponds to the uncertainty in the atoms that are associated with each CG site. Consequently, the labeling entropy effectively transfers configurational information from the lost ensemble into the mapped ensemble. Moreover, our analysis highlights the possibility of resonant mappings that separate the atomic potential into CG and intra-site contributions. We numerically illustrate these considerations with a Gaussian network model for the equilibrium fluctuations of actin. We demonstrate that the spectral quality, Q, provides a simple metric for identifying high quality representations for actin. Conversely, we find that neither maximizing nor minimizing the information content of the mapped ensemble results in high quality representations. However, if one accounts for the labeling uncertainty, Q(M) correlates quite well with the adjusted configurational information loss, Îmap(M), that results from the mapping.
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Affiliation(s)
- Katherine M Kidder
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - W G Noid
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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2
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Dorsey PJ, Lau CL, Chang TC, Doerschuk PC, D'Addio SM. Review of machine learning for lipid nanoparticle formulation and process development. J Pharm Sci 2024:S0022-3549(24)00422-2. [PMID: 39341497 DOI: 10.1016/j.xphs.2024.09.015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2024] [Revised: 09/10/2024] [Accepted: 09/11/2024] [Indexed: 10/01/2024]
Abstract
Lipid nanoparticles (LNPs) are a subset of pharmaceutical nanoparticulate formulations designed to encapsulate, stabilize, and deliver nucleic acid cargoes in vivo. Applications for LNPs include new interventions for genetic disorders, novel classes of vaccines, and alternate modes of intracellular delivery for therapeutic proteins. In the pharmaceutical industry, establishing a robust formulation and process to achieve target product performance is a critical component of drug development. Fundamental understanding of the processes for making LNPs and their interactions with biological systems have advanced considerably in the wake of the COVID-19 pandemic. Nevertheless, LNP formulation research remains largely empirical and resource intensive due to the multitude of input parameters and the complex physical phenomena that govern the processes of nanoparticle precipitation, self-assembly, structure evolution, and stability. Increasingly, artificial intelligence and machine learning (AI/ML) are being applied to improve the efficiency of research activities through in silico models and predictions, and to drive deeper fundamental understanding of experimental inputs to functional outputs. This review will identify current challenges and opportunities in the development of robust LNP formulations of nucleic acids, review studies that apply machine learning methods to experimental datasets, and provide discussion on associated data science challenges to facilitate collaboration between formulation and data scientists, aiming to accelerate the advancement of AI/ML applied to LNP formulation and process optimization.
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Affiliation(s)
- Phillip J Dorsey
- Pharmaceutical Sciences & Clinical Supply, MRL, Merck & Co., Inc., Rahway, NJ 07065, USA; University of Pittsburgh School of Medicine, Pittsburgh, PA 15213, USA
| | - Christina L Lau
- Cornell University, School of Electrical and Computer Engineering, Ithaca, NY 14853, USA
| | - Ti-Chiun Chang
- Pharmaceutical Sciences & Clinical Supply, MRL, Merck & Co., Inc., Rahway, NJ 07065, USA
| | - Peter C Doerschuk
- Cornell University, School of Electrical and Computer Engineering, Ithaca, NY 14853, USA
| | - Suzanne M D'Addio
- Pharmaceutical Sciences & Clinical Supply, MRL, Merck & Co., Inc., Rahway, NJ 07065, USA.
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3
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Spencer RKW, Smirnova YG, Soleimani A, Müller M. Transient pores in hemifusion diaphragms. Biophys J 2024; 123:2455-2475. [PMID: 38867448 PMCID: PMC11365115 DOI: 10.1016/j.bpj.2024.06.009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2024] [Revised: 05/07/2024] [Accepted: 06/07/2024] [Indexed: 06/14/2024] Open
Abstract
Exchange of material across two membranes, as in the case of synaptic neurotransmitter release from a vesicle, involves the formation and poration of a hemifusion diaphragm (HD). The nontrivial geometry of the HD leads to environment-dependent control, regarding the stability and dynamics of the pores required for this kind of exocytosis. This work combines particle simulations, field-based calculations, and phenomenological modeling to explore the factors influencing the stability, dynamics, and possible control mechanisms of pores in HDs. We find that pores preferentially form at the HD rim, and that their stability is sensitive to a number of factors, including the three line tensions, membrane tension, HD size, and the ability of lipids to "flip-flop" across leaflets. Along with a detailed analysis of these factors, we discuss ways that vesicles or cells may use them to open and close pores and thereby quickly and efficiently transport material.
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Affiliation(s)
- Russell K W Spencer
- Institute for Theoretical Physics, Georg-August University, Göttingen, Germany.
| | - Yuliya G Smirnova
- Institute for Theoretical Physics, Georg-August University, Göttingen, Germany; Technische Universität Dortmund, Dortmund, Germany
| | - Alireza Soleimani
- Institute for Theoretical Physics, Georg-August University, Göttingen, Germany
| | - Marcus Müller
- Institute for Theoretical Physics, Georg-August University, Göttingen, Germany.
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4
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Bussoletti M, Gallo M, Bottacchiari M, Abbondanza D, Casciola CM. Mesoscopic elasticity controls dynamin-driven fission of lipid tubules. Sci Rep 2024; 14:14003. [PMID: 38890460 PMCID: PMC11189461 DOI: 10.1038/s41598-024-64685-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2024] [Accepted: 06/12/2024] [Indexed: 06/20/2024] Open
Abstract
Mesoscale physics bridges the gap between the microscopic degrees of freedom of a system and its large-scale continuous behavior and highlights the role of a few key quantities in complex and multiscale phenomena, like dynamin-driven fission of lipid membranes. The dynamin protein wraps the neck formed during clathrin-mediated endocytosis, for instance, and constricts it until severing occurs. Although ubiquitous and fundamental for life, the cooperation between the GTP-consuming conformational changes within the protein and the full-scale response of the underlying lipid substrate is yet to be unraveled. In this work, we build an effective mesoscopic model from constriction to fission of lipid tubules based on continuum membrane elasticity and implicitly accounting for ratchet-like power strokes of dynamins. Localization of the fission event, the overall geometry, and the energy expenditure we predict comply with the major experimental findings. This bolsters the idea that a continuous picture emerges soon enough to relate dynamin polymerization length and membrane rigidity and tension with the optimal pathway to fission. We therefore suggest that dynamins found in in vivo processes may optimize their structure accordingly. Ultimately, we shed light on real-time conductance measurements available in literature and predict the fission time dependency on elastic parameters.
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Affiliation(s)
- Marco Bussoletti
- Department of Mechanical and Aerospace Engineering, Sapienza University of Rome, Rome, Italy
| | - Mirko Gallo
- Department of Mechanical and Aerospace Engineering, Sapienza University of Rome, Rome, Italy
| | - Matteo Bottacchiari
- Department of Mechanical and Aerospace Engineering, Sapienza University of Rome, Rome, Italy
- Department of Basic and Applied Sciences for Engineering, Sapienza University of Rome, Rome, Italy
| | - Dario Abbondanza
- Department of Mechanical and Aerospace Engineering, Sapienza University of Rome, Rome, Italy
| | - Carlo Massimo Casciola
- Department of Mechanical and Aerospace Engineering, Sapienza University of Rome, Rome, Italy.
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5
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Blasco S, Sukeník L, Vácha R. Nanoparticle induced fusion of lipid membranes. NANOSCALE 2024; 16:10221-10229. [PMID: 38679949 PMCID: PMC11138393 DOI: 10.1039/d4nr00591k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2024] [Accepted: 04/23/2024] [Indexed: 05/01/2024]
Abstract
Membrane fusion is crucial for infection of enveloped viruses, cellular transport, and drug delivery via liposomes. Nanoparticles can serve as fusogenic agents facilitating such membrane fusion for direct transmembrane transport. However, the underlying mechanisms of nanoparticle-induced fusion and the ideal properties of such nanoparticles remain largely unknown. Here, we used molecular dynamics simulations to investigate the efficacy of spheroidal nanoparticles with different size, prolateness, and ligand interaction strengths to enhance fusion between vesicles. By systematically varying nanoparticle properties, we identified how each parameter affects the fusion process and determined the optimal parameter range that promotes fusion. These findings provide valuable insights for the design and optimization of fusogenic nanoparticles with potential biotechnological and biomedical applications.
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Affiliation(s)
- Sofía Blasco
- CEITEC - Central European Institute of Technology, Kamenice 5, 625 00 Brno, Czech Republic.
- National Centre for Biomolecular Research, Faculty of Science, Masaryk University, Kamenice 5, 625 00 Brno, Czech Republic
| | - Lukáš Sukeník
- CEITEC - Central European Institute of Technology, Kamenice 5, 625 00 Brno, Czech Republic.
- Department of Condensed Matter Physics, Faculty of Science, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic
| | - Robert Vácha
- CEITEC - Central European Institute of Technology, Kamenice 5, 625 00 Brno, Czech Republic.
