1
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Duque CM, Hall DM, Tyukodi B, Hagan MF, Santangelo CD, Grason GM. Limits of economy and fidelity for programmable assembly of size-controlled triply periodic polyhedra. Proc Natl Acad Sci U S A 2024; 121:e2315648121. [PMID: 38669182 PMCID: PMC11067059 DOI: 10.1073/pnas.2315648121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2023] [Accepted: 03/11/2024] [Indexed: 04/28/2024] Open
Abstract
We propose and investigate an extension of the Caspar-Klug symmetry principles for viral capsid assembly to the programmable assembly of size-controlled triply periodic polyhedra, discrete variants of the Primitive, Diamond, and Gyroid cubic minimal surfaces. Inspired by a recent class of programmable DNA origami colloids, we demonstrate that the economy of design in these crystalline assemblies-in terms of the growth of the number of distinct particle species required with the increased size-scale (e.g., periodicity)-is comparable to viral shells. We further test the role of geometric specificity in these assemblies via dynamical assembly simulations, which show that conditions for simultaneously efficient and high-fidelity assembly require an intermediate degree of flexibility of local angles and lengths in programmed assembly. Off-target misassembly occurs via incorporation of a variant of disclination defects, generalized to the case of hyperbolic crystals. The possibility of these topological defects is a direct consequence of the very same symmetry principles that underlie the economical design, exposing a basic tradeoff between design economy and fidelity of programmable, size controlled assembly.
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Affiliation(s)
- Carlos M. Duque
- Max Planck Institute of Molecular Cell Biology and Genetics, Dresden01307, Germany
- Center for Systems Biology Dresden, Dresden01307, Germany
- Department of Physics, University of Massachusetts, Amherst, MA01003
| | - Douglas M. Hall
- Department of Polymer Science and Engineering, University of Massachusetts, Amherst, MA01003
| | - Botond Tyukodi
- Department of Physics, Babes-Bolyai University, Cluj-Napoca400084, Romania
- Martin A. Fisher School of Physics, Brandeis University, Waltham, MA02453
| | - Michael F. Hagan
- Martin A. Fisher School of Physics, Brandeis University, Waltham, MA02453
| | - Christian D. Santangelo
- Department of Physics, University of Massachusetts, Amherst, MA01003
- Department of Physics, Syracuse University, Syracuse, NY13210
| | - Gregory M. Grason
- Department of Polymer Science and Engineering, University of Massachusetts, Amherst, MA01003
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2
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Asor R, Singaram SW, Levi-Kalisman Y, Hagan MF, Raviv U. Effect of ionic strength on the assembly of simian vacuolating virus capsid protein around poly(styrene sulfonate). THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:107. [PMID: 37917241 DOI: 10.1140/epje/s10189-023-00363-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2023] [Accepted: 10/09/2023] [Indexed: 11/04/2023]
Abstract
Virus-like particles (VLPs) are noninfectious nanocapsules that can be used for drug delivery or vaccine applications. VLPs can be assembled from virus capsid proteins around a condensing agent, such as RNA, DNA, or a charged polymer. Electrostatic interactions play an important role in the assembly reaction. VLPs assemble from many copies of capsid protein, with a combinatorial number of intermediates. Hence, the mechanism of the reaction is poorly understood. In this paper, we combined solution small-angle X-ray scattering (SAXS), cryo-transmission electron microscopy (TEM), and computational modeling to determine the effect of ionic strength on the assembly of Simian Vacuolating Virus 40 (SV40)-like particles. We mixed poly(styrene sulfonate) with SV40 capsid protein pentamers at different ionic strengths. We then characterized the assembly product by SAXS and cryo-TEM. To analyze the data, we performed Langevin dynamics simulations using a coarse-grained model that revealed incomplete, asymmetric VLP structures consistent with the experimental data. We found that close to physiological ionic strength, [Formula: see text] VLPs coexisted with VP1 pentamers. At lower or higher ionic strengths, incomplete particles coexisted with pentamers and [Formula: see text] particles. Including the simulated structures was essential to explain the SAXS data in a manner that is consistent with the cryo-TEM images.
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Affiliation(s)
- Roi Asor
- Institute of Chemistry and the Center for Nanoscience and Nanotechnology, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, 9190401, Jerusalem, Israel
| | - Surendra W Singaram
- Department of Physics, Brandeis University, 415 South Street, Waltham, 02453, MA, USA
| | - Yael Levi-Kalisman
- Institute of Life Sciences and the Center for Nanoscience and Nanotechnology, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, 9190401, Jerusalem, Israel
| | - Michael F Hagan
- Department of Physics, Brandeis University, 415 South Street, Waltham, 02453, MA, USA.
| | - Uri Raviv
- Institute of Chemistry and the Center for Nanoscience and Nanotechnology, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, 9190401, Jerusalem, Israel.
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3
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Das A, Limmer DT. Nonequilibrium design strategies for functional colloidal assemblies. Proc Natl Acad Sci U S A 2023; 120:e2217242120. [PMID: 37748070 PMCID: PMC10556551 DOI: 10.1073/pnas.2217242120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2022] [Accepted: 08/17/2023] [Indexed: 09/27/2023] Open
Abstract
We use a nonequilibrium variational principle to optimize the steady-state, shear-induced interconversion of self-assembled nanoclusters of DNA-coated colloids. Employing this principle within a stochastic optimization algorithm allows us to identify design strategies for functional materials. We find that far-from-equilibrium shear flow can significantly enhance the flux between specific colloidal states by decoupling trade-offs between stability and reactivity required by systems in equilibrium. For isolated nanoclusters, we find nonequilibrium strategies for amplifying transition rates by coupling a given reaction coordinate to the background shear flow. We also find that shear flow can be made to selectively break detailed balance and maximize probability currents by coupling orientational degrees of freedom to conformational transitions. For a microphase consisting of many nanoclusters, we study the flux of colloids hopping between clusters. We find that a shear flow can amplify the flux without a proportional compromise on the microphase structure. This approach provides a general means of uncovering design principles for nanoscale, autonomous, functional materials driven far from equilibrium.
