Comparative study of the stability of poplar plastocyanin isoforms

The stability of the two isoforms of poplar plastocyanin (PCa and PCb) was studied with differential scanning calorimetry (DSC) technique. It was shown that the thermal unfolding of both isoforms is an irreversible process with two endothermic and one exothermic peaks. The melting temperature of PCb was found to be 1.3+/-0.2 K degrees higher than of PCa, which indicates that PCb is more stable. The enthalpy of unfolding was estimated from the heat capacity curves and was found to be significantly higher for PCb at salt concentration I=0.1 M. In addition, PCb unfolding enthalpy and melting temperature are much more sensitive to the changes in the salt concentration as found in the experiments done at different ionic strength. The experiments were complemented with numerical calculations. The salt effect on the stability was modeled using the X-ray structure of PCa and a homology modeled structure of PCb. It was found, in agreement with the experimental data, that the stability of PCb changes by 4.7 kJ more than PCa, as the salt concentration increases from zero to 0.1 M. Thus, the differences in only 12 amino acid positions between "a" and "b" isoforms result in a measurable difference in the folding enthalpy and a significant difference in the salt dependence. The optimization of the electrostatic energies of PCa and PCb were studied and it was shown that PCb is better electrostatically optimized.     

Effects of Potassium Chloride and Sodium Chloride on the Thermal Properties of Gellan Gum Gels

The exothermic and endothermic peaks in cooling and heating curves of differential scanning calorimetry (DSC) for gellan gum gels without and with potassium chloride and sodium chloride were analyzed. The gelling and melting temperatures shifted to higher temperatures with increasing gellan and salt concentration in the concentration range of gellan from 0.3 to 2.0% (w/w). The exothermic and endothermic enthalpy increased with increasing gellan and salt concentrations. Cooling DSC curves showed one exothermic peak for samples with salts and at low gellan concentration. Heating DSC curves showed many peaks for all samples except 0.3% (w/w) gellan gum gels. The sol-gel transition of samples was examined numerically by using a zipper model approach. The introduction of cations increases the number of junction zones or zippers and decreases the rotational freedom of parallel links. This makes the structure of junction zones more heat resistant, and increases the elastic modulus of the gel.     

Fine structures in denaturation curves of bacteriophage lambda DNA. Their relation to the intramolecular heterogeneity in base compositon.

Precise recording of polyphasic optical melting curves was carried out for three kinds of bacteriophage lambda DNA differing in length (lambdac1857s7, lambdacIb2 and lambdacIb2b5). Each of denaturation steps in melting profiles was characterized by two parameters, the melting temperature and the relative size. Any difference in fine structures in melting profiles was not recognized between the intact lambdacI857s7DNA and the DNA fragmented into halves. The change in fine structures in melting profiles caused by the deletions of the b2 and b5 region agreed qualitatively well with the prediction based on the physical and the genetical maps of phage lambda chromosome. The combined results indicate that, first, the well-known linear relationship between melting temperature and G+C content may apply also to each of denaturation steps in polyphasic melting curves due to heterogeneity of nucleotide distribution in a single DNA species, and, second, the effect of molecular ends on melting fine structures can be neglected at moderate salt concentration (0.01 M less than or equal to Na+ less than or equal to 0.2 M) for such a high molecular weight DNA. The heterogeneous distribution of nucleotides was derived for lambdaDNA and for its b2 and b5 regions.     

Relationship between helix-coil transition and gene organization of ColE1 plasmid DNA. Differential scanning calorimetric and theoretical studies

Differential scanning calorimetry (DSC) was carried out to analyze the transition of helix to coil state of DNA, using ColE1 DNA molecules digested with EcoRI. The DSC curves showed multimodal transition, consisting of nine to 11 peaks over a temperature range, depending on the ionic strength of the DNA solution. These DSC curves were essentially in good agreement with the optical melting curves of ColE1 DNA. The theoretical melting profiles of ColE1 DNA were predicted from calculations based on the helix-coil transition theory and the nucleotide sequence of the DNA. These profiles resembled the DSC curves and made it possible to assign the peaks seen in the DSC curves to the helix-coil transition of particular regions of the nucleotide sequence of ColE1. The helix-coil transition of each of the small genes gave rise to a single peak in the DSC curve, while the helix-coil transition of large genes contributed to two or more peaks in the DSC curve. This multimodal transition within a single coding region might correspond to the melting of individual segments encoding the different domains of the proteins. The helix-coil transition at the specific sites including ori, the origin of replication of ColE1, was also found to occur in a particular temperature range. DSC, a simple method, is thus useful for analyzing the multimodal helix-coil transition of DNA, and for providing information on the genetic organization of DNA.     