- National Centre for Biomolecular Research, Faculty of Science, Masaryk University, Kamenice 5, 625 00 Brno, Czech Republic
- Department of Condensed Matter Physics, Faculty of Science, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic
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6
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Sadeghi M, Rosenberger D. Dynamic framework for large-scale modeling of membranes and peripheral proteins. Methods Enzymol 2024; 701:457-514. [PMID: 39025579 DOI: 10.1016/bs.mie.2024.03.018] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/20/2024]
Abstract
In this chapter, we present a novel computational framework to study the dynamic behavior of extensive membrane systems, potentially in interaction with peripheral proteins, as an alternative to conventional simulation methods. The framework effectively describes the complex dynamics in protein-membrane systems in a mesoscopic particle-based setup. Furthermore, leveraging the hydrodynamic coupling between the membrane and its surrounding solvent, the coarse-grained model grounds its dynamics in macroscopic kinetic properties such as viscosity and diffusion coefficients, marrying the advantages of continuum- and particle-based approaches. We introduce the theoretical background and the parameter-space optimization method in a step-by-step fashion, present the hydrodynamic coupling method in detail, and demonstrate the application of the model at each stage through illuminating examples. We believe this modeling framework to hold great potential for simulating membrane and protein systems at biological spatiotemporal scales, and offer substantial flexibility for further development and parametrization.
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Affiliation(s)
- Mohsen Sadeghi
- Department of Mathematics and Computer Science, Freie Universität Berlin, Berlin, Germany.
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7
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Spencer RKW, Santos-Pérez I, Rodríguez-Renovales I, Martinez Galvez JM, Shnyrova AV, Müller M. Membrane fission via transmembrane contact. Nat Commun 2024; 15:2793. [PMID: 38555357 PMCID: PMC10981662 DOI: 10.1038/s41467-024-47122-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2023] [Accepted: 03/20/2024] [Indexed: 04/02/2024] Open
Abstract
Division of intracellular organelles often correlates with additional membrane wrapping, e.g., by the endoplasmic reticulum or the outer mitochondrial membrane. Such wrapping plays a vital role in proteome and lipidome organization. However, how an extra membrane impacts the mechanics of the division has not been investigated. Here we combine fluorescence and cryo-electron microscopy experiments with self-consistent field theory to explore the stress-induced instabilities imposed by membrane wrapping in a simple double-membrane tubular system. We find that, at physiologically relevant conditions, the outer membrane facilitates an alternative pathway for the inner-tube fission through the formation of a transient contact (hemi-fusion) between both membranes. A detailed molecular theory of the fission pathways in the double membrane system reveals the topological complexity of the process, resulting both in leaky and leakless intermediates, with energies and topologies predicting physiological events.
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Affiliation(s)
- Russell K W Spencer
- Institute for Theoretical Physics, Georg-August University, Göttingen, Germany.
| | - Isaac Santos-Pérez
- Electron Microscopy and Crystallography Platform, Center for Cooperative Research in Biosciences (CIC bioGUNE), Derio, Spain
| | - Izaro Rodríguez-Renovales
- BREM Basque Resource for Electron Microscopy, Leioa, Spain
- Instituto Biofisika (CSIC, UPV/EHU), Barrio Sarriena, Leioa, Spain
| | - Juan Manuel Martinez Galvez
- Instituto Biofisika (CSIC, UPV/EHU), Barrio Sarriena, Leioa, Spain
- Department of Biochemistry and Molecular Biology, University of the Basque Country, Leioa, Spain
| | - Anna V Shnyrova
- Instituto Biofisika (CSIC, UPV/EHU), Barrio Sarriena, Leioa, Spain.
- Department of Biochemistry and Molecular Biology, University of the Basque Country, Leioa, Spain.
| | - Marcus Müller
- Institute for Theoretical Physics, Georg-August University, Göttingen, Germany.
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8
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Eggers J, Liverpool TB, Mietke A. Rheology of Suspensions of Flat Elastic Particles. PHYSICAL REVIEW LETTERS 2023; 131:194002. [PMID: 38000428 DOI: 10.1103/physrevlett.131.194002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2023] [Accepted: 09/06/2023] [Indexed: 11/26/2023]
Abstract
We consider a suspension of noninteracting flat elastic particles in a Newtonian fluid. We model a flat shape as three beads, carried along by the flow according to Stokes law, and connected by nonlinear springs, chosen such that the energy is quadratic in the area. In analogy with common dumbbell models involving two beads connected by linear springs, we solve the stochastic equations of motion exactly to compute the constitutive law for the stress tensor of a flat elastic particle suspension. A lower convected time derivative naturally arises as part of the constitutive law, but surprisingly the rheological response in strong extensional and strong contracting flows is similar to that of the classical Oldroyd-B model associated with dumbbell suspensions.
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Affiliation(s)
- Jens Eggers
- School of Mathematics, University of Bristol, Fry Building, Bristol BS8 1UG, United Kingdom
| | - Tanniemola B Liverpool
- School of Mathematics, University of Bristol, Fry Building, Bristol BS8 1UG, United Kingdom
| | - Alexander Mietke
- School of Mathematics, University of Bristol, Fry Building, Bristol BS8 1UG, United Kingdom
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9
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Islam K, Razizadeh M, Liu Y. Coarse-grained molecular simulation of extracellular vesicle squeezing for drug loading. Phys Chem Chem Phys 2023; 25:12308-12321. [PMID: 37082907 PMCID: PMC10337604 DOI: 10.1039/d3cp00387f] [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] [Indexed: 04/08/2023]
Abstract
In recent years, extracellular vesicles have become promising carriers as next-generation drug delivery platforms. Effective loading of exogenous cargos without compromising the extracellular vesicle membrane is a major challenge. Rapid squeezing through nanofluidic channels is a widely used approach to load exogenous cargoes into the EV through the nanopores generated temporarily on the membrane. However, the exact mechanism and dynamics of nanopore opening, as well as cargo loading through nanopores during the squeezing process remains unknown and it is impossible to visualize or quantify it experimentally due to the small size of the EV and the fast transient process. This paper developed a systemic algorithm to simulate nanopore formation and predict drug loading during extracellular vesicle (EV) squeezing by leveraging the power of coarse-grain (CG) molecular dynamics simulations with fluid dynamics. The EV CG beads are coupled with implicit the fluctuating lattice Boltzmann solvent. The effects of EV properties and various squeezing test parameters, such as EV size, flow velocity, channel width, and length, on pore formation and drug loading efficiency are analyzed. Based on the simulation results, a phase diagram is provided as a design guide for nanochannel geometry and squeezing velocity to generate pores on the membrane without damaging the EV. This method can be utilized to optimize the nanofluidic device configuration and flow setup to obtain desired drug loading into EVs.
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Affiliation(s)
- Khayrul Islam
- Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, Pennsylvania 18015, USA.
| | - Meghdad Razizadeh
- Department of Developmental Neurobiology, St. Jude Children's Research Hospital, Memphis, TN 38105, USA
| | - Yaling Liu
- Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, Pennsylvania 18015, USA.
- Department of Bioengineering, Lehigh University, Bethlehem, Pennsylvania 18015, USA
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10
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Varma M, Deserno M. Distribution of cholesterol in asymmetric membranes driven by composition and differential stress. Biophys J 2022; 121:4001-4018. [PMID: 35927954 PMCID: PMC9674969 DOI: 10.1016/j.bpj.2022.07.032] [Citation(s) in RCA: 21] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2022] [Revised: 07/11/2022] [Accepted: 07/27/2022] [Indexed: 11/25/2022] Open
Abstract
Many lipid membranes of eukaryotic cells are asymmetric, which means the two leaflets differ in at least one physical property, such as lipid composition or lateral stress. Maintaining this asymmetry is helped by the fact that ordinary phospholipids rarely transition between leaflets, but cholesterol is an exception: its flip-flop times are in the microsecond range, so that its distribution between leaflets is determined by a chemical equilibrium. In particular, preferential partitioning can draw cholesterol into a more saturated leaflet, and phospholipid number asymmetry can force it out of a compressed leaflet. Combining highly coarse-grained membrane simulations with theoretical modeling, we investigate how these two driving forces play against each other until cholesterol's chemical potential is equilibrated. The theory includes two coupled elastic sheets and a Flory-Huggins mixing free energy with a χ parameter. We obtain a relationship between χ and the interaction strength between cholesterol and lipids in either of the two leaflets, and we find that it depends, albeit weakly, on lipid number asymmetry. The differential stress measurements under various asymmetry conditions agree with our theoretical predictions. Using the two kinds of asymmetries in combination, we find that it is possible to counteract the phospholipid number bias, and the resultant stress in the membrane, via the control of cholesterol mixing in the leaflets.
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Affiliation(s)
- Malavika Varma
- Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania
| | - Markus Deserno
- Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania.