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Affiliation(s)
- Avishek Das
- Department of Chemistry, University of California, Berkeley, CA94720
| | - David T. Limmer
- Department of Chemistry, University of California, Berkeley, CA94720
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA94720
- Material Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA94720
- Kavli Energy NanoSciences Institute, University of California, Berkeley, CA94720
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4
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Hagan MF, Mohajerani F. Self-assembly coupled to liquid-liquid phase separation. PLoS Comput Biol 2023; 19:e1010652. [PMID: 37186597 PMCID: PMC10212142 DOI: 10.1371/journal.pcbi.1010652] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2022] [Revised: 05/25/2023] [Accepted: 04/26/2023] [Indexed: 05/17/2023] Open
Abstract
Liquid condensate droplets with distinct compositions of proteins and nucleic acids are widespread in biological cells. While it is known that such droplets, or compartments, can regulate irreversible protein aggregation, their effect on reversible self-assembly remains largely unexplored. In this article, we use kinetic theory and solution thermodynamics to investigate the effect of liquid-liquid phase separation on the reversible self-assembly of structures with well-defined sizes and architectures. We find that, when assembling subunits preferentially partition into liquid compartments, robustness against kinetic traps and maximum achievable assembly rates can be significantly increased. In particular, both the range of solution conditions leading to productive assembly and the corresponding assembly rates can increase by orders of magnitude. We analyze the rate equation predictions using simple scaling estimates to identify effects of liquid-liquid phase separation as a function of relevant control parameters. These results may elucidate self-assembly processes that underlie normal cellular functions or pathogenesis, and suggest strategies for designing efficient bottom-up assembly for nanomaterials applications.
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Affiliation(s)
- Michael F. Hagan
- Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts, United States of America
| | - Farzaneh Mohajerani
- Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts, United States of America
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5
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Abstract
Charge detection mass spectrometry (CDMS) is a single-particle technique where the masses of individual ions are determined from simultaneous measurement of their mass-to-charge ratio (m/z) and charge. Masses are determined for thousands of individual ions, and then the results are binned to give a mass spectrum. Using this approach, accurate mass distributions can be measured for heterogeneous and high-molecular-weight samples that are usually not amenable to analysis by conventional mass spectrometry. Recent applications include heavily glycosylated proteins, protein complexes, protein aggregates such as amyloid fibers, infectious viruses, gene therapies, vaccines, and vesicles such as exosomes.
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Affiliation(s)
- Martin F Jarrold
- Chemistry Department, Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47404, United States
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6
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Hagan MF, Grason GM. Equilibrium mechanisms of self-limiting assembly. REVIEWS OF MODERN PHYSICS 2021; 93:025008. [PMID: 35221384 PMCID: PMC8880259 DOI: 10.1103/revmodphys.93.025008] [Citation(s) in RCA: 34] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/08/2023]
Abstract
Self-assembly is a ubiquitous process in synthetic and biological systems, broadly defined as the spontaneous organization of multiple subunits (e.g. macromolecules, particles) into ordered multi-unit structures. The vast majority of equilibrium assembly processes give rise to two states: one consisting of dispersed disassociated subunits, and the other, a bulk-condensed state of unlimited size. This review focuses on the more specialized class of self-limiting assembly, which describes equilibrium assembly processes resulting in finite-size structures. These systems pose a generic and basic question, how do thermodynamic processes involving non-covalent interactions between identical subunits "measure" and select the size of assembled structures? In this review, we begin with an introduction to the basic statistical mechanical framework for assembly thermodynamics, and use this to highlight the key physical ingredients that ensure equilibrium assembly will terminate at finite dimensions. Then, we introduce examples of self-limiting assembly systems, and classify them within this framework based on two broad categories: self-closing assemblies and open-boundary assemblies. These include well-known cases in biology and synthetic soft matter - micellization of amphiphiles and shell/tubule formation of tapered subunits - as well as less widely known classes of assemblies, such as short-range attractive/long-range repulsive systems and geometrically-frustrated assemblies. For each of these self-limiting mechanisms, we describe the physical mechanisms that select equilibrium assembly size, as well as potential limitations of finite-size selection. Finally, we discuss alternative mechanisms for finite-size assemblies, and draw contrasts with the size-control that these can achieve relative to self-limitation in equilibrium, single-species assemblies.
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Affiliation(s)
- Michael F Hagan
- Martin Fisher School of Physics, Brandeis University, Waltham, MA 02454, USA
| | - Gregory M Grason
- Department of Polymer Science and Engineering, University of Massachusetts, Amherst, MA 01003, USA
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7
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Mohajerani F, Sayer E, Neil C, Inlow K, Hagan MF. Mechanisms of Scaffold-Mediated Microcompartment Assembly and Size Control. ACS NANO 2021; 15:4197-4212. [PMID: 33683101 PMCID: PMC8058603 DOI: 10.1021/acsnano.0c05715] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
This article describes a theoretical and computational study of the dynamical assembly of a protein shell around a complex consisting of many cargo molecules and long, flexible scaffold molecules. Our study is motivated by bacterial microcompartments, which are proteinaceous organelles that assemble around a condensed droplet of enzymes and reactants. As in many examples of cytoplasmic liquid-liquid phase separation, condensation of the microcompartment interior cargo is driven by flexible scaffold proteins that have weak multivalent interactions with the cargo. Our results predict that the shell size, amount of encapsulated cargo, and assembly pathways depend sensitively on properties of the scaffold, including its length and valency of scaffold-cargo interactions. Moreover, the ability of self-assembling protein shells to change their size to accommodate scaffold molecules of different lengths depends crucially on whether the spontaneous curvature radius of the protein shell is smaller or larger than a characteristic elastic length scale of the shell. Beyond natural microcompartments, these results have important implications for synthetic biology efforts to target alternative molecules for encapsulation by microcompartments or viral shells. More broadly, the results elucidate how cells exploit coupling between self-assembly and liquid-liquid phase separation to organize their interiors.
