Large-scale prediction of protein geometry and stability changes for arbitrary single point mutations.

We have developed a method to both predict the geometry and the relative stability of point mutants that may be used for arbitrary mutations. The geometry optimization procedure was first tested on a new benchmark of 2141 ordered pairs of X-ray crystal structures of proteins that differ by a single point mutation, the largest data set to date. An empirical energy function, which includes terms representing the energy contributions of the folded and denatured proteins and uses the predicted mutant side chain conformation, was fit to a training set consisting of half of a diverse set of 1816 experimental stability values for single point mutations in 81 different proteins. The data included a substantial number of small to large residue mutations not considered by previous prediction studies. After removing 22 (approximately 2%) outliers, the stability calculation gave a standard deviation of 1.08 kcal/mol with a correlation coefficient of 0.82. The prediction method was then tested on the remaining half of the experimental data, giving a standard deviation of 1.10 kcal/mol and covariance of 0.66 for 97% of the test set. A regression fit of the energy function to a subset of 137 mutants, for which both native and mutant structures were available, gave a prediction error comparable to that for the complete training set with predicted side chain conformations. We found that about half of the variation is due to conformation-independent residue contributions. Finally, a fit to the experimental stability data using these residue parameters exclusively suggests guidelines for improving protein stability in the absence of detailed structure information.

Boundary element solution of the linear Poisson-Boltzmann equation and a multipole method for the rapid calculation of forces on macromolecules in solution.

The Poisson-Boltzmann equation is widely used to describe the electrostatic potential of molecules in an ionic solution that is treated as a continuous dielectric medium. The linearized form of this equation, applicable to many biologic macromolecules, may be solved using the boundary element method. A single-layer formulation of the boundary element method, which yields simpler integral equations than the direct formulations previously discussed in the literature, is given. It is shown that the electrostatic force and torque on a molecule may be calculated using its boundary element representation and also the polarization charge for two rigid molecules may be rapidly calculated using a noniterative scheme. An algorithm based on a fast adaptive multipole method is introduced to further increase the speed of the calculation. This method is particularly suited for Brownian dynamics or molecular dynamics simulations of large molecules, in which the electrostatic forces must be calculated for many different relative positions and orientations of the molecules. It has been implemented as a set of programs in C++, which are used to study the accuracy and speed of this method for two actin monomers.