Stabilization of protein crystals by electrostatic interactions as revealed by a numerical approach

We developed a novel algorithm to solve numerically the Poisson-Boltzmann equations under a periodic boundary condition. By employing this algorithm to calculate the electrostatic potentials in two different types of protein crystals, a bovine pancreatic trypsin inhibitor (BPTI) orthorhombic crystal and a pig-insulin cubic crystal, the energy contributions of the electrostatic interactions to the crystals' stability were evaluated. At a high ionic strength, the condensed state of proteins in the crystal was stabilized electrostatically compared with that isolated in dilute solution because the attractive electrostatic interactions between neighboring protein molecules overcame the repulsive forces that originated from the same net charges of the equivalent protein molecules. On the other hand, at a low ionic strength the electrostatic interactions destabilized the crystalline state of both proteins, although a different dependence on the ionic strength was found between them. Here, the insulin crystal was more stable than the BPTI one because of the higher charge density in the BPTI crystal. In all of the solvent ionic strengths investigated, the attractive electrostatic interactions between charge pairs separated by less than 5 A on the respective protein molecules prominently stabilize the protein crystals. Therefore, two protein molecules in the crystals are oriented to compensate each other for their opposite charges on the surfaces. We also found a specific role for bound phosphate ions in the stabilization of the BPTI crystal, based on comparison of the electrostatic energies of the two crystals with and without the ions. By determining the contribution of each atomic charge in the crystals to the electrostatic energy, it was revealed that several electrostatic pairs specifically contributed to the crystal's stability. On the basis of our numerical calculation results, we propose a new method to design protein molecules that adopt stable crystals by replacing destabilizing residues with stabilizing ones and by introducing specific hydrogen bonds or salt bridges between neighboring protein molecules.