The importance of charge-charge interactions in the thermal stability of proteins is widely known. pH and ionic strength play a crucial role in these electrostatic interactions, as well as in the arrangement of ionizable residues in each protein-folding stage. In this study, two coarse-grained models were used to evaluate the effect of pH and salt concentration on the thermal stability of a protein G variant (1PGB-QDD), which was chosen due to the quantity of experimental data exploring these effects on its stability. One of these coarse-grained models, the TKSA, calculates the electrostatic free energy of the protein in the native state via the Tanford-Kirkwood approach for each residue. The other one, CpHMD-SBM, uses a Coulomb screening potential in addition to the structure-based model C. Both models simulate the system in constant pH. The comparison between the experimental stability analysis and the computational results obtained by these simple models showed a good agreement. Through the TKSA method, the role of each charged residue in the protein's thermal stability was inferred. Using CpHMD-SBM, it was possible to evaluate salt and pH effects throughout the folding process. Finally, the computational pK values were calculated by both methods and presented a good level of agreement with the experiments. This study provides, to our knowledge, new information and a comprehensive description of the electrostatic contribution to protein G stability.
The influence of soft, hydration-mediated ion-ion and ion-surface interactions on the differential capacitance of an electric double layer is investigated using Monte Carlo simulations and compared to various mean-field models. We focus on a planar electrode surface at physiological concentration of monovalent ions in a uniform dielectric background. Hydration-mediated interactions are modeled on the basis of Yukawa potentials that add to the Coulomb and excluded volume interactions between ions. We present a mean-field model that includes hydration-mediated anion-anion, anion-cation, and cation-cation interactions of arbitrary strengths. In addition, finite ion sizes are accounted for through excluded volume interactions, described either on the basis of the Carnahan-Starling equation of state or using a lattice gas model. Both our Monte Carlo simulations and mean-field approaches predict a characteristic double-peak (the so-called camel shape) of the differential capacitance; its decrease reflects the packing of the counterions near the electrode surface. The presence of hydration-mediated ion-surface repulsion causes a thin charge-depleted region close to the surface, which is reminiscent of a Stern layer. We analyze the interplay between excluded volume and hydration-mediated interactions on the differential capacitance and demonstrate that for small surface charge density our mean-field model based on the Carnahan-Starling equation is able to capture the Monte Carlo simulation results. In contrast, for large surface charge density the mean-field approach based on the lattice gas model is preferable.
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