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George Thurston, Michael Martini, Chris Wahle, Dawn Hollenbeck, David Ross, John Hamilton; Statistical-thermodynamic model for charge-regulation properties of bovine γB-crystallin. Invest. Ophthalmol. Vis. Sci. 2013;54(15):4965. doi: https://doi.org/.
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© ARVO (1962-2015); The Authors (2016-present)
To model interacting-site protonation equilibria of γB-crystallin to aid in quantifying screened, charge-regulated electrostatic γB-γB interactions.
We model screened, site-specific charge regulation in γB-crystallin and neighboring pairs of γB-crystallin molecules, adapting our recent formulation (Hollenbeck et al, Phys. Rev. E 2010) to use γB-crystallin crystallographic coordinates. Using a simplified dielectric model, we solve a screened electrostatic partial differential equation model to calculate a 51 x 51 work-of-charging matrix, and use relevant data to model site-specific proton affinities. We use Monte Carlo simulations to calculate the grand canonical partition function and the probabilities of leading proton occupancy configurations, for 4 < pH < 8 and Debye screening length values from 6 to 30 Angstroms.
The work of charging matrix can be put into an approximate block-diagonal form in which blocks correspond to interacting patches of titratable sites that include long-recognized charge pairing in γB-crystallin. The predicted average net protein charge fits available near-neutral pH potentiometric titration data on γB-crystallin reasonably well, but deviates at low and high pH. For neighboring γB molecule pairs, the relevant 102x102 enlarged work-of-charging matrix depends on relative intermolecular proximity and orientation, making protonation configurations interdependent for near neighbors. At pH 7.0 and Debye length 6 Angstroms, the most prominent γB-crystallin proton occupancy configuration is only predicted to occur less than a tenth of the time, the first hundred configurations account for only 75% of the total, and nearly a thousand are needed to account for 95%. Proton occupancy probability distributions broaden remarkably as pH is lowered to close to 4.5, then sharpen again; over a thousand configurations account for only 30% of the total at pH 4.5. Raising the Debye screening length considerably sharpens the proton configuration probability distributions, due to strengthened site-site interactions.
The broad width of γB-crystallin proton occupancy probability distributions, and their interdependence in neighboring γB molecules, suggest that charge regulation is one important aspect of screened electrostatic contributions to orientation-dependent γB-γB interactions.
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