Salt-specific effects in lysozyme solutions

The effects of additions of low-molecular-mass salts on the properties of aqueous lysozyme solutions are examined by using the cloud-point temperature, $T_{cloud}$, measurements. Mixtures of protein, buffer, and simple salt in water are studied at pH=6.8 (phosphate buffer) and pH=4.6 (acetate buffer). We show that an addition of buffer in the amount above $I_{buffer} = 0.6$ mol dm$^{-3}$ does not affect the $T_{cloud}$ values. However, by replacing a certain amount of the buffer electrolyte by another salt, keeping the total ionic strength constant, we can significantly change the cloud-point temperature. All the salts de-stabilize the solution and the magnitude of the effect depends on the nature of the salt. Experimental results are analyzed within the framework of the one-component model, which treats the protein-protein interaction as highly directional and of short-range. We use this approach to predict the second virial coefficients, and liquid-liquid phase diagrams under conditions, where $T_{cloud}$ is determined experimentally.

does not change upon further increase of the buffer concentration. In continuation of this interesting work, Taratuta and coworkers added low-molecular-mass salts to the buffer, at the same time decreasing the buffer content to keep the total ionic strength equal to 0.6 mol dm −3 . In other words, they varied the composition of the low-molecular-mass electrolyte, keeping its total ionic strength constant. In the present experimental study we follow this approach to examine the effects of the added low-molecularmass salts on the stability of protein solutions.
Recently [38] we proposed a new approach to analyze the cloud-point temperature measurements. We modelled protein molecules as hard spheres, with a number of square-well attractive sites located on the surface. To obtain measurable quantities we applied the thermodynamic perturbation theory developed by Wertheim [43,44]. The approach was used to analyze experimental data for T cloud in lysozyme solutions. The calculations provided good fits to the cloud-point curves of lysozyme in buffer-salt mixtures as a function of the type and concentration of salt. In a spirit of the chemical engineering theories, the approach was capable of predicting full coexistence curves, osmotic compressibilities and second virial coefficients within the domain of concentrations where T cloud were measured.
The work presented here is a continuation of our previous study [38] with one major difference that we analyze our own T cloud measurements performed recently. The review of literature revealed that experimental studies of salt-specific effects are rarely systematic: sometimes salts are added to protein solution in addition to buffer, sometimes alone, forming the protein-salt mixture. Further, for the chosen experimental method, the data collected in different laboratories may scatter much more than it is suggested by the precision of a single measurement. One reason for this lies in the details of protein solution preparation, which appears to be more important than it is actually recognized by most of the researchers. The protein solutions are prone to "age" and one can obtain different results with the freshly prepared or a few weeks old samples. Such differences can be seen even within a single paper [15].
Taking all these into account, and to avoid possible experimental inconsistencies, we decided to perform our own T cloud measurements on the well characterized solutions. The data were taken on lysozyme samples purchased from a single producer (Merck, Germany). We took all the necessary precautions in preparing the solutions, for details see the experimental part of the manuscript, to ensure a consistency of the results and a fair comparison with theory. The measurements were analyzed using the onecomponent model published recently [38]. Based on this analysis and on our new T cloud measurements, we predicted other thermodynamic quantities, including the full binodal curves and osmotic second virial coefficients for lysozyme in phosphate and acetate buffers in presence of low-molecular-mass salts.

