Fluctuation spectra of free and supported membrane pairs

TL;DR

This paper analyzes the fluctuation spectra of coupled membrane systems, comparing discrete tether models with continuous potentials, and explores how these interactions influence membrane displacements and fluctuation behaviors.

Contribution

It provides a comparative analysis of discrete and continuous models for membrane fluctuations, revealing conditions for nonmonotonic spectra and displacement alterations.

Findings

Discrete tethers can cause nonmonotonic fluctuation spectra.

Supported membrane pairs exhibit altered displacement profiles.

Nonmonotonic spectra occur with stiff tethers and varying membrane rigidities.

Abstract

Fluctuation spectra of fluid compound membrane systems are calculated. The systems addressed contain two (or more) almost parallel membranes that are connected by harmonic tethers or by a continuous, harmonic confining potential. Additionally, such a compound system can be attached to a supporting substrate. We compare quasi-analytical results for tethers with analytical results for corresponding continuous models and investigate under what circumstances the discrete nature of the tethers actually influences the fluctuations. A tethered, supported membrane pair with similar bending rigidities and stiff tethers can possess a nonmonotonic fluctuation spectrum with a maximum. A nonmonotonic spectrum with a maximum and a minimum can occur for an either free or supported membrane pair of rather different bending rigidities and for stiff tethers. Typical membrane displacements are calculated for supported membrane pairs with discrete or continuous interacting potentials. Thereby an estimate of how close the constituent two membranes and the substrate typically approach each other is given. For a supported membrane pair with discrete or continuous interactions, the typical displacements of each membrane are altered with respect to a single supported membrane, where those of the membrane near the substrate are diminished and those of the membrane further away are enhanced.