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Affiliation(s)
- Farzaneh Mohajerani
- Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, United States
| | - Evan Sayer
- Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, United States
| | - Christopher Neil
- Department of Biochemistry, Brandeis University, Waltham, Massachusetts 02453, United States
| | - Koe Inlow
- Department of Biochemistry, Brandeis University, Waltham, Massachusetts 02453, United States
| | - Michael F Hagan
- Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, United States
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8
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Hopkins SS, Chakrabarti A, Schmit JD. Effects of non-pairwise repulsion on nanoparticle assembly. J Chem Phys 2019; 151:034901. [PMID: 31325921 PMCID: PMC6635123 DOI: 10.1063/1.5092130] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2019] [Accepted: 06/21/2019] [Indexed: 11/14/2022] Open
Abstract
Electrostatic interactions provide a convenient way to modulate interactions between nanoparticles, colloids, and biomolecules because they can be adjusted by the solution pH or salt concentration. While the presence of salt provides an easy method to control the net interparticle interaction, the nonlinearities arising from electrostatic screening make it difficult to quantify the strength of the interaction. In particular, when charged particles assemble into clusters or aggregates, nonlinear effects render the interactions strongly non-pairwise. Here, we report Brownian dynamics simulations to investigate the effect that the non-pairwise nature of electrostatic interactions has on nanoparticle assembly. We compare these simulations to a system in which the electrostatics are modeled by a strictly pairwise Yukawa potential. We find that both systems show a narrow range in parameter space where the particles form well-ordered crystals. Bordering this range are regions where the net interactions are too weak to stabilize aggregated structures or strong enough that the system becomes kinetically trapped in a gel. The non-pairwise potential differs from the pairwise system in the appearance of an amorphous state for strongly charged particles. This state appears because the many-body electrostatic interactions limit the maximum density achievable in an assembly.
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Affiliation(s)
- Sawyer S Hopkins
- Department of Physics, Kansas State University, Manhattan, Kansas 66506, USA
| | | | - Jeremy D Schmit
- Department of Physics, Kansas State University, Manhattan, Kansas 66506, USA
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9
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Pinchaipat R, Campo M, Turci F, Hallett JE, Speck T, Royall CP. Experimental Evidence for a Structural-Dynamical Transition in Trajectory Space. PHYSICAL REVIEW LETTERS 2017; 119:028004. [PMID: 28753337 DOI: 10.1103/physrevlett.119.028004] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2016] [Indexed: 06/07/2023]
Abstract
Among the key insights into the glass transition has been the identification of a nonequilibrium phase transition in trajectory space which reveals phase coexistence between the normal supercooled liquid (active phase) and a glassy state (inactive phase). Here, we present evidence that such a transition occurs in experiments. In colloidal hard spheres, we find a non-Gaussian distribution of trajectories leaning towards those rich in locally favored structures (LFSs), associated with the emergence of slow dynamics. This we interpret as evidence for a nonequilibrium transition to an inactive LFS-rich phase. Reweighting trajectories reveals a first-order phase transition in trajectory space between a normal liquid and a LFS-rich phase. We also find evidence for a purely dynamical transition in trajectory space.
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Affiliation(s)
- Rattachai Pinchaipat
- H.H. Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
- Centre for Nanoscience and Quantum Information, Tyndall Avenue, Bristol BS8 1FD, United Kingdom
| | - Matteo Campo
- Graduate School Materials Science in Mainz, Staudinger Weg 9, 55128 Mainz, Germany
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
| | - Francesco Turci
- H.H. Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
- Centre for Nanoscience and Quantum Information, Tyndall Avenue, Bristol BS8 1FD, United Kingdom
| | - James E Hallett
- H.H. Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
- Centre for Nanoscience and Quantum Information, Tyndall Avenue, Bristol BS8 1FD, United Kingdom
| | - Thomas Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
| | - C Patrick Royall
- H.H. Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
- Centre for Nanoscience and Quantum Information, Tyndall Avenue, Bristol BS8 1FD, United Kingdom
- School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS, United Kingdom
- Department of Chemical Engineering, Kyoto University, Kyoto 615-8510, Japan
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10
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Midya J, Das SK. Kinetics of Vapor-Solid Phase Transitions: Structure, Growth, and Mechanism. PHYSICAL REVIEW LETTERS 2017; 118:165701. [PMID: 28474902 DOI: 10.1103/physrevlett.118.165701] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2016] [Indexed: 06/07/2023]
Abstract
The kinetics of the separation between low and high density phases in a single component Lennard-Jones model is studied via molecular dynamics simulations, at very low temperatures, in the space dimension d=2. For densities close to the vapor branch of the coexistence curve, disconnected nanoscale clusters of the high density phase exhibit essentially ballistic motion. Starting from nearly circular shapes, at the time of nucleation, these clusters grow via sticky collisions, gaining filamentlike nonequilibrium structure at a later time, with a very low fractal dimensionality. The origin of the latter is shown to lie in the low mobility of the constituent particles, in the corresponding cluster reference frame, due to the (quasi-long-range) crystalline order. Standard self-similarity in the domain pattern, typically observed in the kinetics of phase transitions, is found to be absent. This invalidates the common method, that provides a growth law comparable to that in solid mixtures, of quantifying growth. An appropriate alternative approach, involving the fractality, quantifies the growth of the characteristic "length" to be a power law with time, the exponent being strongly temperature dependent. The observed growth law is in agreement with the outcome of a nonequilibrium kinetic theory.
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Affiliation(s)
- Jiarul Midya
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
| | - Subir K Das
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
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11
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Frechette L, Stratt RM. The inherent dynamics of isotropic- and nematic-phase liquid crystals. J Chem Phys 2017; 144:234505. [PMID: 27334177 DOI: 10.1063/1.4953618] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
The geodesic (shortest) pathways through the potential energy landscape of a liquid can be thought of as defining what its dynamics would be if thermal noise were removed, revealing what we have called the "inherent dynamics" of the liquid. We show how these inherent paths can be located for a model liquid crystal former, showing, in the process, how the molecular mechanisms of translation and reorientation compare in the isotropic and nematic phases of these systems. These mechanisms turn out to favor the preservation of local orientational order even under macroscopically isotropic conditions (a finding consistent with the experimental observation of pseudonematic domains in these cases), but disfavor the maintenance of macroscopic orientational order, even in the nematic phase. While the most efficient nematic pathways that maintain nematic order are indeed shorter than those that do not, it is apparently difficult for the system to locate these paths, suggesting that molecular motion in liquid-crystal formers is dynamically frustrated, and reinforcing the sense that there are strong analogies between liquid crystals and supercooled liquids.
