Charge-charge interactions are key determinants of the pK values of ionizable groups in ribonuclease Sa (pI=3.5) and a basic variant (pI=10.2)

The pK values of the titratable groups in ribonuclease Sa (RNase Sa) (pI=3.5), and a charge-reversed variant with five carboxyl to lysine substitutions, 5K RNase Sa (pI=10.2), have been determined by NMR at 20 °C in 0.1 M NaCl. In RNase Sa, 18 pK values and in 5K, 11 pK values were measured. The carboxyl group of Asp33, which is buried and forms three intramolecular hydrogen bonds in RNase Sa, has the lowest pK (2.4), whereas Asp79, which is also buried but does not form hydrogen bonds, has the most elevated pK (7.4). These results highlight the importance of desolvation and charge–dipole interactions in perturbing pK values of buried groups. Alkaline titration revealed that the terminal amine of RNase Sa and all eight tyrosine residues have significantly increased pK values relative to model compounds. A primary objective in this study was to investigate the influence of charge–charge interactions on the pK values by comparing results from RNase Sa with those from the 5K variant. The solution structures of the two proteins are very similar as revealed by NMR and other spectroscopic data, with only small changes at the N terminus and in the α-helix. Consequently, the ionizable groups will have similar environments in the two variants and desolvation and charge–dipole interactions will have comparable effects on the pK values of both. Their pK differences, therefore, are expected to be chiefly due to the different charge–charge interactions. As anticipated from its higher net charge, all measured pK values in 5K RNase are lowered relative to wild-type RNase Sa, with the largest decrease being 2.2 pH units for Glu14. The pK differences (pKSa−pK5K) calculated using a simple model based on Coulomb's Law and a dielectric constant of 45 agree well with the experimental values. This demonstrates that the pK differences between wild-type and 5K RNase Sa are mainly due to changes in the electrostatic interactions between the ionizable groups. pK values calculated using Coulomb's Law also showed a good correlation (R=0.83) with experimental values. The more complex model based on a finite-difference solution to the Poisson–Boltzmann equation, which considers desolvation and charge–dipole interactions in addition to charge–charge interactions, was also used to calculate pK values. Surprisingly, these values are more poorly correlated (R=0.65) with the values from experiment. Taken together, the results are evidence that charge–charge interactions are the chief perturbant of the pK values of ionizable groups on the protein surface, which is where the majority of the ionizable groups are positioned in proteins.This work was supported by grants GM-37039 and GM-52483 from the National Institutes of Health (USA), grants BE-1060 and BE-1281 from the Robert A. Welch Foundation, and a grant PB-93-06777 to M.R. from the Dirección General de Investigación Cientı́fica y Técnica (Spain

Anisotropic Diffusion Effects on the Barnase–Barstar Encounter Kinetics

We investigated effects of hydrodynamic anisotropy on the kinetics of a diffusional encounter of a bacterial ribonuclease, barnase, and its natural inhibitor barstar, using the rigid-body Brownian dynamics technique. We performed atomistically detailed Brownian dynamics simulations of barnase and barstar under periodic boundary conditions, taking into account excluded volume and electrostatic and hydrophobic interactions between the proteins. We studied their specific (i.e., orientationally restricted by their configuration in the X-ray complex) and nonspecific association, either taking into account hydrodynamic anisotropy of the proteins or treating them as hydrodynamically equivalent spheres. We found that even relatively small anisotropy of associating proteins may influence the rate of their encounter and this effect is quantitatively measurable in the simulations. The role of the anisotropic diffusion manifests itself only in case of specific encounters while the association toward nonspecific complexes is not influenced by anisotropic diffusion. Association rate constants obtained from Brownian dynamics simulations for the studied system are up to 20% larger when hydrodynamic anisotropies of barnase and barstar are taken into account. Moreover, the dissociation from the specific complex is also accelerated in case of anisotropic diffusion

Toward an Accurate Modeling of Hydrodynamic Effects on the Translational and Rotational Dynamics of Biomolecules in Many-Body Systems

Proper treatment of hydrodynamic interactions is of importance in evaluation of rigid-body mobility tensors of biomolecules in Stokes flow and in simulations of their folding and solution conformation, as well as in simulations of the translational and rotational dynamics of either flexible or rigid molecules in biological systems at low Reynolds numbers. With macromolecules conveniently modeled in calculations or in dynamic simulations as ensembles of spherical frictional elements, various approximations to hydrodynamic interactions, such as the two-body, far-field Rotne–Prager approach, are commonly used, either without concern or as a compromise between the accuracy and the numerical complexity. Strikingly, even though the analytical Rotne–Prager approach fails to describe (both in the qualitative and quantitative sense) mobilities in the simplest system consisting of two spheres, when the distance between their surfaces is of the order of their size, it is commonly applied to model hydrodynamic effects in macromolecular systems. Here, we closely investigate hydrodynamic effects in two and three-body systems, consisting of bead–shell molecular models, using either the analytical Rotne–Prager approach, or an accurate numerical scheme that correctly accounts for the many-body character of hydrodynamic interactions and their short-range behavior. We analyze mobilities, and translational and rotational velocities of bodies resulting from direct forces acting on them. We show, that with the sufficient number of frictional elements in hydrodynamic models of interacting bodies, the far-field approximation is able to provide a description of hydrodynamic effects that is in a reasonable qualitative as well as quantitative agreement with the description resulting from the application of the virtually exact numerical scheme, even for small separations between bodies