Springer Online Journal Archives 1860-2000
Abstract We consider four models of the lateral distribution of proteins in lipid bilayer membranes and study the fraction of lipids which are adjacent to at least one protein (adjacent lipids) and how this quantity depends upon protein concentration. The models are (i) hard hexagons free to move from one lattice site to another; (ii) hard disks moving on a continuum; (iii) a mixture of two sizes of “nearly-hard” disks moving on a continuum; (iv) a modification of (ii). The hexagons or disks represent proteins, while unocupied lattice sites or the remainder of the continuum represents lipids. In (iii) large disks represent proteins and small disks represent lipids. In (iv) some of the continuum between pairs of disks, where packing defects might occur, is not occupied by lipids. We find that an analytical expression for the adjacent lipids (Hoffmann et al. 1981), which is in excellent agreement with the results of the Hexagon model (i), breaks down at a packing density of f A≊0.805, and we show by considering the hexagon pair correlation function, that this indicates the onset of random close packing, and that a transition to ordered close packing occurs at f A=0.866. We thus obtain an operational definition for a “random” distribution of hexagons: distributions of packing densities≲0.805. We show that the Disk model (ii) gives results for adjacent lipids that are greater than the Hexagon model and compare these results to the Two Disk model (iii) which gives a result substantially less than the Hexagon model (Mountain et al. 1986). We show that the Modified Disk model (iv) gives results in essential agreement with the Hexagon model except for f A≳0.77. Finally we discuss the general appearance of the “motion restricted” ESR spectrum and conclude that, of these four models, the Modified Disk or the Hexagon models best account for the data. We discuss why this is so with reference to the representation of a 3-dimensional membrane by a 2-dimensional plane.
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