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Affiliation(s)
- Layne Frechette
- Department of Chemistry, Brown University, Providence, Rhode Island 02912, USA
| | - Richard M Stratt
- Department of Chemistry, Brown University, Providence, Rhode Island 02912, USA
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12
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Whitelam S. Hierarchical assembly may be a way to make large information-rich structures. SOFT MATTER 2015; 11:8225-8235. [PMID: 26350267 DOI: 10.1039/c5sm01375e] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Self-assembly in the laboratory can now yield 'information-rich' nanostructures in which each component is of a distinct type and has a defined spatial position. Ensuring the thermodynamic stability of such structures requires inter-component interaction energies to increase logarithmically with structure size, in order to counter the entropy gained upon mixing component types in solution. However, self-assembly in the presence of strong interactions results in general in kinetic trapping, so suggesting a limit to the size of an (equilibrium) structure that can be self-assembled from distinguishable components. Here we study numerically a two-dimensional hierarchical assembly scheme already considered in experiment. We show that this scheme is immune to the kinetic traps associated with strong 'native' interactions (interactions designed to stabilize the intended structure), and so, in principle, offers a way to make large information-rich structures. In this scheme the size of an assembled structure scales exponentially with the stage of assembly, and assembly can continue as long as random motion is able to bring structures into contact. The resulting superstructure could provide a template for building in the third dimension. The chief drawback of this scheme is that it is particularly susceptible to kinetic traps that result from 'non-native' interactions (interactions not required to stabilize the intended structure); the scale on which such a scheme can be realized therefore depends upon how effectively this latter kind of interaction can be suppressed.
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Affiliation(s)
- Stephen Whitelam
- Molecular Foundry, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA.
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13
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Ashton DJ, Ivell SJ, Dullens RPA, Jack RL, Wilding NB, Aarts DGAL. Self-assembly and crystallisation of indented colloids at a planar wall. SOFT MATTER 2015; 11:6089-6098. [PMID: 26133286 DOI: 10.1039/c5sm01043h] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We report experimental and simulation studies of the structure of a monolayer of indented ("lock and key") colloids, on a planar surface. On adding a non-absorbing polymer with prescribed radius and volume fraction, depletion interactions are induced between the colloids, with controlled range and strength. For spherical particles, this leads to crystallisation, but the indented colloids crystallise less easily than spheres, in both simulation and experiment. Nevertheless, simulations show that indented colloids do form plastic (rotator) crystals. We discuss the conditions under which this occurs, and the possibilities of lower-symmetry crystal states. We also comment on the kinetic accessibility of these states.
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14
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Lash MH, Fedorchak MV, McCarthy JJ, Little SR. Scaling up self-assembly: bottom-up approaches to macroscopic particle organization. SOFT MATTER 2015; 11:5597-5609. [PMID: 25947543 DOI: 10.1039/c5sm00764j] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
This review presents an overview of recent work in the field of non-Brownian particle self-assembly. Compared to nanoparticles that naturally self-assemble due to Brownian motion, larger, non-Brownian particles (d > 6 μm) are less prone to autonomously organize into crystalline arrays. The tendency for particle systems to experience immobilization and kinetic arrest grows with particle radius. In order to overcome this kinetic limitation, some type of external driver must be applied to act as an artificial "thermalizing force" upon non-Brownian particles, inducing particle motion and subsequent crystallization. Many groups have explored the use of various agitation methods to overcome the natural barriers preventing self-assembly to which non-Brownian particles are susceptible. The ability to create materials from a bottom-up approach with these characteristics would allow for precise control over their pore structure (size and distribution) and surface properties (topography, functionalization and area), resulting in improved regulation of key characteristics such as mechanical strength, diffusive properties, and possibly even photonic properties. This review will highlight these approaches, as well as discuss the potential impact of bottom-up macroscale particle assembly. The applications of such technology range from customizable and autonomously self-assembled niche microenvironments for drug delivery and tissue engineering to new acoustic dampening, battery, and filtration materials, among others. Additionally, crystals made from non-Brownian particles resemble naturally derived materials such as opals, zeolites, and biological tissue (i.e. bone, cartilage and lung), due to their high surface area, pore distribution, and tunable (multilevel) hierarchy.
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Affiliation(s)
- M H Lash
- Department of Chemical and Petroleum Engineering, 940 Benedum Hall, 3700 O'Hara Street, Pittsburgh, PA 15261, USA.
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15
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The Role of Packaging Sites in Efficient and Specific Virus Assembly. J Mol Biol 2015; 427:2451-2467. [PMID: 25986309 DOI: 10.1016/j.jmb.2015.05.008] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2015] [Revised: 04/21/2015] [Accepted: 05/10/2015] [Indexed: 12/25/2022]
Abstract
During the life cycle of many single-stranded RNA viruses, including many human pathogens, a protein shell called the capsid spontaneously assembles around the viral genome. Understanding the mechanisms by which capsid proteins selectively assemble around the viral RNA amidst diverse host RNAs is a key question in virology. In one proposed mechanism, short sequences (packaging sites) within the genomic RNA promote rapid and efficient assembly through specific interactions with the capsid proteins. In this work, we develop a coarse-grained particle-based computational model for capsid proteins and RNA that represents protein-RNA interactions arising both from nonspecific electrostatics and from specific packaging site interactions. Using Brownian dynamics simulations, we explore how the efficiency and specificity of assembly depend on solution conditions (which control protein-protein and nonspecific protein-RNA interactions) and the strength and number of packaging sites. We identify distinct regions in parameter space in which packaging sites lead to highly specific assembly via different mechanisms and others in which packaging sites lead to kinetic traps. We relate these computational predictions to in vitro assays for specificity in which cognate viral RNAs compete against non-cognate RNAs for assembly by capsid proteins.
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16
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Affiliation(s)
- Stephen Whitelam
- Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720;
| | - Robert L. Jack
- Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom;
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17
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Abstract
I present a review of the theoretical and computational methodologies that have been used to model the assembly of viral capsids. I discuss the capabilities and limitations of approaches ranging from equilibrium continuum theories to molecular dynamics simulations, and I give an overview of some of the important conclusions about virus assembly that have resulted from these modeling efforts. Topics include the assembly of empty viral shells, assembly around single-stranded nucleic acids to form viral particles, and assembly around synthetic polymers or charged nanoparticles for nanotechnology or biomedical applications. I present some examples in which modeling efforts have promoted experimental breakthroughs, as well as directions in which the connection between modeling and experiment can be strengthened.
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18
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Zhang L, Lua LHL, Middelberg APJ, Sun Y, Connors NK. Biomolecular engineering of virus-like particles aided by computational chemistry methods. Chem Soc Rev 2015; 44:8608-18. [DOI: 10.1039/c5cs00526d] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
Multi-scale investigation of VLP self-assembly aided by computational methods is facilitating the design, redesign, and modification of functionalized VLPs.
