Model for screened, charge-regulated electrostatics of an eye lens protein: Bovine gammaB-crystallin

Christopher W. Wahle, K. Michael Martini, Dawn M. Hollenbeck, Andreas Langner, David S. Ross, John F. Hamilton, George M. Thurston

We model screened, site-specific charge regulation of the eye lens protein bovine gammaB-crystallin (γB) and study the probability distributions of its proton occupancy patterns. Using a simplified dielectric model, we solve the linearized Poisson-Boltzmann equation to calculate a 54×54 work-of-charging matrix, each entry being the modeled voltage at a given titratable site, due to an elementary charge at another site. The matrix quantifies interactions within patches of sites, including γB charge pairs. We model intrinsic pK values that would occur hypothetically in the absence of other charges, with use of experimental data on the dependence of pK values on aqueous solution conditions, the dielectric model, and literature values. We use Monte Carlo simulations to calculate a model grand-canonical partition function that incorporates both the work-of-charging and the intrinsic pK values for isolated γB molecules and we calculate the probabilities of leading proton occupancy configurations, for 4<pH<8 and Debye screening lengths from 6 to 20 Å. We select the interior dielectric value to model γB titration data. At pH 7.1 and Debye length 6.0 Å, on a given γB molecule the predicted top occupancy pattern is present nearly 20% of the time, and 90% of the time one or another of the first 100 patterns will be present. Many of these occupancy patterns differ in net charge sign as well as in surface voltage profile. We illustrate how charge pattern probabilities deviate from the multinomial distribution that would result from use of effective pK values alone and estimate the extents to which γB charge pattern distributions broaden at lower pH and narrow as ionic strength is lowered. These results suggest that for accurate modeling of orientation-dependent γB-γB interactions, consideration of numerous pairs of proton occupancy patterns will be needed.