Pressure perturbation calorimetric studies of the solvation properties and the thermal unfolding of proteins in solution—experiments and theoretical interpretation

Abstract

We used pressure perturbation calorimetry (PPC), a relatively new and efficient technique, to study the solvation and volumetric properties of amino acids and peptides as well as of proteins in their native and unfolded state. In PPC, the coefficient of thermal expansion of the partial volume of the protein is deduced from the heat consumed or produced after small isothermal pressure jumps, which strongly depends on the interaction of the protein with the solvent or cosolvent at the protein–solvent interface. Furthermore, the effects of various chaotropic and kosmotropic cosolvents on the volume and expansivity changes of proteins were measured over a wide concentration range with high precision. Depending on the type of cosolvent and its concentration, specific differences were found for the solvation properties and unfolding behaviour of the proteins, and the volume change upon unfolding may even change sign. To yield a molecular interpretation of the different terms contributing to the partial protein volume and its temperature dependence, and hence a better understanding of the PPC data, molecular dynamics computer simulations on SNase were also carried out and compared with the experimental data. The PPC studies introduced aim to obtain more insight into the basic thermodynamic properties of protein solvation and volume effects accompanying structural transformations of proteins in various cosolvents on one hand, as these form the basis for understanding their physiological functions and their use in drug designing and formulations, but also to initiate further valuable applications in studies of other biomolecular and chemical systems.

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1. Introduction

Understanding the stability and thermodynamics of the folded state of proteins has fascinated protein chemists and biophysicists for many years and still remains one of the most challenging issues in the field. In general, the stability of proteins depends on temperature, pressure, its hydration capacity and on the solvent properties.^1–24 In this regard, volumetric properties of proteins, such as its partial specific volume, and even more significantly, the temperature and pressure derivatives thereof, have proven to be sensitive measures of hydration effects.^6,23 It is well-known that the cytoplasm of the cell is relatively crowded, and surface to surface gaps of neighbouring organelles and biopolymers are, on average, less than 5 nm containing a rather complex solvent mixture.^25–27 In the context of such proximity, we can expect the structure and dynamics of the solvent to be largely determined by the properties of the biomolecular surfaces, and—vice versa—the properties of the biomolecular systems will depend drastically on their direct solvent environment.

Proteins in their native, folded configurations contain both hydrophilic and hydrophobic surface groups. As an illustrating example, Fig. 1 shows the surface groups and the first hydration layer of native SNase. Vicinal water molecules close to charged residues are expected to be oriented to the surface charges, leading to a more or less layered structure.^23,28 In fact, this layering, if substantial, should be reflected in the thermodynamic properties of the protein, such as the partial molar volume and its apparent coefficient of thermal expansion, α. How many water layers with properties different from bulk solvent may form at the protein surface, depends principally on two factors: the charge density and its spatial distribution and the strength of the thermal forces that tend to disrupt the induced organization. Increase of temperature is expected to lead to a disruption of the solvent layer, which, in turn, should be reflected in the temperature dependence of α.

Fig. 1 Arrangement of water molecules in the hydration shell from an MD simulation study on SNase (T = 300 K, cut-off distance from the protein surface: d = 4.5 Å). (A) The different types of atoms at the molecular surface are shown in different colours: N blue, O red, C cyan, S yellow and H white. (B) The various types of residues at the molecular surface of SNase are shown: nonpolar: white, acidic: red, basic: blue and polar: green). The hydration water molecules near the hydrophilic atoms are more tightly packed and exhibit a complex hydrogen bonding pattern, whereas the water molecules near the hydrophobic atoms are more loosely packed and form a hydrogen bonded network with chain-like arrangements of water molecules.³⁶

The influence of the protein’s surface on adjacent water and how this might be reflected in the apparent expansivity data of proteins has been discussed extensively by Lin et al.²⁹ Their seminal work indicates that exposed hydrophilic groups, such as charged or polar side chains of proteins, show a pattern characteristic of water structure breakers, with a large positive apparent expansion coefficient of the protein, in particular at low temperature, which decreases drastically with increasing temperature. On the contrary, apolar, hydrophobic amino acid side groups act in the reverse manner, as structure makers, by enhancing the space consuming hydrogen bonded network structure of water typical for hydrophobic hydration. Hence, for proteins in aqueous solution, the temperature dependent coefficient of thermal expansion is drastically influenced by protein–water interactions and therefore also by the magnitude and nature of the solvent accessible surface area (ASA) of the protein. Furthermore, irrespective of whether cosolvents directly bind to or are excluded from the protein surface, they are expected to induce significant changes in the quantity of “bound” water and its associated physical properties. In general, not only the degree of protein hydration, but also the structural and dynamic properties of the hydration layer change in the course of protein un- and refolding, aggregation, amyloidogenesis and binding events.

In this article, we review recent, published studies and introduce new work on PPC measurements of amino acids, tripeptides and proteins. The PPC technique is complementary to densimetric measurements^23,30–34 and has the high sensitivity which is necessary to detect small volumetric changes. In fact, the relative volume changes of protein unfolding can be either positive or negative and are usually very small (ΔV/V < 1%). To complete the thermodynamic data, DSC results are given for some of the systems studied. In the first part, we introduce the PPC technique and discuss results on amino acids and tripeptides. We then present data on the solvation and volumetric properties of two enzymes, ribonuclease A (RNase A) and staphylococcal nuclease (SNase), in their native and unfolded states. Moreover, the effects of various chaotropic and kosmotropic cosolvents (glycerol, sorbitol, sucrose, urea, guanidinium hydrochloride (GuHCl), guanidinium sulfate (Gu₂SO₄), potassium sulfate (K₂SO₄), ethanol (EtOH), trifluoroethanol (TFE)) on the solvation and unfolding behaviour of the proteins is discussed. The influence of these cosolvents on α and hence on the hydrational properties of the protein provides insight into the underlying contributions to the volume changes accompanying unfolding. To yield a molecular interpretation of the different terms contributing to the partial protein volume and its temperature dependence and hence a better understanding of the PPC data, molecular dynamics (MD) computer simulations on SNase were also carried out and compared with experimental data.

2. Materials and methods

2.1 Materials

The amino acids alanine, leucine, glutamine, methionine and phenylalanine, of >99% minimum purity, were obtained from Sigma Aldrich, the tripeptides of >99% minimum purity from Bachem. All chemicals were dissolved in deionized water without further purification. The partial specific volumes of the amino acids and tripeptides were calculated according to the method of Reading et al.³⁰ Bovine pancreatic ribonuclease A (RNase A) was purchased from Sigma Chemical Co. and used without further purification. Recombinant SNase with the sequence of nuclease A from the V8 strain of Staphylococcus aureus was obtained using the λ expression system in the Escherichia coli strain Arλ9 and purified as previously described.^35,36 The salts, alcohols and osmolytes were obtained from Aldrich and used without further purification. Phosphate buffer (10 mM) (di-sodium hydrogen phosphate, Na₂HPO₄, anhydrous, from Merck) at pH 5.5 was used for all experiments, except where mentioned.

2.2 DSC and PPC measurements

The differential scanning calorimetric traces were measured by means of a high precision VP DSC micro-calorimeter from MicroCal, Northampton, MA, USA. The reference cell was filled with matching buffer/cosolvent solution. Both buffer and protein solutions were degassed before being injected into the respective cells. The instrument is also equipped with a pressuring cap that allows application of 1.8 bar to the cells in order to avoid air bubbles at elevated temperatures. The instrument was operated in the high gain mode at a rate of 40 °C h⁻¹. Baseline subtraction (pure buffer/cosolvent) and normalization with respect to the protein concentration were performed by the instrument software, yielding the temperature-dependent apparent molar heat capacity of the protein, C_p with respect to the buffer/cosolvent solution. The sample concentration of the proteins in 10 mM phosphate buffer was 0.5 wt% with a known quantity of cosolvent, except where mentioned.

