Date Published: July 21, 2015
Publisher: Public Library of Science
Author(s): Andrea Pica, Giuseppe Graziano, Piero Andrea Temussi.
Both sodium chloride and sodium sulfate are able to stabilize yeast frataxin, causing an overall increase of its thermodynamic stability curve, with a decrease in the cold denaturation temperature and an increase in the hot denaturation one. The influence of low concentrations of these two salts on yeast frataxin stability can be assessed by the application of a theoretical model based on scaled particle theory. First developed to figure out the mechanism underlying cold denaturation in water, this model is able to predict the stabilization of globular proteins provided by these two salts. The densities of the salt solutions and their temperature dependence play a fundamental role.
It is widely recognized that globular proteins undergo cold denaturation in aqueous media , as further confirmed in the last years by means of detailed experimental studies [2, 3]. Careful analysis of NMR and CD investigations [4, 5] has shown that: (1) yeast frataxin, Yfh1, undergoes cold denaturation at a temperature above 0°C, (2) the transition is exothermic and reversible, (3) the two denatured states (obtained upon cold and hot denaturation, respectively) are very similar from a structural point of view .
Two macro-states are accessible to protein molecules: the ensemble of native conformations, N-state, and the ensemble of denatured conformations, D-state. According to the theoretical approach [9, 10, 12], the denaturation Gibbs energy change (ΔGd) in both water and aqueous salt solutions is given by:
where ΔGc(D) and ΔGc(N) are the Gibbs energy changes associated with the creation in aqueous media of the cavity hosting the D-state and N-state, respectively; ΔSconf represents the increase in conformational entropy of the protein chain upon denaturation; Ea(D) and Ea(N) are the energies obtained by taking into account all the interactions waters and ions establish with the protein in the D-state and N-state, respectively; ΔEa(intra) is the intra-protein energy loss upon denaturation. It is worth noting that in Eq (1) no contribution from the structural rearrangement of water H-bonds has been considered. For the latter process an almost complete enthalpy-entropy compensation holds [13, 14]. Furthermore, it can be assumed that the second square bracket in Eq (1), labelled ΔE, is close to zero. This assumption relies on the consideration that the sum of the intra-molecular interactions in the N-state and the inter-molecular interactions of N-state with waters are almost entirely counterbalanced by the inter-molecular interactions of D-state with waters (for a more detailed discussion, see ref.  and S1 Text). This assumption is considered to hold also in the case of aqueous solutions of NaCl and Na2SO4. It is firmly established that the Na+, Cl- and SO42- ions preferentially interact with waters [15, 16], and so should be excluded from the protein solvation shell of both the N-state and D-state. Indeed, the analysis of several frataxin X-ray structures, from different sources (pdb id: 2fql , 1ekg , 1ew4 ), revealed no interaction between the N-state of the protein and sulfate, chloride or sodium ions, even though these ions are very abundant in the crystallization conditions. Since the protein-solvent interactions involve always water molecules, the same assumption made in the case of pure water should hold in aqueous solutions of NaCl and Na2SO4. It is well known that also the Na+, Cl- and SO42- ions can be bound by some globular proteins due to specific structural and electrostatic features of the binding sites . The present approach, however, cannot account for such binding effects on the conformational stability of globular proteins.
A sphere of radius a = 15 Å is selected to model the N-state, whereas three prolate spherocylinders, with different values of radius (a) and cylindrical length (l), are selected to model the D-state (this should be important to test the “robustness” of the model). The spherocylinder sizes are: (1) a = 6.0 Å and l = 117.0 Å for D-state I; (2) a = 5.34 Å and l = 150.7 Å for D-state II; (3) a = 5.0 Å and l = 173.3 Å for D-state III. All these objects (representing the N-state and D-states) have the same van der Waals volume (VvdW = 14137 Å3), but a markedly different water accessible surface area (WASA). A summary of the geometric properties of the sphere and the spherocylinders is reported in Table 1 (see also S2 Text). These numbers correspond to a 138-residue globular protein, since the van der Waals volume of an average residue is 102.5 Å3 , and should be reliable for a comparison with Yfh1, that consists of 123 residues. It is worth noting that detailed Monte Carlo simulations by Tran and Pappu (accounting exclusively for the repulsive interactions among residues) indicate that average shapes of the D-state for 23 globular proteins are consistent with prolate ellipsoids . The latter are similar to the prolate spherocylinders considered in the present work [9, 10, 16].
The profile of the functions ΔΔGc(H2O), ΔΔGc(0.1 m NaCl), ΔΔGc(0.1 m Na2SO4) and T ΔSconf, calculated in the temperature range from -30 to 70°C, is shown in Fig 2 for all the considered cases. A qualitatively similar trend is obtained in the 0.05 m salt solutions; data not shown. The larger is ∆WASA (defined as WASA(D-state)—WASA(N-state)) the larger is the value of ∆∆Gc; ∆WASA is in fact a measure of the rise in solvent-excluded volume effect associated with chain unfolding. More importantly, the Gc functions show a parabola-like profile, which originates from the peculiar temperature dependence of aqueous solution densities (see Fig 1 for the densities of pure water and 0.1 m salt solutions). Indeed, while the density of a common liquid increases on decreasing the temperature, water shows a temperature of maximum density (TMD) at 4.0°C. The TMD value of salt solutions depends upon the salt type and concentration and it is always lower than that of pure water [38, 39]. In particular, TMD is 2.5°C for the 0.1 m NaCl solution, and 1.0°C for the 0.1 m Na2SO4 solution . The TMD values of all the considered solutions are listed in Table 2. All the ∆∆Gc functions decrease on lowering the temperature as a direct consequence of both the density decrease and the decrease in random thermal energy of the solvent particles bombarding the cavity surface (i.e., the RT factor present in all the formulas to calculate the work of cavity creation [26, 27]).
To the best of our knowledge, the salt effect on cold denaturation has been investigated only in the case of yeast frataxin, Yfh1 . Therefore, the experimental results on Yfh1 motivated the present analysis. The latter, however, having a statistical mechanical ground, is not aimed to quantitatively reproduce the results obtained in the case of Yfh1, but to provide a general and qualitative rationalization of the stabilization afforded by small concentrations of NaCl or Na2SO4. In this respect, it is worth noting that these two salts have shown a similar shift of the collapse transition temperature (akin to the cold denaturation temperature) in the case of the uncharged poly(N-isopropylacrylamide), PNIPAM, and elastin-like polypeptides .