Kirkwood-Buff theory of molecular and protein association, aggregation, and cellular crowding

Abstract

An analysis of the effect of a cosolvent on the association of a solute in solution using the Kirkwood-Buff theory of solutions is presented. The approach builds on the previous results of Ben-Naim by extending the range of applicability to include any number of components at finite concentrations in both closed and semiopen systems. The derived expressions, which are exact, provide a foundation for the analysis and rationalization of cosolvent effects on molecular and biomolecular equilibria including protein association, aggregation, and cellular crowding. A slightly different view of cellular crowding is subsequently obtained. In particular, it is observed that the addition of large cosolvents still favors the associated form even when traditional excluded volume effects are absent.

Figure 1

The two representations of the same system used in this study. The system contains a solvent (1, shaded spheres), a solute (2), and a cosolvent (3, open spheres). In this case the solute can exist in two forms: One being the monomer (M) and the other being an aggregate (A) of n=6 monomers. The monomer can adopt different shapes in the associated and free forms.

Figure 2

SI results for the effects of a single crowder (3) on the association equilibrium (nM→A) of an infinitely dilute solute (2) in a primary solvent (1) in a closed system. The data were obtained using Eq. 54 for different molar volume ratios (r) of the crowder and solvent such that V₃=rV₁. The results are plotted as a function of cosolvent volume fraction (φ₃=ρ₃V₃), cosolvent mole fraction (x₃), and cosolvent molality (m₃) with water as the solvent. In this case x₃=φ₃∕[φ₃+r(1−φ₃)] and m₃=1000φ₃∕r(1−φ₃)∕18.015. For reference, the molar volume of pure water is V₁=18 cm³∕mol and so r=1000 would correspond to a 25 kDa protein of approximately 225 residues. All curves are truncated at a cosolvent volume fraction of 0.5.