Conformational analysis and stability of collagen peptides by CD and by 1H- and 13C-NMR spectroscopies

Four small type I collagen CNBr peptides containing complete natural sequences were purified from bovine skin and investigated by CD and 1H- and 13C-nmr spectroscopies to obtain information concerning their conformation and thermal stability. CD showed that a triple helix was formed at 10 degrees C in acidic aqueous solution by peptide alpha l(I) CB2 only, and to lesser extent, by alpha 1(I) CB4, whereas peptides alpha 1(I) CB5 and alpha 2(I) CB2 remained unstructured. Analytical gel filtration confirmed that peptides alpha 1(I) CB2 and alpha 1(I) CB4 only were able to form trimeric species at temperature between 14 and 20 degrees C, and indicated that the monomer = trimer equilibrium was influenced by the chaotropic nature of the salt present in the eluent, by its concentration, and by temperature variations. CD measurements at increasing temperatures showed that alpha 1(I) CB2 was less stable than its synthetic counterpart due to incomplete prolyl hydroxylation of the preparation from the natural source. 1H- and 13C-nmr spectra acquired in the temperature range 0-47 and 0-27 degrees C, respectively, indicated that with decreasing temperature the most abundant from of alpha 1(I) CB2 was in slow exchange with an assembled form, characterized by broad lines, as expected for the triple-helical conformation. A large number of trimer cross peaks was observed both in the proton and carbon spectra, and these were most likely due to the nonequivalence of the environments of the three chains in the triple helix. This nonequivalence may have implications for the aggregation of collagen molecules and for collagen binding to other molecules. The thermal transition from trimer to monomer was also monitored by 1H-nmr following the change in area of the signal belonging to one of the two beta protons of the C-terminal homoserine. The unfolding process was found to be fully reversible with a melting temperature of 13.4 degrees C, in agreement with CD results. The qualitative superposition of the melting curves obtained by CD for the peptide bond characteristics and by nmr for a side chain suggests that triple-helical backbone and side chains constitute a single unit.     

The effect of low ionic strength on the radiation chemistry and physical properties of calf thymus DNA

Studies of ultraviolet and circular dichroism spectra of aqueous solutions of calf thymus (CT) DNA confirm the tendency of DNA to change conformation at low ionic strength. The qualitative shape and transition width of 260 nm melting curves below 1 mM NaCl differed significantly from those previously published for DNA solutions containing 1 mM NaCl and above. Neutral aqueous solutions of CT DNA at low ionic strengths (0.1 mM-10 mM NaCl) were irradiated with low doses of gamma-rays. The melting temperature, Tm, of irradiated DNA samples increased below 1 mM NaCl suggesting interstrand crosslinking of the denatured DNA or formation of regions of more thermally stable DNA conformation. The magnitudes of these radiation responses were found to be a function of the time elapsed between salt concentration changes and irradiation as well as time after irradiation. These results are consistent with the hypothesis that the purine and pyrimidine base chromophores in double stranded DNA are sheltered from radical attack by the sugar phosphate backbone. Low dose radiation studies (0.8-8.0 Gy) of CT DNA in 1 mM NaCl and below showed a split dose and dose rate dependence for the sample melting curves.     

Salt effects on the denaturation of DNA. IV. A calorimetric study of the helix-coil conversion of the alternating copolymer poly[d(A-T)].

The enthalpy deltaH, entropy deltaS, and the temperature Tm of the conformational transition of poly[d (A-T)] from the ordered to the randomly oriented state have been determined at pH 6.8 with the help of an adiabatic differential scanning calorimeter in Na2SO4 solutions of increasing ionic strength. Spectrophotometric denaturation experiments supplemented the calorimetric measurements. All thermodynamic parameters were found to vary strongly with salt concentration: both deltaH and Tm increase linearly with the logarithm of the mean molal activity alpha plus or minus of Na2SO4. However, whereas the dependence of Tm on salt activity remains linear over the entire salt concentration range employed deltaH decreases abruptly in the most concentrated Na2SO4 solutions. The entropy of melting changes with salt concentration in a pattern similar to that displayed by deltaH. The data on deltaH as well as data derived from the maximum slopes of the calorimetric heat denaturation curves were used to calculate the cooperative length Lh, the stacking free energy epsilon, and the cooperativity parameter sigma of poly[d(A-T)] as a function of ionic strength. Lh decreases with increasing salt concentration whereas sigma increases. Epsilon assumes more positive values with increasing salt molality. These changes then are in agreement with the generally held belief that an increase in salt concentration leads to an increase in the "loop" content of the copolymer.     

