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Waltmann C, Shrestha A, Olvera de la Cruz M. Patterning of multicomponent elastic shells by gaussian curvature. Phys Rev E 2024; 109:054409. [PMID: 38907410 DOI: 10.1103/physreve.109.054409] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Accepted: 04/19/2024] [Indexed: 06/24/2024]
Abstract
Recent findings suggest that shell protein distribution and the morphology of bacterial microcompartments regulate the chemical fluxes facilitating reactions which dictate their biological function. We explore how the morphology and component patterning are coupled through the competition of mean and gaussian bending energies in multicomponent elastic shells that form three-component irregular polyhedra. We observe two softer components with lower bending rigidities allocated on the edges and vertices while the harder component occupies the faces. When subjected to a nonzero interfacial line tension, the two softer components further separate and pattern into subdomains that are mediated by the gaussian curvature. We find that this degree of fractionation is maximized when there is a weaker line tension and when the ratio of bending rigidities between the two softer domains ≈2. Our results reveal a patterning mechanism in multicomponent shells that can capture the observed morphologies of bacterial microcompartments, and moreover, can be realized in synthetic vesicles.
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Affiliation(s)
| | | | - Monica Olvera de la Cruz
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA
- Center for Computation and Theory of Soft Materials, Northwestern University, Evanston, Illinois 60208, USA
- Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA
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Sun F, Brunk NE, Jadhao V. Shape control of deformable charge-patterned nanoparticles. Phys Rev E 2023; 107:014502. [PMID: 36797885 DOI: 10.1103/physreve.107.014502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2022] [Accepted: 12/05/2022] [Indexed: 06/18/2023]
Abstract
Deformable nanoparticles (NPs) offer unprecedented opportunities as dynamic building blocks that can spontaneously reconfigure during assembly in response to environmental cues. Designing reconfigurable materials based on deformable NPs hinges on an understanding of the shapes that can be engineered in these NPs. We solve for the low-energy shapes of charge-patterned deformable NPs by using molecular dynamics-based simulated annealing to minimize a coarse-grained model Hamiltonian characterized with NP elastic and electrostatic energies subject to a volume constraint. We show that deformable spherical NPs of radius 50 nm whose surface is tailored with octahedrally distributed charged patches and double-cap charged patches adapt their shape differently in response to changes in surface charge coverage and ionic strength. We find shape transitions to rounded octahedra, faceted octahedra, faceted bowls, oblate spheroids, spherocylinders, dented beans, and dimpled rounded bowls. We demonstrate that similar shape transitions can be achieved in deformable NPs of different sizes. The effects of counterion condensation on the free-energetic drive associated with the observed deformations are examined via Manning model calculations that utilize simulation-derived estimates for the NP Coulomb energy under salt-free conditions. The charge-pattern-based shape control of deformable NPs has implications for the design of responsive nanocontainers and for assembling reconfigurable materials whose functionality hinges on the shape-shifting properties of their nanoscale building blocks.
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Affiliation(s)
- Fanbo Sun
- Intelligent Systems Engineering, Indiana University, Bloomington, Indiana 47408, USA
| | - Nicholas E Brunk
- Wolfram Research, Champaign, Illinois 61820, USA
- American Regent, Norristown, Pennsylvania 19403, USA
| | - Vikram Jadhao
- Intelligent Systems Engineering, Indiana University, Bloomington, Indiana 47408, USA
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Chemically controlled pattern formation in self-oscillating elastic shells. Proc Natl Acad Sci U S A 2021; 118:2025717118. [PMID: 33649242 DOI: 10.1073/pnas.2025717118] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
Patterns and morphology develop in living systems such as embryos in response to chemical signals. To understand and exploit the interplay of chemical reactions with mechanical transformations, chemomechanical polymer systems have been synthesized by attaching chemicals into hydrogels. In this work, we design autonomous responsive elastic shells that undergo morphological changes induced by chemical reactions. We couple the local mechanical response of the gel with the chemical processes on the shell. This causes swelling and deswelling of the gel, generating diverse morphological changes, including periodic oscillations. We further introduce a mechanical instability and observe buckling-unbuckling dynamics with a response time delay. Moreover, we investigate the mechanical feedback on the chemical reaction and demonstrate the dynamic patterns triggered by an initial deformation. We show the chemical characteristics that account for the shell morphology and discuss the future designs for autonomous responsive materials.
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Brunk NE, Kadupitiya J, Jadhao V. Designing Surface Charge Patterns for Shape Control of Deformable Nanoparticles. PHYSICAL REVIEW LETTERS 2020; 125:248001. [PMID: 33412054 DOI: 10.1103/physrevlett.125.248001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2020] [Revised: 10/09/2020] [Accepted: 11/12/2020] [Indexed: 06/12/2023]
Abstract
Designing reconfigurable materials based on deformable nanoparticles (NPs) hinges on an understanding of the energetically favored shapes these NPs can adopt. Using simulations, we show that hollow, deformable, patchy NPs tailored with surface charge patterns such as Janus patches, stripes, and polyhedrally distributed patches differently adapt their shape in response to changes in patterns and ionic strength, transforming into capsules, hemispheres, variably dimpled bowls, and polyhedra. The links between anisotropy in NP surface charge, shape, and the elastic energy density are discussed.
