Flexible membranes have been studied for a long time in biology, pharmacology and medicine since they represent the main structural element for the amazing architecture of the living cell. In addition, physicists and chemists have been fascinated by the unusual properties of these structures which are very anisotropic: They consist of bilayers of molecules and thus are very thin with a thickness of only 4 - 5 nanometers; their lateral extension, however, is much larger and can be tens of micrometers. Therefore, flexible membranes are able to bridge the gap between the nano- and the microworld.
So far, our understanding of these structures was based on two rather different theoretical approaches. On the one hand, the behavior of membranes on the micrometer scale is well understood in terms of smooth surfaces as described by differential geometry. In this way, one can explain the many different shapes and topologies as observed in the optical microscope. On the other hand, our view about the membranes on the nanometer scale comes from computer simulations in which one studies discrete molecular models with atomic resolution. However, these two approaches have remained rather distinct and unrelated.
Recently, researchers at the Max Planck Institute of Colloids and Interfaces (Physical Review Letters 82, 4 January 1999) have made the first explicit connection between these two different levels corresponding to the nano- and the microworld, respectively . Using Molecular Dynamics simulations of rather large membrane segments, they studied both the self-assembly process and the physical properties of such bilayer membranes, compare Fig.1. On molecular scales, these membranes are observed to be rather mobile and to have rough surfaces arising from molecular protrusions, i.e., from the relative displacements of individual molecules. On length scales, which are only somewhat larger than the membrane thickness, however, the membranes are found to undergo smooth bending undulations.
Using these computer simulations, it was even possible to estimate the bending rigidity, the most important elastic constant which enters the description on the micrometer scale. This elastic constant was extracted from a detailed analysis of thermally-excited membrane fluctuations. Surprisingly, the numerical value of the bending rigidity as determined from the fluctuation spectrum turns out to be consistent with a relatively simple model in which one treats each monolayer of the bilayer as a thin structureless film with vanishing 2-dimensional shear modulus.
In the article published in Physical Review Letters, this approach has been applied to rather simple membrane models. It is obvious, however, that the same approach can also be used for more complex models. It will then be possible to study how the elastic properties of the membranes depend on the precise molecular architecture and how these properties vary with the membrane composition.
Typical configuration of a bilayer membrane composed of 1152 amphiphilic molecules. At small scales, one sees individual molecules which protrude from the bilayer membrane. On length scales, which are only somewhat larger than the membrane thickness, the bilayer looks already like an elastic sheet which is curved in a smooth way.
Published: 22-12-98
Contact: Thomas Weikl
Max Planck Institute of Colloids and Interfaces, Teltow/Germany
Phone: 49-3328-46-590
Fax: 49-3328-46-232
Journal
Physical Review Letters