Biophys J, December 2002, p. 2898-2905, Vol. 83, No. 6

The Many-Body Problem for Anisotropic Membrane Inclusions and the Self-Assembly of "Saddle" Defects into an "Egg Carton"

Paul G. Dommersnes^* and Jean-Baptiste Fournier

 ^*Department of Physics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway, and  Laboratoire de Physico-Chimie Théorique et FR CNRS 2438 "Matière et Systèmes Complexes," ESPCI, F-75231 Paris cedex 05, France

We calculate the many-body, nonpairwise interaction between N rigid, anisotropic membrane inclusions by modeling them as point-like constraints on the membrane's curvature tensor and by minimizing the membrane's curvature energy. Because multipolar distortions of higher-order decay on very short distances, our calculation gives the correct elastic interaction energy for inclusions separated by distances of the order of several times their size. As an application, we show by thermally equilibrating the many-body elastic energy using a Monte Carlo algorithm, that inclusions shaped as "saddles" attract each other and build an "egg-carton" structure. The latter is reminiscent of some patterns observed in membranes obtained from biological extracts, the origin of which is still mysterious.

Biophys J, December 2002, p. 2898-2905, Vol. 83, No. 6
© 2002 by the Biophysical Society   0006-3495/02/12/2898/08  $2.00