Prediction of protein solubility from calculation of transfer free energy

Abstract

Solubility plays a major role in protein purification, and has serious implications in many diseases. We studied the effects of pH and mutations on protein solubility by calculating the transfer free energy from the condensed phase to the solution phase. The condensed phase was modeled as an implicit solvent, with a dielectric constant lower than that of water. To account for the effects of pH, the protonation states of titratable side chains were sampled by running constant-pH molecular dynamics simulations. Conformations were then selected for calculations of the electrostatic solvation energy: once for the condensed phase, and once for the solution phase. The average transfer free energy from the condensed phase to the solution phase was found to predict reasonably well the variations in solubility of ribonuclease Sa and insulin with pH. This treatment of electrostatic contributions combined with a similar approach for nonelectrostatic contributions led to a quantitative rationalization of the effects of point mutations on the solubility of ribonuclease Sa. This study provides valuable insights into the physical basis of protein solubility.

FIGURE 1

(A) Structure of RNase Sa. Eleven carboxyl side chains, two histidines, and residue T76 are labeled and displayed as red, cyan, and yellow sticks, respectively. The N-terminal residue happens to be an aspartate. The side chain of this residue was not titrated in the constant-pH simulations, and is not shown here. (B) Structure of zinc-insulin hexamer. The two trimers are shown in the foreground and background in green and gray, respectively. The two zinc ions and the coordinating histidines and water molecules are shown. In addition, the five titrated side chains of one monomer are labeled and shown as sticks.

FIGURE 2

(A) Crystalline phase of RNase Sa, and (B) its modeling as an effective dielectric medium. In the crystalline phase, a single RNase Sa monomer, shown in red, is surrounded by its crystalline replicas. The space between the replicas is filled by water. In the implicit model for the crystalline phase, the inhomogeneous environment of the red monomer is approximated by a uniform dielectric medium (depicted by the blue “cloud”), with a dielectric constant intermediate between a high value for water and a low value expected for protein molecules. The red monomer is the solute, which is always assigned a low dielectric constant (specifically, 4).

FIGURE 3

Comparison of calculated and experimental results for the pH dependence of the solubility of RNase Sa.

FIGURE 4

Comparison of calculated and experimental results for the pH dependence of the solubility of insulin. The pH values of the calculated results were shifted downward by 0.75 units to account for anion binding. The experimental results of Desbuquois and Aurbach (37) and Fischel-Ghodsian et al. (12) were for porcine insulin, whereas those of Fredericq and Neurath (36) were for bovine insulin. The two species differ at only two positions, involving uncharged residues, in sequence. Our calculations used the structure of porcine insulin.

FIGURE 5

(A) Electrostatic solvation energy, of a single RNase Sa monomer in the presence of a crystalline array of replicas. The replicas serve to change the dielectric environment of the single monomer. The infinite array is approached by including more and more distant replicas (n = total number of replicas included). The dashed curve through the data points provides guidance for the eye. (B) Reproduction of when the inhomogeneous dielectric environment is replaced by a uniform dielectric medium. The effective dielectric constant, ɛ_c, of the uniform dielectric medium is varied to match as indicated by the horizontal line.

FIGURE 6

Comparison of calculated and experimental results for the variation of solubility among 20 RNase Sa variants with point mutations at position 76. The calculated results for T76 are shown in lighter shades to indicate the wild-type protein.

FIGURE 7

Comparison of calculated and experimental results for the octanol-to-water transfer free energies of pentapeptides AcWL-X-LL. The identity of the guest residue X is shown on the horizontal axis.