LARGE DEVIATIONS OF THE AVERAGE SHAPES OF VESICLES FROM EQUILIBRIUM -EFFECTS OF THERMAL FLUCTUATIONS IN THE PRESENCE OF CONSTRAINTS

In the absence of external stresses, the surface area and the volume o f a closed, flaccid lipid vesicle are practically constant. Thermal sh ape fluctuations of vesicles that are subject to these constraints rec ently have been shown to induce a shift of the average shapes away fro m the equilibrium (zero temperature) shapes. Since only the average sh apes can be determined from observations by optical microscopy, it is important to establish the magnitude of their deviation from the well- studied equilibrium shapes. In this paper we develop a formalism to ca lculate this thermal shift, and we demonstrate that nonlinearities in the constraints may cause it to be unexpectedly large. Allowing for ar bitrary shape deformations, we present numerical calculations revealin g a logarithmic dependence of the thermal shift on the number of fluct uational degrees of freedom of the vesicle membrane or, equivalently, on the number of lipid molecules constituting the membrane. As a conse quence, the surface area (''projected area'') and, to a lesser extent, the volume (''projected volume'') of the average shape are smaller th an their true values. These numerical results are in general agreement with theoretical predictions that have been made so far only for piec es of flat membranes but not for closed lipid membranes subject to the constraints of both constant area and volume. Furthermore, we derive an expression for the correlation function of deviations from equilibr ium including terms of the order of (k(B)T)(2) that involve the (quadr atic) thermal shift. We demonstrate that these terms may actually exce ed the commonly used leading term of the correlation function. This an alysis suggests that the determination of the membrane bending modulus k(c) from observations of thermal vesicle shape fluctuations should b e based on the variances rather than the correlation functions.