Thermodynamic characterization of cytochrome c at low pH. Observation of the molten globule state and of the cold denaturation process.

Several reports have pointed out the existence of intermediate states (both kinetic and equilibrium intermediate) between the native and the denatured states. The molten globule state, a compact intermediate state in which the secondary structure is formed but the tertiary structure fluctuates considerably, is currently being studied intensively because of its possible implication in the folding process of several proteins. We have examined the thermal stability of horse cytochrome c at low pH between 2.0 and 3.2 and different potassium chloride concentrations by absorbance of the Soret band, far and near-ultraviolet circular dichroism (u.v. c.d.) and tryptophan fluorescence using a multidimensional spectrophotometer. The concentration of potassium chloride ranged from 0 M to 0.5 M. The experimental thermal denaturation curves show that: (1) the helical content of cytochrome c remains stable at higher temperature when the concentration of salt is increased; whereas (2) the extent of ordering of the tertiary structure is weakly dependent on salt concentration; and (3) for cytochrome c, the stabilization of the molten globule state is induced by the binding of anions. Other salts such as NaCl, LiCl, potassium ferricyanide (K3Fe(CN)6) and Na2SO4 may also be used to stabilize the molten globule state. The thermodynamic analysis of the denaturation curves of c.d. at 222 nm and c.d. at 282 nm shows that, whereas a two-state (native and denatured) transition is observed at low-salt concentration, the far and near-u.v. c.d. melting curves of cytochrome c do not coincide with each other at high-salt concentration, and a minimum of three different thermodynamic states (IIb, intermediate or IIc, and denatured) is necessary to achieve a sufficient analysis. The intermediate state (called IIc) is attributed to the molten globule state because of its high secondary structure content and the absence of tertiary structure. Therefore, at low pH, cytochrome c is present in at least four states (native, IIb, IIc and denatured) depending on the salt concentration and temperature. The thermodynamic parameters, i.e. the Gibbs free energy differences (delta G), the enthalpy differences (delta H), the midpoint temperatures (Tm) of the transition (IIb in equilibrium intermediate (IIc in equilibrium denatured) are determined. We also give estimates of the heat capacity differences (delta Cp) from the temperature dependence of the enthalpy differences. The enthalpy change and the heat capacity difference of the IIc in equilibrium denatured transition are non-zero. The number of charges (protons or chloride anions) released upon transitions are determined by analysing the pH and chloride anion concentration dependence of the Gibbs free energy.(ABSTRACT TRUNCATED AT 400 WORDS)     

Thermal unfolding of tetrameric melittin: comparison with the molten globule state of cytochrome c.

Whereas melittin at micromolar concentrations is unfolded under conditions of low salt at neutral pH, it transforms to a tetrameric alpha-helical structure under several conditions, such as high peptide concentration, high anion concentration, or alkaline pH. The anion- and pH-dependent stabilization of the tetrameric structure is similar to that of the molten globule state of several acid-denatured proteins, suggesting that tetrameric melittin might be a state similar to the molten globule state. To test this possibility, we studied the thermal unfolding of tetrameric melittin using far-UV CD and differential scanning calorimetry. The latter technique revealed a broad but distinct heat absorption peak. The heat absorption curves were consistent with the unfolding transition observed by CD and were explainable by a 2-state transition mechanism between the tetrameric alpha-helical state and the monomeric unfolded state. From the peptide or salt-concentration dependence of unfolding, the heat capacity change upon unfolding was estimated to be 5 kJ (mol of tetramer)-1 K-1 at 30 degrees C and decreased with increasing temperature. The observed change in heat capacity was much smaller than that predicted from the crystallographic structure (9.2 kJ (mol of tetramer)-1 K-1), suggesting that the hydrophobic residues of tetrameric melittin in solution are exposed in comparison with the crystallographic structure. However, the results also indicate that the structure is more ordered than that of a typical molten globule state. We consider that the conformation is intermediate between the molten globule state and the native state of globular proteins.     

