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Assessing the sequence specificity in the binding of Co(III) to DNA via a thermodynamic approach.

The interaction specificities of Co(III) with DNA were investigated via consideration of thermodynamic characteristics of the duplex to single strand transition for DNA oligomers incubated in the presence of [Co(NH3)5(OH2)](ClO4)3. It has previously been demonstrated that incubation of the DNA oligomer [(5medC-dG)4]2 with this cobalt complex leads to coordination of the cobalt center to the DNA, presumably at N7 of guanine bases [D. C. Calderone, E. J. Mantilla, M. Hicks, D. H. Huchital, W. R. Murphy, Jr. and R. D. Sheardy, (1995) Biochemistry 34, 13841]. In this report, DNA oligomers of different sequence were incubated with [Co(NH3)5(OH2)](ClO4)3 via protocols developed previously and the treated oligomers were subjected to thermal denaturation for comparison to the untreated oligomers. The DNA oligomers were designed in order to investigate the sequence specificity, if any, in the reaction of the cobalt complex with DNA. The values of Tm, delta HvH, and delta n (the differential ion binding term) obtained from the thermal denaturations were used to assess the sequence specificity of the interaction. For all oligomers, treated or untreated, Tm and delta HvH vary linearly with log [Na+] and hence the value of delta n is a function of the Na+ concentration. The results indicate no significant reaction between the cobalt complex and oligomers possessing isolated -GA- or -CG- sites; however, the thermodynamic characteristics of DNA oligomers possessing either an isolated -GG- site or an isolated -GC- site were altered by the treatment. Atomic absorption studies of the treated oligomers demonstrate that only the DNA oligomers possessing isolated -GG- or -GC- sites bind cobalt. Hence, the changes in the thermodynamic properties of these oligomers are a result of cobalt binding with a remarkable sequence specificity.

Binding Sites↗

Thermodynamics of protein folding: a statistical mechanical study of a small all-beta protein.

The thermodynamic properties of a 46-mer beta-barrel protein model are investigated using Langevin dynamics and the histogram analysis method. By obtaining the density of states distribution and using the methods of statistical mechanics, we are able to identify the thermodynamic transitions for this model protein and characterize the nature of these transitions. Consistent with an earlier study of this model, we find that the transition from a random coil state to a manifold of collapsed but nonnative states is a continuous transition, and the transition from the manifold of collapsed states to the native state is first order-like. However, our calculations indicate that the folding transition is only weakly first order. Most importantly, we are able to characterize the free energy surface of the protein model, as well as the processes of compaction and native structure formation, from a statistical point of view. We also examined the thermodynamic transition state. By combining the earlier kinetic analysis for the same protein model, we provide a more complete description of this model protein and propose possible further modifications of the model to improve its stability and foldability.

Kinetics↗

Derivation of nearest-neighbor properties from data on nucleic acid oligomers. II. Thermodynamic parameters of DNA.RNA hybrids and DNA duplexes.

Using nearest-neighbor models consisting of independent short sequence combinations of nearest neighbors (ISS models), values of thermodynamic parameters for sets of independent sequences are derived from published oligomer data for DNA.RNA hybrids [N. Sugimoto, S. Nakano, M. Katoh, A. Matsumura, H. Nakamuta, T. Ohmichi, M. Yoneyama, and M. Sasaki (1995) Biochemistry, Vol. 34, pp. 11211-11216] and dsDNA duplexes [J. SantaLucia, Jr., H. T. Allawi, and P. A. Seneviratne (1996) Biochemistry, Vol. 35, pp. 3555-3562]. The results are compared with those from models that assign values of thermodynamic parameters to individual nearest neighbors (INN models). Differences in the use of ISS and INN models are also illustrated in an appendix, which shows examples of analyses for values of a fictitious nearest-neighbor property. INN models that include an initiation parameter contain an implicit assumption that combinations of end neighbors have the same value of a property. It is found that combinations of end neighbors (e.g., base pairs neighboring solvent) in oligomers can have significant and different apparent values of thermodynamic properties, so that the assumption inherent in INN models is not always correct. Even though ISS models do not allow the assignment of values to individual nearest neighbors, except for the like neighbors [such as d(AA)/r(UU), etc., for hybrids and d(AA)/d(TT) and d(GG)/d(CC) for DNA duplexes], they do provide physically meaningful values for the like neighbors, for sequence combinations, and for specified combinations of end neighbors.