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11
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Jarin Z, Agolini O, Pastor RW. Finite-Size Effects in Simulations of Peptide/Lipid Assembly. J Membr Biol 2022; 255:437-449. [PMID: 35854128 PMCID: PMC9581812 DOI: 10.1007/s00232-022-00255-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2022] [Accepted: 06/17/2022] [Indexed: 11/29/2022]
Abstract
Molecular dynamics simulations are an attractive tool for understanding lipid/peptide self-assembly but can be plagued by inaccuracies when the system sizes are too small. The general guidance from self-assembly simulations of homogeneous micelles is that the total number of surfactants should be three to five times greater than the equilibrium aggregate number of surfactants per micelle. Herein, the heuristic is tested on the more complicated self-assembly of lipids and amphipathic peptides using the Cooke and Martini 3 coarse-grained models. Cooke model simulations with 50 to 1000 lipids and no peptide are dominated by finite-size effects, with usually one aggregate (micelle or nanodisc) containing most of the lipids forming at each system size. Approximately 200 systems of different peptide/lipid (P/L) ratios and sizes of up to 1000 lipids yield a "finite-size phase diagram" for peptide driven self-assembly, including a coexistence region of micelles and discs. Insights from the Cooke model are applied to the assembly of dimyristoylphosphatidylcholine and the ELK-neutral peptide using the Martini 3 model. Systems of 150, 450, and 900 lipids with P/L = 1/6.25 form mixtures of lipid-rich discs that agree in size with experiment and peptide-rich micelles. Only the 150-lipid system shows finite-size effects, which arise from the long-tailed distribution of aggregate sizes. The general rule of three to five times the equilibrium aggregate size remains a practical heuristic for the Cooke and Martini 3 systems investigated here.
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Affiliation(s)
- Zack Jarin
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, MD, USA
| | - Olivia Agolini
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, MD, USA
| | - Richard W Pastor
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, MD, USA.
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12
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Allsopp R, Pavlova A, Cline T, Salyapongse AM, Gillilan RE, Di YP, Deslouches B, Klauda JB, Gumbart JC, Tristram-Nagle S. Antimicrobial Peptide Mechanism Studied by Scattering-Guided Molecular Dynamics Simulation. J Phys Chem B 2022; 126:6922-6935. [PMID: 36067064 PMCID: PMC10392866 DOI: 10.1021/acs.jpcb.2c03193] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In an effort to combat rising antimicrobial resistance, our labs have rationally designed cationic, helical, amphipathic antimicrobial peptides (AMPs) as alternatives to traditional antibiotics since AMPs incur bacterial resistance in weeks, rather than days. One highly positively charged AMP, WLBU2 (+13e), (RRWV RRVR RWVR RVVR VVRR WVRR), has been shown to be effective in killing both Gram-negative (G(-)) and Gram-positive (G(+)) bacteria by directly perturbing the bacterial membrane nonspecifically. Previously, we used two equilibrium experimental methods: synchrotron X-ray diffuse scattering (XDS) providing lipid membrane thickness and neutron reflectometry (NR) providing WLBU2 depth of penetration into three lipid model membranes (LMMs). The purpose of the present study is to use the results from the scattering experiments to guide molecular dynamics (MD) simulations to investigate the detailed biophysics of the interactions of WLBU2 with LMMs of Gram-negative outer and inner membranes, and Gram-positive cell membranes, to elucidate the mechanisms of bacterial killing. Instead of coarse-graining, backmapping, or simulating without bias for several microseconds, all-atom (AA) simulations were guided by the experimental results and then equilibrated for ∼0.5 μs. Multiple replicas of the inserted peptide were run to probe stability and reach a combined time of at least 1.2 μs for G(-) and also 2.0 μs for G(+). The simulations with experimental comparisons help rule out certain structures and orientations and propose the most likely set of structures, orientations, and effects on the membrane. The simulations revealed that water, phosphates, and ions enter the hydrocarbon core when WLBU2 is positioned there. For an inserted peptide, the three types of amino acids, arginine, tryptophan, and valine (R, W, V), are arranged with the 13 Rs extending from the hydrocarbon core to the phosphate group, Ws are located at the interface, and Vs are more centrally located. For a surface state, R, W, and V are positioned relative to the bilayer interface as expected from their hydrophobicities, with Rs closest to the phosphate group, Ws close to the interface, and Vs in between. G(-) and G(+) LMMs are thinned ∼1 Å by the addition of WLBU2. Our results suggest a dual anchoring mechanism for WLBU2 both in the headgroup and in the hydrocarbon region that promotes a defect region where water and ions can flow across the slightly thinned bacterial cell membrane.
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Affiliation(s)
- Robert Allsopp
- Department of Chemical and Biomolecular Engineering, University of Maryland, College Park, Maryland 20742, United States
| | - Anna Pavlova
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, United States
| | - Tyler Cline
- Department of Chemical and Biomolecular Engineering, University of Maryland, College Park, Maryland 20742, United States
| | - Aria M Salyapongse
- Biological Physics Group, Physics Department, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States
| | - Richard E Gillilan
- Cornell High Energy Synchrotron Source (CHESS), Cornell University, Ithaca, New York 14853, United States
| | - Y Peter Di
- Department of Environmental and Occupational Health, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - Berthony Deslouches
- Department of Environmental and Occupational Health, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - Jeffery B Klauda
- Department of Chemical and Biomolecular Engineering, University of Maryland, College Park, Maryland 20742, United States
| | - James C Gumbart
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, United States
| | - Stephanie Tristram-Nagle
- Biological Physics Group, Physics Department, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States
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13
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DeLyser MR, Noid WG. Coarse-grained models for local density gradients. J Chem Phys 2022; 156:034106. [DOI: 10.1063/5.0075291] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Affiliation(s)
- Michael R. DeLyser
- Department of Chemistry, Penn State University, University Park, Pennsylvania 16802, USA
| | - W. G. Noid
- Department of Chemistry, Penn State University, University Park, Pennsylvania 16802, USA
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14
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Szukalo RJ, Noid WG. Investigating the energetic and entropic components of effective potentials across a glass transition. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:154004. [PMID: 33498016 DOI: 10.1088/1361-648x/abdff8] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2020] [Accepted: 01/26/2021] [Indexed: 06/12/2023]
Abstract
By eliminating unnecessary details, coarse-grained (CG) models provide the necessary efficiency for simulating scales that are inaccessible to higher resolution models. However, because they average over atomic details, the effective potentials governing CG degrees of freedom necessarily incorporate significant entropic contributions, which limit their transferability and complicate the treatment of thermodynamic properties. This work employs a dual-potential approach to consider the energetic and entropic contributions to effective interaction potentials for CG models. Specifically, we consider one- and three-site CG models for ortho-terphenyl (OTP) both above and below its glass transition. We employ the multiscale coarse-graining (MS-CG) variational principle to determine interaction potentials that accurately reproduce the structural properties of an all-atom (AA) model for OTP at each state point. We employ an energy-matching variational principle to determine an energy operator that accurately reproduces the intra- and inter-molecular energy of the AA model. While the MS-CG pair potentials are almost purely repulsive, the corresponding pair energy functions feature a pronounced minima that corresponds to contacting benzene rings. These energetic functions then determine an estimate for the entropic component of the MS-CG interaction potentials. These entropic functions accurately predict the MS-CG pair potentials across a wide range of liquid state points at constant density. Moreover, the entropic functions also predict pair potentials that quite accurately model the AA pair structure below the glass transition. Thus, the dual-potential approach appears a promising approach for modeling AA energetics, as well as for predicting the temperature-dependence of CG effective potentials.
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Affiliation(s)
- Ryan J Szukalo
- Department of Chemistry, Penn State University, University Park, PA 16802 United States of America
| | - W G Noid
- Department of Chemistry, Penn State University, University Park, PA 16802 United States of America
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15
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DeLyser M, Noid WG. Bottom-up coarse-grained models for external fields and interfaces. J Chem Phys 2020; 153:224103. [PMID: 33317310 DOI: 10.1063/5.0030103] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
Abstract
Bottom-up coarse-grained (CG) models accurately describe the structure of homogeneous systems but sometimes provide limited transferability and a poor description of thermodynamic properties. Consequently, inhomogeneous systems present a severe challenge for bottom-up models. In this work, we examine bottom-up CG models for interfaces and inhomogeneous systems. We first analyze the effect of external fields upon the many-body potential of mean force. We also demonstrate that the multiscale CG (MS-CG) variational principle for modeling the external field corresponds to a generalization of the first Yvon-Born-Green equation. This provides an important connection with liquid state theory, as well as physical insight into the structure of interfaces and the resulting MS-CG models. We then develop and assess MS-CG models for a film of liquid methanol that is adsorbed on an attractive wall and in coexistence with its vapor phase. While pair-additive potentials provide unsatisfactory accuracy and transferability, the inclusion of local-density (LD) potentials dramatically improves the accuracy and transferability of the MS-CG model. The MS-CG model with LD potentials quite accurately describes the wall-liquid interface, the bulk liquid density, and the liquid-vapor interface while simultaneously providing a much improved description of the vapor phase. This model also provides an excellent description of the pair structure and pressure-density equation of state for the bulk liquid. Thus, LD potentials hold considerable promise for transferable bottom-up models that accurately describe the structure and thermodynamic properties of both bulk and interfacial systems.
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Affiliation(s)
- Michael DeLyser
- Department of Chemistry, Penn State University, University Park, Pennsylvania 16802, USA
| | - W G Noid
- Department of Chemistry, Penn State University, University Park, Pennsylvania 16802, USA
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16
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Foley S, Deserno M. Stabilizing Leaflet Asymmetry under Differential Stress in a Highly Coarse-Grained Lipid Membrane Model. J Chem Theory Comput 2020; 16:7195-7206. [PMID: 33126796 DOI: 10.1021/acs.jctc.0c00862] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We present a version of the coarse-grained Cooke lipid model, modified to simulate asymmetric lipid membranes. It is inspired by a method employed by Wang et al. [ Commun. Comput. Phys. 2013, 13, 1093-1106] for artificially penalizing lipid flip-flop but copes more robustly with differential stress, at the cost of one additional bead per lipid and the concomitant increase in computational overhead. Bilayer asymmetry ultimately breaks down beyond a system size dependent critical differential stress, which can be predicted from a simple analytical model. We remeasure many important material parameters for the new model and find it to be consistent with typical fluid lipid membranes. Maintaining a stable stress asymmetry has many applications, and we give two examples: (i) connecting monolayer stress to lipid number asymmetry in order to directly measure the monolayer area modulus and (ii) finding its strain-dependent higher-order correction by monitoring the equilibrium bilayer area.
