Predicting the Orientation of Adsorbed Proteins Steered with Electric Fields Using a Simple Electrostatic Model

Accurate Boundary Integral Formulations for the Calculation of Electrostatic Forces with an Implicit-Solvent Model

An accurate force calculation with the Poisson-Boltzmann equation is challenging, as it requires the electric field on the molecular surface. Here we present a calculation of the electric field on the solute-solvent interface that is exact for piecewise linear variations of the potential and analyze four different alternatives to compute the force using a boundary element method. We performed a verification exercise for two cases: the isolated and two interacting molecules. Our results suggest that the boundary element method outperforms the finite difference method, as the latter needs a much finer mesh than in solvation energy calculations to get acceptable accuracy in the force, whereas the same surface mesh as in a standard energy calculation is appropriate for the boundary element method. Among the four evaluated alternatives of force calculation, we saw that the most accurate one is based on the Maxwell stress tensor. However, for a realistic application, like the barnase-barstar complex, the approach based on variations of the energy functional, which is less accurate, gives equivalent results. This analysis is useful toward using the Poisson-Boltzmann equation for force calculations in applications where high accuracy is key, for example, to feed molecular dynamics models or to enable the study of the interaction between large molecular structures, like viruses adsorbed onto substrates.

Arbitrary-Shape Dielectric Particles Interacting in the Linearized Poisson-Boltzmann Framework: An Analytical Treatment

This work considers the interaction of two dielectric particles of arbitrary shape immersed into a solvent containing a dissociated salt and assuming that the linearized Poisson-Boltzmann equation holds. We establish a new general spherical re-expansion result which relies neither on the conventional condition that particle radii are small with respect to the characteristic separating distance between particles nor on any symmetry assumption. This is instrumental in calculating suitable expansion coefficients for the electrostatic potential inside and outside the objects and in constructing small-parameter asymptotic expansions for the potential, the total electrostatic energy, and forces in ascending order of Debye screening. This generalizes a recent result for the case of dielectric spheres to particles of arbitrary shape and builds for the first time a rigorous (exact at the Debye-Hückel level) analytical theory of electrostatic interactions of such particles at arbitrary distances. Numerical tests confirm that the proposed theory may also become especially useful in developing a new class of grid-free, fast, highly scalable solvers.

Modeling of the Electrostatic Interaction and Catalytic Activity of [NiFe] Hydrogenases on a Planar Electrode

Hydrogenases are a group of enzymes that have caught the interest of researchers in renewable energies, due to their ability to catalyze the redox reaction of hydrogen. The exploitation of hydrogenases in electrochemical devices requires their immobilization on the surface of suitable electrodes, such as graphite. The orientation of the enzyme on the electrode is important to ensure a good flux of electrons to the catalytic center, through an array of iron-sulfur clusters. Here we present a computational approach to determine the possible orientations of a [NiFe] hydrogenase (PDB 1e3d) on a planar electrode, as a function of pH, salinity, and electrode potential. The calculations are based on the solution of the linearized Poisson-Boltzmann equation, using the PyGBe software. The results reveal that electrostatic interactions do not truly immobilize the enzyme on the surface of the electrode, but there is instead a dynamic equilibrium between different orientations. Nonetheless, after averaging over all thermally accessible orientations, we find significant differences related to the solution's salinity and pH, while the effect of the electrode potential is relatively weak. We also combine models for the protein adsoption-desorption equilibria and for the electron transfer between the proteins and the electrode to arrive at a prediction of the electrode's activity as a function of the enzyme concentration.