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Affiliation(s)
- Lin Zhang
- Department of Biochemical Engineering and Key Laboratory of Systems Bioengineering of the Ministry of Education
- School of Chemical Engineering and Technology
- Tianjin University
- Tianjin 300072, People's Republic of China
| | - Linda H. L. Lua
- Protein Expression Facility
- The University of Queensland
- Brisbane, Australia
| | - Anton P. J. Middelberg
- Australian Institute for Bioengineering and Nanotechnology
- The University of Queensland
- Brisbane, Australia
| | - Yan Sun
- Department of Biochemical Engineering and Key Laboratory of Systems Bioengineering of the Ministry of Education
- School of Chemical Engineering and Technology
- Tianjin University
- Tianjin 300072, People's Republic of China
| | - Natalie K. Connors
- Australian Institute for Bioengineering and Nanotechnology
- The University of Queensland
- Brisbane, Australia
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19
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Grünwald M, Geissler PL. Patterns without patches: hierarchical self-assembly of complex structures from simple building blocks. ACS NANO 2014; 8:5891-7. [PMID: 24816138 PMCID: PMC4071109 DOI: 10.1021/nn500978p] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2014] [Accepted: 05/12/2014] [Indexed: 05/26/2023]
Abstract
Nanoparticles with "sticky patches" have long been proposed as building blocks for the self-assembly of complex structures. The synthetic realizability of such patchy particles, however, greatly lags behind predictions of patterns they could form. Using computer simulations, we show that structures of the same genre can be obtained from a solution of simple isotropic spheres, with control only over their sizes and a small number of binding affinities. In a first step, finite clusters of well-defined structure and composition emerge from natural dynamics with high yield. In effect a kind of patchy particle, these clusters can further assemble into a variety of complex superstructures, including filamentous networks, ordered sheets, and highly porous crystals.
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Affiliation(s)
- Michael Grünwald
- Computational Physics, University of Vienna, Sensengasse 8, 1090 Vienna, Austria
| | - Phillip L. Geissler
- Department of Chemistry, University of California, Berkeley, California 94720, United States
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20
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Pierson E, Keifer DZ, Selzer L, Lee LS, Contino NC, Wang JCY, Zlotnick A, Jarrold MF. Detection of late intermediates in virus capsid assembly by charge detection mass spectrometry. J Am Chem Soc 2014; 136:3536-41. [PMID: 24548133 PMCID: PMC3985884 DOI: 10.1021/ja411460w] [Citation(s) in RCA: 105] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2013] [Indexed: 12/13/2022]
Abstract
The assembly of hundreds of identical proteins into an icosahedral virus capsid is a remarkable feat of molecular engineering. How this occurs is poorly understood. Key intermediates have been anticipated at the end of the assembly reaction, but it has not been possible to detect them. In this work we have used charge detection mass spectrometry to identify trapped intermediates from late in the assembly of the hepatitis B virus T = 4 capsid, a complex of 120 protein dimers. Prominent intermediates are found with 104/105, 110/111, and 117/118 dimers. Cryo-EM observations indicate the intermediates are incomplete capsids and, hence, on the assembly pathway. On the basis of their stability and kinetic accessibility we have proposed plausible structures. The prominent trapped intermediate with 104 dimers is attributed to an icosahedron missing two neighboring facets, the 111-dimer species is assigned to an icosahedron missing a single facet, and the intermediate with 117 dimers is assigned to a capsid missing a ring of three dimers in the center of a facet.
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Affiliation(s)
- Elizabeth
E. Pierson
- Department of Chemistry and
Department of Molecular and Cellular Biochemistry, Indiana University, Bloomington, Indiana 47405,United States
| | - David Z. Keifer
- Department of Chemistry and
Department of Molecular and Cellular Biochemistry, Indiana University, Bloomington, Indiana 47405,United States
| | - Lisa Selzer
- Department of Chemistry and
Department of Molecular and Cellular Biochemistry, Indiana University, Bloomington, Indiana 47405,United States
| | - Lye Siang Lee
- Department of Chemistry and
Department of Molecular and Cellular Biochemistry, Indiana University, Bloomington, Indiana 47405,United States
| | - Nathan C. Contino
- Department of Chemistry and
Department of Molecular and Cellular Biochemistry, Indiana University, Bloomington, Indiana 47405,United States
| | - Joseph C.-Y. Wang
- Department of Chemistry and
Department of Molecular and Cellular Biochemistry, Indiana University, Bloomington, Indiana 47405,United States
| | - Adam Zlotnick
- Department of Chemistry and
Department of Molecular and Cellular Biochemistry, Indiana University, Bloomington, Indiana 47405,United States
| | - Martin F. Jarrold
- Department of Chemistry and
Department of Molecular and Cellular Biochemistry, Indiana University, Bloomington, Indiana 47405,United States
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21
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Růžička Š, Allen MP. Collective translational and rotational Monte Carlo moves for attractive particles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:033307. [PMID: 24730967 DOI: 10.1103/physreve.89.033307] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2013] [Indexed: 06/03/2023]
Abstract
Virtual move Monte Carlo is a Monte Carlo (MC) cluster algorithm forming clusters via local energy gradients and approximating the collective kinetic or dynamic motion of attractive colloidal particles. We carefully describe, analyze, and test the algorithm. To formally validate the algorithm through highlighting its symmetries, we present alternative and compact ways of selecting and accepting clusters which illustrate the formal use of abstract concepts in the design of biased MC techniques: the superdetailed balance and the early rejection scheme. A brief and comprehensive summary of the algorithms is presented, which makes them accessible without needing to understand the details of the derivation.