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Affiliation(s)
- Samuel Foley
- Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States
| | - Markus Deserno
- Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States
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17
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Razizadeh M, Nikfar M, Paul R, Liu Y. Coarse-Grained Modeling of Pore Dynamics on the Red Blood Cell Membrane under Large Deformations. Biophys J 2020; 119:471-482. [PMID: 32645292 PMCID: PMC7399477 DOI: 10.1016/j.bpj.2020.06.016] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2020] [Revised: 05/22/2020] [Accepted: 06/16/2020] [Indexed: 12/17/2022] Open
Abstract
Transient pore formation on the membrane of red blood cells (RBCs) under high mechanical tensions is of great importance in many biomedical applications, such as RBC damage (hemolysis) and mechanoporation-based drug delivery. The dynamic process of pore formation, growth, and resealing is hard to visualize in experiments. We developed a mesoscale coarse-grained model to study the characteristics of transient pores on a patch of the lipid bilayer that is strengthened by an elastic meshwork representing the cytoskeleton. Unsteady molecular dynamics was used to study the pore formation and reseal at high strain rates close to the physiological ranges. The critical strain for pore formation, pore characteristics, and cytoskeleton effects were studied. Results show that the presence of the cytoskeleton increases the critical strain of pore formation and confines the pore growth. Moreover, the pore recovery process under negative strain rates (compression) is analyzed. Simulations show that pores can remain open for a long time during the high-speed tank-treading induced stretching and compression process that a patch of the RBC membrane usually experiences under high shear flow. Furthermore, complex loading conditions can affect the pore characteristics and result in denser pores. Finally, the effects of strain rate on pore formation are analyzed. Higher rate stretching of membrane patch can result in a significant increase in the critical areal strain and density of pores. Such a model reveals the dynamic molecular process of RBC damage in biomedical devices and mechanoporation that, to our knowledge, has not been reported before.
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Affiliation(s)
- Meghdad Razizadeh
- Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, Pennsylvania
| | - Mehdi Nikfar
- Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, Pennsylvania
| | - Ratul Paul
- Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, Pennsylvania
| | - Yaling Liu
- Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, Pennsylvania; Department of Bioengineering, Lehigh University, Bethlehem, Pennsylvania.
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18
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Large-scale simulation of biomembranes incorporating realistic kinetics into coarse-grained models. Nat Commun 2020; 11:2951. [PMID: 32528158 PMCID: PMC7289815 DOI: 10.1038/s41467-020-16424-0] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2019] [Accepted: 04/28/2020] [Indexed: 12/12/2022] Open
Abstract
Biomembranes are two-dimensional assemblies of phospholipids that are only a few nanometres thick, but form micrometre-sized structures vital to cellular function. Explicit molecular modelling of biologically relevant membrane systems is computationally expensive due to the large number of solvent particles and slow membrane kinetics. Coarse-grained solvent-free membrane models offer efficient sampling but sacrifice realistic kinetics, thereby limiting the ability to predict pathways and mechanisms of membrane processes. Here, we present a framework for integrating coarse-grained membrane models with continuum-based hydrodynamics. This framework facilitates efficient simulation of large biomembrane systems with large timesteps, while achieving realistic equilibrium and non-equilibrium kinetics. It helps to bridge between the nanometer/nanosecond spatiotemporal resolutions of coarse-grained models and biologically relevant time- and lengthscales. As a demonstration, we investigate fluctuations of red blood cells, with varying cytoplasmic viscosities, in 150-milliseconds-long trajectories, and compare kinetic properties against single-cell experimental observations.
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19
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Pang YT, Ge Z, Zhang B, Xiu P, Li Q, Wang Y. Pore formation induced by nanoparticles binding to a lipid membrane. NANOSCALE 2020; 12:7902-7913. [PMID: 32227042 DOI: 10.1039/c9nr10534d] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
Nanoparticles (NPs) enter a cell primarily via endocytosis, during which they are engulfed by the cell and reside in lipid vesicles named endosomes. Apart from when an endosome is pinched off the plasma membrane, structural integrity of its lipid membrane is usually well maintained. Under certain circumstances, however, such structural integrity can be considerably perturbed by a nanoparticle. For instance, recent experiments [Chu et al., Sci. Rep., 2014, 4, 4495] indicate that nanodiamonds with sharp corners can escape from an endosome by piercing its lipid membrane. Nonetheless, the energetics of this behavior and how it may be controlled by membrane adhesion and NP morphology remain unclear. In this work, we employ continuum modeling to investigate membrane pore formation induced by the spontaneous binding of a sharp nanoparticle. Based on two axial-symmetric NP models, we characterize the indispensable role played by curvature heterogeneity, membrane adhesion, and the sharpness as well as the size of a nanoparticle in 'breaking' a lipid membrane. Apart from revealing a general mechanism of NP binding-induced membrane pore formation, our results provide the reference for improving the endosomal escape of nanoparticles through manipulating their morphology, a direction that can be explored either independently or combined with existing strategies targeting NP surface chemistry.
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Affiliation(s)
- Yui Tik Pang
- Department of Physics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong.
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20
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Khalid S, Rouse SL. Simulation of subcellular structures. Curr Opin Struct Biol 2020; 61:167-172. [DOI: 10.1016/j.sbi.2019.12.017] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2019] [Revised: 12/18/2019] [Accepted: 12/26/2019] [Indexed: 12/21/2022]
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21
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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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22
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Hossein A, Deserno M. Spontaneous Curvature, Differential Stress, and Bending Modulus of Asymmetric Lipid Membranes. Biophys J 2019; 118:624-642. [PMID: 31954503 DOI: 10.1016/j.bpj.2019.11.3398] [Citation(s) in RCA: 110] [Impact Index Per Article: 22.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2019] [Revised: 11/20/2019] [Accepted: 11/25/2019] [Indexed: 12/24/2022] Open
Abstract
Lipid bilayers can exhibit asymmetric states, in which the physical characteristics of one leaflet differ from those of the other. This most visibly manifests in a different lipid composition, but it can also involve opposing lateral stresses in each leaflet that combine to an overall vanishing membrane tension. Here, we use theoretical modeling and coarse-grained simulation to explore the interplay between a compositional asymmetry and a nonvanishing differential stress. Minimizing the total elastic energy leads to a preferred spontaneous curvature that balances torques due to both bending moments and differential stress, with sometimes unexpected consequences. For instance, asymmetric flat bilayers, whose specific areas in each leaflet are matched to those of corresponding tensionless symmetric flat membranes, still exhibit a residual differential stress because the conditions of vanishing area strain and vanishing bending moment differ. We also measure the curvature rigidity of asymmetric bilayers and find that a sufficiently strong differential stress, but not compositional asymmetry alone, can increase the bending modulus. The likely cause is a stiffening of the compressed leaflet, which appears to be related to its gel transition but not identical with it. We finally show that the impact of cholesterol on differential stress depends on the relative strength of elastic and thermodynamic driving forces: if cholesterol solvates equally well in both leaflets, it will redistribute to cancel both leaflet tensions almost completely, but if its partitioning free energy prefers one leaflet over the other, the resulting distribution bias may even create differential stress. Because cells keep most of their lipid bilayers in an asymmetric nonequilibrium steady state, our findings suggest that biomembranes are elastically more complex than previously thought: besides a spontaneous curvature, they might also exhibit significant differential stress, which could strongly affect their curvature energetics.
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Affiliation(s)
- Amirali Hossein
- Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania
| | - Markus Deserno
- Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania.
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23
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Abstract
Low resolution coarse-grained (CG) models are widely adopted for investigating phenomena that cannot be effectively simulated with all-atom (AA) models. Since the development of the many-body dissipative particle dynamics method, CG models have increasingly supplemented conventional pair potentials with one-body potentials of the local density (LD) around each site. These LD potentials appear to significantly extend the transferability of CG models, while also enabling more accurate descriptions of thermodynamic properties, interfacial phenomena, and many-body correlations. In this work, we systematically examine the properties of LD potentials. We first derive and numerically demonstrate a nontrivial transformation of pair and LD potentials that leaves the total forces and equilibrium distribution invariant. Consequently, the pair and LD potentials determined via bottom-up methods are not unique. We then investigate the sensitivity of CG models for glycerol to the weighting function employed for defining the local density. We employ the multiscale coarse-graining (MS-CG) method to simultaneously parameterize both pair and LD potentials. When employing a short-ranged Lucy function that defines the local density from the first solvation shell, the MS-CG model accurately reproduces the pair structure, pressure-density equation of state, and liquid-vapor interfacial profile of the AA model. The accuracy of the model generally decreases as the range of the Lucy function increases further. The MS-CG model provides similar accuracy when a smoothed Heaviside function is employed to define the local density from the first solvation shell. However, the model performs less well when this function acts on either longer or shorter length scales.