Comparative differential scanning calorimetric analysis of vegetable oils: I. Effects of heating rate variation

The melting curves of 11 vegetable oils have been characterised. Vegetable oil samples that were cooled at a constant rate (5 degrees C/min) from the melt showed between one and seven melting endotherms upon heating at four different heating rates (1, 5, 10 and 20 degrees C/min) in a differential scanning calorimeter (DSC). Triacylglycerol (TAG) profiles and iodine value analyses were used to complement the DSC data. Generally, the melting transition temperature shifted to higher values with increased rates of heating. The breadth of the melting endotherm and the area under the melting peak also increased with increasing heating rate. Although the number of endothermic peaks was dependent on heating rate, the melting curves of the oil samples were not straightforward in that there was no correlation between the number of endothermic peaks and heating rates. Multiple melting behaviour in DSC experiments with different heating rates could be explained by: (1) the melting of TAG populations with different melting points; and (2) TAG crystal reorganisation effects. On the basis of the corollary results obtained, vegetable oils and fats may be distinguished from their offset-temperature (Toff) values in the DSC melting curves. The results showed that Toff values of all oil samples were significantly (p < 0.01) different in the melting curves scanned at four different scanning rates. These calorimetric results indicate that DSC is a valuable technique for studying vegetable oils.     

High resolution thermal denaturation analyses of small sequenced DNA restriction fragments containing Escherichia coli lactose genetic control loci.

Differential melting curves are reported for four DNA restriction fragments (789, 301, 203, and 95 base pairs in length) spanning the lactose control region. All but the smallest melt with two or more subtransitions. Maps are proposed which identify the positions of regions of different thermal stability in the sequences. The sizes of regions comprising subtransitions range from 60 to 200 base pairs. An analysis is made of the cooperativity exhibited between regions in the sequence. The effect on the shape of the differential melting curves of Na+ between 10 mM and 0.5 M as well as that of Mg2+ and glycerol has been determined. An 81-bp-long sequence of unusual thermal stability occurs at the lactose promoter. Its TM change, resulting from the above change in salt concentration, is out of step by 1.5 degree C with the neighboring DNA sequence. The potential biological significance of this behavior is discussed.     

The interaction of DNA with sperm-specific histones of the H1 family

We have studied the interactions of DNA with sperm-specific histones of the H1 family of sea urchin Strongylocentrotus intermedius, sea starfish Aphelasterias japonica and bivalve mollusk Chlamis islandicus using circular dichroism and DNA melting analysis. It was shown that echinoderm's sperm H1 protein has additional alpha-helical domains in its C-terminus and it demonstrates stronger DNA compaction. The differential melting curves of DNA-protein complexes have two peaks. The low temperature peak characterized the melting temperature of free DNA within the complex. The higher temperature peak characterizes the melting temperature of DNA bond to protein. DNA is found to be in the most stable state in the complexes with mollusk sperm H1 protein.     

Study of heat denaturation of human serum albumin in water-alcohol and water-salt solutions in the presence of organic ligands

The method of differential scanning microcalorimetry was used to show a decrease in heat stability of serum albumin in the presence of aliphatic alcohols. In aqueous-alcohol media, the melting temperature, denaturation transition enthalpy were decreased, and the protein intermolecular aggregation enhanced. When the alcohol concentration in aqueous solution was elevated, the number of epsilon-amino groups of lysine residues in human serum albumin exposed to the solvent rose from 6-7 in aqueous solution to maximum 20 groups in the aqueous-alcohol solution, respectively. The elevation of ionic strength also induced an increase in the number of exposed lysine residues and was accompanied by an enhancement of protein aggregation. The modification of six amino groups by pyridoxal phosphate or three by glucose in the initial albumin stabilized the protein incubated at 65 degrees-70 degrees C both in the aqueous-alcohol media. At the given concentration and temperature the native protein was denatured and fully aggregated. Aliphatic alcohols displaced fatty acids from the binding sites on the molecule of serum albumin, which resulted in a change in the number of peaks of the melting curve.     

Mechanochemical study of NaDNA and NaDNA-netropsin fibers in ethanol-water and trifluoroethanol-water solutions.