Base Pairing↗

Thermodynamic analysis of protein interactions with biosensor technology.

A methodology using biosensor technology for combined kinetic and thermodynamic analysis of biomolecular interactions is described. Rate and affinity constants are determined with BIAcore. Thermodynamics parameters, changes in free energy, enthalpy and entropy, are evaluated from equilibrium data and by using rate constants and transition state theory. The methodology using van't Hoff theory gives complementary information to microcalorimetry, since only the direct binding is measured with BIAcore whereas microcalorimetry measures all components, including e.g. hydration effects. Furthermore, BIAcore gives possibilities to gain new information by thermodynamic analysis of the rate constants.

Animals↗

Thermodynamics of the helix-coil transition: Binding of S15 and a hybrid sequence, disulfide stabilized peptide to the S-protein.

Pancreatic ribonuclease A may be cleaved to produce two fragments: the S-peptide (residues 1-20) and the S-protein (residues 21-124). The S-peptide, or a truncated version designated as the S15 peptide (residues 1-15), combines with the S-protein to produce catalytically active complexes. The conformation of these peptides and many of their analogues is predominantly random coil at room temperature; however, they populate a significant fraction of helical form at low temperature under certain solution conditions. Moreover, they adopt a helical conformation when bound to the S-protein. A hybrid sequence, disulfide-stabilized peptide (ApaS-25), designed to stabilize the helical structure of the S-peptide in solution, also combines with the S-protein to yield a catalytically active complex. We have performed high-precision titration microcalorimetric measurements to determine the free energy, enthalpy, entropy, and heat capacity changes for the binding of ApaS-25 to S-protein within the temperature range 5-25 degrees C. The thermodynamic parameters for both the complex formation reactions and the helix-to-coil transition also were calculated, using a structure-based approach, by calculating changes in accessible surface area and using published empirical parameters. A simple thermodynamic model is presented in an attempt to account for the differences between the binding of ApaS-25 and the S-peptide. From this model, the thermodynamic parameters of the helix-to-coil transition of S15 can be calculated.

Amino Acids↗

RF nonlinear interactions in living cells-I: nonequilibrium thermodynamic theory.

Some biological experiments report effects that depend on low frequency modulation of a radiofrequency (RF) carrier. Such effects require nonlinear responses in biological preparations, which we show could be observed with great generality by the unique frequency signatures that would appear in the scattered RF energy. Following Illinger [Illinger (1982): Bioelectromagnetics 3:9-16], we considered a two part physical system. The greater part, dominated by the properties of water, interacts linearly with the RF field and is described by equilibrium thermodynamics. However, another, much smaller part, e.g., certain biological molecules and molecular subgroups, supports nonlinear interactions and is described by nonequilibrium thermodynamics. For example, a nonlinear interaction might result from scattering of RF photons from oscillators located in a region of strong field gradients, such as at membrane surfaces. A second nonlinear mechanism could appear if stress (elastic) waves were launched within the confines of the exposure vessel by RF heating. Amplitude modulation at angular frequency Omega of a carrier wave with angular frequency omega (omega << omega) produces two peaks in elastic stress in the cell structure during each period; that is, there is "full-wave demodulation." As a result of coherent nonlinear charge motion, modulation products could appear at frequencies omega +/- 2 omega and, in general, at omega +/- n 2 omega (n = 1, 2, em leader ) if vibrational harmonics at 2 n omega also are excited. Although in principle microwaves can alter the stability of a thermodynamic system by pumping a chemical transition, the degree of nonlinear coupling required for an observable instability is so great that its probability is effectively zero, unless field intensity is extremely high. A companion paper suggests an extremely sensitive method and the related instrumentation for detection of the spectrum scattered by living cells during exposure to amplitude modulated RF energy.

Animals↗

The thermodynamic contribution of the 5-methyl group of thymine in the two- and three-stranded complexes formed by poly(dU) and poly(dT) with poly(dA).

