RENORMALIZATION OF CHIRAL COUPLINGS IN TILTED BILAYER-MEMBRANES

We study the effects of chiral constituent molecules on the macroscopi c shapes attained by lipid bilayer membranes. Such fluid membranes are beautiful examples of statistical ensembles of random shapes, sometim es coupled to in-plane order. We analyze them with methods of continuu m elasticity theory, generalizing the well-known Canham-Helfrich model , and in particular incorporate the effects of thermal fluctuations. T he condition that coordinate choice be immaterial greatly constrains t he possible forms of the statistical weights in these systems, leading to very few independent couplings and hence physically simple models. Thermal fluctuations effectively reduce the chirality of a membrane a t long scales, leading to an anomalous scaling relation for the radius of bilayer tubules and helices as a function of chirality. En route t o this conclusion we develop a perturbative calculation scheme, paying particular attention to the functional measure needed to describe flu ctuations covariantly.