12 Diffusion in Membranes Ilpo Vattulainen and Ole G. Mouritsen 12.1 Introduction Nature is always in motion. As simple as it is, this statement is true in the sense that numerous phenomena in living systems are characterized by non- equilibrium. Our muscles are in constant need of energy provided by the metabolic pathway, the blood flows in our veins as long as the heart keeps going, and yet old cells are constantly being replaced by fresh ones as a typical life time of a cell is on the order of one day. The state of living beings can therefore only rarely be described by equilibrium. However, even if a true equilibrium were possible in living systems, we would find spontaneous thermal fluctuations to occur around the equilibrium state, again implying that the matter were moving in time. This book is devoted to the idea of particles moving in condensed matter systems. Our aim in this chapter is to discuss the role of diffusion in soft biological interfaces known as membranes. In biological systems, diffusion is one of the most intriguing processes that arise from the dynamics of biological molecules. It may sound surprising but many of the diffusion processes in living systems are based on a very simple idea – a random walk. Microtubules – long filaments of proteins that search for other molecules inside cells and serve as highways for transporting them inside the cell – grow and shrink in a manner that reminds us of a random walk [1]. Small bacteria, in turn, swim in a fashion involving a long ballistic movement followed by a period during which the particle “tumbles” in a highly erratic manner, thus choosing a new direction for its motion, again followed by another long jump [2]. Interestingly, this joint motion of rushing and tumbling allows the bacterium to move efficiently around its environment as it searches for the best food markets. Then, if we look at the motion of molecules in cell membranes that act as a permeable barrier between the inside and the outside of the cell, we again may notice that the motion of molecules in the plane of the membrane can essentially be described as a random walk [3]. All these examples are kind of confusing since one might expect that Nature works in a manner that is more orderly and deterministic and less random than finance or lottery, in which the random walk plays a major role [4]. Yet we have plenty of evidence that the diffusion in living systems