Direct molecular level measurements of the electrostatic properties of a protein surface

In this work, we used direct measurements with the surface force apparatus to determine the pH-dependent electrostatic charge density of a single binding face of streptavidin. Mean field calculations have been used with considerable success to model electrostatic potential fields near protein surfaces, but these models and their inherent assumptions have not been tested directly at the molecular level. Using the force apparatus and immobilized, oriented monolayers of streptavidin, we measured a pI of 5–5.5 for the biotin-binding face of the protein. This differs from the pI of 6.3 for the soluble protein and confirms that we probed the local electrostatic features of the macromolecule. With finite difference solutions of the linearized Poisson–Boltzmann equation, we then calculated the pH-dependent charge densities adjacent to the same face of the protein. These calculated values agreed quantitatively with those obtained by direct force measurements. Although our study focuses on the pH-dependence of surface electrostatics, this direct approach to probing the electrostatic features of proteins is applicable to investigations of any perturbations that alter the charge distribution of the surfaces of immobilized molecules.

A fast, high resolution, second-order central scheme for incompressible flows

A high resolution, second-order central difference method for incompressible flows is presented. The method is based on a recent second-order extension of the classic Lax–Friedrichs scheme introduced for hyperbolic conservation laws (Nessyahu H. & Tadmor E. (1990) J. Comp. Physics. 87, 408-463; Jiang G.-S. & Tadmor E. (1996) UCLA CAM Report 96-36, SIAM J. Sci. Comput., in press) and augmented by a new discrete Hodge projection. The projection is exact, yet the discrete Laplacian operator retains a compact stencil. The scheme is fast, easy to implement, and readily generalizable. Its performance was tested on the standard periodic double shear-layer problem; no spurious vorticity patterns appear when the flow is underresolved. A short discussion of numerical boundary conditions is also given, along with a numerical example.