Java application for calculating protein-induced bilayer deformation energies using an analytical solution

The local deformation of a bilayer due to protein-bilayer hydrophobic mismatch has an associated energetic cost, the bilayer deformation energy (ΔGdef), which contributes to the total energetic cost of membrane protein conformational changes (ΔGtotal). We present an analytical solution to the continuum elastic model of protein-induced bilayer deformations (Nielsen et al., 1998, 2000), which allows us to calculate ΔGdef for a cylindrical membrane inclusion, together with a user-friendly Java implementation that calculates ΔGdef for two different states (different hydrophobic lengths) of an inclusion.

This provides for a simple calculation of the bilayer contribution to ΔGtotal (ΔΔGdef, or ΔGbilayer). In the current implementation, ΔGdef varies as a function of the unperturbed bilayer hydrophobic thickness (d0), the inclusion’s hydrophobic length (l), the lipid intrinsic curvature (c0) and the elastic moduli for compression (Ka) and bending (Kc).

The consequences of a non-zero c0 depend on the contact slope at the inclusion boundary (s), which is introduced as in Nielsen and Andersen (2000). Constraints introduced by an energetic penalty for local lipid packing are introduced through different boundary conditions for s, which may be user-defined.

The perturbation of the bilayer, and the radial decomposition of ΔGdef into its component energies can be visualized graphically, and the underlying data can be saved. The tool allows for quick calculations of bilayer deformation energies for a user’s given parameters, which provides for convenient estimates of the bilayer contribution to conformational changes in integral membrane proteins.