Continuum electromechanical modeling of protein-membrane interactions

A continuum electromechanical model is proposed to describe the membrane curvature induced by electrostatic interactions in a solvated protein-membrane system. The model couples the macroscopic strain energy of membrane and the electrostatic solvation energy of the system, and equilibrium membrane deformation is obtained by minimizing the electroelastic energy functional with respect to the dielectric interface. The model is illustrated with the systems with increasing geometry complexity and captures the sensitivity of membrane curvature to the permanent and mobile charge distributions.

Figure 1

(Color online) Illustration of the proposed electromechanical model for protein-membrane interactions. Left: molecular surface of a protein-membrane complex. Atomistic details are retained in the protein but are neglected in membrane. The left and right surfaces of the membrane are negatively charged, and its circular face is charge-free and constrained. Depending on the mobile ion concentration and the partial charge distribution in the protein, the membrane might be attracted to bend toward the protein (middle) or repulsed away from the protein (right).

Figure 2

(Color online) Change of membrane displacement with different parameters for the test systems. Unless specified particularly the charge of atom is $5e$, the mobile ion concentration is 150 mM, and the surface charge density assumes the default value. In the first system (A)–(C) the protein consists of a single atom centered at (0,0,50). In the second problem (D) the overall electrically neutral protein consists of eight model atoms centered at $\left(\pm 6,\pm 6,50\right)$ and $\left(\pm 6,\pm 6,56\right)$. Every atom on $z=50$ and $z=56$ carries a charge of 2 and $-2$, respectively. The center of the membrane is initially placed at (0,0,0) in both problems with its axle aligned with the $z$ axis.

Figure 3

(Color online) First row: the structure of protein 1I4D (left); surface triangulation of the BAR-domain protein-membrane complex (middle) and the electrostatic potential on the protein and membrane surfaces (right). Second row: membrane curvature at various ion concentrations (left) and membrane displacement at various initial separations $D$ (right).