Entropic pressure between biomembranes in a periodic stack due to thermal fluctuations

The phenomenon of thermal fluctuation of a biomembrane within a stack of like membranes was introduced in a pioneering paper [Helfrich W (1978) Z Naturforsch A 33(3): 305-315]. Internal energy arises in a representative membrane through elastic resistance to bending deformation, and membrane motion is further restrained through steric interaction with adjacent membranes. Due to reflective symmetry within the stack, analysis of behavior can be reduced to study of a single membrane fluctuating between parallel rigid planes. The phenomenon is reexamined here from several viewpoints to quantify the dependence of system free energy on the size of the gap between membranes. This analysis is based on essentially the same formulation that was used in the original study, and it is found that analysis based on enforcement of the underlying principles can lead to an exact mathematical solution. On this basis, a self-consistent picture of behavior emerges showing a dependence of free energy on the width of the confining gap that is weaker than has been thought to prevail.