A Simple Computer Model for Liquid Lipid Bilayers

We present a simple coarse-grained bead-and-spring model for lipid bilayers. The system has been developed to reproduce the main (gel-liquid) transition of biological membranes on intermediate length scales of a couple of nanometres and is very efficient from a computational point of view. For the solvent environment, two different models are proposed. The first model forces the lipids to form bilayers by confining their heads in two parallel planes. In the second model, the bilayer is stabilised by a surrounding gas of "phantom" solvent beads, which do not interact with each other. This model takes only slightly more computing time than the first one, while retaining the full membrane flexibility. We calculate the liquid-gel phase boundaries for both models and find that they are very similar.Comment: 11 pages, 6 figure

Connections and the Second Main Theorem for Holomorphic Curves

By means of $C^\infty$-connections we will prove a general second main theorem and some special ones for holomorphic curves. The method gives a geometric proof of H. Cartan's second main theorem in 1933. By applying the same method, we will prove some second main theorems in the case of the product space (\pone)^2 of the Riemann sphere.Comment: 21 page