Measuring Gaussian Rigidity Using Curved Substrates

Fonda, Piermarco; Al-Izzi, Sami C.; Giomi, Luca; Turner, Matthew S.

doi:10.1103/physrevlett.125.188002

Cited by 6 publications

(6 citation statements)

References 35 publications

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“…Conventional lipid bilayer vesicles do not permit easy understanding of how the Gaussian modulus affects their morphology, as the Gauss–Bonnet theorem requires that the Gaussian curvature energy integrates to a system-independent constant value ( 6 , 56 , 57 ). Consequently, measurement and control of the Gaussian modulus in lipid bilayers is challenging ( 58 – 60 ). Open edges of colloidal membranes enabled our study of how the Gaussian modulus influences the stability of flat disk–shaped membranes.…”

Section: Discussionmentioning

confidence: 99%

Controlling the shape and topology of two-component colloidal membranes

Khanra

Jia

Mitchell

et al. 2022

Proc. Natl. Acad. Sci. U.S.A.

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Changes in the geometry and topology of self-assembled membranes underlie diverse processes across cellular biology and engineering. Similar to lipid bilayers, monolayer colloidal membranes have in-plane fluid-like dynamics and out-of-plane bending elasticity. Their open edges and micrometer-length scale provide a tractable system to study the equilibrium energetics and dynamic pathways of membrane assembly and reconfiguration. Here, we find that doping colloidal membranes with short miscible rods transforms disk-shaped membranes into saddle-shaped surfaces with complex edge structures. The saddle-shaped membranes are well approximated by Enneper’s minimal surfaces. Theoretical modeling demonstrates that their formation is driven by increasing the positive Gaussian modulus, which in turn, is controlled by the fraction of short rods. Further coalescence of saddle-shaped surfaces leads to diverse topologically distinct structures, including shapes similar to catenoids, trinoids, four-noids, and higher-order structures. At long timescales, we observe the formation of a system-spanning, sponge-like phase. The unique features of colloidal membranes reveal the topological transformations that accompany coalescence pathways in real time. We enhance the functionality of these membranes by making their shape responsive to external stimuli. Our results demonstrate a pathway toward control of thin elastic sheets’ shape and topology—a pathway driven by the emergent elasticity induced by compositional heterogeneity.

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Section: Discussionmentioning

confidence: 99%

Controlling the shape and topology of two-component colloidal membranes

Khanra

Jia

Mitchell

et al. 2022

Proc. Natl. Acad. Sci. U.S.A.

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show abstract

“…Conventional lipid bilayer vesicles do not permit easy understanding of how Gaussian modulus affects their morphology, as the Gauss-Bonnet theorem requires that the Gaussian curvature energy integrates to a system independent constant value [6,55,56]. Consequently, measurement and control of Gaussian modulus in lipid bilayers is challenging [57][58][59]. Open edges of colloidal membranes enabled our study of how Gaussian modulus influences the stability of flat disk-shaped membranes.…”

Section: Discussionmentioning

confidence: 99%

Controlling the shape and topology of two-component colloidal membranes

Khanra,

Jia,

Mitchell

et al. 2022

Preprint

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Changes in the geometry and topology of self-assembled membranes underlie diverse processes across cellular biology and engineering. Similar to lipid bilayers, monolayer colloidal membranes have in-plane fluid-like dynamics and out-of-plane bending elasticity. Their open edges and micron length scale provide a tractable system to study the equilibrium energetics and dynamic pathways of membrane assembly and reconfiguration. Here, we find that doping colloidal membranes with short miscible rods transforms disk-shaped membranes into saddle-shaped surfaces with complex edge structures. The saddle-shaped membranes are well-approximated by Enneper's minimal surfaces. Theoretical modeling demonstrates that their formation is driven by increasing positive Gaussian modulus, which in turn is controlled by the fraction of short rods. Further coalescence of saddleshaped surfaces leads to diverse topologically distinct structures, including catenoids, tri-noids, four-noids, and higher order structures. At long time scales, we observe the formation of a systemspanning, sponge-like phase. The unique features of colloidal membranes reveal the topological transformations that accompany coalescence pathways in real time. We enhance the functionality of these membranes by making their shape responsive to external stimuli. Our results demonstrate a novel pathway towards control of thin elastic sheets' shape and topology -a pathway driven by the emergent elasticity induced by compositional heterogeneity. RESULTS Assembly of colloidal membranesColloidal membranes are one-rod-length thick fluid monolayers composed of aligned rods that self-assemble

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“…It is necessary to express equation (1) in terms of φ so we might be able to establish the variations of the energy due to the Gaussian curvature similar to Eq. (12). These variations must also be subject to diffusion so we can obtain the dynamic equation that dictates the evolution of the surface.…”

Section: Competing Interestsmentioning

confidence: 99%

“…Lipid bilayers exhibit different stable configurations, depending on the values of the Gaussian and bending energetic moduli. There are no direct experimental measurements of the Gaussian modulus, although a method has been proposed recently 12 . Indirect measurements give a negative value of about κ ≈ −15K B T 13 , and molecular dynamics simulations give similar results 14 .…”

Section: Introductionmentioning

confidence: 99%

On Gaussian Curvature and Membrane Fission

Rueda-Contreras

Gallen

Romero-Arias

et al. 2021

Preprint

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We propose a three-dimensional mathematical model to describe dynamical processes of membrane fission. The model is based on a phase field equation that includes the Gaussian curvature contribution to the bending energy. With the addition of the Gaussian curvature energy term numerical simulations agree with the predictions that tubular shapes can break down into multiple vesicles. A dispersion relation obtained with linear analysis predicts the wavelength of the instability and the number of formed vesicles. Finally, a membrane shape diagram is obtained for the different Gaussian and bending modulus, showing different shape regimes.

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Measuring Gaussian Rigidity Using Curved Substrates

Cited by 6 publications

References 35 publications

Controlling the shape and topology of two-component colloidal membranes

Controlling the shape and topology of two-component colloidal membranes

Controlling the shape and topology of two-component colloidal membranes

On Gaussian Curvature and Membrane Fission

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