Polarizability and Kerr constant of proteins by boundary element methods

Abstract

A precise implementation of the boundary element method has been applied to the computation of the polarizability and the Kerr constant of eight soluble proteins. The method is demonstrated to be accurate and precise by comparison with analytical values for spheroids. Two different integral equations have been solved: (1) an exact equation with explicit dielectric constant dependence, and (2) an exact equation for a metallic body. The dielectric dependence for the metallic body case is built in with a generalization of the ellipsoid formula. Both methods agree quantitatively with each other for low relative dielectric constants. A full tensor expression for the Kerr constant yields perfect agreement with experiment for some proteins and badly under reports for the rest. The protein structure is obtained from a crystallographic database and is assumed rigid throughout the TEB measurement. Electrolyte effects are neglected. The Kerr constant is dominated by the protein dipole moment and is quite sensitive to the orientation of the dipole moment relative to the principal axes of the polarizability tensor. Several possible reasons for the large discrepancy between some computed and measured values are discussed.

Figure 1

Extrapolation to infinite number of triangles. Oblate ellipsoid with axial ratio p =2.

Fig 2

The triangulated surface of lysozyme.

Fig. 3

Dependence of the Kerr constant on the orientation of the dipole moment for tropomyosin. Angles are given in radians (0 < θ < π; 0 < ϕ < 2 π).