The pressure perturbation (PPC) experiments were performed in the DSC calorimeter using the MicroCal PPC accessory.^{11,29,37–40} The reference and sample cell volume are identical (0.5 mL) and they open to a common pressure chamber containing a sensor (Fig. 2A). The protein concentration used for the PPC studies was 5 mg mL⁻¹, except where mentioned. An equal pressure of 5 bar was applied to both cells in a programmed manner using nitrogen gas (Fig. 2B). The software then initiates a pressure release to ambient pressure. The temperature is kept constant by active compensation of the heat change caused by the pressure jump. As the solutions in the sample and reference cell are identical except for the small amount of dissolved solute in the sample cell (solid ellipses in Fig. 2A) counterbalanced by the corresponding volume of buffer (at the same pH) in the reference cell (dashed ellipses), the measured differential heats are quite small. The compensation power returns to the baseline typically within 1 min and integration of the supplied power vs time yields the heat consumed or released by the sample. After complete equilibration, an opposite pressure jump is applied when the PPC controller reconnects the PPC cells with nitrogen gas. The heat peaks upon compression and decompression agree within a few % in absolute values, they are of opposite sign, however. For both compression and decompression experiments, temperature, pressure, and heat flow are recorded as a function of time. The calorimeter is then automatically heated or cooled to the next desired temperature and the next two (compression/decompression) pressure jumps are applied. Refs. 40–42 refer to an earlier debate concerning possible methodological errors within the PPC procedure.

Fig. 2 (A) Schematic drawing for the pressure perturbation calorimetry (PPC) experimental setup (adopted from refs. 37 and 38). The open ellipses in the reference cell represent the volume occupied by solvent in this cell, which counterbalances the volume occupied by the solute molecules in the sample (filled ellipses). (B) Time courses of the cell temperature T, pressure p, and the compensation power dQ/dt upon three (out of typically 20–80) pressure jumps (downward and upward). Before each pressure jump, equilibration of the calorimeter in the isothermal mode at the desired temperature (here 20, 21 and 22 °C) takes place. The compensation power returns to the baseline typically within 1 min and integration of the supplied power over time yields the heat consumed or released by the sample. The heat peaks caused by the upward and downward pressure jumps differ in sign but should agree in absolute values. Integration of dQ/dt yields two data points for Q(T) at a given pressure change. After equilibration, the calorimeter is automatically heated or cooled to the next desired temperature and the next compression/decompression cycle is repeated.

Thermodynamics relates the pressure coefficient of the heat Q_rev exchanged, (∂Q_rev/∂p)_T, in a reversible process to the coefficient of thermal expansion, α = (1/V)(∂V/∂T)_p, of the sample volume. For a sufficiently dilute solution containing m_S grams of solute and m₀ grams of solvent, the volume is given by V = m₀V₀ + m_sV̄_s, where V₀ is the specific volume of the solvent and V̄_s the partial specific volume of the solute. One then finds

(∂Q_rev/∂p)_T = −TVα = −T [m₀V₀α₀ + m_sV̄_s[small alpha, Greek, macron]_s ]. (1)

α₀ = (1/V₀) (∂V₀/∂T)_p and [small alpha, Greek, macron]_s = (1/V̄_s)(∂V̄_s/∂T)_p are the coefficients of thermal expansion associated with the solvent volume and the solute partial volume, respectively.

In the actual differential PPC experiment, the volume occupied by the solute in the sample cell, m_sV̄_s, is replaced by the same volume of solvent in the reference cell. Within small pressure intervals (±5 bar here), the pressure dependence of V and α can be neglected for the systems studied here, and eqn (1) can be integrated to yield the working equation

ΔQ_rev = −T [m_sV̄_s[small alpha, Greek, macron]_s − m_sV̄_sα₀ ] Δp (2)

which then rearranges towhere the total mass of solute, m_s, is obtained by multiplying its concentration c_s by the cell volume. If the solvent is pure or nearly pure water, then α₀ can be obtained directly from density data in the literature. If the solvent contains moderately high concentrations of electrolytes (buffer) and other solutes (cosolvents), which is mostly the case, α₀ must be determined in a separate PPC experiment, with buffer in the sample cell and pure water in the reference cell. In the following, the partial specific value of the volume, V̄_s, and the coefficient of thermal expansion, [small alpha, Greek, macron]_s, of the solute, will be replaced by their apparent values, denoted V and α, respectively. All reported PPC data are of the differential solution-versus-solvent type, adjusted to the same pH.

The relative volume changes ΔV/V at the unfolding transition of proteins, taking place in the temperature interval from T_o to T_e, can be obtained by:

2.3 Molecular dynamics simulations of the protein–water interface

A series of MD simulations was performed on SNase in water at constant temperature and ambient pressure, namely at 300, 360 and 400 K. Details of the simulation method at ambient conditions can be found in our previous paper.⁴³ Briefly, the MD simulations were performed using AMBER 6.0,⁴⁴ the all-atom force field by Cornell et al.⁴⁵ and the particle mesh Ewald (PME)⁴⁶ was used for the calculation of electrostatic interactions. All protein atoms were explicitly included in the simulations and the TIP3P water model was used.⁴⁷ All simulations were performed at constant N, p, T conditions and at a residue-based cut-off of 10 Å for van der Waals interactions. The simulations were continued for 7 to 13 ns. For the analysis, the trajectory from the last 2 ns was used. The program DSSP⁴⁸ was used for the calculation of the solvent-accessible surface area (ASA). The van der Waals volume, V_vdW, of the protein was calculated with the program Mol_Volume.⁴⁹ The solvent-excluded volume, V_SE, and the molecular surface area of the protein were determined using the program MSMS.⁵⁰ A 1.4 Å radius for the probe sphere (H₂O) was used for these calculations. To determine the standard errors of the mean values of fluctuating physical properties derived, we used the usual statistical analysis.^51,52

3. Results and discussion

3.1 Amino acids

Fig. 3A displays selected curves of the temperature dependence of the thermal expansivity of alanine for varying concentrations. For all curves the global behaviour of expansivity of this amino acid in water is dominated by the structure breaking properties of the ionisable moieties. The value of α is large and positive at low temperature, reflecting the capacity of these ionisable moieties to cause a more dense organization of the hydrating water molecules around them compared to bulk water. The value of α decreases significantly as temperature increases, because the degree of interaction is diminished by increasing temperature.

Fig. 3 (A) Temperature dependence of the apparent thermal expansion coefficient α of alanine as a function of concentration (1, 2, 5 and 10 wt%) in phosphate buffer at pH 5.5. (B) Temperature dependence of the apparent thermal expansion coefficient α of alanine at different pH values, corresponding to its isoelectrical point (pI), pK₁ and pK₂ values (pI 6.1, pK₁ 2.3, pK₂ 9.9).

Concentration effect. We note as well that the α values decrease markedly with increasing concentrations above a concentration of about 1 wt% (e.g., 25% from 1 to 10 wt% alanine at low temperature), indicating that intermolecular interactions influence α already at these concentrations. Hence, concentrations of 1 wt% and less are generally used for PPC studies of protein solutions.

Charge effect. Fig. 3B shows the pH dependence of α values for the a.a. alanine. The concentration was 1 wt% and sodium phosphate buffer was used. Measurements were performed for alanine at its isoelectrical point (pI) at pH 6.1. The α value is 2.0 × 10⁻³ K⁻¹ at the lowest temperature (7 °C), and hence smaller than at pH 5.5. The PPC trace measured at pH 2.3 (pK₁) (with charged −NH₃⁺) starts at slightly higher α values than that at pH 5.5 (largely neutral species). The PPC curve of alanine at pH 9.9 (pK₂) shows highest α values (3.75 × 10⁻³ K⁻¹ at the lowest temperature), which is due to the strong hydration of the −COO⁻ group. These results indicate that charged groups (−NH₃⁺, −COO⁻) lead to increased α-values owing to an increased hydration contribution to α, being strongest for the negatively charged carboxyl group.

Different amino acid side chains. Fig. 4 compares the temperature dependence of the expansivity of the amino acids glycine, glutamine, leucine, alanine, methionine and phenylalanine (Fig. 4A) in sodium phosphate buffer at pH 5.5 and a concentration of 1wt%. In comparison to the other amino acids, the α value of glycine at low temperature has a rather high value of ∼4.0 × 10⁻³ K⁻¹, and leucine exhibits the smallest α value of 1.5 × 10⁻³ K⁻¹ at about 7 °C. For all the amino acids tested, α decreases drastically with increasing temperature, most dramatically for glycine and glutamine. Glycine and glutamine are examples of hydrophilic amino acids, whereas leucine, alanine, methionine and phenylalanine have hydrophobic side chains that exhibit PPC curves with lower α and α (T) values.

Fig. 4 (A) Temperature dependence of the apparent thermal expansion coefficient α of various amino acids in 10 mM phosphate buffer at pH 5.5 and a concentration of 1 wt%. (B) To see the net side chain effect of the amino acids, the difference Δα_x−Gly = α_x − α_Gly is displayed.