Materials and solution preparations
Hen egg white lysozyme (M 2 = 14.388 g mol −1 ) was purchased from Merck Milipore, product number 105281, lot K46535581 514. The alkali metal salts (> 99%, KCl, NaCl, KBr, NaBr, NaI, NaNO 3 , NaH 2 PO 4 ·2H 2 O, and Na 2 HPO 4 ) were obtained from Merck Milipore as well, while CH 3 CH 2 COONa and NaSCN were obtained from Sigma Aldrich. The first step was preparation of the lysozyme-buffer and salt-buffer stock solutions. Dialyzing buffer was NaH 2 PO 4 /Na 2 HPO 4 with ionic strength of 0.1 mol dm −3 and pH = 6.8. Lysozyme was dissolved in buffer and dialyzed against it for 24 h, using the Spectra/Por Membrane dialysis membrane with the M w cutoff of 3500 Da. During this time, the buffer was changed three times. Concentrations of protein and salts in stock solution were two times higher than in the solution used in T cloud measurements. As often for mixed electrolytes, the salt and buffer amounts are given in ionic strength, I = 1 2 i c i z 2 i , where sum goes over all ionic species of salt, i of concentration c i and electrovalence z i . For +1:−1 salt I is equal to its concentration, c in mol dm −3 .
The low-molecular-mass salts were in presence of P 2 O 5 dried for two hours at T = 130 • C. Stock saltbuffer solutions were prepared in such a way that solid components were weighted and then filled with distilled water in a filling flask up to the mark. Mixtures of salts and protein were prepared just before the measurements. The lysozyme concentration was determined by measuring the absorbance at λ = 280 nm and 25 • C using a Cary 100 Bio (Varian) spectrophotometer, which uses the Peltier block for temperature regulation. The same instrument was used for the T cloud determination. The extinction coefficient 23601-2 of lysozyme was 2.635 dm 3 g −1 cm −1 at 25 • C. pH was measured using the Iskra pH meter model MA5740 (Ljubljana, Slovenia), using combined glass micro-electrode of type InLab 423 from Mettler Toledo (Schwerzenbach, Switzerland). pH of solutions were determined at the beginning and at the end of the experiment. The deviations from the desired pH values were always within ±0.1.

Cloud-point temperature measurements
T cloud is defined as the temperature where upon cooling the first opacification is noticed in solution under study. The cloudiness was in our case detected by an increase in the solution absorbance at wavelength λ = 340 nm. As noticed before, the measured cloud-point temperatures may depend on the cooling rate [22]. In an initial investigation of the system, we measured T cloud at three different cooling rates: 0.1, 0.5, and 1.0 • C min −1 and extrapolated these results to cooling rate equal to zero. In the T cloud measurements reported here, we used the cooling rate equal to 0.1 • C min −1 , which yields the results very close (within ±0.1 • C) to the extrapolated value. Reversibility of the process was verified by warming up the sample above the T cloud and by cooling it again to repeat the measurement. Like some other authors before us, we measured both the T cloud and T clear ; the latter is the temperature where the solution becomes clear again. The differences between these two temperatures were in the range from 1.0 to 4.0 • C, depending on the salt type and concentration. While other researchers [22] take the average of T cloud and T clear as a final value, we report the actual T cloud values in our results. In view of the observed differences between T cloud and T clear values, the absolute error in temperature of cloud-point determination is estimated to be between ±1.0 and ±2.0 • C.

