# Renormalization of chiral couplings in titled bilayer membranes

@article{Nelson1993RenormalizationOC, title={Renormalization of chiral couplings in titled bilayer membranes}, author={Philip C. Nelson and Thomas R. Powers}, journal={Journal De Physique Ii}, year={1993}, volume={3}, pages={1535-1569} }

We study the effects of chiral constituent molecules on the microscopic shapes attained by lipid bilayer membranes. Such fluid membranes are beautiful examples of statistical ensembles of random shapes, sometimes coupled to in-plane order. We analyze them with methods of continuum elasticity theory, generalizing the well-known Canham-Helfrich model, and in particular incorporate the effects of thermal fluctuations. The condition that coordinate choice be immaterial greatly constrains the…

## 34 Citations

Measure Factors, Tension, and Correlations of Fluid Membranes

- Chemistry, Physics
- 1994

We study two geometrical factors needed for the correct construction of statistical ensembles of surfaces. Such ensembles appear in the study of fluid bilayer membranes, though our results are more…

Novel tilt-curvature coupling in lipid membranes.

- Chemistry, MedicineThe Journal of chemical physics
- 2017

This paper argues that the derivation of a tilt-curvature Hamiltonian based on the elementary assumption of a thin fluid elastic sheet experiencing internal lateral pre-stress unfortunately missed a coupling term between curvature and tilt, and derives a new term that is equivalent to the monolayer Gaussian curvature modulus, κ¯m.

Statistical mechanics of closed fluid membranes.

- Physics, MedicinePhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1995

The combination of undulation and collective mode free energy contributions found here is shown to yield thermodynamic properties for a vesicle phase whose parameter dependence is consistent with the scale invariance of the Helfrich bending energy.

Thermal fluctuations of vesicles and nonlinear curvature elasticity--implications for size-dependent renormalized bending rigidity and vesicle size distribution.

- Physics, MedicineSoft matter
- 2016

The statistical mechanics of closed membranes (vesicles) incorporating both constitutive and geometrical nonlinearities are discussed and results for the renormalized bending rigidity of small vesicles are derived and it is shown that significant stiffening may occur for sub-20 nm vesicle sizes.

Fluctuating Membranes with Tilt Order

- Physics
- 1995

Thermal fluctuations are important for amphiphilic bilayer membranes since typical bending stiffnesses can be a few k B T. The rod-like constituent molecules are generically tilted with respect to…

Theory of cylindrical tubules and helical ribbons of chiral lipid membranes.

- Materials Science, MedicinePhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1996

We present a general theory for the equilibrium structure of cylindrical tubules and helical ribbons of chiral lipid membranes. This theory is based on a continuum elastic free energy that permits…

Flexoelectricity and thermal fluctuations of lipid bilayer membranes: Renormalization of flexoelectric, dielectric, and elastic properties

- Materials Science
- 2013

Thermal fluctuations renormalize the bending elasticity of lipid bilayers. This well-studied effect is a cornerstone in the study of several membrane biophysical phenomena. Analogously, nearly all…

The concept of effective tension for fluctuating vesicles

- Physics
- 1995

Vesicles are closed surfaces of bilayer membranes. Their mean shapes and fluctuations are governed by the competition of curvature energy and geometrical constraints on the enclosed volume and total…

Additional contributions to elastic energy of lipid membranes: Tilt-curvature coupling and curvature gradient.

- Physics, MedicinePhysical review. E
- 2020

A stable elastic energy functional is derived, showing that the squared gradient of the curvature was missed in both of these works, and this change in the energy functional arises from a more accurate consideration of the transverse shear deformation terms and their influence on the membrane stability.

Topological defects on fluctuating surfaces: General properties and the Kosterlitz-Thouless transition.

- Physics, MedicinePhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1996

The Kosterlitz-Thouless transition for hexatic order on a free fluctuating membrane is investigated and both a Coulomb gas and a sine-Gordon Hamiltonian are derived, which derive renormalization group recursion relations that predict a transition with decreasing bending rigidity $\kappa$.

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