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Research Papers

Interaction-Induced Morphological Transitions of Lipid Membranes in Contact With an Elliptical Cross Section of a Rigid Substrate

[+] Author and Article Information
T. Belay

Department of Mechanical Engineering,
University of Alberta,
Edmonton T6G 2G8, Canada
e-mail: tsegay@ualberta.ca

C. I. Kim

Assistant Professor
Department of Mechanical Engineering,
University of Alberta,
Edmonton T6G 2G8, Canada
e-mail: cikim@ualberta.ca

P. Schiavone

Professor
Department of Mechanical Engineering,
University of Alberta,
Edmonton T6G 2G8, Canada
e-mail: P.Schiavone@ualberta.ca

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received July 7, 2015; final manuscript received August 28, 2015; published online October 8, 2015. Assoc. Editor: M Taher Saif.

J. Appl. Mech 83(1), 011001 (Oct 08, 2015) (12 pages) Paper No: JAM-15-1355; doi: 10.1115/1.4031485 History: Received July 07, 2015; Revised August 28, 2015

We present a complete analysis for the deformation profiles of lipid membranes induced by their interactions with solid elliptical cylinder substrates (e.g., proteins). The theoretical framework for the mechanics of lipid membranes is described in terms of the classical Helfrich model, and the resulting shape equation is formulated in general curvilinear coordinates to accommodate the elliptical shape of the contour surrounding the contact area. Admissible boundary conditions for the contact region are taken from the existing literature but reformulated and adapted to the current framework. A complete semi-analytic solution (in terms of Mathieu functions) is obtained within the limitation of superposed incremental deformations and the Monge representation in the deformed configuration functions. The results predict smooth morphological transitions over the domain of interest when a lipid membrane interacts with a rigid substrate through an elliptical contact region.

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References

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Figures

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Fig. 1

Circular, cylindrical, and elliptical structure formed from lipid molecules [14]

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Fig. 2

Schematics of interaction of membrane, substrate, and bulk liquid: (a) three-dimensional and (b) two-dimensional representations

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Fig. 3

Deflection of lipid membrane along the (a) major and (b) minor axes with γ = π/2, e = 0.95, and σ/λ = −3

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Fig. 4

Deflection of lipid membrane along the (a) major and (b) minor axes with γ = π/2, e = 0.95, and σ/λ = −9

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Fig. 5

Deflection of lipid membrane along the (a) major and (b) minor axes with γ = π/2, e = 0.95, and σ/λ = −15

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Fig. 6

Contour plot of lipid membrane deflection with elliptical substrate (γ = π/2, e = 0.75, and σ/λ = −15)

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Fig. 7

Contour plot of lipid membrane deflection with circular substrate interaction (γ = π/2 and σ/λ = −3)

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Fig. 8

Linear solution of lipid membrane circular cylinder substrate interaction (γ = π/2 : (a) σ/λ = −3, (b) σ/λ = −9, and (c) σ/λ = −15)

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Fig. 9

Effect of substrate cylinder radius with (a) μρ0 = 0.05 and (b) μρ0 = 10

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