Effects of hydrated water on protein unfolding

The conformational stability of a protein in aqueous solution is described in terms of the thermodynamic properties such as unfolding Gibbs free energy, which is the difference in the free energy (Gibbs function) between the native and random conformations in solution. The properties are composed of two contributions, one from enthalpy due to intramolecular interactions among constituent atoms and chain entropy of the backbone and side chains, and the other from the hydrated water around a protein molecule. The hydration free energy and enthalpy at a given temperature for a protein of known three-dimensional structure can be calculated from the accessible surface areas of constituent atoms according to a method developed recently. Since the hydration free energy and enthalpy for random conformations are computed from those for an extended conformation, the thermodynamic properties of unfolding are evaluated quantitatively. The evaluated hydration properties for proteins of known transition temperature (Tm) and unfolding enthalpy (delta Hm) show an approximately linear dependence on the number of constituent heavy atoms. Since the unfolding free energy is zero at Tm, the enthalpy originating from interatomic interactions of a polypeptide chain and the chain entropy are evaluated from an experimental value of delta Hm and computed properties due to the hydrated water around the molecule at Tm. The chain enthalpy and entropy thus estimated are largely compensated by the hydration enthalpy and entropy, respectively, making the unfolding free energy and enthalpy relatively small. The computed temperature dependences of the unfolding free energy and enthalpy for RNase A, T4 lysozyme, and myoglobin showed a good agreement with the experimental ones.(ABSTRACT TRUNCATED AT 250 WORDS)     

Elucidating protein thermodynamics from the three-dimensional structure of the native state using network rigidity

Given the three-dimensional structure of a protein, its thermodynamic properties are calculated using a recently introduced distance constraint model (DCM) within a mean-field treatment. The DCM is constructed from a free energy decomposition that partitions microscopic interactions into a variety of constraint types, i.e., covalent bonds, salt-bridges, hydrogen-bonds, and torsional-forces, each associated with an enthalpy and entropy contribution. A Gibbs ensemble of accessible microstates is defined by a set of topologically distinct mechanical frameworks generated by perturbing away from the native constraint topology. The total enthalpy of a given framework is calculated as a linear sum of enthalpy components over all constraints present. Total entropy is generally a nonadditive property of free energy decompositions. Here, we calculate total entropy as a linear sum of entropy components over a set of independent constraints determined by a graph algorithm that builds up a mechanical framework one constraint at a time, placing constraints with lower entropy before those with greater entropy. This procedure provides a natural mechanism for enthalpy-entropy compensation. A minimal DCM with five phenomenological parameters is found to capture the essential physics relating thermodynamic response to network rigidity. Moreover, two parameters are fixed by simultaneously fitting to heat capacity curves for histidine binding protein and ubiquitin at five different pH conditions. The three free parameter DCM provides a quantitative characterization of conformational flexibility consistent with thermodynamic stability. It is found that native hydrogen bond topology provides a key signature in governing molecular cooperativity and the folding-unfolding transition.     

Comparative thermodynamic analysis of DNA--protein interactions using surface plasmon resonance and fluorescence correlation spectroscopy

We report a kinetic and thermodynamic analysis of interactions between ssDNA and replication protein A (RPA) using surface plasmon resonance (SPR) and fluorescence correlation spectroscopy (FCS) at variable temperature. The two methods yield different values for the Gibbs free energy but nearly the same value for the reaction enthalpy of ssDNA-RPA complex formation. The Gibbs free energy was determined by SPR and FCS to be -62.6 and -54.7 kJ/mol, respectively. The values for the reaction enthalpy are -64.4 and -66.5 kJ/mol. It is concluded that the difference in Gibbs free energy measured by the two methods is due to different reaction entropies. The entropic contribution to the free energy at 25 degrees C is -1.8 kJ/mol for SPR and -11.8 kJ/mol for FCS. In SPR, the reaction is restricted to two dimensions because of immobilization of the DNA molecules to the sensor surface. In contrast, FCS is able to follow complex formation without spatial restrictions. In consequence, the reaction entropy determined from SPR experiments is lower than for FCS experiments.     