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Affiliation(s)
- Michael R DeLyser
- Department of Chemistry, Penn State University, University Park, Pennsylvania 16802, USA
| | - W G Noid
- Department of Chemistry, Penn State University, University Park, Pennsylvania 16802, USA
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24
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Lebold KM, Noid WG. Dual-potential approach for coarse-grained implicit solvent models with accurate, internally consistent energetics and predictive transferability. J Chem Phys 2019; 151:164113. [PMID: 31675902 DOI: 10.1063/1.5125246] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Abstract
The dual-potential approach promises coarse-grained (CG) models that accurately reproduce both structural and energetic properties, while simultaneously providing predictive estimates for the temperature-dependence of the effective CG potentials. In this work, we examine the dual-potential approach for implicit solvent CG models that reflect large entropic effects from the eliminated solvent. Specifically, we construct implicit solvent models at various resolutions, R, by retaining a fraction 0.10 ≤ R ≤ 0.95 of the molecules from a simple fluid of Lennard-Jones spheres. We consider the dual-potential approach in both the constant volume and constant pressure ensembles across a relatively wide range of temperatures. We approximate the many-body potential of mean force for the remaining solutes with pair and volume potentials, which we determine via multiscale coarse-graining and self-consistent pressure-matching, respectively. Interestingly, with increasing temperature, the pair potentials appear increasingly attractive, while the volume potentials become increasingly repulsive. The dual-potential approach not only reproduces the atomic energetics but also quite accurately predicts this temperature-dependence. We also derive an exact relationship between the thermodynamic specific heat of an atomic model and the energetic fluctuations that are observable at the CG resolution. With this generalized fluctuation relationship, the approximate CG models quite accurately reproduce the thermodynamic specific heat of the underlying atomic model.
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Affiliation(s)
- Kathryn M Lebold
- Department of Chemistry, Penn State University, University Park, Pennsylvania 16802, USA
| | - W G Noid
- Department of Chemistry, Penn State University, University Park, Pennsylvania 16802, USA
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25
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Recent Advances in Coarse-Grained Models for Biomolecules and Their Applications. Int J Mol Sci 2019; 20:ijms20153774. [PMID: 31375023 PMCID: PMC6696403 DOI: 10.3390/ijms20153774] [Citation(s) in RCA: 65] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2019] [Revised: 07/28/2019] [Accepted: 07/30/2019] [Indexed: 12/23/2022] Open
Abstract
Molecular dynamics simulations have emerged as a powerful tool to study biological systems at varied length and timescales. The conventional all-atom molecular dynamics simulations are being used by the wider scientific community in routine to capture the conformational dynamics and local motions. In addition, recent developments in coarse-grained models have opened the way to study the macromolecular complexes for time scales up to milliseconds. In this review, we have discussed the principle, applicability and recent development in coarse-grained models for biological systems. The potential of coarse-grained simulation has been reviewed through state-of-the-art examples of protein folding and structure prediction, self-assembly of complexes, membrane systems and carbohydrates fiber models. The multiscale simulation approaches have also been discussed in the context of their emerging role in unravelling hierarchical level information of biosystems. We conclude this review with the future scope of coarse-grained simulations as a constantly evolving tool to capture the dynamics of biosystems.
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26
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Dunn NJH, Gutama B, Noid WG. Simple Simulation Model for Exploring the Effects of Solvent and Structure on Asphaltene Aggregation. J Phys Chem B 2019; 123:6111-6122. [DOI: 10.1021/acs.jpcb.9b04275] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Nicholas J. H. Dunn
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Besha Gutama
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - W. G. Noid
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
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27
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Rosenberger D, van der Vegt NFA. Relative entropy indicates an ideal concentration for structure-based coarse graining of binary mixtures. Phys Rev E 2019; 99:053308. [PMID: 31212527 DOI: 10.1103/physreve.99.053308] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2019] [Indexed: 06/09/2023]
Abstract
Many methodological approaches have been proposed to improve systematic or bottom-up coarse-graining techniques to enhance the representability and transferability of the derived interaction potentials. Transferability describes the ability of a coarse-grained (CG) model to be predictive, i.e., to describe a system at state points different from those chosen for parametrization. Whereas the representability characterizes the accuracy of a CG model to reproduce target properties of the underlying reference or fine-grained model at a given state point. In this article, we shift the focus away from methodological aspects and rather raise the question whether we can overcome the disadvantages of a given method in terms of representability and transferability by systematically selecting the state point at which the CG model gets parametrized. We answer this question by applying the inverse Monte Carlo (IMC) approach-a structure-based coarse-graining method-to derive effective interactions for binary mixtures of simple Lennard-Jones (LJ) particles, which are different in size. For such simple systems we indeed can identify a concentration where the derived potentials show the best performance in terms of structural representability and transferability. This specific concentration is identified by computing the relative entropy which quantifies the information loss between different IMC models and the reference LJ model at varying mixture compositions. Further, we show that an IMC model for mixtures of n-hexane and n-perfluorohexane shows the same trend in transferability as the IMC models for the LJ system. All derived models are more transferable in the direction of increasing concentration of the larger-sized compound.
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Affiliation(s)
- David Rosenberger
- Eduard Zintl Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Darmstadt, 64287, Germany
| | - Nico F A van der Vegt
- Eduard Zintl Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Darmstadt, 64287, Germany
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28
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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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29
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Leonard AN, Wang E, Monje-Galvan V, Klauda JB. Developing and Testing of Lipid Force Fields with Applications to Modeling Cellular Membranes. Chem Rev 2019; 119:6227-6269. [DOI: 10.1021/acs.chemrev.8b00384] [Citation(s) in RCA: 53] [Impact Index Per Article: 10.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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30
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Smith DJ, Klauda JB, Sodt AJ. Simulation Best Practices for Lipid Membranes [Article v1.0]. LIVING JOURNAL OF COMPUTATIONAL MOLECULAR SCIENCE 2019; 1:5966. [PMID: 36204133 PMCID: PMC9534443 DOI: 10.33011/livecoms.1.1.5966] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/06/2023]
Abstract
We establish a reliable and robust standardization of settings for practical molecular dynamics (MD) simulations of pure and mixed (single- and multi-component) lipid bilayer membranes. In lipid membranes research, particle-based molecular simulations are a powerful tool alongside continuum theory, lipidomics, and model, in vitro, and in vivo experiments. Molecular simulations can provide precise and reproducible spatiotemporal (atomic- and femtosecond-level) information about membrane structure, mechanics, thermodynamics, kinetics, and dynamics. Yet the simulation of lipid membranes can be a daunting task, given the uniqueness of lipid membranes relative to conventional liquid-liquid and solid-liquid interfaces, the immense and complex thermodynamic and statistical mechanical theory, the diversity of multiscale lipid models, limitations of modern computing power, the difficulty and ambiguity of simulation controls, finite size effects, competitive continuum simulation alternatives, and the desired application, including vesicle experiments and biological membranes. These issues can complicate an essential understanding of the field of lipid membranes, and create major bottlenecks to simulation advancement. In this article, we clarify these issues and present a consistent, thorough, and user-friendly framework for the design of state-of-the-art lipid membrane MD simulations. We hope to allow early-career researchers to quickly overcome common obstacles in the field of lipid membranes and reach maximal impact in their simulations.
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Affiliation(s)
- David J. Smith
- Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara, CA, USA
| | - Jeffery B. Klauda
- Department of Chemical and Biomolecular Engineering and Biophysics Program, University of Maryland, College Park, MD, USA
| | - Alexander J. Sodt
- Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, MD, USA
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31
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Tesei G, Vazdar M, Lund M. Coarse-grained model of titrating peptides interacting with lipid bilayers. J Chem Phys 2018; 149:244108. [PMID: 30599743 DOI: 10.1063/1.5058234] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Molecular-level computer simulations of peptide aggregation, translocation, and protonation at and in biomembranes are impeded by the large time and length scales involved. We present a computationally efficient, coarse-grained, and solvent-free model for the interaction between lipid bilayers and peptides. The model combines an accurate description of mechanical membrane properties with a new granular representation of the dielectric mismatch between lipids and the aqueous phase. All-atom force fields can be easily mapped onto the coarse-grained model, and parameters for coarse-grained monopeptides accurately extrapolate to membrane permeation free energies for the corresponding dipeptides and tripeptides. Acid-base equilibria of titratable amino acid residues are further studied using a constant-pH ensemble, capturing protonation state changes upon membrane translocation. Important differences between histidine, lysine, and arginine are observed, which are in good agreement with experimental observations.