To assess the thermodynamic contribution of the 5-methyl group of thymine, we have studied the two-stranded helical complexes poly(dA).poly(dU) and poly(dA).poly(dT) and the three-stranded complexes--poly(dA).2poly(dU), poly(dA).poly(dT).poly(dU) and poly(dA).2poly(dT)--by differential scanning calorimetry, and uv optical melting experiments. The thermodynamic quantities associated with the 3 --> 2, 2 --> 1, and 3 --> 1 melting transitions are found to vary with salt concentration and temperature in a more complex manner than commonly believed. The transition temperatures, T(m), are generally not linear in the logarithm of concentration or activity of NaCl. The change in enthalpy and in entropy upon melting varies with salt concentration and temperature, and a change in heat capacity accompanies each transition. The poly(dA).2poly(dU) triple helix is markedly different from poly(dA).2poly(dT) in both its CD spectrum and thermodynamic behavior, while the poly(dA).poly(dT).poly(dU) triple helix resembles poly(dA).2poly(dT) in these properties. In comparing poly(dA).2poly(dT) with either the poly(dA).poly(dT).poly(dU) or the poly(dA).2poly(dU) triplexes, the substitution of thymine for uracil in the third strand results in an enhancement of stability against the 3 --> 2 dissociation of deltadeltaG degrees = -135 +/- 85 cal (mol A)(-1) at 37 degrees C. This represents a doubling of the absolute stability toward dissociation compared to the triplexes with poly(dU) as the third strand. The poly (dA).poly (dT) duplex is more stable than poly(dA).poly(dU) by deltadeltaG degrees = -350 +/- 60 cal (mol base pair)(-1) at 37 degrees C. Poly(dA).poly(dT) has 50% greater stability than poly(dA).poly(dU) as a result of the dT for dU substitution in the duplex.

Adenine↗

Polymyxin B-lipid interactions in Langmuir-Blodgett monolayers of Escherichia coli lipids: a thermodynamic and atomic force microscopy study.

The dramatically increased frequency of antibiotic resistance has led to intensive efforts towards developing new families of antibiotics. Membrane-active antibiotic peptides such as polymyxin B (PxB) hold promise as the next generation of antibiotics, since they rarely spur the evolution of resistance. At low concentrations in the membrane, PxB forms vesicle-vesicle contacts and induces lipid exchange without leakage or fusion, a phenomenon that can explain its specificity towards gram-negative bacteria by contact formation between the two phospholipids interfaces in the periplasmatic space. In this work, the interaction of PxB and the nonantibiotic derivative polymyxin B nonapeptide (PxB-NP) with monolayers of Escherichia coli membrane lipids (ECL) has been studied by thermodynamic and structural methods. PxB inserts itself into ECL monolayers as a conformation that forms intermembrane contacts with vesicles injected underneath, and induces lipid exchange when the monolayer surface pressure is set at 32 mN/m (membrane equivalence pressure) or net transfer vesicle-to-monolayer at lower surface pressures. Thermodynamic analysis of the compression isotherms of mixed monolayers indicates that PxB inserts into the monolayer with an expansion of the mean molecular area, implying that peptide and lipids form nonideal mixtures. At low concentrations, corresponding to the membrane-membrane contact form of PxB, the mixed monolayers present positive excess energy values (deltaGm(Ex)), and atomic force microscopy (AFM) imaging reveals structures of approximately 120-nm diameter that protrude from the lipid surface approximately 0.7 nm. At concentrations of PxB above 4 mol %, thermodynamic analysis gives a very high deltaGm(Ex), corresponding to nonfavorable interactions, and AFM images show round structures of 20-30 nm diameter. PxB-NP behaves in a totally different way, in agreement with its inability to form vesicle-vesicle contacts and its lack of antibiotic effect. These results are discussed in the light of the mechanism of action of PxB on the membrane of gram-negative bacteria.

Anti-Bacterial Agents↗

A molecular thermodynamic approach to predict the secondary structure of homopolypeptides in aqueous systems.