Highly oriented calf-thymus NaDNA fibers, prepared by a wet-spinning method, were complexed with netropsin in ethanol-water and trifluoroethanol (TFE)-water solutions. The relative fiber length, L/L0, was measured at room temperature as a function of ethanol or TFE concentration to obtain information on the B-A conformational transition. The B-A transition point and transition cooperativity of the fibers were calculated. The binding of netropsin to NaDNA fibers was found to stabilize B form and to displace the B-A transition to higher ethanol concentration, as indicated by its elongational effect on the fiber bundles. An increased salt concentration was found to reduce netropsin binding. In netropsin-free ethanol solution, the dissociation of bound netropsin from the DNA fibers was observable. Pure B-NaDNA fibers were found to be more stable in TFE solution than in ethanol solution. This was interpreted as being due to a different steric factor and a larger polarity of TFE compared with ethanol, resulting in its smaller capacity to reduce the water activity and dielectric constant of the medium in the immediate vicinity of DNA fibers. Therefore, the effect of netropsin binding on the B-A transition of NaDNA fibers became less obvious in TFE solution. In another series of experiments, L/L0 was measured as a function of temperature to obtain information on the helix-coil transition, or melting, as well as the B-A transition of NaDNA and NaDNA-netropsin fibers. The melting temperature and helix-coil transition width were calculated from the melting curves. A phenomenological approach was used to describe the melting behavior of the fibers in and around the B-A transition region. The effect of netropsin on the melting of DNA fibers was attributed mainly to the stabilization of B-DNA and to a higher melting cooperativity in the B-DNA region.     

Study of DNA melting in the region of the inversion of relative stability of AT and GC pairs]

Systematic data on the dependence of the melting curve parameters of DNA from different organisms on the concentration of salt (C2H5)5NBr have been obtained. The melting curves were studied by spectrophotometric as well as by microcalorimetric methods. The DNA melting range width is shown to pass through the minimum value delta0T = 0.6 +/- 0.1 degrees at the point of inversion of relative stability of AT and GC pairs that corresponds to the concentration of (C2H5)4NBr equal to 2.9 +/- 0.1 M. This concentration, as well as the value of delta0T, are the same for different DNA's of common chemical structure. The T2 and T4 DNA containing hydroxymethylated and glucosylated cytosine residues show an anomalous behaviour. The enthalpy of melting falls very slowly as the salt concentration increases. The possible causes of the observed value of delta0T are discussed. A conclusion is drawn that the main factor which governs the DNA melting process in the region of inversion of the relative stability of AT and GC pairs is the heterogeneity of stacking interaction between different base pairs.     

Volume changes accompanying the thermal denaturation of deoxyribonucleic acid. I. Denaturation at neutral pH

Dilatometric measurements were made to determine the change in apparent specific volume φ of DNA resulting from thermal denaturation in neutral solution, φ increased continuously with temperature in the range 10–85°C. No deviations from a monotonically rising curve were observed in the φ versus temperature profile in the region of the melting temperature. The results are interpreted in terms of a partial loss of the preferentially bound DNA hydration shell. The nature of the well known buoyant density difference between native and denatured DNA was investigated by evaluating the densities in a series of cesium salt gradients at constant temperature. Extrapolation of the results to zero water activity indicates that the partial specific volumes of anhydrous native and denatured DNA are equal. The density difference at nonzero water activities is attributed to decreased hydration in the denatured state. The absence of a related change in φ accompanying the denaturation in the dilatometric experiments suggests that the probable volume change associated with loss of bound water during denaturation is accompanied by other compensatory volume effects. The possible nature of these volume effects is discussed.     

Melting of local ordered structures in yeast 5S ribosomal RNA in aqueous salts.

Equilibrium and kinetics of thermal melting of yeast 5S ribosomal RNA in aqueous NaCl with or without Mg2+ were investigated by differential thermal melting and temperature jump methods. Two peaks (1 and 2) and a shoulder were observed in each of melting curves at ionic strength I=0.002-0.5 and linearity between each of melting temperatures T1m and T2m and log I was found at I=0.01-0.5 in the Mg2+-free solution. The local structures were found to be stabilized considerably by Mg2+. The temperature jump measurements gave the kinetic melting curve of the structure 1 at I=0.03 without Mg2+ or with 0.5 mM Mg2+. The kinetic Tm coincided well with the corresponding static Tm. For the structure 1, various parameters were calculated from the kinetic data, which indicated a double helical character of the structure 1. In terms of the values of Tm, G-C content, and enthalpy change of the transition of the structure 1 or 2, appropriateness of each of the secondary structure models of eukaryotic 5S RNA proposed previously was discussed.     