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Affiliation(s)
- Giulio Tesei
- Division of Theoretical Chemistry, Lund University, P.O. Box 124, SE-22100 Lund, Sweden
| | - Mario Vazdar
- Division of Organic Chemistry and Biochemistry, Rudjer Bošković Institute, P.O. Box 180, HR-10002 Zagreb, Croatia
| | - Mikael Lund
- Division of Theoretical Chemistry, Lund University, P.O. Box 124, SE-22100 Lund, Sweden
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32
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Pannuzzo M, McDargh ZA, Deserno M. The role of scaffold reshaping and disassembly in dynamin driven membrane fission. eLife 2018; 7:39441. [PMID: 30561335 PMCID: PMC6355196 DOI: 10.7554/elife.39441] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2018] [Accepted: 12/13/2018] [Indexed: 12/11/2022] Open
Abstract
The large GTPase dynamin catalyzes membrane fission in eukaryotic cells, but despite three decades of experimental work, competing and partially conflicting models persist regarding some of its most basic actions. Here we investigate the mechanical and functional consequences of dynamin scaffold shape changes and disassembly with the help of a geometrically and elastically realistic simulation model of helical dynamin-membrane complexes. Beyond changes of radius and pitch, we emphasize the crucial role of a third functional motion: an effective rotation of the filament around its longitudinal axis, which reflects alternate tilting of dynamin’s PH binding domains and creates a membrane torque. We also show that helix elongation impedes fission, hemifission is reached via a small transient pore, and coat disassembly assists fission. Our results have several testable structural consequences and help to reconcile mutual conflicting aspects between the two main present models of dynamin fission—the two-stage and the constrictase model. When cells take up material from their surroundings, they must first transport this cargo across their outer membrane, a flexible sheet of tightly organized fat molecules that act as a barrier to the environment. Cells can achieve this by letting their membrane surround the object, pulling it inwards until it is contained in a pouch that bulges into the cell. This bag is then corded up so it splits off from the outer membrane. The ‘cord’ is a protein called dynamin, which is thought to form a tight spiral around the bag’s neck, closing it over and pinching it away. The structure of dynamin is fairly well known, and yet several theories compete to explain how it may snap the bag off the outer membrane. Here, Pannuzzo et al. have created a computer simulation that faithfully replicates the geometry and the elasticity of the membrane and of dynamin, and used it to test different ways the protein could work. The first test featured simple constriction, where the dynamin spiral contracts around the membrane to pinch it; this only separated the bag from the membrane after implausibly tight constriction. The second test added elongation, with the spiral lengthening as well as reducing its diameter, but this further reduced the ability for the protein to snap off the membrane. The final test combined constriction and rotation, whereby dynamin ‘twirls’ as it presses on the neck of the bag: this succeeded in efficiently severing the membrane once the dynamin spiral disassembled. Indeed, the simulations suggested that dynamin might start to dismantle while it constricts, without compromising its role. In fact, getting rid of excess length as the protein contracts helps to dissolve any remnants of a membrane connection. Defects in dynamin are associated with conditions such as centronuclear myopathy and Charcot‐Marie‐Tooth peripheral neuropathy. Recent research also indicates that the protein is involved in a much wider range of neurological disorders that include Alzheimer's, Parkinson's, Huntington's, and amyotrophic lateral sclerosis. The models created by Pannuzzo et al. are useful tools to understand how dynamin and similar proteins work and sometimes fail.
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Affiliation(s)
- Martina Pannuzzo
- Department of Physics, Carnegie Mellon University, Pittsburgh, United States
| | - Zachary A McDargh
- Department of Physics, Carnegie Mellon University, Pittsburgh, United States
| | - Markus Deserno
- Department of Physics, Carnegie Mellon University, Pittsburgh, United States
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33
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Diggins P, Liu C, Deserno M, Potestio R. Optimal Coarse-Grained Site Selection in Elastic Network Models of Biomolecules. J Chem Theory Comput 2018; 15:648-664. [PMID: 30514085 PMCID: PMC6391041 DOI: 10.1021/acs.jctc.8b00654] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
Elastic network models, simple structure-based representations of biomolecules where atoms interact via short-range harmonic potentials, provide great insight into a molecule's internal dynamics and mechanical properties at extremely low computational cost. Their efficiency and effectiveness have made them a pivotal instrument in the computer-aided study of proteins and, since a few years, also of nucleic acids. In general, the coarse-grained sites, i.e. those effective force centers onto which the all-atom structure is mapped, are constructed based on intuitive rules: a typical choice for proteins is to retain only the C α atoms of each amino acid. However, a mapping strategy relying only on the atom type and not the local properties of its embedding can be suboptimal compared to a more careful selection. Here, we present a strategy in which the subset of atoms, each of which is mapped onto a unique coarse-grained site of the model, is selected in a stochastic search aimed at optimizing a cost function. The latter is taken to be a simple measure of the consistency between the harmonic approximation of an elastic network model and the harmonic model obtained through exact integration of the discarded degrees of freedom. The method is applied to two representatives of structurally very different types of biomolecules: the protein adenylate kinase and the RNA molecule adenine riboswitch. Our analysis quantifies the substantial impact that an algorithm-driven selection of coarse-grained sites can have on a model's properties.
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Affiliation(s)
- Patrick Diggins
- Department of Physics , Carnegie Mellon University , Pittsburgh , Pennsylvania 15213 , United States
| | - Changjiang Liu
- Department of Physics , Carnegie Mellon University , Pittsburgh , Pennsylvania 15213 , United States.,Department of Biophysics , University of Michigan , Ann Arbor , Michigan 48109 , United States
| | - Markus Deserno
- Department of Physics , Carnegie Mellon University , Pittsburgh , Pennsylvania 15213 , United States
| | - Raffaello Potestio
- Physics Department , University of Trento , via Sommarive, 14 I-38123 Trento , Italy.,INFN-TIFPA, Trento Institute for Fundamental Physics and Applications , I-38123 Trento , Italy
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34
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Ramakrishnan N, Bradley RP, Tourdot RW, Radhakrishnan R. Biophysics of membrane curvature remodeling at molecular and mesoscopic lengthscales. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:273001. [PMID: 29786613 PMCID: PMC6066392 DOI: 10.1088/1361-648x/aac702] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/19/2023]
Abstract
At the micron scale, where cell organelles display an amazing complexity in their shape and organization, the physical properties of a biological membrane can be better-understood using continuum models subject to thermal (stochastic) undulations. Yet, the chief orchestrators of these complex and intriguing shapes are a specialized class of membrane associating often peripheral proteins called curvature remodeling proteins (CRPs) that operate at the molecular level through specific protein-lipid interactions. We review multiscale methodologies to model these systems at the molecular as well as at the mesoscopic and cellular scales, and also present a free energy perspective of membrane remodeling through the organization and assembly of CRPs. We discuss the morphological space of nearly planar to highly curved membranes, methods to include thermal fluctuations, and review studies that model such proteins as curvature fields to describe the emergent curved morphologies. We also discuss several mesoscale models applied to a variety of cellular processes, where the phenomenological parameters (such as curvature field strength) are often mapped to models of real systems based on molecular simulations. Much insight can be gained from the calculation of free energies of membranes states with protein fields, which enable accurate mapping of the state and parameter values at which the membrane undergoes morphological transformations such as vesiculation or tubulation. By tuning the strength, anisotropy, and spatial organization of the curvature-field, one can generate a rich array of membrane morphologies that are highly relevant to shapes of several cellular organelles. We review applications of these models to budding of vesicles commonly seen in cellular signaling and trafficking processes such as clathrin mediated endocytosis, sorting by the ESCRT protein complexes, and cellular exocytosis regulated by the exocyst complex. We discuss future prospects where such models can be combined with other models for cytoskeletal assembly, and discuss their role in understanding the effects of cell membrane tension and the mechanics of the extracellular microenvironment on cellular processes.
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Affiliation(s)
- N Ramakrishnan
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, United States of America
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35
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Chen L, Li X, Zhang Y, Chen T, Xiao S, Liang H. Morphological and mechanical determinants of cellular uptake of deformable nanoparticles. NANOSCALE 2018; 10:11969-11979. [PMID: 29904774 DOI: 10.1039/c8nr01521j] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Understanding the interactions of nanoparticles (NPs) with cell membranes and regulating their cellular uptake processes are of fundamental importance to the design of drug delivery systems with minimum toxicity, high efficiency and long circulation time. Employing the procedure of coarse-graining, we built an elastically deformable NP model with tunable morphological and mechanical properties. We found that the cellular uptake of deformable NPs depends on their shape: an increase in the particle elasticity significantly slows the uptake rate of spherical NPs, slightly retards that of prolate NPs, and promotes the uptake of oblate NPs. The intrinsic mechanisms have been carefully investigated through analysis of the endocytic mechanisms and free energy calculations. These findings provide unique insights into how deformable NPs penetrate across cell membranes and offer novel possibilities for designing effective NP-based carriers for drug delivery.
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Affiliation(s)
- Liping Chen
- CAS Key Laboratory of Soft Matter Chemistry, iChEM (Collaborative Innovation Center of Chemistry for Energy Materials), Department of Polymer Science and Engineering, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China.