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Affiliation(s)
- Nicholas E Brunk
- Intelligent Systems Engineering, Indiana University, Bloomington, Indiana 47408, USA
- Wolfram Research, Champaign, Illinois 61820, USA
| | - Jcs Kadupitiya
- Intelligent Systems Engineering, Indiana University, Bloomington, Indiana 47408, USA
| | - Vikram Jadhao
- Intelligent Systems Engineering, Indiana University, Bloomington, Indiana 47408, USA
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Brunk NE, Jadhao V. Computational studies of shape control of charged deformable nanocontainers. J Mater Chem B 2020; 7:6370-6382. [PMID: 31642850 DOI: 10.1039/c9tb01003c] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
Biological matter is often compartmentalized by soft membranes that dynamically change their shape in response to chemical and mechanical cues. Deformable soft-matter-based nanoscale membranes or nanocontainers that mimic this behavior can be used as drug-delivery carriers that can adapt to evolving physiological conditions, or as dynamic building blocks for the design of novel hierarchical materials via assembly engineering. Here, we connect the intrinsic features of charged deformable nanocontainers such as their size, charge, surface tension, and elasticity with their equilibrium shapes for a wide range of solution conditions using molecular dynamics simulations. These links identify the fundamental mechanisms that establish the chemical and materials design control strategies for modulating the equilibrium shape of these nanocontainers. We show that flexible nanocontainers of radii ranging from 10-20 nm exhibit sphere-to-rod-to-disc shape transitions yielding rods and discs over a wide range of aspect ratio λ (0.3 < λ < 5). The shape transitions can be controlled by tuning salt and/or surfactant concentration as well as material elastic parameters. The shape changes are driven by reduction in the global electrostatic energy and are associated with dramatic changes in local surface elastic energy distributions. To illustrate the shape transition mechanisms, exact analytical calculations for idealized spheroidal nanocontainers in salt-free conditions are performed. Explicit counterion simulations near nanocontainers and associated Manning model calculations provide an assessment of the stability of observed shape deformations in the event of ion condensation.
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Affiliation(s)
- Nicholas E Brunk
- Intelligent Systems Engineering, Indiana University, Bloomington, Indiana 47408, USA.
| | - Vikram Jadhao
- Intelligent Systems Engineering, Indiana University, Bloomington, Indiana 47408, USA.
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Su J, Yao Z, de la Cruz MO. Vesicle Geometries Enabled by Dynamically Trapped States. ACS NANO 2016; 10:2287-2294. [PMID: 26795199 DOI: 10.1021/acsnano.5b06991] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Understanding and controlling vesicle shapes is a fundamental challenge in biophysics and materials design. In this paper, we design dynamic protocols for enlarging the shape space of both fluid and crystalline vesicles beyond the equilibrium zone. By removing water from within the vesicle at different rates, we numerically produced a series of dynamically trapped stable vesicle shapes for both fluid and crystalline vesicles in a highly controllable fashion. In crystalline vesicles that are continuously dehydrated, simulations show the initial appearance of small flat areas over the surface of the vesicles that ultimately merge to form fewer flat faces. In this way, the vesicles transform from a fullerene-like shape into various faceted polyhedrons. We perform analytical elasticity analysis to show that these salient features are attributable to the crystalline nature of the vesicle. The potential to use dynamic protocols, such as those used in this study, to engineer vesicle shape transformations is helpful for exploiting the richness of vesicle geometries for desired applications.
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Affiliation(s)
- Jiaye Su
- Department of Applied Physics, Nanjing University of Science and Technology , Nanjing, Jiangsu 210094, China
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Abstract
Manipulating the shape of nanoscale objects in a controllable fashion is at the heart of designing materials that act as building blocks for self-assembly or serve as targeted drug delivery carriers. Inducing shape deformations by controlling external parameters is also an important way of designing biomimetic membranes. In this paper, we demonstrate that electrostatics can be used as a tool to manipulate the shape of soft, closed membranes by tuning environmental conditions such as the electrolyte concentration in the medium. Using a molecular dynamics-based simulated annealing procedure, we investigate charged elastic shells that do not exchange material with their environment, such as elastic membranes formed in emulsions or synthetic nanocontainers. We find that by decreasing the salt concentration or increasing the total charge on the shell's surface, the spherical symmetry is broken, leading to the formation of ellipsoids, discs, and bowls. Shape changes are accompanied by a significant lowering of the electrostatic energy and a rise in the surface area of the shell. To substantiate our simulation findings, we show analytically that a uniformly charged disc has a lower Coulomb energy than a sphere of the same volume. Further, we test the robustness of our results by including the effects of charge renormalization in the analysis of the shape transitions and find the latter to be feasible for a wide range of shell volume fractions.
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Sknepnek R, Olvera de la Cruz M. Nonlinear elastic model for faceting of vesicles with soft grain boundaries. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:050501. [PMID: 23004693 DOI: 10.1103/physreve.85.050501] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2012] [Indexed: 06/01/2023]
Abstract
We use an elastic model to explore faceting of solid-wall vesicles with elastic heterogeneities. We show that faceting occurs in regions where the vesicle wall is softer, such as areas of reduced wall thicknesses or concentrated in crystalline defects. The elastic heterogeneities are modeled as a second component with reduced elastic parameters. Using simulated annealing Monte Carlo simulations we obtain the vesicle shape by optimizing the distributions of facets and boundaries. Our model allows us to reduce the effects of the residual stress generated by crystalline defects, and reveals a robust faceting mechanism into polyhedra other than the icosahedron.
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Affiliation(s)
- Rastko Sknepnek
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA.
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