Under physiological conditions, many polypeptide chains spontaneously fold into discrete and tightly packed three-dimensional structures. The folded polypeptide chain conformation is believed to represent a minimum Gibbs energy of the system, governed by the weak interactions that operate between the amino acid residues and between the residues and the solvent. A semiempirical molecular thermodynamic model is proposed to represent the Gibbs energy of folding of aqueous homopolypeptide systems. The model takes into consideration both the entropy contribution and the enthalpy contribution of folding homopolypeptide chains in aqueous solutions. The entropy contribution is derived from the Flory-Huggins expression for the entropy of mixing. It accounts for the entropy loss in folding a random-coiled polypeptide chain into a specific polypeptide conformation. The enthalpy contribution is derived from a molecular segment-based Non-Random Two Liquid (NRTL) local composition model [H. Renon and J. M. Prausnitz (1968) AIChE J., Vol. 14, pp. 135-142; C.-C. Chen and L. B. Evans (1986) AIChE J., Vol. 32, pp. 444-454], which takes into consideration of the residue-residue, residue-solvent, and solvent-solvent binary physical interactions along with the local compositions of amino acid residues in aqueous homopolypeptides. The UNIFAC group contribution method [A. Fredenslund, R. L. Jones, and J. M. Prausnitz (1975) AIChE J., 21, 1086-1099; A. Fredenslund, J. Gmehling, and P. Rasmussen (1977) Vapor-Liquid Equilibrium Using UNIFAC, Elsevier Scientific Publishing Company, Amsterdam], developed originally to estimate the excess Gibbs energy of solutions of small molecules, was used to estimate the NRTL binary interaction parameters. The model yields a hydrophobicity scale for the 20 amino acid side chains, which compares favorably with established scales [Y. Nozaki and C. Tanford (1971) Journal of Biological Chemistry, Vol. 46, pp. 2211-2217; E. B. Leodidis and T. A. Hatton (1990) Journal of Physical Chemistry, Vol. 94, pp. 6411-6420]. In addition, the model generates qualitatively correct thermodynamic constants and it accurately predicts thermodynamically favorable folding of a number of aqueous homopolypeptides from random-coiled states into alpha-helices. The model further facilitates estimation of the Zimm-Bragg helix growth parameter s and the nucleation parameter sigma for amino acid residues [B. H. Zimm and J. K. Bragg (1959) Journal of Chemical Physics, Vol. 31, pp. 526-535]. The calculated values of the two parameters fall into the ranges suggested by Zimm and Bragg.

Models, Molecular↗

Thermodynamic basis of site-specific cooperativity.

Cooperative phenomena in biological macromolecules arise from the interaction of many distinct subsystems, such as structural domains or binding sites. Cooperative properties of the system as a whole, like protein folding or allosteric transitions, are subject to the restrictions imposed by thermodynamic stability. These restrictions, however, do not apply in the case of individual subsystems open to interactions with the rest of the macromolecule. The site-specific properties of such subsystems can be understood in general thermodynamic terms from those of a multicomponent system under particular conditions. The analogy provides a thermodynamic basis for site-specific cooperativity.

Binding Sites↗

Kinetic and thermodynamic characterization of DNA duplex-hairpin interconversion for two DNA decamers: d(CAACGGGTTG) and d(CAACCCGTTG).

The duplex-hairpin interconversion of two DNA decamers, d(CAACGGGTTG) and d(CAACCCGTTG), has been characterized thermodynamically and kinetically by using uv-melting and nmr relaxation methods. Separately, each decamer shows slow exchange between hairpin and duplex conformations. The hairpin conformations have melting points of 47 and 50 degrees C, respectively, and exhibit similar thermodynamic stabilities. The enthalpies of duplex formation, measured by nmr, were found to be very similar (delta HDH = 26 +/- 3 kcal/mole) for both decamers at low salt concentrations (< 50 mM NaCl). However, as the salt concentration was increased the behavior of delta HDH and kinetics is significantly different for each decamer. The d(CAACGGGTTG) decamer forms a duplex containing two central G.G mismatches at high salt and DNA concentration. Based upon the measurement of high interconversion activation energies and a decrease in hairpin formation rate with increasing salt, the interconversion between hairpin and duplex was concluded to proceed by complete strand dissociation. In contrast, the d(CAACCCGTTG) decamer was determined to form a duplex with two centrally located C.C mismatches at pH values less than 6.2, consistent with the formation of a hemiprotonated C+.C mismatch. At pH values greater than 6.4, the hairpin-duplex equilibrium is almost completely shifted toward the hairpin conformation at DNA concentrations of 0.5-7.0 mM and salt concentrations of 10-100 mM. The interconversion of duplex and hairpin conformations was ascertained by means of both kinetic and thermodynamic measurements to proceed by a slightly different mechanism than its complementary decamer. Although the interconversion proceeds by complete strand separation as suggested by high duplex-hairpin interconversion activation enthalpies, the increasing hairpin formation rate with increasing ionic strength as well as the delta HDH dependence on salt indicate that an intermediate internally bulged duplex (no C+.C formation) is stabilized by increasing ionic strength. These data support an interconversion mechanism where an intermediate internally bulged duplex may be the rate limiting step before strand separation.