In order to eliminate the effect of the ionisable moieties on the value of α(T) and to evaluate the effect of the nature of the side chains R of the amino acids, the difference Δα_x−Gly = α_x − α_Gly was calculated (Fig. 4B). All glycine corrected curves start at negative Δα_x−Gly values at low temperatures and reach positive values only at rather high temperatures >40 °C; the alanine side chain shows the most extreme behaviour, with Δα_x−Gly becoming positive only at temperatures above 60 °C. Leucine exhibits the most negative value at low temperature, while that of glutamine is the smallest in absolute value.

It has been pointed out²⁹ that solutes which increase the amount of structure in liquid water should have small positive or even negative α values at low temperature and a large positive temperature coefficient of α. Solutes that decrease the structure in water will show the opposite behaviour, with large positive α values at low temperature and a large negative temperature coefficient of α. This is simply the result of either increasing or decreasing, respectively, those features prominent in the behaviour of bulk liquid water that are attributable to tetrahedral structure melting.^27,53 Such a scenario is fully consistent with our data on single amino acids, which show that Δα at low temperature becomes more negative with increased hydrophobicity of the a.a. side chain as measured by some hydrophobicity scale or transfer free energy measurement of a.a. side chains (e.g., from cyclohexane to H₂O [kJ mol⁻¹]:¹ leucine, 20.59; phenylalanine, 12.47; methionine, 9.83; alanine, 7.57; glycine, 3.93; and glutamine: −23.18).

3.2 Tripeptides

Another means of evaluating the effect of the specific nature of the side chains of amino acids on their hydration and volumetric properties is to place the amino acid residue of interest in the context of a tripeptide, GXG, and subtract the PPC curve of the GGG tri-peptide from that of the GXG tri-peptide. This configuration has the advantage that the residue of interest is present in a configuration more closely resembling that of a polypeptide chain.^31,32Fig. 5A shows the PPC curves of all tripeptides measured in sodium phosphate buffer at pH 5.5 and a concentration of 1 wt%. The coefficient of thermal expansion of GGG is the largest (α = 1.5 × 10⁻³ K⁻¹) at low temperature, but still smaller than that of glycine (Fig. 3). All tripeptides show α values which are either smaller or larger than the corresponding single amino acids, except leucine where both α(T) values are similar. Fig. 5B shows the net effect of the side chains on the α values of the tripeptides (GXG) by subtracting the triglycine data (GGG): Δα_GXG−GGG = α_GXG − α_GGG (i.e., for comparing the α values of specific GXG tripeptides with the corresponding value of triglycine, we assumed—in a first approximation—additivity of α values). In comparison to the single amino acids, all tripeptides show less negative α values (e.g., the side chain of alanine has an α value of about −1.5 × 10⁻³ K⁻¹, whereas α = −1.5 × 10⁻³ K⁻¹ for the alanine side chain in GAG at T = 7 °C, i.e., there is a shielding effect of the neighbouring amino acids in the tripeptide, rendering the differential hydration contribution of the central a.a. residue to α less hydrophobic. Leucine shows the most negative α values for both the single amino acid side chain and for the tripeptide side chain with α values of −2.4 × 10⁻³ K⁻¹ and −1.4 × 10⁻³ K⁻¹, respectively, again indicating that the nearby hydration layers of the flanking amino acids markedly change (in this case decrease) the contribution of the central a.a. residue to α.

Fig. 5 (A) Temperature dependence of the apparent thermal expansion coefficient α of substituted triglycine in 10 mM phosphate buffer at pH 5.5 and a concentration of 1 wt%. (B) To visualize the net effect of the side chains on the α values of the tripeptides (GXG), we show the subtracted triglycine data (GGG), Δα_GXG−GGG = α_GXG − α_GGG.

The temperature dependence of the partial molar volumes of tripeptides of the sequence GXG has also been determined using differential scanning densimetry in order to evaluate a group additivity scheme for unfolded proteins.^31,32 It is apparent from a perusal of the temperature dependence of the amino acid side-chain volumes in these studies that the side-chains may also be divided into two groups, typically hydrophobic (“structure-making” in terms of their effect on the solvent) and polar/ionic (“structure-breaking”), which have characteristic volume–temperature profiles with slopes which are qualitatively similar to our PPC data.^31,32

Blocked termini. In order to determine the effect of the net charges at the N- and C-termini of the single amino acids and the tripeptides we also performed measurements on blocked ends (Ac–N– for H–N– and –OMe for –OH at the N– and C–terminus, respectively). Fig. 6A shows the PPC curves of alanine with “blocked” ends with respect to pure alanine. Fig. 6B displays the corresponding data for the tripeptide, trialanine. Both α values of the systems with blocked ends are smaller and exhibit much smaller slopes for α(T), again pointing to the drastic hydration contribution of charged groups to the apparent thermal expansion coefficient.

Fig. 6 Temperature dependence of the apparent thermal expansion coefficient α of (A) alanine and (B) trialanine with “blocked” ends measured in phosphate buffer at pH 5.5 and a concentration of 1 wt%.

3.3 Proteins

RNase A – H₂O (buffer). Fig. 7 shows the PPC and complementary DSC data of 0.5 wt% of RNase A in 10 mM phosphate buffer at pH 5.5 measured. For a better understanding of the discussion of the data, the curves are subdivided into pre-transition (< 40 °C), post-transition (>75 °C) and transition (40 < T/°C < 75) regions. In the PPC graph, the midpoint of the thermal unfolding transition (T_m) is indicated by a negative peak, which occurs at 62.0 ± 0.5 °C, which is in close agreement with the T_m value of the DSC result. Since the isoelectric point of RNase A is 9.6, at pH 5.5 it is positively charged (net charge +7). The apparent coefficient of thermal expansion, α, at lower temperatures is rather high (α = 0.76 × 10⁻³ K⁻¹ at 10 °C), and its slope is strongly negative in the native state, i.e., up to ∼40 °C (Δα₁₀₋₄₀ = α₁₀ − α₄₀ = 1.3 × 10⁻⁴ K⁻¹, or (dα/dT) = −4.3 × 10⁻⁶ K⁻²). This is the expected behaviour, since the preponderance of protein groups contacting water will be of the structure breaking hydrophilic type, which includes polar and charged side chains as well as peptide groups (as an example, see Fig. 1). The structure-making aliphatic side chains constitute less than a third of the solvent exposed side chains of the average folded protein and their structure-making effect is diminished by the hydrophilic nature of the peptide groups to which they are attached. Above T_m, α increases again to a relatively constant level with a value around 0.7 × 10⁻³ K⁻¹. Beyond 70 °C, α decreases slightly again. The slight reduction in α is probably due to increased thermal motion that causes still more or less weakly bound water molecules to leave the protein surface.

Fig. 7 (A) PPC temperature dependence of the apparent thermal expansion coefficient α. (B) Background corrected DSC spectrum (scan rate 40 °C h⁻¹) of 5 mg mL⁻¹ RNase A in 10 mM phosphate buffer at pH 5.5.

Using the post- and pre-transition base lines extrapolated to T_m, the change in α upon unfolding, Δα = 1.6 × 10⁻⁴ K⁻¹ is obtained. The magnitude of Δα can be attributed to the exposure of most of the buried groups during thermal unfolding of RNase A. Lin et al.²⁹ determined also α of reduced carboxymethylated (largely unfolded) RNase A between 4 and 95 °C from PPC measurements and found a value for Δα₁₀₋₄₀ of approximately 3.0 × 10⁻⁴ K⁻¹, which is much larger (43%) than that of native RNase A. From this value, the ASA of the native protein can be estimated as 43% of that accessible to the reduced unfolded form.

The area between the experimental data and the progress base line drawn between pre- and post-transition base lines projected into the transition region is utilized to calculate the area under the transitional peak (eqn (4)). The fractional volume change of unfolding, ΔV/V is obtained by integrating α over the temperature range where the transition occurs. By doing so, we obtain ΔV/V = −2.7 × 10⁻³ (−0.27%) for RNase A. The absolute volume change upon unfolding, ΔV, can be calculated from ΔV/V using the molar mass of RNase A (13.7 kDa) and its partial specific volume,⁵⁴ which yields ΔV = −26 mL mol⁻¹. Using densimetric measurements, at pH 2.5, also a negative volume change of unfolding has been observed for RNase A, however of smaller amplitude (ΔV = −10 mL mol⁻¹).²³ The observed negative volume change upon protein unfolding might be due to the opening of void volume and the electrostriction effect of the polar and charged groups of the increased ASA, overcompensating the positive effects of thermal volume and the changes in the hydrophilic–hydrophobic balance of the surface groups. The quality of the data thus clearly shows that, even with the low protein concentration chosen, the method is efficient enough to detect these small volume changes.

