Digital Object Identifier (DOI) 10.1007/s001610100078 Continuum Mech. Thermodyn. (2002) 14: 127–136 Original Article Dynamics of kinks in biological membranes Riccardo Rosso, Andr´ e M. Sonnet and Epifanio G. Virga Dipartimento di Matematica, Istituto Nazionale di Fisica della Materia, Universit` a di Pavia, Via Ferrata 1, 27100 Pavia, Italy Received November 6, 2001 / Published online February 4, 2002 – c  Springer-Verlag 2002 Communicated by Kolumban Hutter, Darmstadt We propose a two-dimensional model for the dynamics of the kinks created in a biological membrane by the interaction with a movable bead. We arrive at the evolution equations for both the bead and the membrane, whence we conclude that the force exerted on the bead by a fixed membrane points in the direction along which the curvature of the membrane is more concentrated. This is the first step towards understanding the basic mechanism behind the dynamics of protein aggregation which takes place on biological membranes. 1 Introduction In the past three decades, many efforts have been devoted to the mathematical modelling of biological membranes, which are basic components of living matter. Biological membranes are complex as they consist of lipids, proteins, and, to a minor extent, also of carbohydrates, ions, and water. Among lipids, a basic distinction is made between polar lipids, like phospholipids and glycolipids, and non-polar lipids, like sterols. In particular, phospholipids are common to all membranes, and their peculiar structure is ultimately responsible for the intriguing properties of biological membranes. They consist of amphiphilic molecules which have a hydrophilic polar head connected with a hydrophobic tail formed by aliphatic chains. It is thus advantageous for amphiphilic molecules dispersed in water to form aggregates where the contact between the hydrophobic tails and the aqueous environment is reduced as much as possible. This explains why lipid bilayers, where the tails hide themselves from the surrounding water molecules, are the most common organizations of amphiphilic molecules (see Fig. 1). Fig. 1. Sketch of a lipid bilayer It should be noted, however, that also non-bilayer aggregates are possible, such as for example direct and inverse micellar phases. This is so because the extremely complex interactions among lipids can modify the tendency induced by the hydrophobic effect: a comprehensive classification of non-bilayer phases can be found in Chapter 16 of Israelachvili’s book [1]. Lipid aggregates in the bilayer phase can further reduce the unfavourable contact between aliphatic chains and water by bending themselves to form vesicles, which are closed membranes. Since the order of magnitude Dedicated to Professor Ingo M¨ uller on the occasion of his 65th birthday