Base Sequence↗

Esterification by immobilized lipase in solvent-free media: kinetic and thermodynamic arguments.

The aim of this study is to characterize, in solvent-free systems (SFS), the kinetic and thermodynamic performance of batch lipase-catalyzed esterification. SFS are compared to a conventional organic solvent, n-hexane. The esterification of oleic acid with ethanol was chosen as a model reaction. The TABEK (thermodynamic activity-based enzyme kinetics) approach was used to rationally analyze kinetics. Influence of the reaction medium on final conversions was also studied. Several factors, such as initial molar ratio of substrates, reactant availability, initial water content, and quantity of immobilized enzyme, were examined. Special attention was also turned to enzyme stability and reuse after reaction, this last item being a prerequisite in the development of industrial processes. SFS proved to be almost as efficient as n-hexane from a kinetic and thermodynamic point of view and offered a better volumetric production.

Enzymes, Immobilized↗

Thermodynamic analysis of product formation in mesophilic acidogenesis of lactose.

Thermodynamic analysis on the acidogenesis of lactose was performed to evaluate the different acidogenic patterns and mechanisms by using Gibbs free energy calculation. Batch acidogenesis of lactose was investigated by using an enriched culture at 37 degrees C, pH 5.5 and varied substrate levels. In addition to usual acidogenic products, i-butyrate, valerate, i-valerate, caproate, and propanol were also produced at a significant level. Thermodynamic analysis shows that valerate might be formed through the reaction requiring hydrogen as electron donor and consuming of propionate and carbon dioxide. Caproate was most likely produced directly from butyrate, hydrogen, and carbon dioxide. The minimum amount of Gibbs free energies needed to sustain isomerization of butyrate and valerate were approximately 5.7-5.8 and 4.5-4.6 kJ/mol, respectively. Propanol was produced from acetate, hydrogen, and carbon dioxide with a minimum amount of Gibbs free energy of 41.8-42.0 kJ/mol. Formation of butanol was controlled more by substrate level or population dynamics than by thermodynamics.

Alcohols↗

How reliable are thermodynamic feasibility statements of biochemical pathways?

The driving force for organo- or lithotrophic growth as well as for each step in the metabolic network is the Gibbs reaction energy. For each enzymatic step it must be negative. Thermodynamics contributes therefore to the in-silico description of living systems. It may be used for assessing the feasibility of a given pathway because it provides a further constraint for those pathways which are feasible from the point of view of mass balance calculations (metabolic flux analysis) and the genetic potential of an organism. However, when this constraint was applied to lactic acid fermentation according to a method proposed by Mavrovouniotis (1993a, ISMB 93:273-283) it turned out that an unrealistically wide metabolite concentration range had to be assumed to make this well-known glycolytic pathway thermodynamically feasible. During a search for the reasons of this surprising result the insufficient consideration of the activity coefficients was identified as main cause. However, it is shown in the present contribution that the influence of the activity coefficients on Gibbs reaction energy can be easily taken into account based on the intracellular ionic strength. The uncertainty of the tabulated equilibrium constants and of the apparent standard Gibbs energies derived from them was found to be the second most important reason for the erroneous result of the feasibility analysis. Deviations of intracellular pH from the standard value and bad estimations of currency metabolites, e.g., NAD(+) and NADH, were found to be of lesser importance but not negligible. The pH dependency of Gibbs reaction enthalpy was proved to be easily taken into account. Therefore, the application of thermodynamics for a better in-silico prediction of the behavior of living cell factories calls predominantly for better equilibrium data determined under well defined conditions and also for a more detailed knowledge about the intracellular ionic strength and pH value.

Cell Physiological Phenomena↗

Engineering of protein thermodynamic, kinetic, and colloidal stability: Chemical Glycosylation with monofunctionally activated glycans.