Thermodynamic studies on the interaction between sodium n-dodecyl sulphate and histone H2B

The thermodynamic parameters for the interaction of the anionic detergent sodium n-dodecyl sulphate (SDS) with H2B at pH 3.2, 6.4 and 10 have been measured at 27 degrees C and 37 degrees C by equilibrium dialysis to determine the Gibbs energies of detergent binding. The data have been used to obtain the enthalpy of interaction from the temperature dependence of the equilibrium constants from the Van't Hoff relation. The enthalpy of interaction between H2B and SDS is endothermic at pH 3.2, 6.4 and 10. The shapes of the enthalpy curves at pH 3.2 and 10 show some small exothermic contribution which probably indicates folding of H2B. The interactions of H2B-SDS are dominated by the increase in entropy on detergent binding. The larger negative free energy, enthalpy and entropy changes at pH 6.4 are consistent with greater denaturation relative to pH 3.2 and 10.     

The Hydrophobic Effect: A New Insight from Cold Denaturation and a Two-State Water Structure

Herein we provide a new insight into the hydrophobic effect in protein folding. Our proposition explains the molecular basis of cold denaturation, and of intermediate states in heat and their absence in cold denaturation. The exposure of non-polar surface reduces the entropy and enthalpy of the system, at low and at high temperatures. At low temperatures the favorable reduction in enthalpy overcomes the unfavorable reduction in entropy, leading to cold denaturation. At high temperatures, folding/unfolding is a two-step process: in the first, the entropy gain leads to hydrophobic collapse, in the second, the reduction in enthalpy due to protein-protein interactions leads to the native state. The different entropy and enthalpy contributions to the Gibbs energy change at each step at high, and at low, temperatures can be conveniently explained by a two-state model of the water structure. The model provides a clear view of the dominant factors in protein folding and stability. Consequently, it appears to provide a microscopic view of the hydrophobic effect and is consistently linked to macroscopic thermodynamic parameters.     

The hydrophobic effect: a new insight from cold denaturation and a two-state water structure

Herein we provide a new insight into the hydrophobic effect in protein folding. Our proposition explains the molecular basis of cold denaturation, and of intermediate states in heat and their absence in cold denaturation. The exposure of non-polar surface reduces the entropy and enthalpy of the system, at low and at high temperatures. At low temperatures the favorable reduction in enthalpy overcomes the unfavorable reduction in entropy, leading to cold denaturation. At high temperatures, folding/unfolding is a two-step process: in the first, the entropy gain leads to hydrophobic collapse, in the second, the reduction in enthalpy due to protein-protein interactions leads to the native state. The different entropy and enthalpy contributions to the Gibbs energy change at each step at high, and at low, temperatures can be conveniently explained by a two-state model of the water structure. The model provides a clear view of the dominant factors in protein folding and stability. Consequently, it appears to provide a microscopic view of the hydrophobic effect and is consistently linked to macroscopic thermodynamic parameters.     

Thermodynamics of the temperature-induced unfolding of globular proteins.

The heat capacity, enthalpy, entropy, and Gibbs energy changes for the temperature-induced unfolding of 11 globular proteins of known three-dimensional structure have been obtained by microcalorimetric measurements. Their experimental values are compared to those we calculate from the change in solvent-accessible surface area between the native proteins and the extended polypeptide chain. We use proportionality coefficients for the transfer (hydration) of aliphatic, aromatic, and polar groups from gas phase to aqueous solution, we estimate vibrational effects, and we discuss the temperature dependence of each constituent of the thermodynamic functions. At 25 degrees C, stabilization of the native state of a globular protein is largely due to two favorable terms: the entropy of non-polar group hydration and the enthalpy of interactions within the protein. They compensate the unfavorable entropy change associated with these interactions (conformational entropy) and with vibrational effects. Due to the large heat capacity of nonpolar group hydration, its stabilizing contribution decreases quickly at higher temperatures, and the two unfavorable entropy terms take over, leading to temperature-induced unfolding.     

