Abstract
We present a theory describing the solubility of protein crystals as a function of pH, salt concentration, and temperature. There are four terms in the model. The neutral terms arise from 1) the translational entropy of the soluble proteins, and 2) H-bond and hydrophobic attractive interactions which we obtain from a fitting procedure. The two electrostatic terms are a result of counterions confined in the crystal to satisfy charge neutrality. These counterions contribute 3) an entropic penalty from the trapping of ions in the crystal, and 4) a favorable enthalpy from the interaction of each protein with its counterion cloud. This theory quantitatively describes the solubility of tetragonal and orthorhombic lysozyme crystals as determined by Pusey et al. According to the theory, the reduced solubility at high salt concentrations comes, not from increased screening, but from a reduced entropy of counterion confinement. The theory correctly describes the weak pH dependence of the solubility, which is a result of the compensating effects of the two electrostatic terms. We discuss the implications of this theory for crystal nucleation and the success of the “crystallization slot”.
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