In this work we establish the relationship between chemical glycosylation and protein thermodynamic, kinetic, and colloidal stability. While there have been reports in the literature that chemical glycosylation modulates protein stability, mechanistic details still remain uncertain. To address this issue, we designed and coupled monofunctional activated glycans (lactose and dextran) to the model protein alpha-chymotrypsin (alpha-CT). This resulted in a series of glycoconjugates with variations in the glycan size and degree of glycosylation. Thermodynamic unfolding, thermal inactivation, and temperature-induced aggregation experiments revealed that chemical glycosylation increased protein thermodynamic (Delta G(25 degrees C)), kinetic (t(1/2)(45 degrees C)), and colloidal stability. These results highlight the potential of chemical glycosylation with monofunctional activated glycans as a technology for increasing the long-term stability of liquid protein formulations for industrial and biotherapeutic applications.

Chemical Engineering↗

Electrostatic effects on the thermodynamics of protonation of reduced plastocyanin.

The L12E, L12K, Q88E, and Q88K variants of spinach plastocyanin have been electrochemically investigated. The effects of insertion of net charges near the metal site on the thermodynamics of protonation and detachment from the copper(I) ion of the His87 ligand have been evaluated. The mutation-induced changes in transition enthalpy cannot be explained by electrostatic considerations. The existence of enthalpy/entropy (H/S) compensation within the protein series indicates that solvent-reorganization effects control the differences in transition thermodynamics. Once these compensating contributions are factorized out, the resulting modest differences in transition enthalpies turn out to be those that can be expected on purely electrostatic grounds. Therefore, this work shows that the acid transition in cupredoxins involves a reorganization of the H-bonding network within the hydration sphere of the molecule in the proximity of the metal center that dominates the observed transition thermodynamics and masks the differences that are due to protein-based effects.

Amino Acid Substitution↗

Structural basis of light chain amyloidogenicity: comparison of the thermodynamic properties, fibrillogenic potential and tertiary structural features of four Vlambda6 proteins.

Primary (AL) amyloidosis results from the pathologic deposition of monoclonal light chains as amyloid fibrils. Studies of recombinant-derived variable region (VL) fragments of these proteins have shown an inverse relationship between thermodynamic stability and fibrillogenic potential. Further, ionic interactions within the VL domain were predicted to influence the kinetics of light chain fibrillogenicity, as evidenced from our analyses of a relatively stable Vlambda6 protein (Jto) with a long range electrostatic interaction between Asp and Arg side chains at position 29 and 68, respectively, and an unstable, highly fibrillogenic Vlambda6 protein (Wil) that had neutral amino acids at these locations. To test this hypothesis, we have generated two Jto-related mutants designed to disrupt the interaction between Asp 29 and Arg 68 (JtoD29A and JtoR68S). Although the thermodynamic stabilities of unfolding for these two molecules were identical, they exhibited very different kinetics of fibril formation: the rate of JtoD29A fibrillogenesis was slow and comparable to the parent molecule, whereas that of JtoR68S was significantly faster. High-resolution X-ray diffraction analyses of crystals prepared from the two mutants having the same space group and unit cell dimensions revealed no significant main-chain conformational changes. However, several notable side-chain alterations were observed in JtoR68S, as compared with JtoD29A, that resulted in the solvent exposure of a greater hydrophobic surface and modifications in the electrostatic potential surface. We posit that these differences contributed to the enhanced fibrillogenic potential of the Arg 68 mutant, since both Jto mutants lacked the intrachain ionic interaction and were equivalently unstable. The information gleaned from our studies has provided insight into structural parameters that in addition to overall thermodynamic stability, contribute to the fibril forming propensity of immunoglobulin light chains.

Amino Acid Sequence↗

Phase equilibria and thermodynamics of p-hydroxybenzoic acid.

The prevalence of phases and associated solubilities of p-hydroxybenzoic acid have been investigated in methanol, acetonitrile, acetic acid, acetone, water, and ethyl acetate at temperatures from 10 to 50 degrees C. Thermodynamic data was acquired through determination of van't Hoff enthalpy of solution, enthalpy of fusion, and melting temperature. Indications of polymorphic enantiotropy were found primarily through solubility analysis and FTIR-ATR. A comprehensive thermodynamic investigation disclosed correlation between the van't Hoff enthalpy of solution and the solubility in different solvents. A higher solubility is linked to a lower van't Hoff enthalpy of solution. A thermodynamic analysis to discriminate between different solid phases is presented.

Acetates↗