Differential scanning calorimetric and theoretical studies of ColE1 DNA

The differential scanning calorimetry (DSC) of plasmid ColE1 DNA was carried out. The DSC curve under the solvent condition of 1.0 X SSC buffer gave eleven clear peaks over the temperature range of 83 to 98 degrees C. The DSC curves obtained here were essentially in good agreement with the optical melting curves of ColE1 DNA reported previously. The theoretical melting profiles of ColE1 DNA calculated from its entire nucleotide sequence showed a good agreement with the DSC curves. The theoretical analysis made by constructing the thermal stability map showed that there was the positional correlation between the boundaries of the cooperatively melting regions and the ends of the protein coding regions of genes of ColE1. It was shown that the helix-coil transition of many of the small genes had a single cooperatively melting region. However, the large genes such as cea and mob3 had two or more cooperatively melting regions. It was suggested that this is closely related to the domain structures of the proteins encoded by such genes.     

Comparison of the effects of NaCl on the thermotropic behaviour of sn-1' and sn-3' stereoisomers of 1,2-dimyristoyl-sn-glycero-3-phosphatidylglycerol

The phase behaviour of liposomes of 1,2-dimyristoyl-sn-glycero-3-phosphatidyl-sn-1'-glycerol (1'-DMPG) and the corresponding sn-3' stereoisomer (3'-DMPG) were studied by DSC as a function of NaCl concentration. The melting of the metastable gel phase to the liquid-crystalline phase was similar for both lipids. However, in the presence of salt and at 6 degrees C (T less than Tp) the gel phase of both stereoisomers of DMPG was shown to be metastable and a new phase nominated here as the highly crystalline phase was formed as the stable state. However, significant differences in the formation and melting of the highly crystalline phase were evident between the two polar headgroup stereoisomers. For 3'-DMPG in the presence of 300 mM NaCl the melting enthalpy of this phase is approx. 82 kJ/mol and the transition temperature about 11 degrees higher (at 33.6 degrees C) than for the gel to liquid-crystalline phase transition (25 kJ/mol at 23.0 degrees C). In the presence of 0.15-1.2 M NaCl at 6 to 10 degrees C the formation of the highly crystalline phase of 3'-DMPG is complete within 2 to 5 days, increasing [NaCl] facilitates the rate. For a 1:1 mixture of 1'- and 3'-DMPG the formation of the highly crystalline phase requires several weeks and melts at about 20 degrees higher than the gel phase (at approx. 40 degrees C). For 1'-DMPG partial conversion into the highly crystalline phase requires several months. For 3'-DMPG several intermediate phases appeared as endothermic peaks between the main phase transition temperature and the melting temperature of the highly crystalline phase. In contrast, for 1'-DMPG and the 1:1 mixture the subgel phase appears to be the only metastable intermediate phase. Different monovalent cations differ in their effect on the metastable behaviour.     

On the application of polyelectrolyte “limiting laws” to the helix-coil transition of DNA. I. Excess univalent cations

A general theory of polyelectrolyte solutions is here used to calculate the differences in Gibbs free energy, enthalpy, and entropy between the coil and helix forms of DNA at any temperature and salt concentration. The salt has univalent cations and is assumed present in excess over the base concentration. The results are restricted to sufficiently dilute solutions. It is shown that the salt concentrations effect is entirely entropic in origin. When applied to the melting temperature, the calculations yield a relation between the enthalpy difference at the melting temperature and the slope of the plot of melting temperature vs. the logarithm of the salt concentration. In accord with observation, both the Gibbs free energy difference at any fixed temperature and the melting temperature are predicted to be linear functions of the log of the salt concentration. However, the theory is not in quantitative agreement with enthalpy data. Data on various colligative and transport properties of both helix and coil forms are reviewed in the text and in Appendix B, and good agreement is found with theory for both forms. No attempt is made to explain why the theory is quantitative for these properties but not for heat measurements. Finally, in Appendix A, an approximate calculation is made of the free energy contributions due to ionic effects not associated with the salt concentration.