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Affiliation(s)
- Štěpán Růžička
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Michael P Allen
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
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22
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Multistep kinetic self-assembly of DNA-coated colloids. Nat Commun 2013; 4:2007. [DOI: 10.1038/ncomms3007] [Citation(s) in RCA: 98] [Impact Index Per Article: 8.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2013] [Accepted: 05/12/2013] [Indexed: 01/25/2023] Open
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23
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Klotsa D, Jack RL. Controlling crystal self-assembly using a real-time feedback scheme. J Chem Phys 2013; 138:094502. [DOI: 10.1063/1.4793527] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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24
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Simulations of HIV capsid protein dimerization reveal the effect of chemistry and topography on the mechanism of hydrophobic protein association. Biophys J 2013; 103:1363-9. [PMID: 22995509 DOI: 10.1016/j.bpj.2012.08.016] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2012] [Revised: 07/31/2012] [Accepted: 08/06/2012] [Indexed: 01/17/2023] Open
Abstract
Recent work has shown that the hydrophobic protein surfaces in aqueous solution sit near a drying transition. The tendency for these surfaces to expel water from their vicinity leads to self-assembly of macromolecular complexes. In this article, we show with a realistic model for a biologically pertinent system how this phenomenon appears at the molecular level. We focus on the association of the C-terminal domain (CA-C) of the human immunodeficiency virus capsid protein. By combining all-atom simulations with specialized sampling techniques, we measure the water density distribution during the approach of two CA-C proteins as a function of separation and amino acid sequence in the interfacial region. The simulations demonstrate that CA-C protein-protein interactions sit at the edge of a dewetting transition and that this mesoscopic manifestation of the underlying liquid-vapor phase transition can be readily manipulated by biology or protein engineering to significantly affect association behavior. Although the wild-type protein remains wet until contact, we identify a set of in silico mutations, in which three hydrophilic amino acids are replaced with nonpolar residues, that leads to dewetting before association. The existence of dewetting depends on the size and relative locations of substituted residues separated by nanometer length scales, indicating long-range cooperativity and a sensitivity to surface topography. These observations identify important details that are missing from descriptions of protein association based on buried hydrophobic surface area.
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25
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Grant J, Jack RL, Whitelam S. Analyzing mechanisms and microscopic reversibility of self-assembly. J Chem Phys 2012; 135:214505. [PMID: 22149800 DOI: 10.1063/1.3662140] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023] Open
Abstract
We use computer simulations to investigate self-assembly in a system of model chaperonin proteins, and in an Ising lattice gas. We discuss the mechanisms responsible for rapid and efficient assembly in these systems, and we use measurements of dynamical activity and assembly progress to compare their propensities for kinetic trapping. We use the analytic solution of a simple minimal model to illustrate the key features associated with such trapping, paying particular attention to the number of ways that particles can misbind. We discuss the relevance of our results for the design and control of self-assembly in general.
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Affiliation(s)
- James Grant
- Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom
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26
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Grant J, Jack RL. Quantifying reversibility in a phase-separating lattice gas: an analogy with self-assembly. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:021112. [PMID: 22463158 DOI: 10.1103/physreve.85.021112] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2011] [Revised: 01/13/2012] [Indexed: 05/31/2023]
Abstract
We present dynamic measurements of a lattice gas during phase separation, which we use as an analogy for self-assembly of equilibrium ordered structures. We use two approaches to quantify the degree of reversibility of this process: First, we count events in which bonds are made and broken; second, we use correlation-response measurements and fluctuation-dissipation ratios to probe reversibility during different time intervals. We show how correlation and response functions can be related directly to microscopic (ir)reversibility and we discuss the time dependence and observable dependence of these measurements, including the role of fast and slow degrees of freedom during assembly.
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Affiliation(s)
- James Grant
- Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom.
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27
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Lander B, Seifert U, Speck T. Effective confinement as origin of the equivalence of kinetic temperature and fluctuation-dissipation ratio in a dense shear-driven suspension. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:021103. [PMID: 22463149 DOI: 10.1103/physreve.85.021103] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2011] [Indexed: 05/31/2023]
Abstract
We study response and velocity autocorrelation functions for a tagged particle in a shear driven suspension governed by underdamped stochastic dynamics. We follow the idea of an effective confinement in dense suspensions and exploit a time scale separation between particle reorganization and vibrational motion. This allows us to approximately derive the fluctuation-dissipation theorem in a "hybrid" form involving the kinetic temperature as an effective temperature and an additive correction term. We show numerically that even in a moderately dense suspension the latter is negligible. We discuss similarities and differences with a simple toy model, a single trapped particle in shear flow.
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Affiliation(s)
- Boris Lander
- II. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, DE-70550 Stuttgart, Germany
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28
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Hagan MF, Elrad OM, Jack RL. Mechanisms of kinetic trapping in self-assembly and phase transformation. J Chem Phys 2012; 135:104115. [PMID: 21932884 DOI: 10.1063/1.3635775] [Citation(s) in RCA: 76] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Abstract
In self-assembly processes, kinetic trapping effects often hinder the formation of thermodynamically stable ordered states. In a model of viral capsid assembly and in the phase transformation of a lattice gas, we show how simulations in a self-assembling steady state can be used to identify two distinct mechanisms of kinetic trapping. We argue that one of these mechanisms can be adequately captured by kinetic rate equations, while the other involves a breakdown of theories that rely on cluster size as a reaction coordinate. We discuss how these observations might be useful in designing and optimising self-assembly reactions.
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Affiliation(s)
- Michael F Hagan
- Department of Physics, Brandeis University, Waltham, Massachusetts 02254, USA
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29
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Whitelam S. Approximating the dynamical evolution of systems of strongly interacting overdamped particles. MOLECULAR SIMULATION 2011. [DOI: 10.1080/08927022.2011.565758] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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30
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Abstract
The coat proteins of many viruses spontaneously form icosahedral capsids around nucleic acids or other polymers. Elucidating the role of the packaged polymer in capsid formation could promote biomedical efforts to block viral replication and enable use of capsids in nanomaterials applications. To this end, we perform Brownian dynamics on a coarse-grained model that describes the dynamics of icosahedral capsid assembly around a flexible polymer. We identify several mechanisms by which the polymer plays an active role in its encapsulation, including cooperative polymer-protein motions. These mechanisms are related to experimentally controllable parameters such as polymer length, protein concentration and solution conditions. Furthermore, the simulations demonstrate that assembly mechanisms are correlated with encapsulation efficiency, and we present a phase diagram that predicts assembly outcomes as a function of experimental parameters. We anticipate that our simulation results will provide a framework for designing in vitro assembly experiments on single-stranded RNA virus capsids.
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Affiliation(s)
- Oren M Elrad
- Department of Physics, Brandeis University, Waltham, MA, USA
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31
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Mechanisms of capsid assembly around a polymer. Biophys J 2010; 99:619-28. [PMID: 20643082 DOI: 10.1016/j.bpj.2010.04.035] [Citation(s) in RCA: 50] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2010] [Revised: 04/13/2010] [Accepted: 04/15/2010] [Indexed: 11/23/2022] Open
Abstract
Capsids of many viruses assemble around nucleic acids or other polymers. Understanding how the properties of the packaged polymer affect the assembly process could promote biomedical efforts to prevent viral assembly or nanomaterials applications that exploit assembly. To this end, we simulate on a lattice the dynamical assembly of closed, hollow shells composed of several hundred to 1000 subunits, around a flexible polymer. We find that assembly is most efficient at an optimum polymer length that scales with the surface area of the capsid; polymers that are significantly longer than optimal often lead to partial-capsids with unpackaged polymer "tails" or a competition between multiple partial-capsids attached to a single polymer. These predictions can be tested with bulk experiments in which capsid proteins assemble around homopolymeric RNA or synthetic polyelectrolytes. We also find that the polymer can increase the net rate of subunit accretion to a growing capsid both by stabilizing the addition of new subunits and by enhancing the incoming flux of subunits; the effects of these processes may be distinguishable with experiments that monitor the assembly of individual capsids.