154 Protein folding and binding funnels: a common driving force and a common mechanism

Under the free energy landscape theory, both the protein-folding and protein–ligand binding processes are driven by the decrease in total Gibbs free energy of the protein-solvent or protein–ligand-solvent system, which involves the non-complementary changes between the entropy and enthalpy, ultimately leading to a global free energy minimization of these thermodynamic systems (Ji & Liu, 2011; Liu et al., 2012; Yang, Ji & Liu, 2012). In the case of protein folding, the lowering of the system free energy coupled with the gradual reduction in conformational degree of freedom of the folding intermediates determines that the shape of the free energy landscape for protein folding must be funnel-like (Dill & Chan, 1997), rather than non-funneled shapes (Ben-Naim, 2012). In the funnel-like free energy landscape, protein folding can be viewed as going down the hill via multiple parallel routes from a vast majority of individual non-native states on surface outside the funnel to the native states located around the bottom of the funnel. The first stage of folding, i.e. the rapid hydrophobic collapse process, is driven by the solvent entropy maximization. Concretely, the water molecules squeeze and sequestrate the hydrophobic amino acid side chains within the interior of the folding intermediates while exposing the polar and electrostatically charged side chains on the intermediate surface so as to minimize the solvent-accessible surface area of the solute and thus, the minimal contacts between the folding intermediates and the water molecules. This will maximize the entropy of the solvent, thus contributing substantially to lowering of the system free energy due to an absolute advantage of the solvent in both quantity and mass (Yang, Ji & Liu, 2012). The resulting molten globule states (Ohgushi & Wada, 1983), within which a few transient secondary structural components and tertiary contacts have been formed but many native contacts or close residue–residue interactions has yet to form, need to be further sculptured into the native states. This is a relatively slow “bottleneck” process because the competitive interactions between protein residues within the folding intermediates and between residues and water molecules may repeat many rounds to accumulate a large enough number of stable noncovalent bonds capable of counteracting the conformational entropy loss of the intermediates, thus putting this bottleneck stage under the enthalpy control (i.e. negative enthalpy change), contributing further to the lowering of the system free energy. Although the protein–ligand association occurs around the rugged bottom of the free energy landscape, the exclusion of water from the binding interfaces and the formation of noncovalent bonds between the two partners can still lower the system free energy. In conjunction with the loss of the rotational and translational degrees of freedom of the two partners as well as the loss of the conformational entropy of the protein, these processes could merge, downwards expand, and further narrow the free energy wells within which the protein–ligand binding process takes place, thereby making them look like a funnel, which we term the binding funnel. In this funnel, the free energy downhill process follows a similar paradigm to the protein-folding process. For example, if the initial collisions/contacts occur between the properly complementary interfaces of the protein and ligand, a large amount of water molecules (which usually form a water network around the solute surface) will be displaced to suit the need for maximizing the solvent entropy. This process is similar to that of the hydrophobic collapse during protein folding, resulting in a loosely associated protein–ligand complex that needs also to be further adapted into a tight complex, i.e. the second step which is mainly driven by the negative enthalpy change through intermolecular competitive interactions to gradually accumulate the noncovalent bonds and ultimately, to stabilize the complex at a tightly bound state. Taken together, we conclude that whether in the protein-folding or in the protein–ligand binding process, both the entropy-driven first step and the enthalpy-driven second step contribute to the lowering of the system free energy, resulting in the funnel-like folding or binding free energy landscape.     

Survey of the year 2008: applications of isothermal titration calorimetry

Isothermal titration calorimetry (ITC) is a fast, accurate and label‐free method for measuring the thermodynamics and binding affinities of molecular associations in solution. Because the method will measure any reaction that results in a heat change, it is applicable to many different fields of research from biomolecular science, to drug design and materials engineering, and can be used to measure binding events between essentially any type of biological or chemical ligand. ITC is the only method that can directly measure binding energetics including Gibbs free energy, enthalpy, entropy and heat capacity changes. Not only binding thermodynamics but also catalytic reactions, conformational rearrangements, changes in protonation and molecular dissociations can be readily quantified by performing only a small number of ITC experiments. In this review, we highlight some of the particularly interesting reports from 2008 employing ITC, with a particular focus on protein interactions with other proteins, nucleic acids, lipids and drugs. As is tradition in these reviews we have not attempted a comprehensive analysis of all 500 papers using ITC, but emphasize those reports that particularly captured our interest and that included more thorough discussions we consider exemplify the power of the technique and might serve to inspire other users. Copyright © 2010 John Wiley & Sons, Ltd.     

Evaluation of free energy landscape for base-amino acid interactions using ab initio force field and extensive sampling

Structural data of protein-DNA complex show redundancy and flexibility in base-amino acid interactions. To understand the origin of the specificity in protein-DNA recognition, we calculated the interaction free energy, enthalpy, entropy, and minimum energy maps for AT-Asn, GC-Asn, AT-Ser, and GC-Ser by means of a set of ab initio force field with extensive conformational sampling. We found that the most preferable interactions in these pairs are stabilized by hydrogen bonding, and are mainly enthalpy driven. However, minima in the free energy maps are not necessarily the same as those in the minimum energy map or enthalpy maps, due to the entropic effect. The effect of entropy is particularly important in the case of GC-Asn. Experimentally observed structures of base-amino acid interactions are within preferable regions in the calculated free energy maps, where there are many different interaction configurations with similar energy. The full geometry optimization procedure using ab initio molecular orbital method was applied to get the optimal interaction geometries for AT-Asn, GC-Asn, AT-Ser, and GC-Ser. We found that there are various base-amino acid combinations with similar interaction energies. These results suggest that the redundancy and conformational flexibility in the base-amino acid interactions play an important role in the protein-DNA recognition.     