From the corresponding DSC data, we can derive the midpoint of the thermal unfolding temperature (T_m) and the area under the transition curve, the enthalpy change of the transition, ΔH. The enthalpy change obtained by integration over the DSC peak amounts to 435 ± 4 kJ mol⁻¹. We can find an increase in C_p of 5.2 ± 0.2 kJ mol⁻¹ K⁻¹ between the unfolded and native state, a value which is typical for proteins and indicates an increased number of water–biopolymer contacts and hence hydration contribution during unfolding as also seen from the PPC graph. All these parameters derived from the PPC and DSC experiments for RNase A are taken as a reference to discuss their relative changes in the presence of various cosolvents (Table 1).

Table 1 RNase A PPC and DSC experimental data (on average, the error for ΔV is up to 7% (taking into account also the temperature dependence of V), T_m ± 0.2 °C, for ΔH ∼1% and for ΔC_p ∼5%)

Solvent	PPC Results						DSC Results
	T m/ °C	α 10/ 10^−3 K^−1	Δα10−40/ 10^−4 K^−1	ΔV/V/ 10^−3	ΔV/ mL mol^−1	Δα/ 10^−4 K^−1	T m/ °C	ΔH/ kJ mol^−1	ΔCp/ kJ K^−1 mol^−1
RNase A (5.5 mg mL^−1)	62.5	0.76	1.3	−2.7	−26.0	1.6	62.0	435	5.2
RNase A (12.5 mg mL^−1)	63.0	0.66	0.7	−2.6	−25.0	1.5	62.1	424	5.4
RNase A (21.0 mg mL^−1)	63.0	0.62	0.6	−2.5	−24.0	1.3	62.1	420	5.4
+ 0.5 M GuHCl	57.0	0.5	0.3	−3	−29.0	2.1	57.8	349	3.1
+ 1.5 M GuHCl	48.2	0.53	0.2	−3.5	−34.0	1.8	48.5	295	3.9
+ 2.5 M GuHCl	40.0	0.74	∼0	−3.6	−35.0	0.8	40.1	226	4.6
+ 0.5 M Sucrose	64.0	0.84	1.7	−1.9	−18.3	1.2	64.2	436	2.2
+ 1.5 M Sucrose	68.1	0.68	1.3	+1.3	+12.5	0.8	67.8	448	1.6
+ 0.5 M Gu2SO4	61.0	0.6	−0.2	−2.2	−21.2	1.3	61.5	371	2.6
+ 1.5 M Gu2SO4	61.5	0.58	∼0.4	0	0	0.9	62.0	385	3.3
+ 2.5 M Gu2SO4	65.0	0.54	∼0	+1.5	+14.5	1.0	66.0	376	3.5
+ 0.5 M EtOH	60.5	0.84	2.1	−2.6	–25.1	1.6	60.6	405	4.0
+ 1.5 M EtOH	59.5	0.84	1.6	−2.2	−21.2	1.5	58.6	420	1.0
+ 2.5 M EtOH	57	0.86	1.4	−2.0	−19.3	1.4	56.8	456	3.4
+ 3.5 M EtOH	55	0.92	0.9	−1.7	−16.4	1.2	54.8	440	4.0
+ 4.5 M EtOH	53	1.3	2.9	−1.4	−13.5	1.0	54.0	457	4.4
+ 0.5 M TFE	61.5	0.6	1.0	−1.6	+15.4	1.26	60.0	436	3.3
+ 1.5 M TFE	55.1	0.46	0.9	∼0	∼0	0.93	56.0	453	3.4
+ 2.5 M TFE	51.5	−0.05	1.6	+1.9	+18.3	0.75	52.9	427	3.2

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RNase A – H₂O (buffer) – concentration effects. We also carried out measurements at different concentrations (5.5, 12.5 and 21 mg mL⁻¹) of RNase A in 10 mM phosphate buffer. Inspection of Fig. 8 and Table 1 shows that the α and dα/dT values depend significantly on the protein concentration above 5 mg mL⁻¹. In particular, in the pretransitional region, a decrease of these values with increasing concentration is clearly visible. This effect might be due to intermolecular interactions and self-association. However, ΔV, ΔH, T_m, and ΔC_p are less affected by the protein concentration (Table 1).

Fig. 8 Temperature dependence of the apparent thermal expansion coefficient α of 5 (filled squares), 12.5 (open triangles) and 21 mg mL⁻¹ RNase A (continuous line) in 10 mM phosphate buffer solution at pH 5.5.

RNase A – H₂O – sucrose. Glycerol, sorbitol and other polyolic cosolvents have been shown to lead to a “preferential hydration” of the protein, i.e., the exclusion of the cosolvent molecules from the protein surface.^5,55–59 Being strongly hydrophilic cosolvents, they interact strongly with H₂O and have a relatively weak affinity to the polar residues on the protein surface, thus leading to preferential hydration of the protein. In addition, due to steric exclusion, the volume fraction occupied by the cosolvent at the surface of the protein should be less than that in the bulk solvent, which again leads to preferential hydration of the protein by H₂O.⁵ For sugars (e.g., sucrose), glycerol and polyhydric alcohols (e.g., ethylene glycerol, sorbitol), the preferential hydration was found to induce also protein stabilization.

As an example, we show PPC experiments at 0.5 M (∼17 wt%) and 1.5 M (∼51 wt%) sucrose as cosolvent in 10 mM phosphate buffer. As can be clearly seen in Fig. 9, the hydration changes due to sucrose are significant. The comparison of α and (dα/dT)_10–40 values of RNase A/0.5 M sucrose (−5.7 × 10⁻⁶ K⁻²) and RNase A in pure buffer solution (−4.3 × 10⁻⁶ K⁻²) indicates that there is a higher solvation (stronger hydration layer) of the native protein in the sucrose containing solvent, which also acts as an effective stabilizing agent as indicated by the higher T_m values (Fig. 9B, Table 1). The volume change upon unfolding is much smaller, −18.3 mL mol⁻¹ in 0.5 M sucrose as compared to −26.0 mL mol⁻¹ in the pure phosphate buffer system, which may indicate a less disordered unfolded state structure. This decrease in the absolute value of ΔV is also due to the fact that unfolding occurs at higher temperature and that the magnitude of ΔV decreases with increasing temperature. Above a sucrose concentration of ∼1 M, the volume change upon unfolding of the protein actually changes its sign; for example, in the 1.5 M sucrose solution, ΔV = +12.5 mL mol⁻¹. Interestingly, at high sucrose concentrations, α decreases markedly, even below the value in the pure buffer system, indicating a significant decrease in protein hydration at these high cosolvent concentrations where the properties of bulk water are largely altered and specific cosolute binding to the protein becomes more likely. Also increased osmolyte-driven protein–protein interactions cannot be ruled out. According to the DSC data (Fig. 9B), the T_m value increases from 62 °C to 64 and 68 °C for the 0.5 and 1.5 M sucrose-RNase A systems, respectively. An incomplete thermal unfolding is also suggested by the reduced ΔC_p values (Table 1).

Fig. 9 (A) Temperature dependence of the apparent thermal expansion coefficient α of RNase A (protein concentration 5 mg mL⁻¹) in 10 mM phosphate buffer solution at pH 5.5 (filled squares) as well as in 0.5 M (open triangles) and 1.5 M (continuous thin line) sucrose in 10 mM phosphate buffer solution at pH 5.5. (B) Corresponding DSC traces of RNase A (thick line) and in the presence of 0.5 M (thin line) and 1.5 M (dashed dot line) sucrose.

The PPC data of further osmolytes are discussed elsewhere ³⁸ (see also Fig. 10). Briefly, for glycerol, the steric exclusion effect is expected to be smaller and as a result, hydration changes and stabilization due to glycerol are less pronounced. Sorbitol takes an intermediate position with regard to solvation of the native protein, to the protein stability, and the effect of cosolvent concentration on ΔV/V. With increasing cosolvent concentration, also for these polyols the volume change of unfolding becomes positive, however at much higher molar concentrations. A similar behaviour is observed for SNase.³⁹

Fig. 10 Relative volume changes, ΔV/V, of (a) RNase A and (b) SNase upon unfolding (protein concentration 5 mg mL⁻¹, in 10 mM phosphate buffer solution) for various cosolvents as a function of cosolvent concentration. Please note that the unfolding temperatures T_m also vary as a function of cosolvent concentration (Table 1).