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32
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Whitelam S. Control of pathways and yields of protein crystallization through the interplay of nonspecific and specific attractions. PHYSICAL REVIEW LETTERS 2010; 105:088102. [PMID: 20868132 DOI: 10.1103/physrevlett.105.088102] [Citation(s) in RCA: 46] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2010] [Indexed: 05/29/2023]
Abstract
We use computer simulation to study crystal-forming model proteins equipped with interactions that are both orientationally specific and nonspecific. Distinct dynamical pathways of crystal formation can be selected by tuning the strengths of these interactions. When the nonspecific interaction is strong, liquidlike clustering can precede crystallization; when it is weak, growth can proceed via ordered nuclei. Crystal yields are in certain parameter regimes enhanced by the nonspecific interaction, even though it promotes association without local crystalline order. Our results suggest that equipping nanoscale components with weak nonspecific interactions (such as depletion attractions) can alter both their dynamical pathway of assembly and optimize the yield of the resulting material.
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Affiliation(s)
- Stephen Whitelam
- Molecular Foundry, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA.
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33
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Russo J, Sciortino F. How do self-assembling polymers and gels age compared to glasses? PHYSICAL REVIEW LETTERS 2010; 104:195701. [PMID: 20866977 DOI: 10.1103/physrevlett.104.195701] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/23/2009] [Revised: 10/10/2009] [Indexed: 05/29/2023]
Abstract
Experiments on gels have provided contradictory results concerning the relation between correlation and response functions during aging. To clarify this puzzle, we numerically investigate the fluctuation-dissipation plot in equilibrium polymers and in network forming gels employing two distinct observables, (i) the density Fourier transform and (ii) the single-particle potential energy, to probe (i) diffusional processes and (ii) the development of a bond network. The plot behaves very differently for the two cases. Violation from the equilibrium behavior is found only for the second observable. The experimental implications of the discovered sensitivity to the choice of the probe are discussed, in particular, with respect to the existing experimental results.
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Affiliation(s)
- John Russo
- Dipartimento di Fisica and CNR-ISC, Sapienza-Università di Roma, Piazzale A. Moro 2, 00185 Roma, Italy
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34
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Gnan N, Maggi C, Schrøder TB, Dyre JC. Predicting the effective temperature of a glass. PHYSICAL REVIEW LETTERS 2010; 104:125902. [PMID: 20366549 DOI: 10.1103/physrevlett.104.125902] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2009] [Indexed: 05/29/2023]
Abstract
We explain the findings by Di Leonardo et al. [Phys. Rev. Lett. 84, 6054 (2000)10.1103/PhysRevLett.84.6054] that the effective temperature of a Lennard-Jones glass depends only on the final density in the volume and/or temperature jump that produces the glass. This is not only a property of the Lennard-Jones liquid, but a feature of all strongly correlating liquids. For such liquids data from a single quench simulation provide enough information to predict the effective temperature of any glass produced by jumping from an equilibrium state. This prediction is validated by simulations of the Kob-Andersen binary Lennard-Jones liquid and shown not to apply for the nonstrongly correlating monatomic Lennard-Jones Gaussian liquid.
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Affiliation(s)
- Nicoletta Gnan
- DNRF Center Glass and Time, IMFUFA, Department of Sciences, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark.
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35
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Wilber AW, Doye JPK, Louis AA. Self-assembly of monodisperse clusters: Dependence on target geometry. J Chem Phys 2010; 131:175101. [PMID: 19895042 DOI: 10.1063/1.3243580] [Citation(s) in RCA: 52] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We apply a simple model system of patchy particles to study monodisperse self-assembly using the Platonic solids as target structures. We find marked differences between the assembly behaviors of the different systems. Tetrahedra, octahedral, and icosahedra assemble easily, while cubes are more challenging and dodecahedra do not assemble. We relate these differences to the kinetics and thermodynamics of assembly, with the formation of large disordered aggregates a particular important competitor to correct assembly. In particular, the free energy landscapes of those targets that are easy to assemble are funnel-like, whereas for the dodecahedral system the landscape is relatively flat with little driving force to facilitate escape from disordered aggregates.
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Affiliation(s)
- Alex W Wilber
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
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36
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Malins A, Williams SR, Eggers J, Tanaka H, Royall CP. Geometric frustration in small colloidal clusters. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:425103. [PMID: 21715858 DOI: 10.1088/0953-8984/21/42/425103] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We study the structure of clusters in a model colloidal system with competing interactions using Brownian dynamics simulations. A short-ranged attraction drives clustering, while a weak, long-ranged repulsion is used to model electrostatic charging in experimental systems. The former is treated with a short-ranged Morse attractive interaction, the latter with a repulsive Yukawa interaction. We consider the yield of clusters of specific structure as a function of the strength of the interactions, for clusters with m = 3,4,5,6,7,10 and 13 colloids. At sufficient strengths of the attractive interaction (around 10k(B)T), the average bond lifetime approaches the simulation timescale and the system becomes nonergodic. For small clusters, m≤5, where geometric frustration is not relevant, despite nonergodicity, for sufficient strengths of the attractive interaction the yield of clusters which maximize the number of bonds approaches 100%. However for m = 7 and higher, in the nonergodic regime we find a lower yield of these structures where we argue geometric frustration plays a significant role. m = 6 is a special case, where two structures, of octahedral and C(2v) symmetry, compete, with the latter being favoured by entropic contributions in the ergodic regime and by kinetic trapping in the nonergodic regime. We believe that our results should be valid as long as the one-component description of the interaction potential is valid. A system with competing electrostatic repulsions and van der Waals attractions may be such an example. However, in some cases, the one-component description of the interaction potential may not be appropriate.
