Molecules dancing in membranes

In 1828, a botanist named Robert Brown found that small pollen particles suspended in water migrated in an erratic fashion. Later it was realized that the dance Brown observed was essentially a two-dimensional random walk driven by thermal fluctuations, thus this Brownian motion was more intense at higher temperatures. The pioneering ideas and observations by Brown have inspired people for a long time to think about the fascinating aspects of random walks, and hence of diffusion. In this brief contribution, we consider this topic at complex biological interfaces known as cellular membranes and discuss how the dance of lipids and small molecules can be quantified through experiments and theoretical approaches. Some illustrative examples of diffusion in membrane systems are discussed