RNase A – H₂O (buffer) – GuHCl and Gu₂SO₄. Chemical denaturation, with an agent such as urea and GuHCl, is one of the primary methods employed to assess protein stability, the effects of mutations on stability, and protein un- and refolding behaviour.¹ It is well known that the destabilizing nature of these agents is mainly caused by their preferential binding to the peptide group.^60,61 This leads to protein unfolding with exposure to the solvent of a large number of previously buried peptide groups with which urea or GuHCl interacts favourably. As a consequence, the protein attains a more or less random coil like structure. The PPC results of RNase A in 0.5 mol GuHCl salt solution are shown in Fig. 11 (see also Table 1). The α values at low temperatures are much smaller than those of RNase A in pure buffer solution, and Δα₁₀₋₄₀ = 0.3 × 10⁻⁴ K⁻¹. The T_m value decreases from 62 °C for RNase A in pure buffer solution to 57.0 °C in the presence of 0.5 M GuHCl. These findings are a consequence of specific binding of guanidinium ions to the protein, thereby replacing water molecules and releasing them into the bulk phase, such that the hydration of the protein and hence α is largely diminished in the presence of the salt, prior to denaturation. The ΔV value of −29 mL mol⁻¹ value of RNase A in 0.5 mol GuHCl buffer solution is much greater (∼12%) than that of RNase A in the pure buffer solution at the 5 °C higher temperature. Again, these changes in the magnitude of the volume change of unfolding probably result from a combined effect of the additive on the structure of the unfolded state and the fact that unfolding occurs at a lower temperature. The increased Δα value of 2.1 × 10⁻⁴ K⁻¹ supports the idea of formation of a largely unfolded (large increase of SAS), random-coil-like structure of the denatured protein in the presence of GuHCl. Interestingly, in the post-transitional region α of the RNase A-GuHCl system, α(T) tends to be flat, which is an indication that further temperature increase has rather little influence on the hydration changes which might be due the extended ligand binding of the guanidinium ions, thereby replacing water from the protein surface. Beyond a concentration of ∼2.5 M of urea or GuHCl, it is not possible to calculate ΔV accurately as the protein does not unfold in a cooperative manner any more.

Fig. 11 (A) Temperature dependence of the apparent thermal expansion coefficient α of RNase A (protein concentration 5 mg mL⁻¹) in 10 mM phosphate buffer solution at pH 5.5 (filled squares) and in 0.5 M GuHCl/10 mM phosphate buffer solution at pH 5.5 (open triangles). (B) Temperature dependence of the apparent thermal expansion coefficient α of RNase A (protein concentration 5 mg mL⁻¹) in 10 mM phosphate buffer solution at pH 5.5 (filled squares) and in 0.5 M (open triangles), 1.5 M (continuous thin line) and 2.5 M Gu₂SO₄ (open circles) in 10 mM phosphate buffer solution at pH 5.5.

The lowered T_m value of 57.8 °C obtained from the DSC trace is in close agreement with the PPC result. ΔH of 349 kJ mol⁻¹ in the presence of 0.5 M GuHCl is ∼20% smaller than the enthalpy change of unfolding of RNase A in pure buffer solution.

The major mechanism of stabilization by salt anions is known to be due to a reduction of the net positive charge of positively charged amino acid side groups on the protein surface through charge screening. Hofmeister anions,^9,62,63 such as sulfate, are thought to also weakly interact with the peptide groups, whereas they interact unfavourably with nonpolar peptide side chains. From the PPC results for RNase A dissolved in 0.5 M K₂SO₄ buffer solution, we have shown³⁸ that the shift in the T_m value from 62.0 to 69.0 °C is an indication that the salt acts as a strong stabilizing agent. By contrast to the osmolytes glycerol, sorbitol and sucrose, the apparent expansion coefficient of the native protein is markedly smaller, even smaller than that of the protein in pure buffer solution. Hence, even though the low α-value indicates a drastic net reduction in hydration, similar to urea and GuHCl, the K₂SO₄/buffer system increases the stability of the protein.

Here we show additional data where we replaced K⁺ by the strongly chaotropic guanidinium cation. We varied the Gu₂SO₄ concentration from 0.5 to 2.5 mol and the results of PPC and DSC scans are presented in Fig. 11B. It appears that at low concentrations, the guanidinium cations destabilize the protein as is visible by a slight shift of the T_m value to 64 °C. However, above 1.5 M Gu₂SO₄, the protein is stabilized and T_m increases to 66 °C at 2.5 M Gu₂SO₄, where the strongly stabilizing sulfate anions overcome the denaturing effect of the guanidinium cations. A decrease in the magnitude of ΔV and a reduction in ΔH values is observed (Table 1), both indicating that the protein is undergoing an incomplete unfolding. Above ∼0.5 mol Gu₂SO₄, the solvent contributions to α, and Δα₁₀₋₄₀ are small. We should emphasize at this point, however, that a direct correlation between the denaturation volume of proteins and the denatured state structure is difficult and has to be treated with care owing to the different contributions to V and the complex interplay of these contributions. The water structuring tendencies are nearly eliminated in 2.8 M guanidinium sulfate where a long-range hydrogen-bonded water structure is largely absent. An almost constant value of α near 0.55 × 10⁻³ K⁻¹ for native RNase A in 2.5 M Gu₂SO₄ buffer may represent the expansion of the intrinsic protein volume.

Thus, at high enough sulfate concentrations, the destabilizing effect of the guanidinium cation to native proteins is overcompensated by the strongly stabilizing and compaction-driving SO₄²⁻ anion. As a consequence, also the ΔV value changes sign at high Gu₂SO₄ concentration, due, again, to a decrease in the magnitude of ΔV with increasing temperature and an increased compaction of the unfolded state. The negative contribution of the loss of void volume is minimized under these conditions, and therefore the positive contribution of the exposure of hydrophobic residues, coupled to the decrease in hydration of the polar moieties due to binding of the additive, may lead to the overall increase in volume upon unfolding, as has been observed before.²⁹

RNase A – H₂O – alcohols EtOH and TFE. More subtle effects are observed in the case of monoalcohols, such as ethanol, and their fluorinated derivatives, such as 2,2,2-trifluoroethanol (TFE), which is assumed to be particularly potent in inducing structural conversions within proteins, due likely to an additive effect of fluorination.⁶⁴ It is generally observed that alcohols promote secondary structure, especially α-helix formation, but at the same time act as destabilizers of tertiary and quaternary interactions within the folded protein, occasionally leading to partially unfolded “molten globule”-like conformations.⁶⁵ However, their modes of action are still a matter of debate. Alcohols exhibit a lower dielectric constant than water and are much weaker hydrogen bond acceptors. These properties give rise to a series of proposed interaction mechanisms, including perturbation of the protein’s water shell,^66,67 diminution of hydrophobic interactions,⁶⁸ strengthening of intra-protein hydrogen bonding and less shielding of electrostatic interactions due to the lower polarity of alcohols.⁶⁴ Other mechanisms stress preferential binding with simultaneous dehydration in the immediate vicinity of the protein,^69–71 and the impact of clustering to provide local regions of low polarity.¹⁸ The effects of alcohols on protein folding have been shown to depend on the alcohol concentration in a non-monotonic fashion.^72,73

Fig. 12A presents PPC scans of RNase A as a function of ethanol concentration in 10 mM phosphate buffer at pH 5.5 (for all the thermodynamic data derived from PPC and DSC, see Table 1). The reduced T_m values are an indication of the slight destabilising effect of ethanol. Interestingly, the magnitude of the reduction in volume is smaller than that of RNase A in pure buffer at a higher temperature, even at 4.5 M ethanol, indicating that the protein unfolds only partially. The solvent contribution to α and Δα₁₀₋₄₀ is enhanced with increasing ethanol concentration, however. Hence, in contrast to the case of GuHCl, while like GuHCl ethanol displays a slightly destabilizing effect on T_m, the hydration contribution of the protein to the value and temperature dependence of α is increased.

