Excluded Volume in Solvation: Sensitivity of Scaled-Particle Theory to Solvent Size and Density

Abstract

Changes in solvent environment greatly affect macromolecular structure and stability. To investigate the role of excluded volume in solvation, scaled-particle theory is often used to calculate delta G(tr)(ev), the excluded-volume portion of the solute transfer free energy, delta G(tr). The inputs to SPT are the solvent radii and molarities. Real molecules are not spheres. Hence, molecular radii are not uniquely defined and vary for any given species. Since delta G(tr)(ev) is extremely sensitive to solvent radii, uncertainty in these radii causes a large uncertainty in delta G(tr)(ev)-several kcal/mol for amino acid solutes transferring from water to aqueous mixtures. This uncertainty is larger than the experimental delta G(tr) values. Also, delta G(tr)(ev) can be either positive or negative. Adding neutral crowding molecules may not necessarily reduce solubility. Lastly, delta G(tr)(ev) is very sensitive to solvent density, rho. A few percent error in rho may even cause qualitative deviations in delta G(tr)(ev). For example, if rho is calculated by assuming the hard-sphere pressure to be constant, then delta G(tr)(ev) values and uncertainties are now only tenths of a kcal/mol and are positive. Because delta G(tr)(ev) values calculated by scaled-particle theory are strongly sensitive to solvent radii and densities, determining the excluded-volume contribution to transfer free energies using SPT may be problematic.

Urea interactions with protein groups: A volumetric study

“…37,38,74 However, in contrast to differential cavity volume DDV C , differential free energy of cavity formation, DDG C , is not insignificant and cannot be ignored. 45 It is the general consensus that the cavity formation term, DDG C , contributes unfavorably to the water-to-urea transfer free energy, DG tr , while the contribution of the interaction term, DDG I , is favorable. 39,45 The differential free energy of cavity formation, DDG C , can be calculated based on scaled particle theory (SPT).…”

“…45 It is the general consensus that the cavity formation term, DDG C , contributes unfavorably to the water-to-urea transfer free energy, DG tr , while the contribution of the interaction term, DDG I , is favorable. 39,45 The differential free energy of cavity formation, DDG C , can be calculated based on scaled particle theory (SPT). [43][44][45] However, such calculations may be quite unreliable due to their critical dependence on the assumed hard sphere diameter of the cosolvent molecule.…”

“…39,45 The differential free energy of cavity formation, DDG C , can be calculated based on scaled particle theory (SPT). [43][44][45] However, such calculations may be quite unreliable due to their critical dependence on the assumed hard sphere diameter of the cosolvent molecule. 45 The latter is not easy to determine given the necessity to approximate a nonspherical molecule by a sphere.…”

“…[43][44][45] However, such calculations may be quite unreliable due to their critical dependence on the assumed hard sphere diameter of the cosolvent molecule. 45 The latter is not easy to determine given the necessity to approximate a nonspherical molecule by a sphere. 45 The interaction contribution, DDG I 5 2(n/r)RT ln[(a 1 / a 10 ) r 1 k(a 3 /a r 10 )], on the other hand, can be readily calculated for a solute or a functional group from its equilibrium constant, k. Figure 2 presents the simulated urea-dependences of DDG I for the 19 naturally occurring amino acid side chains and the glycyl unit.…”

“…A standard way to evaluate the differential free energy of cavity formation, DDG C , is based on scaled particle theory (SPT) calculations. 41,[43][44][45] However, SPT-based calculations may be unreliable due to the critical sensitivity of calculated DDG C on the assumed diameters of solvent and cosolvent molecules. 45 We describe here a novel way of probing solute-cosolvent interactions which is based on high precision volumetric measurements.…”