Theoretical part
The theoretical model used in this study [38] is based on the observation that the range and directionality of the attractive interactions between protein molecules determine their phase behaviour [20,24,[45][46][47]. Previous studies suggested the appearance of a liquid-liquid coexistence region, which turns out to be meta-stable with respect to the solidification [19,24,48,49]. This is in contrast with the behavior of the systems composed of van der Waals type of particles, where the range of interaction between molecules is comparable with their size. Theoretical methods suitable to the study of systems of molecules interacting with strong directional forces have been proposed by Wertheim [43,44] and further developed by many other authors [50,51]. The one-component model of protein solution, which in some aspects resembles simple water models [52,53], has recently been used to analyze the experimental data for phase diagrams of lysozyme and γ-crystallin solutions [38]. For convenience of a reader, the descriptions of the model and theory are briefly repeated below.
We model the solution as a system of N protein molecules with number density ρ = N /V at temperature T and volume V . Protein molecule is pictured as a sphere of diameter σ with the attractive squarewell sites through which it interacts with other protein molecules. The solution is treated as a quasi one-component system, where the solvent (water, buffer, and low-molecular-mass salt) merely modifies the interaction between solutes. We assume the protein-protein pair potential to be composed of: (i) the hard-sphere part u R (r ) and (ii) attractive contributions, u AB , caused by the (short-range) square-well sites localized on the surface of the protein [43] In this expression, r (r = |r|) is the vector between the centers of molecules, x AB is the vector connecting sites A and B on two different protein molecules and Γ denotes the set of sites, see figure 1. We examine the case where M equal sites are distributed over the surface of the spherical protein; in other words, the displacement length d is 0.5σ. The pairwise additive potential is then written as follows: Here, ε W (> 0) is the square-well potential depth and a W is its range. The interaction between the sites is only effective for the site-site distance |x AB | being smaller than a W . The multiple site bonding is prevented by applying the condition [43,54] 0 < a W < σ − 3d . As usually in such studies, the additivity of the free energy terms is assumed where A id is the ideal part [55], A hs is the hard-sphere part [56], while A ass stands for the site-site association contribution [43,44,51] βA ass  Further, the ∆ AB term is related to the hard-sphere fluid through the radial distribution function g hs (r ) via the expression [54] ∆ AB = 4πg hs (σ) 2d +a W σf ass (r )r 2 dr. (3.8) The radial distribution function g hs (r ) is calculated by the Ornstein-Zernike integral equation theory using the Percus-Yevick (PY) closure [55], yielding where η = πρσ 3 /6 is the packing fraction of hard spheres. Further,f ass (r ), is the angular average of the Mayer function, obtained analytically [54] (3.10) Once the Helmholtz free energy, equation (3.5), is known, other thermodynamic quantities, among them the osmotic pressure Π and chemical potential of the protein species, µ, can be calculated. By using equations (3.6), (3.7) and (3.9), we get expressions for osmotic pressure and then for the chemical potential (3.12) Ideal and hard sphere contributions to the free energy and pressure can be found elsewhere [55]. At this step we can calculate the cloud point temperature, as well as the whole liquid-liquid coexistence curve, by applying the Maxwell construction. Another important theoretical and experimental quantity is the second virial coefficient, B 2 , defined as: We calculated this quantity as suggested by Bianchi et al. [32] B 2 = B (hs) 2 − 2πM 2 2d +a W σf ass (r )r 2 dr. (3.14) Here, B (hs) 2 = 2πσ 3 /3 is the second virial coefficient of hard spheres. Note that the integral in equations

Cloud-point temperatures for lysozyme-buffer-salt mixtures
Taratuta et al. [15] noticed that after a sufficient amount of buffer is added, T cloud becomes insensitive to a further increase of ionic strength. This observation suggests that at certain ionic strength, the Coulomb interaction between proteins becomes sufficiently screened. We confirmed this finding for lysozyme in mixture with phosphate buffer (pH = 6.8) and NaBr (see figure 2). In this graph we present  T cloud taken as a function of the ionic strength of the added sodium bromide (I salt ≡ c salt ) at a constant total ionic strength I total = I salt + I buffer , with I total equal to 0.7, 0.8, and 0.9 mol dm −3 , respectively. Symbols representing the measurements at different I total fall -within the experimental error -on the same curve. These results indicate that for a given value of I salt 0, T cloud is insensitive to the I total variations above 0.6 mol dm −3 . Due to the experimental limitations of our apparatus, no T cloud values could be determined below −6 • C.

23601-5
In figure 3, the experimental results for T cloud at pH = 6.8, lysozyme concentration γ = 90 g dm −3 , and total ionic strength (I buffer + I salt ) equal to 0.6 mol dm −3 are shown. Analogous results for acetate buffer are shown in figure 4. The experiments suggest a square root functional dependence between the T cloud and ionic strength of the added electrolyte. Notice that the T cloud at I salt = 0 should be the same for all the salts. The extrapolated value of T cloud to I salt = 0, as we have already mentioned, this point is experimentally not accessible, is −12 ± 2 • C. The salt-specific effects in T cloud measurements have been observed in several previous experimental papers [5,15]. An increase of the cloud-point temperature can be interpreted as a decrease of stability of the system. Considering that the total ionic strength is constant for all the samples studied in figure 3, this instability has been ascribed to the salt adsorption occurring at the protein surface [15]. Lysozyme solutions at pH = 6.8 assume a positive net charge. That is why the effects of anions are strong.
In our model, the strength of the protein-protein attraction can only be regulated by the depth of the attractive square-well potential, W . In view of the new experimental results, shown in figure 3, we suggest this quantity to be correlated with the ionic strength of the added low-molecular-mass salt (I salt ) as follows: The parameters of this equation, leading to a good agreement with experimental data for solutions in phosphate buffer, are given in table 2. As we see, the slope of equation (4.1) (parameter a) varies from salt to salt. Table 2. Parameters a and b defining equation (4.1) -phosphate buffer (pH = 6.8), protein concentration γ = 90 g dm −3 .
NaSCN 1055 2293 NaI 807 NaNO 3 625 NaBr 426 NaCl 235 The parameters leading to a good agreement with experimental data for acetate buffer, are given in table 3. The extrapolated value of T cloud at I salt = 0 is in this case equal to −31 ± 2 • C. It is of interest to correlate the slope in equation (4.1), which depends solely on the potential well-depth, with the hydration free energy of the salt anion. These results are shown in figure 5 for two different buffers -phosphate (lower curve) and acetate (upper curve). As we see, the two lines show the same trend. The ion dependent shift between the two lines seem to reflect the effects of the buffers present in systems. We see that, as found before for polyelectrolyte [58] and lysozyme solutions [38,59], the strength of protein-protein interaction is roughly correlated with the free energy of counterion solvation ∆G hydr .