Fig. 12 (A) Temperature dependence of the apparent thermal expansion coefficient α of RNase A (protein concentration 5 mg mL⁻¹) in 10 mM phosphate buffer solution at pH 5.5 (filled squares) and in 0.5 M (open triangles), 2.5 M (open circles), 3.5 M (stars) and 4.5 M ethanol (open squares) in 10 mM phosphate buffer solution at pH 5.5. (B) Temperature dependence of the apparent thermal expansion coefficient α of RNase A (protein concentration 5 mg mL⁻¹) in 10 mM phosphate buffer solution at pH 5.5 (filled squares) and in 0.5 M (open triangles), 1.5 M (continuous thin line), and 2.5 M TFE (open circles) in 10 mM phosphate buffer solution at pH 5.5.

We have also studied the effect of 0.5 to 3.5 M TFE on RNase A solutions (Fig. 12B, Table 1). As can be clearly seen, TFE destabilizes the protein and, contrary to the cosolvent EtOH, it drastically reduces the hydration around the protein, as can be seen by a drastic reduction in α values. Surprisingly, at and above 1.5 M TFE, the volume change of unfolding, ΔV, of the protein changes sign and becomes positive. Hence, not only stabilizing osmolytes at high concentration, but also alcohols are able to induce positive ΔV values. The striking difference between the ethanol and TFE destabilisation scenarios is that TFE greatly disturbs the hydration layer around the protein by binding to the protein, thus drastically destabilising the protein’s tertiary structure. The ΔH and ΔC_p values support the aforementioned conclusion that TFE greatly reduces the hydration by preferential solvation without marked unfolding of the secondary structure elements. A mere protein swelling (molten globule kind of state) upon denaturation might explain the positive ΔV values at high TFE concentrations.

3.4 Contributions to the partial protein volume and its coefficient of thermal expansion for native and unfolding proteins

As previously discussed by Chalikian,⁶ changes in partial specific volume, V, and hence in α of a protein can be considered to be dissected into essentially three different contributions: (1) the intrinsic volume, V_intr, which originates from the van der Waals volume of the constituent atoms plus the volume of intrinsic voids within the water-inaccessible protein interior; (2) a hydrational term, ΔV_h, or “interaction volume”, describing—with regard to the bulk solvent—the solvent volume associated with the hydration of solvent-accessible protein atomic groups, resulting from solute–solvent interactions around the charged (electrostriction), polar (hydrogen-bonding), and nonpolar (hydrophobic hydration) atomic groups on the protein surface; and (3) the thermal volume, V_therm, which results from thermally induced mutual molecular vibrations and re-orientations of the solute and the solvent: V ≈ V_intr + ΔV_h + V_therm. The thermal expansivity of the protein interior is generally expected to be small, which has yet to be verified (see below). The thermal volume increases with temperature leading to a positive contribution to α. The solvation effect may be expected to decrease with increasing temperature, as thermal activation leads to a continuous release of the “condensed” layered water from the protein surface (but see MD simulation results below). Once the water is released, it no longer contributes to the partial volume of the protein and hence to α. Such behaviour for α(T) of proteins has indeed been found in our experiments, pointing to the fact that the hydrational term plays a major role in determining the apparent thermal expansion coefficient of proteins. The negative volume change of unfolding observed for the two proteins at the transition temperature is probably due to the opening of void volume and the increase in hydrophilic hydration of more charged and polar groups. In the unfolded state, α increases due to a large increase of ASA and hence of the hydration contribution to α, in addition to the positive effects of thermal volume and the increased contribution of hydrophobic hydration in the unfolded state.

We have seen that ΔV drastically depends on the type of cosolvent. However, the volume change that accompanies the unfolding transition of proteins is expected to depend also on the temperature at which the transition occurs. This is obvious given the fact that the expansivities of the folded states of proteins are different from those of the unfolded state and highly temperature dependent. Since the temperature dependences of the specific volume of the two states are different, the difference in volume between these two states cannot be constant with temperature. In fact, since the addition of osmolytes (glycerol, sorbitol, sucrose) stabilizes the folded state, such that the T_m increases with increasing glycerol concentration, and the relative volume change upon unfolding of RNase A, d(ΔV/V)/dT, decreases roughly at a rate of 5 × 10⁻⁴ K⁻¹ (Fig. 10). Since the volume change of unfolding is expected to decrease with increasing temperature (as noted above), we may conclude that at least part of the observed effect of the stabilizing cosolvents on ΔV is due to the increase in transition temperature (leading to an increase of V_therm), and not only due to differential conformational or hydrational effects. In fact, such an explanation should also hold for the observed slight increase in the absolute value of ΔV as a function of increasing urea or GuHCl concentration (d(ΔV/V)/dT ≈ 4.7 × 10⁻⁵ K⁻¹ for RNase A, Fig. 10), as these cosolvents destabilize the folded state of the protein leading to a decrease in the T_m with increasing denaturant concentration.

Drastic temperature dependence of V would also be consistent with the pH dependence of the PPC curves of RNase A (data not shown). For example, the T_m value decreases from 63 °C at pH 7.7 (pI = 9.6) to 41 °C at pH 2, where the protein is strongly positively charged, and ΔV decreases concomitantly from −14.5 mL mol⁻¹ at 63 °C to −38.6 mL mol⁻¹ at 41 °C. The differences in d(ΔV/V)/dT values observed for the different cosolvents imply, however, that the different ΔV values observed for the various types of cosolvents can only partially be explained by the temperature dependence of ΔV. An additional contribution is probably due to a more or less completely unfolded state structure. Detailed small-angle scattering and CD/FT-IR spectroscopic measurements are needed to verify these assumptions.

3.5 Properties of the hydration water at the protein interface of SNase by MD computer simulations

To yield a molecular interpretation of the different terms contributing to the partial protein volume and its temperature dependence and hence a better understanding of the PPC data, MD computer simulations on SNase were also carried out and compared with the experimental data. Please note that a quantitative comparison of absolute volumetric and expansibility data with the experimental data is difficult owing to the fact that the absolute values of these parameters still depend on the water model and force field used in the MD simulation. In a recent MD study on SNase we studied in detail the water structure at the protein surface.⁴³ We found that the structural properties of the water and hydrogen bonding pattern (network) at the protein surface are very complex and depend on its chemical and topographical properties. We classified the interfacial water molecules in the following way. A first type, water near hydrophobic residues, which induces bonding between neighbouring water molecules, gives raise to more pentagonal and hexagonal structural elements, which may grow into cage-like networks, forming disordered clathrate-like structures. A second type of interfacial water is the one near hydrophilic groups, such as charged or polar side chains of the protein. They interact strongly with water molecules, inducing a specific orientation of the water dipole. To investigate the influence of the protein surface on the structure of water, we calculated the local density profile of water as a function of the distance from the protein atoms. For precise evaluation of the water-density profile, we first calculated the volume of shells with thickness 0.1 Å as a function of the distance d from the nearest heavy atoms (N, O, C and S) of the protein. For calculation of the water local density profile, we counted the number of water molecules (the position of the water molecule was defined as the center of the oxygen atom) within the same shell and divided this number by the corresponding volume of their shell.⁴³Fig. 13 shows the local density profiles of water from the simulation runs at ambient pressure and different temperatures, normalized by the density of bulk water at the same conditions. With increasing temperature, the height of the maximum of the water density profile, which corresponds to the hydration water (“bound water”), decreases and broadens, indicating a temperature-induced weakening of the water–protein interactions and smearing out of the structure of the hydration shell. Such behaviour should be reflected in the hydration contribution to α(T).

Fig. 13 MD results for the local density profile of water, ρ(d), near the surface of SNase as a function of distance (d) from nearest protein heavy atoms, normalized by the density of bulk water at the same conditions. At p = 1 bar and T = 300, 360 and 400 K.

