# Membrane-mediated interactions

## TL;DR

This paper reviews how inclusions like proteins influence membrane behavior through shape and fluctuation constraints, highlighting generic, non-chemical interactions in biological membranes.

## Contribution

It provides a comprehensive overview of membrane-mediated interactions arising from shape and thickness constraints, emphasizing generic physical mechanisms.

## Key findings

- Long-range interactions from curvature and fluctuation constraints
- Short-range interactions from hydrophobic mismatch
- Use of coarse-grained models for analysis

## Abstract

Interactions mediated by the cell membrane between inclusions, such as membrane proteins or antimicrobial peptides, play important roles in their biological activity. They also constitute a fascinating challenge for physicists, since they test the boundaries of our understanding of self-assembled lipid membranes, which are remarkable examples of two-dimensional complex fluids. Inclusions can couple to various degrees of freedom of the membrane, resulting in different types of interactions. In this chapter, we review the membrane-mediated interactions that arise from direct constraints imposed by inclusions on the shape of the membrane. These effects are generic and do not depend on specific chemical interactions. Hence, they can be studied using coarse-grained soft matter descriptions. We deal with long-range membrane-mediated interactions due to the constraints imposed by inclusions on membrane curvature and on its fluctuations. We also discuss the shorter-range interactions that arise from the constraints on membrane thickness imposed by inclusions presenting a hydrophobic mismatch with the membrane.