Biophys J, November 2000, p. 2583-2604, Vol. 79, No. 5

Inclusion-Induced Bilayer Deformations: Effects of Monolayer Equilibrium Curvature

Claus Nielsen^* and Olaf S. Andersen^*

 ^*Department of Physiology and Biophysics, Cornell University, Weill Medical College, New York, New York 10021 USA, and  August Krogh Institute, University of Copenhagen, Copenhagen DK-2100, Denmark

The energetics of protein-induced bilayer deformation in systems with finite monolayer equilibrium curvature were investigated using an elastic membrane model. In this model the bilayer deformation energy G_def has two major components: a compression-expansion component and a splay-distortion component, which includes the consequences of a bilayer curvature frustration due to a monolayer equilibrium curvature, c₀, that is different from zero. For any choice of bilayer material constants, the value of G_def depends on global bilayer properties, as described by the bilayer material constants, as well as the energetics of local lipid packing adjacent to the protein. We introduce this dependence on lipid packing through the contact slope, s, at the protein-bilayer boundary. When c₀ = 0, G_def can be approximated as a biquadratic function of s and the monolayer deformation at the protein/bilayer boundary, u₀: G_def = a₁u₀² + a₂u₀s + a₃s², where a₁, a₂, and a₃ are functions of the bilayer thickness, the bilayer compression-expansion and splay-distortion moduli, and the inclusion radius (this expression becomes exact when the Gaussian curvature component of G_def is negligible). When c₀  0, the curvature frustration contribution is determined by the choice of boundary conditions at the protein-lipid boundary (by the value of s), and G_def is the sum of the energy for c₀ = 0 plus the curvature frustration-dependent contribution. When the energetic penalty for the local lipid packing can be ignored, G_def will be determined only by the global bilayer properties, and a c₀ > 0 will tend to promote a local inclusion-induced bilayer thinning. When the energetic penalty for local lipid packing is large, s will be constrained by the value of c₀. In a limiting case, where s is determined only by geometric constraints imposed by c₀, a c₀ > 0 will impede such local bilayer thinning. One cannot predict curvature effects without addressing the proper choice of boundary conditions at the protein-bilayer contact surface.

Biophys J, November 2000, p. 2583-2604, Vol. 79, No. 5
© 2000 by the Biophysical Society   0006-3495/00/11/2583/22  $2.00

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