The hydration shell of SNase. Different definitions of the hydration water layer of proteins are possible. Rupley and Careri⁷⁴ suggested that the hydration shell could be defined as the water associated with the protein at the hydration end point, namely until a level of hydration is reached beyond which further addition of water produces no further changes in the thermodynamics and dynamics of the protein and only dilutes it. One may assume that this shell represents essentially a monolayer coverage of the protein surface. To define the hydration water, we used a simple distance criterion: water molecules belong to the hydration shell when they are closer to any heavy atom of the protein than some cut-off distance. For estimation of the average density of the hydration shell of the protein, we are then able to calculate the number of water molecules within the hydration shell, and the volume accessible to these water molecules is defined by the difference between the volume within the shell of a given cut-off distance from the centres of any heavy atom and the corresponding solvent-excluded volume, V_SE.⁷⁵ Due to hydrogen bond formation between the hydration water and the protein surface, it is difficult to define a clear-cut interface between the protein and the hydration water and to separate which volume corresponds to the protein and to the hydration water, respectively. To clarify this problem, we calculated the solvent-excluded volume of the protein with and without hydrogen atoms of the protein. We obtain a 0.3% density increase over the bulk in a shell of 4.5 Å and of 0.6% in a shell of 4.0 Å, when we use only the heavy atoms of SNase for calculating V_SE. We may use these values as a lower limit for the density of the hydration water. In the case of implicit hydrogens of the protein we obtain a 6.7 and 5.5% density increase over the bulk in shells of 4.0 and 4.5 Å, respectively. We may use these values as an upper limit for the density of the hydration water. These data are in quantitative agreement with recently reported data obtained using small-angle X-ray and neutron scattering techniques.¹⁵ To define the hydration shell, one may also use different cut-off distances for different types of the protein atoms (hydrophobic and hydrophilic). In fact, we have seen that the minima of the water local density profile near the protein surface are located at distances of 3.5 and 4.5 Å for hydrophilic (N, O and S) and hydrophobic (C) atoms of the protein, respectively.⁴³ We obtain a density increase of about 11% over the bulk in a hydration shell with these mixed cut-off distances, which is good agreement with other simulations.^76,77

In this study, we used one cut-off distance for all heavy atoms of the protein to define the hydration shell of SNase, and all atoms were used for calculating the physical surface properties of the protein molecule. Fig. 14 shows the average density of the hydration shell of SNase as a function of the cut-off distance d at different temperatures. A pronounced average density maximum close to the protein interface can be identified in all simulations, and appears at a similar distance of about 3.8 Å. As expected, this density maximum broadens with increasing temperature. About two water layers are perturbed at the protein surface and have different densities compared to bulk water.

Fig. 14 The average number density of the hydration water shell near the surface of SNase as a function of the cut-off distance (d) from nearest protein heavy atoms. At p = 1 bar and T = 300, 360 and 400 K.

The thermal expansion coefficient, α = −ρ⁻¹(∂ρ/∂T)_p of the hydration shell has been determined from simulations at two (ρ, T) data points using α = −(2/([small rho, Greek, macron]₁ + [small rho, Greek, macron]₂)([small rho, Greek, macron]₂ − [small rho, Greek, macron]₁)/(T₂ − T₁)) , where [small rho, Greek, macron]₁, [small rho, Greek, macron]₂ are the mean values of the density at temperatures T₁ and T₂, respectively. Fig. 15 exhibits the thermal expansion coefficient of the water within the hydration shell of SNase as a function of the cut-off distance, d. It can be clearly seen that α is much larger at low temperatures close to the protein interface, and drastically decreases at the higher temperature. To be able to compare the properties of the hydration and bulk water, we also determined α for the bulk TIP3P water by simulation of pure water under the same conditions (Table 2). The results are in agreement with previous simulations.⁷⁸ TIP3P bulk water-like behaviour is observed above ∼5.5 Å i.e., beyond the second hydration layer.

Fig. 15 Thermal expansion coefficient α of the hydration shell of SNase as a function of the cut-off distance d from nearest protein heavy atoms.

Table 2 The thermal expansion coefficient of the bulk TIP3P and hydration water of SNase at different temperature conditions. Errors are standard error estimates

	α/10^−3 K^−1
	Bulk water	Hydration water
T 1 = 300 K, T2 = 360 K	1.06 ± 0.02	1.90 ± 0.06
T 1 = 360 K, T2 = 400 K	1.38 ± 0.03	1.60 ± 0.09

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Surface and volumetric properties of the hydrated protein. In Fig. 16, we schematically illustrate three types of protein surfaces, namely: the solvent-accessible surface, the molecular surface, and the van der Waals surface. As originally defined by Lee and Richards,⁷⁹ the solvent-accessible surface is that surface which is traced out by the center of a probe sphere solvent molecule as it rolls over the van der Waals surface of the protein. As defined by Richards,⁸⁰ the molecular surface of a protein has two components, namely that part of the van der Waals protein surface which contacts a rolling probe solvent molecule; and a re-entrant surface, which corresponds to a series of patches formed by the interior-facing domain of the probe when it simultaneously contacts more than one atom on the protein surface. The van der Waals surface is defined by the intersections of the atomic van der Waals spheres which correspond to each atom of the protein. In the discussion below, we consider only the solvent-accessible and the molecular surface. The molecular surface is chemically important because it represents the interface of the protein to the solvent. Analysis of the solvent-accessible surface furnishes information about the hydration shell because it is directly related to the possible number of water molecules at the protein surface.

Fig. 16 Schematic representation of the solvent accessible, molecular, and van der Waals surfaces of a protein.

The molecular and the solvent-accessible surface areas of SNase at different temperatures are shown in Table 3. In addition, we divided the ASA into different types of residues by their physicochemical properties: nonpolar, polar neutral, positively or negatively charged. The molecular and solvent-accessible surface areas of SNase slightly increase (∼0.8 and 0.3%, respectively) with increasing temperature to 360 K, but slightly decrease again at 400 K compared to ambient temperature conditions. The reason is a drastic surface area increase of polar neutral and nonpolar groups of about 8–10% and a concomitant, largely compensating decrease of surface areas of positively and negatively charged groups. Hence, a significant redistribution of surface residues is revealed, leading to a higher population of nonpolar and polar neutral residues. Upon further temperature increase, only a reduction in the number of nonpolar surface area essentially occurs. These findings probably depend on the specific surface topography of the protein under consideration.

Table 3 The molecular surface and solvent-accessible surface areas of various types of a.a. residues of SNase for MD simulations at different temperatures. Errors are standard error estimates. Standard deviations are given in parentheses

	Area (Å^2)
System	Molecular surface	Solvent-accessible surface
		All residues	Nonpolar	Polar, neutral	Positively charged	Negatively charged
SNase, 300 K, 1 bar	7359 ± 12 (107)	9417 ± 18 (160)	1871 ± 7 (60)	2271 ± 8 (70)	3792 ± 8 (74)	1483 ± 6 (50)
SNase, 360 K, 1 bar	7418 ± 14 (131)	9446 ± 24 (216)	2054 ± 7 (66)	2455 ± 11 (95)	3615 ± 10 (90)	1322 ± 9 (80)
SNase, 400 K, 1 bar	7334 ± 14 (124)	9395 ± 20 (180)	1984 ± 8 (77)	2468 ± 12 (110)	3607 ± 11 (96)	1336 ± 8 (72)

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For each type of protein surface group, we can define a corresponding protein volume, which is enclosed by the corresponding surface. The van der Waals volume, V_vdW, of the protein is the volume enclosed within the van der Waals surface of the protein. The volume enclosed within the molecular surface is denoted solvent-excluded volume,⁷⁵V_SE, of the protein, which is equal to the sum of the van der Waals volumes of the protein and the volume of voids, V_void, of the protein resulting from imperfect internal packing. The partial volume, V_P, of a protein in solution is defined as the volume of the solution minus the volume of the solvent in the absence of solute. The MD partial specific volume, V_S = V_P/m_P, of SNase slightly changes from 0.680 cm³ g⁻¹ at ambient temperature (T = 300 K) to 0.684 cm³ g⁻¹ at T = 400 K (still far from MD unfolding conditions), respectively. Experimental data on SNase⁸¹ show a similar increase of V_S(T) in the native state, though the absolute values are slightly larger (∼4%). At low temperatures, the temperature dependence of V_S is larger than at higher temperatures just before the unfolding temperature. Such behaviour is in agreement with our simulations: with increasing temperature from 300 to 360 K, we obtain an increase of about 0.6% in the V_S value. Further increase of temperature does not change the V_S value significantly.

In Table 4, the various protein volumes of SNase obtained for the different temperatures are shown. In general, V_P can be represented by the sum of the intrinsic geometrical volume, V_int = V_vdW + V_void, occupied by the protein molecule itself (which can be approximated by the solvent excluded volume V_SE of the protein molecule) and by the changes in the solvent volume, ΔV_h, resulting from its interaction with accessible a. a. side chains, i.e., V_P = V_vdW + V_void + ΔV_h.^82,83 The hydration contribution, ΔV_h, to the partial volume of the protein molecule reflects the interaction volume associated with the hydration of solvent accessible protein residues. ΔN = ΔV_hρ_bulk is defined here as the number of water molecules that have to be added or released to the hydration shell in order to yield the bulk density value (ρ_bulk is the number density of water under the same temperature conditions).