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Affiliation(s)
- Alex Malins
- School of Chemistry, University of Bristol, Bristol BS8 1TS, UK
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37
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Nguyen HD, Reddy VS, Brooks CL. Invariant polymorphism in virus capsid assembly. J Am Chem Soc 2009; 131:2606-14. [PMID: 19199626 DOI: 10.1021/ja807730x] [Citation(s) in RCA: 91] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
Directed self-assembly of designed viral capsids holds significant potential for applications in materials science and medicine. However, the complexity of preparing these systems for assembly and the difficulty of quantitative experimental measurements on the assembly process have limited access to critical mechanistic questions that dictate the final product yields and isomorphic forms. Molecular simulations provide a means of elucidating self-assembly of viral proteins into icosahedral capsids and are the focus of the present study. Using geometrically realistic coarse-grained models with specialized molecular dynamics methods, we delineate conditions of temperature and coat protein concentration that lead to the spontaneous self-assembly of T = 1 and T = 3 icosahedral capsids. In addition to the primary product of icosahedral capsids, we observe a ubiquitous presence of nonicosahedral yet highly symmetric and enclosed aberrant capsules in both T = 1 and T = 3 systems. This polymorphism in assembly products recapitulates the scope and morphology of particle types that have been observed in mis-assembly experiments of virus capsids. Moreover, we find that this structural polymorphism in the end point structures is an inherent property of the coat proteins and arises from condition-dependent kinetic mechanisms that are independent of the elemental mechanisms of capsid growth (as long as the building blocks of the coat proteins are all monomeric, dimeric, or trimeric) and the capsid T number. The kinetic mechanisms responsible for self-assembly of icosahedral capsids and aberrant capsules are deciphered; the self-assembly of icosahedral capsids requires a high level of assembly fidelity, whereas self-assembly of nonicosahedral capsules is a consequence of an off-pathway mechanism that is prevalent under nonoptimal conditions of temperature or protein concentration during assembly. The latter case involves kinetically trapped dislocations of pentamer-templated proteins with hexameric organization. These findings provide insights into the complex processes that govern viral capsid assembly and suggest some features of the assembly process that can be exploited to control the assembly of icosahedral capsids and nonicosahedral capsules.
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Affiliation(s)
- Hung D Nguyen
- Department of Chemistry and Biophysics Program, 930 North University Avenue, University of Michigan, Ann Arbor, Michigan 48109, USA
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38
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Whitelam S, Feng EH, Hagan MF, Geissler PL. The role of collective motion in examples of coarsening and self-assembly. SOFT MATTER 2009; 5:1251-1262. [PMID: 23227104 PMCID: PMC3516813 DOI: 10.1039/b810031d] [Citation(s) in RCA: 97] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
The simplest prescription for building a patterned structure from its constituents is to add particles, one at a time, to an appropriate template. However, self-organizing molecular and colloidal systems in nature can evolve in much more hierarchical ways. Specifically, constituents (or clusters of constituents) may aggregate to form clusters (or clusters of clusters) that serve as building blocks for later stages of assembly. Here we evaluate the character and consequences of such collective motion in a set of prototypical assembly processes. We do so using computer simulations in which a system's capacity for hierarchical dynamics can be controlled systematically. By explicitly allowing or suppressing collective motion, we quantify its effects. We find that coarsening within a two dimensional attractive lattice gas (and an analogous off-lattice model in three dimensions) is naturally dominated by collective motion over a broad range of temperatures and densities. Under such circumstances, cluster mobility inhibits the development of uniform coexisting phases, especially when macroscopic segregation is strongly favored by thermodynamics. By contrast, the assembly of model viral capsids is not frustrated but is instead facilitated by collective moves, which promote the orderly binding of intermediates consisting of several monomers.
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Affiliation(s)
- Stephen Whitelam
- Systems Biology Centre, University of Warwick, Coventry CV4 7AL, UK ; Department of Chemistry, University of California at Berkeley, Berkeley, CA 94720, USA ; Physical Biosciences and Materials Sciences Divisions, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
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39
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Elrad OM, Hagan MF. Mechanisms of size control and polymorphism in viral capsid assembly. NANO LETTERS 2008; 8:3850-7. [PMID: 18950240 PMCID: PMC2742690 DOI: 10.1021/nl802269a] [Citation(s) in RCA: 58] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
We simulate the assembly dynamics of icosahedral capsids from subunits that interconvert between different conformations (or quasi-equivalent states). The simulations identify mechanisms by which subunits form empty capsids with only one morphology but adaptively assemble into different icosahedral morphologies around nanoparticle cargoes with varying sizes, as seen in recent experiments with brome mosaic virus (BMV) capsid proteins. Adaptive cargo encapsidation requires moderate cargo-subunit interaction strengths; stronger interactions frustrate assembly by stabilizing intermediates with incommensurate curvature. We compare simulation results to experiments with cowpea chlorotic mottle virus empty capsids and BMV capsids assembled on functionalized nanoparticles and suggest new cargo encapsidation experiments. Finally, we find that both empty and templated capsids maintain the precise spatial ordering of subunit conformations seen in the crystal structure even if interactions that preserve this arrangement are favored by as little as the thermal energy, consistent with experimental observations that different subunit conformations are highly similar.
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40
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Hagan MF. Controlling viral capsid assembly with templating. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:051904. [PMID: 18643099 PMCID: PMC2758267 DOI: 10.1103/physreve.77.051904] [Citation(s) in RCA: 55] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2007] [Indexed: 05/07/2023]
Abstract
We develop coarse-grained models that describe the dynamic encapsidation of functionalized nanoparticles by viral capsid proteins. We find that some forms of cooperative interactions between protein subunits and nanoparticles can dramatically enhance rates and robustness of assembly, as compared to the spontaneous assembly of subunits into empty capsids. For large core-subunit interactions, subunits adsorb onto core surfaces en masse in a disordered manner, and then undergo a cooperative rearrangement into an ordered capsid structure. These assembly pathways are unlike any identified for empty capsid formation. Our models can be directly applied to recent experiments in which viral capsid proteins assemble around functionalized inorganic nanoparticles [Sun, Proc. Natl. Acad. Sci. U.S.A. 104, 1354 (2007)]. In addition, we discuss broader implications for understanding the dynamic encapsidation of single-stranded genomic molecules during viral replication and for developing multicomponent nanostructured materials.
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Affiliation(s)
- Michael F Hagan
- Department of Physics, Brandeis University, Waltham, Massachusetts, 02454, USA
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