Protein stability in mixed solvents: a balance of contact interaction and excluded volume

Abstract

Changes in excluded volume and contact interaction with the surface of a protein have been suggested as mechanisms for the changes in stability induced by cosolvents. The aim of the present paper is to present an analysis that combines both effects in a quantitative manner. The result is that both processes are present in both stabilizing and destabilizing interactions and neither can be ignored. Excluded volume was estimated using accessible surface area calculations of the kind introduced by Lee and Richards. The change in excluded volume on unfolding, deltaX, is quite large. For example, deltaX for ribonuclease is 6.7 L in urea and approximately 16 L in sucrose. The latter number is greater than the molar volume of the protein. Direct interaction with the protein is represented as the solvent exchange mechanism, which differs from ordinary association theory because of the weakness of the interaction and the high concentrations of cosolvents. The balance between the two effects and their contribution to overall stability are most simply presented as bar diagrams as in Fig. 3. Our finding for five proteins is that excluded volume contributes to the stabilization of the native structure and that contact interaction contributes to destabilization. This is true for five proteins and four cosolvents including both denaturants and osmolytes. Whether a substance stabilizes a protein or destabilizes it depends on the relative size of these two contributions. The constant for the cosolvent contact with the protein is remarkably uniform for four of the proteins, indicating a similarity of groups exposed during unfolding. One protein, staphylococcus nuclease, is anomalous in almost all respects. In general, the strength of the interaction with guanidinium is about twice that of urea, which is about twice that of trimethylamine-N-oxide and sucrose. Arguments are presented for the use of volume fractions in equilibrium equations and the ignoring of activity coefficients of the cosolvent. It is shown in the Appendix that both the excluded volume and the direct interaction can be extracted in a unified way from the McMillan-Mayer formula for the second virial coefficient.

FIGURE 1

Representation of a solvated protein. The small circles represent water molecules. Cross-hatched circles depict the solvation layer in contact with the protein. The black triple circles represent modes of contact of cosolvent molecules interacting with the protein by replacing a contact water molecule. Cosolvents making double contacts with the protein, like the one at 10 o'clock in the diagram, are not specifically considered in the model.

FIGURE 2

The nature of excluded volume. The center of the small probe sphere is restricted from a volume that is the sum of the volume of the large sphere plus the gap volume indicated in the drawing. The larger outer sphere is the accessible surface area for the smaller probe. The volume within the ASA is the excluded volume.

FIGURE 3

The balance of forces involved in stabilization or destabilization (see Eq. 10). The stability of the folded form is proportional to ΔB, which is directly related to m values. Negative ΔB is a measure of instability. ΔB is the balance of two thermodynamic forces: the change in excluded volume and the change in interaction with the cosolvent are represented by ΔX and , respectively. For unfolding, ΔX is always positive. For denaturants, the interaction is sufficiently strong that the stabilizing effect of the excluded volume is overbalanced, leading to a negative ΔB. A–C are bar diagrams for urea, guanidinium, and TMAO, respectively.

FIGURE 3

The balance of forces involved in stabilization or destabilization (see Eq. 10). The stability of the folded form is proportional to ΔB, which is directly related to m values. Negative ΔB is a measure of instability. ΔB is the balance of two thermodynamic forces: the change in excluded volume and the change in interaction with the cosolvent are represented by ΔX and , respectively. For unfolding, ΔX is always positive. For denaturants, the interaction is sufficiently strong that the stabilizing effect of the excluded volume is overbalanced, leading to a negative ΔB. A–C are bar diagrams for urea, guanidinium, and TMAO, respectively.

FIGURE 3

The balance of forces involved in stabilization or destabilization (see Eq. 10). The stability of the folded form is proportional to ΔB, which is directly related to m values. Negative ΔB is a measure of instability. ΔB is the balance of two thermodynamic forces: the change in excluded volume and the change in interaction with the cosolvent are represented by ΔX and , respectively. For unfolding, ΔX is always positive. For denaturants, the interaction is sufficiently strong that the stabilizing effect of the excluded volume is overbalanced, leading to a negative ΔB. A–C are bar diagrams for urea, guanidinium, and TMAO, respectively.

FIGURE 4

Demonstration that is essentially linear in x. Values of and C_m were taken from data for the denaturation of ribonuclease A in urea. See text.