Label-free detection of enhanced saccharide binding at pH 7.4 to nanoparticulate benzoboroxole based receptor units

Nanoparticles modified with either 6-amino-1-hydroxy-2,1-benzoxaborolane (3-aminobenzoboroxole) or 3-aminophenylboronic acid were prepared by nucleophilic substitution of a styrene-co-DVB-co-vinylbenzylchloride latex (25 nm). Isothermal titration calorimetry (ITC) was used as a label-free detection method for the analysis of the binding between monosaccharides and these two differently derivatized nanoparticle systems at pH 7.4. Because ITC reveals, thermodynamical parameters such as the changes in enthalpy ΔH, free energy ΔG, and entropy ΔS, possible explanations for the higher binding constants can be derived in terms of entropy and enthalpy changes. In case of the modified nanoparticles, the free energy of binding is dominated by the entropy term. This shows that interfacial effects, besides the intrinsic affinity, lead to a higher binding constant compared with the free ligand. The highest binding constant was found for fructose binding to the benzoboroxole modified nanoparticles: Its value of 1150 M(-1) is twice as high as for the free benzoboroxole and five times as high as with phenylboronic acid or 3-aminophenylboronic acid. In contrast to the binding of fructose to free boronic acids, which is an enthalpically driven process, the binding of fructose to the modified nanoparticles is dominated by the positive entropy term.     

Contribution of the trifluoroacetyl group in the thermodynamics of antigen–antibody binding

We analyzed the binding of the 7C8 antibody to the chloramphenicol phosphonate antigens—one containing a trifluoroacetyl group (CP‐F) and the other containing an acetyl group (CP‐H)—by using isothermal titration calorimetry (ITC). The thermodynamic difference due to the substitution of F by H was evaluated using free energy calculations based on molecular dynamics (MD) simulations. We have previously shown that another antibody, namely, 6D9, binds more weakly to CP‐H than to CP‐F, mainly due to the different hydration free energies of the dissociated state and not due to the unfavorable hydrophobic interactions with the antibody in the bound state. Unlike in the binding of the trifluoroacetyl group with 6D9, in its binding with 7C8, it is exposed to the solvent, as seen in the crystal structure of the complex of 7C8 with CP‐F. The thermodynamic analysis performed in this study showed that the binding affinity of 7C8 for CP‐H is similar to that for CP‐F, but this binding to CP‐H is accompanied with less favorable enthalpy and more favorable entropy changes. The free energy calculations indicated that, upon the substitution of F by H, enthalpy and entropy changes in the associated and dissociated states were decreased, but the magnitude of enthalpy and entropy changes in the dissociated state was larger than that in the associated state. The differences in binding free energy, enthalpy, and entropy changes determined by the free energy calculations for the substitution of F by H are in good agreement with the experimental results. Copyright © 2009 John Wiley & Sons, Ltd.     

Thermodynamic assessment of the stability of thrombin receptor antagonistic peptides in hydrophobic environments

In this paper, a general procedure is described to determine thermodynamic parameters associated with the interaction of thrombin receptor antagonistic peptides (TRAPs) with immobilized nonpolar ligands. The results show that these interactions were associated with nonlinear van't Hoff dependencies over a wide temperature range. Moreover, changes in relevant thermodynamic parameters, namely the changes in Gibbs free energy of interaction, DeltaG(0)assoc, enthalpy of interaction, DeltaH(0)assoc, entropy of interaction, DeltaS(0)assoc, and heat capacity, DeltaC(0)p, have been related to the structural properties of these TRAP analogs. The implications of these investigations for the design of thrombin receptor agonists/antagonists with structures stabilized by intramolecular hydrophobic interactions are discussed.     