From T cloud to B 2 and liquid-liquid phase-diagram
We can use experimental information collected in tables (2)  of the corresponding anions. The lines are the best least-square fit through the data. The upper curve belongs to pH = 4.6 and the lower one belongs to pH = 6.8.
It is important to stress that for proteins, the liquid-liquid boundary is located below the solid-liquid boundary, indicating the meta-stability of such systems [24,27]. When the saturated protein solution is cooled, it may undergo liquid-liquid phase transition before it actually crystalizes. This discriminates proteins from most of low-molecular weight mixtures, where such meta-stabilities were not observed. The liquid-liquid coexistence curve can be determined experimentally [5,18].
Another quantity of interest is the second virial coefficient B 2 , a critical parameter in controlling the protein aggregation. The latter process is of practical interest for pharmaceutical industry [40,60]. Wilson and co-workers [61,62] discovered that in order to grow well-defined crystals, the second virial coefficient should be slightly negative. The salt-specific effects can be observed also in figure 7. For each of the two buffers (they determine the pH of solutions), the reduced second virial coefficient decreases with increasing I salt . The decrease is faster in case of the phosphate buffer (pH = 6.8), where the protein net charge is around +7 [63]. For a certain amount of the added low-molecular-mass salt, the stability of the solutions (as indicated by B * 2 values) decreases in the order: Cl − > Br − > I − . This is the so-called inverse Hofmeister series, which has been observed experimentally in several papers [5,64]. Unfortunately, the experimental results for the exact conditions studied in figure 7 are not available so far.

Concluding remarks
We present new measurements of the cloud-point temperature, T cloud , for various lysozyme-buffersalt mixtures. The salts mixed with the protein were NaSCN, NaI, NaNO 3 , NaBr, and NaCl in phosphate buffer (pH = 6.8) and NaSCN, NaI, NaNO 3 , and KBr in acetate buffer (pH = 4.6). Our measurements, in agreement with some previous studies, suggest strong salt-specific effects. The T cloud values, after a certain amount of buffer is added, do not depend any more on the total ionic strength of the present electrolyte (I buffer + I salt ) but rather on its composition; i.e., on I salt content. The cloud-point temperature values can be modelled as a function of the square root of I salt ; cf. equation (4.1). From the measurements we extracted an information on the protein-protein interaction under conditions where I salt varies. Using this information, we predicted the relevant liquid-liquid phase diagrams and reduced second virial coefficients. The critical temperature of the phase diagram increases with an increasing salt content, but for iodide salts, the effect is much stronger than for bromide salts. This holds true for both buffers studied here. The results for reduced second virial coefficients, B * 2 , are consistent with these observations: the addition of iodide salt destabilizes the protein solutions more than the addition of bromide salt. We believe that the reason lies in a relatively high (comparing to Cl − or Br − ions) hydration free energy of I − ion, which is prone to release some hydration water upon binding to the protein charges. This assumption is supported by figure 5, where the correlation between the strength of the protein-protein interaction and the free energy of solvation of various counterions is shown.