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36
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Sadeghi M, Weikl TR, Noé F. Particle-based membrane model for mesoscopic simulation of cellular dynamics. J Chem Phys 2018; 148:044901. [PMID: 29390800 DOI: 10.1063/1.5009107] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
We present a simple and computationally efficient coarse-grained and solvent-free model for simulating lipid bilayer membranes. In order to be used in concert with particle-based reaction-diffusion simulations, the model is purely based on interacting and reacting particles, each representing a coarse patch of a lipid monolayer. Particle interactions include nearest-neighbor bond-stretching and angle-bending and are parameterized so as to reproduce the local membrane mechanics given by the Helfrich energy density over a range of relevant curvatures. In-plane fluidity is implemented with Monte Carlo bond-flipping moves. The physical accuracy of the model is verified by five tests: (i) Power spectrum analysis of equilibrium thermal undulations is used to verify that the particle-based representation correctly captures the dynamics predicted by the continuum model of fluid membranes. (ii) It is verified that the input bending stiffness, against which the potential parameters are optimized, is accurately recovered. (iii) Isothermal area compressibility modulus of the membrane is calculated and is shown to be tunable to reproduce available values for different lipid bilayers, independent of the bending rigidity. (iv) Simulation of two-dimensional shear flow under a gravity force is employed to measure the effective in-plane viscosity of the membrane model and show the possibility of modeling membranes with specified viscosities. (v) Interaction of the bilayer membrane with a spherical nanoparticle is modeled as a test case for large membrane deformations and budding involved in cellular processes such as endocytosis. The results are shown to coincide well with the predicted behavior of continuum models, and the membrane model successfully mimics the expected budding behavior. We expect our model to be of high practical usability for ultra coarse-grained molecular dynamics or particle-based reaction-diffusion simulations of biological systems.
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Affiliation(s)
- Mohsen Sadeghi
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Thomas R Weikl
- Department of Theory and Bio-Systems, Max Planck Institute of Colloids and Interfaces, Science Park Golm, 14424 Potsdam, Germany
| | - Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
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37
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Wan M, Gao L, Fang W. Implicit-solvent dissipative particle dynamics force field based on a four-to-one coarse-grained mapping scheme. PLoS One 2018; 13:e0198049. [PMID: 29795682 PMCID: PMC5967728 DOI: 10.1371/journal.pone.0198049] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2018] [Accepted: 05/12/2018] [Indexed: 11/30/2022] Open
Abstract
A new set of efficient solvent-free dissipative particle dynamics (DPD) force fields was developed for phospholipids and peptides. To enhance transferability, this model maps around four heavy atoms and their connected hydrogen atoms into a coarse-grained elementary bead based on functional group. The effective hybrid potential between any pair of beads is composed of a short-range repulsive soft-core potential that directly adopts the form of an explicit-solvent DPD model and a long-range attractive hydrophobic potential. The parameters of the attractive potentials for lipid molecules were obtained by fitting the explicit-solvent DPD simulation of one bead of any type in a water box, then finely tuning it until the bilayer membrane properties obtained in the explicit-solvent model were matched. These parameters were further extended to amino acids according to bead type. The structural and elastic properties of bilayer membranes, free energy profiles for a lipid flip-flop and amino acid analogues translocating across the membrane, and membrane pore formation induced by antimicrobial peptides obtained from this solvent-free DPD force field considerably agreed with the explicit-solvent DPD results. Importantly, the efficiency of this method is guaranteed to accelerate the assembly of vesicles composed of several thousand lipids by up to 50-fold, rendering the experimental liposome dynamics as well as membrane-peptide interactions feasible at accessible computational expense.
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Affiliation(s)
- Mingwei Wan
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing, China
| | - Lianghui Gao
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing, China
- * E-mail:
| | - Weihai Fang
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing, China
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38
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Kuo AT, Okazaki S, Shinoda W. Transferable coarse-grained model for perfluorosulfonic acid polymer membranes. J Chem Phys 2017; 147:094904. [DOI: 10.1063/1.4986287] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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39
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Sevink GJA, Schmid F, Kawakatsu T, Milano G. Combining cell-based hydrodynamics with hybrid particle-field simulations: efficient and realistic simulation of structuring dynamics. SOFT MATTER 2017; 13:1594-1623. [PMID: 28128838 DOI: 10.1039/c6sm02252a] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We have extended an existing hybrid MD-SCF simulation technique that employs a coarsening step to enhance the computational efficiency of evaluating non-bonded particle interactions. This technique is conceptually equivalent to the single chain in mean-field (SCMF) method in polymer physics, in the sense that non-bonded interactions are derived from the non-ideal chemical potential in self-consistent field (SCF) theory, after a particle-to-field projection. In contrast to SCMF, however, MD-SCF evolves particle coordinates by the usual Newton's equation of motion. Since collisions are seriously affected by the softening of non-bonded interactions that originates from their evaluation at the coarser continuum level, we have devised a way to reinsert the effect of collisions on the structural evolution. Merging MD-SCF with multi-particle collision dynamics (MPCD), we mimic particle collisions at the level of computational cells and at the same time properly account for the momentum transfer that is important for a realistic system evolution. The resulting hybrid MD-SCF/MPCD method was validated for a particular coarse-grained model of phospholipids in aqueous solution, against reference full-particle simulations and the original MD-SCF model. We additionally implemented and tested an alternative and more isotropic finite difference gradient. Our results show that efficiency is improved by merging MD-SCF with MPCD, as properly accounting for hydrodynamic interactions considerably speeds up the phase separation dynamics, with negligible additional computational costs compared to efficient MD-SCF. This new method enables realistic simulations of large-scale systems that are needed to investigate the applications of self-assembled structures of lipids in nanotechnologies.
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Affiliation(s)
- G J A Sevink
- Leiden Institute of Chemistry, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands.
| | - F Schmid
- Institut for Physik, Johannes Gutenberg Univeristat Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
| | - T Kawakatsu
- Department of Physics, Tohoku University, Aoba, Aoba-ku, Sendai 980-8578, Japan
| | - G Milano
- Dipartimento di Chimica e Biologia, Universit degli Studi di Salerno, via Ponte don Melillo, Fisciano, Italy
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40
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41
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Dunn NJH, Foley TT, Noid WG. Van der Waals Perspective on Coarse-Graining: Progress toward Solving Representability and Transferability Problems. Acc Chem Res 2016; 49:2832-2840. [PMID: 27993007 DOI: 10.1021/acs.accounts.6b00498] [Citation(s) in RCA: 71] [Impact Index Per Article: 8.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
Low-resolution coarse-grained (CG) models provide the necessary efficiency for simulating phenomena that are inaccessible to more detailed models. However, in order to realize their considerable promise, CG models must accurately describe the relevant physical forces and provide useful predictions. By formally integrating out the unnecessary details from an all-atom (AA) model, "bottom-up" approaches can, at least in principle, quantitatively reproduce the structural and thermodynamic properties of the AA model that are observable at the CG resolution. In practice, though, bottom-up approaches only approximate this "exact coarse-graining" procedure. The resulting models typically reproduce the intermolecular structure of AA models at a single thermodynamic state point but often describe other state points less accurately and, moreover, tend to provide a poor description of thermodynamic properties. These two limitations have been coined the "transferability" and "representability" problems, respectively. Perhaps, the simplest and most commonly discussed manifestation of the representability problem regards the tendency of structure-based CG models to dramatically overestimate the pressure. Furthermore, when these models are adjusted to reproduce the pressure, they provide a poor description of the compressibility. More generally, it is sometimes suggested that CG models are fundamentally incapable of reproducing both structural and thermodynamic properties. After all, there is no such thing as a "free lunch"; any significant gain in computational efficiency should come at the cost of significant model limitations. At least in the case of structural and thermodynamic properties, though, we optimistically propose that this may be a false dichotomy. Accordingly, we have recently re-examined the "exact coarse-graining" procedure and investigated the intrinsic consequences of representing an AA model in reduced resolution. These studies clarify the origin and inter-relationship of representability and transferability problems. Both arise as consequences of transferring thermodynamic information from the high resolution configuration space and encoding this information into the many-body potential of mean force (PMF), that is, the potential that emerges from an exact coarse-graining procedure. At least in principle, both representability and transferability problems can be resolved by properly addressing this thermodynamic information. In particular, we have demonstrated that "pressure-matching" provides a practical and rigorous means for addressing the density dependence of the PMF. The resulting bottom-up models accurately reproduce the structure, equilibrium density, compressibility, and pressure equation of state for AA models of molecular liquids. Additionally, we have extended this approach to develop transferable potentials that provide similar accuracy for heptane-toluene mixtures. Moreover, these potentials provide predictive accuracy for modeling concentrations that were not considered in their parametrization. More generally, this work suggests a "van der Waals" perspective on coarse-graining, in which conventional structure-based methods accurately describe the configuration dependence of the PMF, while independent variational principles infer the thermodynamic information that is necessary to resolve representability and transferability problems.
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Affiliation(s)
- Nicholas J. H. Dunn
- Department
of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Thomas T. Foley
- Department
of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - William G. Noid
- Department
of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
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42
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Kheyfets B, Galimzyanov T, Drozdova A, Mukhin S. Analytical calculation of the lipid bilayer bending modulus. Phys Rev E 2016; 94:042415. [PMID: 27841551 DOI: 10.1103/physreve.94.042415] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2016] [Indexed: 11/07/2022]
Abstract
Bending and Gaussian moduli of a homogenious single-component lipid bilayer are calculated analytically using microscopic model of the lipid hydrocarbon chains. The approach allows for thermodynamic averaging over different chains conformations. Each chain is modeled as a flexible string with finite bending rigidity and an incompressible cross-section area. The interchain steric repulsion is accounted for self-consistently determined single-chain confining parabolic potential. The model provides a simple analytical expression for the membrane bending modulus, which falls within a range of experimental values. An observed dependence of the modulus on hydrocarbon chain length is also reproduced. Correspondence between our microscopic model and the membrane theory of elasticity is established.