Table 4 The solvent-excluded, van der Waals, void and partial volumes of the SNase at different temperatures (p = 1 bar). Also, the hydration contribution to the partial volume and ΔN = ΔV_hρ_bulk are given. Errors are standard error estimates. Standard deviations are given in parentheses

	Volume/Å^3
System	Solvent-excluded volume, VSE	Van der Waals volume, VvdW	Void volume, Vvoid	Partial protein volume, Vp	Hydration contribution to the partial volume	ΔN = ΔVhρbulk
SNase, 300 K, 1 bar	21482 ± 10 (86)	18472 ± 2 (21)	3010 ± 8 (73)	18987 ± 43 (393)	−2495 ± 6 (52)	−82
SNase, 360 K, 1 bar	21604 ± 14 (109)	18476 ± 2 (21)	3127 ± 11 (100)	19113 ± 49 (446)	−2491 ± 6 (58)	−77
SNase, 400 K, 1 bar	21665 ± 15 (111)	18480 ± 2 (22)	3186 ± 11 (99)	19059 ± 56 (512)	−2606 ± 8 (70)	−76

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Hence, at least for a semiquantitative interpretation of the partial volume of the protein in terms of hydration,⁸⁴ we may use the following relationship

V_P = V_SE + n_h (V_h − V₀), (5)

V₀ and V_h being the partial volumes of water in the bulk and in the hydration shell of the solute, respectively, and n_h is the “hydration number”, that is, the number of water molecules in the hydration shell of the solute. In case of protein hydration, we have to consider V_h as an average effective partial volume of water in the hydration shell due to the presence of different types of the amino acid residues at the protein surface.

The partial volume in the simulation is simply the difference between the volumes of the system before and after adding the protein to the solution. We determined the partial volume of SNase from the simulations, using:

V_P = V_BOX −m_W/ρ_bulk − V_CI, (6)

where V_BOX is the volume of the simulation box, m_W is the mass of water in the simulation box, ρ_bulk is the density of bulk water at the same conditions and V_CI is the partial volume of the counter ions, which we determined by considering the ions as spheres with radius r = r_vdW + 0.5 Å, where r_vdW is their van der Waals radius and 0.5 Å is the thickness of the empty layer surrounding the counter ion.^82,85

It is well known that for polar solutes, ΔV_h is negative and for nonpolar solutes positive.⁸⁶ Around a hydrophilic solute the water molecules are more tightly packed while in the presence of the hydrophobic solutes the water structure is less dense.⁸⁶ For proteins, ΔV_h is generally found to be negative. Remarkably, with increasing temperature, the absolute value of ΔV_h increases (for nonpolar and polar solutes), as the decrease of the bulk water density is faster than the decrease of the hydration water density with increasing temperature. As expected, V_vdW is more or less independent of temperature. Due to a marked increase of V_void (∼4%) up to 360 K, V_SE of SNase increases (∼1%) with increasing temperature. The van der Waals and void volumes make up 86 and 14% of the solvent excluded volume, respectively, at T = 300 K. The void volume of the protein increases markedly with increasing temperature (∼4%), from 3010 ų at 300 K to 3127 ų at 360 K. For these two temperatures, the negative values of the hydration contribution to the partial volume are essentially the same, which is probably due to some surface rearrangement of the protein, leading to a decrease of the polar and concomitant increase of nonpolar and polar neutral protein surface area as discussed above (Table 3). This leads to a decreasing absolute value of ΔV_h. At the higher temperature of 360 K, the magnitude of ΔV_h increases in fact, as the decay of the bulk water density with increasing temperature is larger than the decay of the water density of the hydration water.

With further increasing the temperature from 360 to 400 K, a further but less pronounced increase of the void volume is visible. Obviously, the temperature dependence of the void volume is largest at lower temperatures and reaches a limiting value at high temperatures, probably since a further expansion without unfolding of the protein is not feasible any more. As the contribution of the polar and nonpolar amino acid residues at the protein surface remains the same at 360 and 400 K, we observe an increase of the absolute value of ΔV_h due to the temperature increase in this case.

Additionally, we determined the thermal expansion coefficient of the different protein volumes (Table 5A) using the same dissection method as described above. In a first approximation, the thermal expansion coefficient of the protein partial volume may be expressed as:

α_VP = φ_VvdWα_VvdW + φ_Vvoidα_Vvoid + φ_ΔVhα_ΔVh, (7)

where φ_i is the volume fraction of the corresponding protein volume, φ_i = V_i/V_P (see Table 5B).

Table 5 The thermal expansion coefficients α_i (a) and relative contributions φ_iα_i (b) of the different contributions to the partial protein volume of SNase at different temperatures. Errors are standard error estimates

(a) α/10^−3 K^−1
SNase	Solvent excluded volume	Van der Waals volume	Void volume	Hydration contribution to the partial volume	Protein partial volume
T 1 = 300 K, T2 = 360 K	0.094 ± 0.009	0.004 ± 0.003	0.63 ± 0.08	≈0	0.10 ± 0.01
T 1 = 360 K, T2 = 400 K	0.07 ± 0.02	0.005 ± 0.005	0.33 ± 0.13	1.13 ± 0.41	−0.06 ± 0.03

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(b) φiαi/10^−3 K^−1
SNase	Van der Waals volume	Void volume	Hydration contribution to the partial volume	Protein partial volume
T 1 = 300 K, T2 = 360 K	0.00389	0.102	≈0	0.10 ± 0.01
T 1 = 360 K, T2 = 400 K	0.00484	0.0546	−0.151	−0.06 ± 0.03

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As can be seen from Table 5B, for the temperature interval from 300 to 360 K, the main contribution to the expansion coefficient of the protein partial volume is due to the expansion of the void volume of the protein (0.13% K⁻¹). At higher temperatures (360 to 400 K) we observe a competition between a decreasing but still positive contribution of the void volume (0.05% K⁻¹) to the expansion coefficient of the protein and an increasing negative hydration contribution to the partial protein volume (−0.12% K⁻¹). The drastic decrease of the expansion coefficient of the protein partial volume with increasing temperature, which has also been observed experimentally using PPC, can thus be attributed to a decrease of the expansibility of voids with increasing temperature and a decrease of the expansibility contribution of the hydration layer.

Finally, these volumetric data indicate that, because the void volume contribution of the unfolded state’s partial volume is probably negligible, the decrease in the absolute value of the volume change of unfolding, ΔV, with increasing temperature is essentially due to a decrease in the void volume and a more negative hydration contribution to the partial volume of the folded protein. The latter contributions also lead, as we have seen above (Table 5), to a decrease of the coefficient of thermal expansion of the folded protein at higher temperatures.

4. Concluding remarks

To conclude, pressure perturbation calorimetry has been found to be an effective tool to measure the apparent thermal expansion coefficient and volume changes of proteins in solution with very high precision, and valuable information related to volume changes upon unfolding and denaturation of proteins can be obtained. The thermodynamic data determined drastically depend on the interfacial solvent conditions, which influence the conformation as well as the stability of the biopolymer. The large body of results for various chaotropic and kosmotropic cosolvents clearly shows that the cosolvents change markedly not only the stability of a protein, but also its solvation, and hence may also alter the conformation of the protein in its unfolded, denatured state. The magnitude and even the sign of the volume change of unfolding drastically depend on the cosolvent concentration and strongly decrease with increasing temperature. The MD computer simulations revealed that the thermal expansion coefficient of the native protein’s partial volume is largely determined by the expansibility of its internal voids and by a significant hydration contribution, and both contributions decrease with increasing temperature. More generally, the present results demonstrate that the PPC technique provides an exquisitely sensitive handle on measurements of the hydration properties of biomolecules, the understanding of which is a prerequisite for the comprehension of their stability, structure and conformational dynamics. We may expect in the very near future that this method will show its great potential also in studies of proteins involved in more biologically and medically relevant research, such as in studies of amyloidogenesis of proteins.^87–89

Acknowledgements

Financial support from the Deutsche Forschungsgemeinschaft (DFG) and the Fonds der Chemischen Industrie is gratefully acknowledged.

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