Kinetic and thermodynamic characterization of HIV-1 protease inhibitors

Interaction kinetic and thermodynamic analyses provide information beyond that obtained in general inhibition studies, and may contribute to the design of improved inhibitors and increased understanding of molecular interactions. Thus, a biosensor-based method was used to characterize the interactions between HIV-1 protease and seven inhibitors, revealing distinguishing kinetic and thermodynamic characteristics for the inhibitors. Lopinavir had fast association and the highest affinity of the tested compounds, and the interaction kinetics were less temperature-dependent as compared with the other inhibitors. Amprenavir, indinavir and ritonavir showed non-linear temperature dependencies of the kinetics. The free energy, enthalpy and entropy (DeltaG, DeltaH, DeltaS) were determined, and the energetics of complex association (DeltaG(on), DeltaH(on), DeltaS(on)) and dissociation (DeltaG(off), DeltaH(off), DeltaS(off)) were resolved. In general, the energetics for the studied inhibitors was in the same range, with the negative free energy change (DeltaG < 0) due primarily to increased entropy (DeltaS > 0). Thus, the driving force of the interaction was increased degrees of freedom in the system (entropy) rather than the formation of bonds between the enzyme and inhibitor (enthalpy). Although the DeltaG(on) and DeltaG(off) were in the same range for all inhibitors, the enthalpy and entropy terms contributed differently to association and dissociation, distinguishing these phases energetically. Dissociation was accompanied by positive enthalpy (DeltaH(off) > 0) and negative entropy (DeltaS(off) < 0) changes, whereas association for all inhibitors except lopinavir had positive entropy changes (DeltaS(on) > 0), demonstrating unique energetic characteristics for lopinavir. This study indicates that this type of data will be useful for the characterization of target-ligand interactions and the development of new inhibitors of HIV-1 protease.     

Thermodynamics of the daunomycin-DNA interaction: ionic strength dependence of the enthalpy and entropy

Fluorescence and absorbance methods were used to study the interaction of daunomycin with calf-thymus DNA over a wide range of temperatures and NaCl concentrations. van't Hoff analysis provided estimates for the enthalpy of the binding reaction over the NaCl range of 0.05–1.0 M. Daunomycin binding is exothermic over this entire range, and the favorable binding free energy arises primarily from the large, negative enthalpy. Both the enthalpy change and entropy change are strong functions of ionic strength. Possible molecular contributions to the enthalpy and entropy are discussed, leading to the tentative conclusion that hydrogen-bonding interactions at the interacalation site are the primary contributors to the observed thermodynamic parameters. The dependence of the enthalpy on the ionic strength is well beyond the predictions of current polyelectrolyte theory and cannot be fully accounted for. The enthalpy and entropy changes observed compensate one another to produce relatively small free-energy changes over the range of solution conditions studied.     

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.     

Application of atomic force microscopy for characteristics of single intermolecular interactions

Atomic force microscopy (AFM) can be used to make measurements in vacuum, air, and water. The method is able to gather information about intermolecular interaction forces at the level of single molecules. This review encompasses experimental and theoretical data on the characterization of ligand-receptor interactions by AFM. The advantage of AFM in comparison with other methods developed for the characterization of single molecular interactions is its ability to estimate not only rupture forces, but also thermodynamic and kinetic parameters of the rupture of a complex. The specific features of force spectroscopy applied to ligand-receptor interactions are examined in this review from the stage of the modification of the substrate and the cantilever up to the processing and interpretation of the data. We show the specificities of the statistical analysis of the array of data based on the results of AFM measurements, and we discuss transformation of data into thermodynamic and kinetic parameters (kinetic dissociation constant, Gibbs free energy, enthalpy, and entropy). Particular attention is paid to the study of polyvalent interactions, where the definition of the constants is hampered due to the complex stoichiometry of the reactions.     

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.     

Thermodynamic properties of model CdTe/CdSe mixtures

We report on the thermodynamic properties of binary compound mixtures of model groups II–VI semiconductors. We use the recently introduced Stillinger–Weber Hamiltonian to model binary mixtures of CdTe and CdSe. We use molecular dynamics simulations to calculate the volume and enthalpy of mixing as a function of mole fraction. The lattice parameter of the mixture closely follows Vegard's law: a linear relation. This implies that the excess volume is a cubic function of mole fraction. A connection is made with hard sphere models of mixed fcc and zincblende structures. The potential energy exhibits a positive deviation from ideal soluton behaviour; the excess enthalpy is nearly independent of temperatures studied (300 and 533 K) and is well described by a simple cubic function of the mole fraction. Using a regular solution approach (combining non-ideal behaviour for the enthalpy with ideal solution behaviour for the entropy of mixing), we arrive at the Gibbs free energy of the mixture. The Gibbs free energy results indicate that the CdTe and CdSe mixtures exhibit phase separation. The upper consolute temperature is found to be 335 K. Finally, we provide the surface energy as a function of composition. It roughly follows ideal solution theory, but with a negative deviation (negative excess surface energy). This indicates that alloying increases the stability, even for nano-particles.