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Affiliation(s)
- Boris Kheyfets
- National University of Science and Technology MISIS, Leninskiy prospekt 4, Moscow 119049, Russia
| | - Timur Galimzyanov
- National University of Science and Technology MISIS, Leninskiy prospekt 4, Moscow 119049, Russia
| | - Anna Drozdova
- National University of Science and Technology MISIS, Leninskiy prospekt 4, Moscow 119049, Russia
| | - Sergei Mukhin
- National University of Science and Technology MISIS, Leninskiy prospekt 4, Moscow 119049, Russia
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43
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Gardner JM, Deserno M, Abrams CF. Effect of intrinsic curvature and edge tension on the stability of binary mixed-membrane three-junctions. J Chem Phys 2016; 145:074901. [DOI: 10.1063/1.4960433] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jasmine M. Gardner
- Department of Chemical and Biological Engineering, Drexel University, 3141 Chestnut St., Philadelphia, Pennsylvania 19104, USA
| | - Markus Deserno
- Department of Physics, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, Pennsylvania 15213, USA
| | - Cameron F. Abrams
- Department of Chemical and Biological Engineering, Drexel University, 3141 Chestnut St., Philadelphia, Pennsylvania 19104, USA
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44
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Sigurdsson JK, Atzberger PJ. Hydrodynamic coupling of particle inclusions embedded in curved lipid bilayer membranes. SOFT MATTER 2016; 12:6685-6707. [PMID: 27373277 DOI: 10.1039/c6sm00194g] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We develop theory and computational methods to investigate particle inclusions embedded within curved lipid bilayer membranes. We consider the case of spherical lipid vesicles where inclusion particles are coupled through (i) intramembrane hydrodynamics, (ii) traction stresses with the external and trapped solvent fluid, and (iii) intermonolayer slip between the two leaflets of the bilayer. We investigate relative to flat membranes how the membrane curvature and topology augment hydrodynamic responses. We show how both the translational and rotational mobility of protein inclusions are effected by the membrane curvature, ratio of intramembrane viscosity to solvent viscosity, and intermonolayer slip. For general investigations of many-particle dynamics, we also discuss how our approaches can be used to treat the collective diffusion and hydrodynamic coupling within spherical bilayers.
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Affiliation(s)
| | - Paul J Atzberger
- Department of Mathematics, University of California, Santa Barbara, USA.
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45
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Kreis K, Potestio R. The relative entropy is fundamental to adaptive resolution simulations. J Chem Phys 2016; 145:044104. [DOI: 10.1063/1.4959169] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Affiliation(s)
- Karsten Kreis
- Max-Planck-Institut für Polymerforschung, Ackermannweg 10, 55128 Mainz, Germany
- Graduate School Materials Science in Mainz, Staudingerweg 9, 55128 Mainz, Germany
| | - Raffaello Potestio
- Max-Planck-Institut für Polymerforschung, Ackermannweg 10, 55128 Mainz, Germany
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46
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Nagai T, Pantelopulos GA, Takahashi T, Straub JE. On the use of mass scaling for stable and efficient simulated tempering with molecular dynamics. J Comput Chem 2016; 37:2017-28. [PMID: 27338239 DOI: 10.1002/jcc.24430] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2016] [Revised: 04/30/2016] [Accepted: 05/30/2016] [Indexed: 01/12/2023]
Abstract
Simulated tempering (ST) is a generalized-ensemble algorithm that employs trajectories exploring a range of temperatures to effectively sample rugged energy landscapes. When implemented using the molecular dynamics method, ST can require the use of short time steps for ensuring the stability of trajectories at high temperatures. To address this shortcoming, a mass-scaling ST (MSST) method is presented in which the particle mass is scaled in proportion to the temperature. Mass scaling in the MSST method leads to velocity distributions that are independent of temperature and eliminates the need for velocity scaling after the accepted temperature updates that are required in conventional ST simulations. The homogeneity in time scales with changing temperature improves the stability of simulations and allows for the use of longer time steps at high temperatures. As a result, the MSST is found to be more efficient than the standard ST method, particularly for cases in which a large temperature range is employed. © 2016 Wiley Periodicals, Inc.
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Affiliation(s)
- Tetsuro Nagai
- Department of Bioinformatics, College of Life Sciences, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan
| | | | - Takuya Takahashi
- Department of Bioinformatics, College of Life Sciences, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan
| | - John E Straub
- Department of Chemistry, Boston University, Boston, Massachusetts, 02215
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47
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Foley TT, Shell MS, Noid WG. The impact of resolution upon entropy and information in coarse-grained models. J Chem Phys 2016; 143:243104. [PMID: 26723589 DOI: 10.1063/1.4929836] [Citation(s) in RCA: 91] [Impact Index Per Article: 11.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
By eliminating unnecessary degrees of freedom, coarse-grained (CG) models tremendously facilitate numerical calculations and theoretical analyses of complex phenomena. However, their success critically depends upon the representation of the system and the effective potential that governs the CG degrees of freedom. This work investigates the relationship between the CG representation and the many-body potential of mean force (PMF), W, which is the appropriate effective potential for a CG model that exactly preserves the structural and thermodynamic properties of a given high resolution model. In particular, we investigate the entropic component of the PMF and its dependence upon the CG resolution. This entropic component, SW, is a configuration-dependent relative entropy that determines the temperature dependence of W. As a direct consequence of eliminating high resolution details from the CG model, the coarsening process transfers configurational entropy and information from the configuration space into SW. In order to further investigate these general results, we consider the popular Gaussian Network Model (GNM) for protein conformational fluctuations. We analytically derive the exact PMF for the GNM as a function of the CG representation. In the case of the GNM, -TSW is a positive, configuration-independent term that depends upon the temperature, the complexity of the protein interaction network, and the details of the CG representation. This entropic term demonstrates similar behavior for seven model proteins and also suggests, in each case, that certain resolutions provide a more efficient description of protein fluctuations. These results may provide general insight into the role of resolution for determining the information content, thermodynamic properties, and transferability of CG models. Ultimately, they may lead to a rigorous and systematic framework for optimizing the representation of CG models.
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Affiliation(s)
- Thomas T Foley
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - M Scott Shell
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA
| | - W G Noid
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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48
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Wang X, Deserno M. Determining the Lipid Tilt Modulus by Simulating Membrane Buckles. J Phys Chem B 2016; 120:6061-73. [DOI: 10.1021/acs.jpcb.6b02016] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Affiliation(s)
- Xin Wang
- Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States
| | - Markus Deserno
- Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States
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49
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Dunn NJH, Noid WG. Bottom-up coarse-grained models that accurately describe the structure, pressure, and compressibility of molecular liquids. J Chem Phys 2015; 143:243148. [DOI: 10.1063/1.4937383] [Citation(s) in RCA: 76] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
Affiliation(s)
- Nicholas J. H. Dunn
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - W. G. Noid
- Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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Zhang L, Yethiraj A, Cui Q. Free Energy Calculations for the Peripheral Binding of Proteins/Peptides to an Anionic Membrane. 1. Implicit Membrane Models. J Chem Theory Comput 2015; 10:2845-59. [PMID: 26586509 DOI: 10.1021/ct500218p] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
The binding of peptides and proteins to the surface of complex lipid membranes is important in many biological processes such as cell signaling and membrane remodeling. Computational studies can aid experiments by identifying physical interactions and structural motifs that determine the binding affinity and specificity. However, previous studies focused on either qualitative behaviors of protein/membrane interactions or the binding affinity of small peptides. Motivated by this observation, we set out to develop computational protocols for bimolecular binding to charged membranes that are applicable to both peptides and large proteins. In this work, we explore a method based on an implicit membrane/solvent model (generalized Born with a simple switching in combination with the Gouy-Chapman-Stern model for a charged interface), which we expect to lead to useful results when the binding does not implicate significant membrane deformation and local demixing of lipids. We show that the binding free energy can be efficiently computed following a thermodynamic cycle similar to protein-ligand binding calculations, especially when a Bennett acceptance ratio based protocol is used to consider both the membrane bound and solution conformational ensembles. Test calculations on a series of peptides show that our computational approach leads to binding affinities in encouraging agreement with experimental data, including for the challenging example of the bringing of flexible MARCKS-ED peptides to membranes. The calculations highlight that for a membrane with a significant fraction of anionic lipids, it is essential to include the effect of ion adsorption using the Stern model, which significantly modifies the effective surface charge. This implicit membrane model based computational protocol helps lay the groundwork for more systematic analysis of protein/peptide binding to membranes of complex shape and composition.
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Affiliation(s)
- Leili Zhang
- Department of Chemistry and Theoretical Chemistry Institute, University of Wisconsin-Madison , 1101 University Avenue, Madison, Wisconsin 53706, United States
| | - Arun Yethiraj
- Department of Chemistry and Theoretical Chemistry Institute, University of Wisconsin-Madison , 1101 University Avenue, Madison, Wisconsin 53706, United States
| | - Qiang Cui
- Department of Chemistry and Theoretical Chemistry Institute, University of Wisconsin-Madison , 1101 University Avenue, Madison, Wisconsin 53706, United States
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