Renormalization of chiral couplings in titled bilayer membranes

  title={Renormalization of chiral couplings in titled bilayer membranes},
  author={Philip C. Nelson and Thomas R. Powers},
  journal={Journal De Physique Ii},
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… 
Measure Factors, Tension, and Correlations of Fluid Membranes
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.
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.
  • Morse, R Milner
  • Physics, Medicine
    Physical 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.
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
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.
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
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
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.
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.
  • Park, Lubensky
  • Physics, Medicine
    Physical 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 $\kappa$.


Theory of chiral lipid tubules.
We present a continuum theory for the self-assembly of cylindrical tubules from chiral lipid bilayers in any tilted fluid phase. This theory shows that tubule formation is driven by an intrinsic
On the scale dependence, due to thermal fluctuations, of the elastic properties of membranes
Abstract Motivated by conflicting results of two recent papers, we reconsider the influence of thermal fluctuations on the rigidity of fluid membranes (such as lipid bilayers) with small surface
Fluctuations in membranes with reduced symmetry
We discuss the effects of in-plane ordering of amphiphilic membranes on the statistics of their shape fluctuations. Effects of flexo- and ferroelectricity as well as of several kinds of orientational
Fluctuations in membranes with crystalline and hexatic order
We study the interplay between crystalline (or hexatic) order and thermal fluctuations in membranes with vanishing surface tension. If the connectivity of the crystalline state is preserved, the
Theory of "Ripple" Phases of Lipid Bilayers.
It is shown that chiral bilayers can exhibit phase transitions from symmetric to asymmetric ripples as the temperature is lowered, and it is predicted that more than one distinct ripple phase made possible by the two-dimensional nature of the tilt order parameter is possible.
Intrinsic bending force in anisotropic membranes made of chiral molecules.
  • Helfrich, Prost
  • Physics, Medicine
    Physical review. A, General physics
  • 1988
A linear term linked to molecular chirality occurs in the bending energy of membranes with C/sub 2/ or D/sub 2/ symmetry. We find it to alternate in sign, depending on the direction of a cylindrical
Theory of helical structures of tilted chiral lipid bilayers.
  • Ou-Yang, Liu
  • Medicine, Physics
    Physical review. A, Atomic, molecular, and optical physics
  • 1991
The general formula that explains the aggregation of narrow and prolate ribbon structures is derived, including more terms of elasticity free energy into the theory, and the size of the helical structure is obtained and is shown to agree with experimental observations.
Thermal softening of curvature elasticity in membranes
Abstract Recently, there have been three determinations of the reduction of curvature elasticity due to thermal fluctuations. The results obtained by Helfrich, Peliti and Leibler, and Forster are
Chiral symmetry breaking in Langmuir monolayers and smectic films.
Langmuir monolayers and freely suspended smectic films can exhibit a spontaneous breaking of chiral symmetry, which leads to the spontaneous formation of complex equilibrium patterns with either 1D or 2D modifications in the direction of molecular tilt.
Optical microscopic study of helical superstructures of chiral bilayer membranes
Donnees sur l'observation directe de surstructures helicoidales, formees a partir de membranes en couches bimoleculaires d'amphiphiles d'ammonium chiraux. Cas, par exemple, d'amphiphiles d'ammonium a