Electrostatic models for calcium binding proteins

The binding of calcium ions to biomolecules has been investigated by comparing three continuum models, all presupposing the dominance of Coulombic interactions. To reflect disparity in polarization response of protein and solvent, the "refined" model (RM) incorporates an inhomogeneous static dielectric constant but admits only approximate analysis within the mean field ansatz. Conversely, the "primitive" model (PM), with a uniform dielectric response, yields to essentially exact solutions of the statistical mechanical problem by Monte Carlo simulation techniques. The "elementary" model (EM) further assumes linear thermal response and ignores steric constraints altogether to obtain a trivially evaluated, analytic result. Two contrasting biomolecules are considered: the large, positively charged, extracellular serine protease subtilisin exhibiting a low affinity binding site and the smaller, negatively charged, intracellular, nonenzymatic protein buffer calbindin that binds calcium tenaciously. As functions of protein (fixed) charge mutations and solution ionic strength, the EM shows consistently good agreement with observed shifts in equilibrium binding constants (DpKa). Predictions from simulation and finite difference solutions of both Poisson - Boltzmann and Debye - Hückel equations in the PM are essentially identical. They also conform closely to experiment, though with systematic deviations at high ionic strength. Evidently both long and short range correlations are suppressed or mitigated in these systems, while nonlinear thermal effects appear to be unimportant even up to 1.0 M monovalent salt. With standard parameters, RM calculations generally overestimate DpKa's, while the differences between RM and PM results are independent of salt concentration. Large electrostatic potentials arising in the RM possibly indicate strained protein conformations, though structural relaxation is not accounted for in any of the models studied. Motivated by exact analysis of salt free cases in planar and spherical geometries, alternative mechanisms explaining the theoretical deviations are discussed, in particular self-image correlation of mobile ions and the location of an effective dielectric interface.