Curvature mediated elastic interactions between inclusions in lipid membranes have been analyzed using both theoretical and computational methods. Entropic corrections to these interactions have also been studied. Here we show that elastic and entropic forces between inclusions in membranes can compete under certain conditions to a yield a maximum in the free energy at a critical separation. If the distance between the inclusions is less than this critical separation then entropic interactions dominate and there is an attractive force between them, while if the distance is more than the critical separation then elastic interactions dominate and there is a repulsivemore »
Axisymmetric membranes with edges under external force: buckling, minimal surfaces, and tethers
We use theory and numerical computation to determine the shape of an axisymmetric fluid membrane with a resistance to bending and constant area. The membrane connects two rings in the classic geometry that produces a catenoidal shape in a soap film. In our problem, we find infinitely many branches of solutions for the shape and external force as functions of the separation of the rings, analogous to the infinite family of eigenmodes for the Euler buckling of a slender rod. Special attention is paid to the catenoid, which emerges as the shape of maximal allowable separation when the area is less than a critical area equal to the planar area enclosed by the two rings. A perturbation theory argument directly relates the tension of catenoidal membranes to the stability of catenoidal soap films in this regime. When the membrane area is larger than the critical area, we find additional cylindrical tether solutions to the shape equations at large ring separation, and that arbitrarily large ring separations are possible. These results apply for the case of vanishing Gaussian curvature modulus; when the Gaussian curvature modulus is nonzero and the area is below the critical area, the force and the membrane tension more »
- Award ID(s):
- 2020098
- Publication Date:
- NSF-PAR ID:
- 10287703
- Journal Name:
- Soft Matter
- Volume:
- 17
- Issue:
- 31
- Page Range or eLocation-ID:
- 7268 to 7286
- ISSN:
- 1744-683X
- Sponsoring Org:
- National Science Foundation
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Curvature mediated elastic interactions between inclusions in lipid membranes have been analyzed using both theoretical and computational methods. Entropic corrections to these interactions have also been studied. Here we show that elastic and entropic forces between inclusions in membranes can compete under certain conditions to a yield a maximum in the free energy at a critical separation. If the distance between the inclusions is less than this critical separation then entropic interactions dominate and there is an attractive force between them, while if the distance is more than the critical separation then elastic interactions dominate and there is a repulsivemore »
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