Phase transitions, Kauzmann curves, and inverse melting

Walter Kauzmann's classic 1948 review of liquid supercooling and glass formation drew attention to the temperatures at which (by extrapolation) enthalpies and entropies of liquid and crystal phases would appear to become equal. In the temperature-pressure (T, p) plane, the collection of such 'Kauzmann temperatures' generate characteristic curves. The present study examines the connection of those Kauzmann loci to equilibrium inverse melting phenomena, i.e. cases where isobaric heating causes freezing of the liquid. Such cases are associated with local minima or maxima in the melting curve p(m)(T), and we point out the possible relevance of melting curve maxima to the thermodynamics of protein folding. Both equal-enthalpy and equal-entropy Kauzmann curves must pass through melting curve extrema. Three thermodynamic identities have been obtained to describe the vicinity of these points; they involve, respectively, the slopes of the two Kauzmann curves, and the second temperature derivative of the melting pressure. The second of these three equations is formally identical to the first Ehrenfest relation for second-order phase transitions, but carries no phase-transition implication. For purposes of specific numerical illustration, the inverse-melting behavior displayed by (3)He at low temperature has been analyzed in detail.     

Thermodynamics of barnase unfolding.

The thermodynamics of barnase denaturation has been studied calorimetrically over a broad range of temperature and pH. It is shown that in acidic solutions the heat denaturation of barnase is well approximated by a 2-state transition. The heat denaturation of barnase proceeds with a significant increase of heat capacity, which determines the temperature dependencies of the enthalpy and entropy of its denaturation. The partial specific heat capacity of denatured barnase is very close to that expected for the completely unfolded protein. The specific denaturation enthalpy value extrapolated to 130 degrees C is also close to the value expected for the full unfolding. Therefore, the calorimetrically determined thermodynamic characteristics of barnase denaturation can be considered as characteristics of its complete unfolding and can be correlated with structural features--the number of hydrogen bonds, extent of van der Waals contacts, and the surface areas of polar and nonpolar groups. Using this information and thermodynamic information on transfer of protein groups into water, the contribution of various factors to the stabilization of the native structure of barnase has been estimated. The main contributors to the stabilization of the native state of barnase appear to be intramolecular hydrogen bonds. The contributions of van der Waals interactions between nonpolar groups and those of hydration effects of these groups are not as large if considered separately, but the combination of these 2 factors, known as hydrophobic interactions, is of the same order of magnitude as the contribution of hydrogen bonding.     

A model on the origin of RNA

The theory of the liquid-glass transition is extended to describe the polymerization of RNA in a nucleotide-condensed state. In the glassy state the ribose subunits are joined by a 2'-5' or 3'-5' phosphodiester linkage to form the ribose-phosphate backbone similar to oligosaccharides and polysaccharides. The occurrence of the glass transition requires two conditions: (1) a supercooled state in a nucleotide-condensed state should exist below the temperature at which the whole RNA hydrolyzes; (2) the Gibbs free energy due to the Kauzmann entropy, which obeys a Curie law with a negative sign, must be larger than the height of the potential barrier for nucleotides to overcome to form the binding.     

Thermodynamic aspects of vitrification

Vitrification is a process in which a liquid begins to behave as a solid during cooling without any substantial change in molecular arrangement or thermodynamic state variables. The physical phenomenon of vitrification is relevant to both cryopreservation by freezing, in which cells survive in glass between ice crystals, and cryopreservation by vitrification in which a whole sample is vitrified. The change from liquid to solid behavior is called the glass transition. It is coincident with liquid viscosity reaching 10¹³ Poise during cooling, which corresponds to a shear stress relaxation time of several minutes. The glass transition can be understood on a molecular level as a loss of rotational and translational degrees of freedom over a particular measurement timescale, leaving only bond vibration within a fixed molecular structure. Reduced freedom of molecular movement results in decreased heat capacity and thermal expansivity in glass relative to the liquid state. In cryoprotectant solutions, the change from liquid to solid properties happens over a ∼10 °C temperature interval centered on a glass transition temperature, typically near −120 °C (±10 °C) for solutions used for vitrification. Loss of freedom to quickly rearrange molecular position causes liquids to depart from thermodynamic equilibrium as they turn into a glass during vitrification. Residual molecular mobility below the glass transition temperature allows glass to very slowly contract, release heat, and decrease entropy during relaxation toward equilibrium. Although diffusion is practically non-existent below the glass transition temperature, small local movements of molecules related to relaxation have consequences for cryobiology. In particular, ice nucleation in supercooled vitrification solutions occurs at remarkable speed until at least 15 °C below the glass transition temperature.     

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)     

Computer Simulation of Liquid Crystal Films

Abstract

We present the results of extensive Monte Carlo simulations of liquid crystal films of various thicknesses. A simple nearest-neighbour lattice model, the Lebwohl-Lasher model, is employed, with periodic boundaries in two directions and free, planar, surfaces in the third. Particular attention is devoted to locating the temperature of the order-disorder (nematic-isotropic) phase transition. Weak first-order behaviour apparently persists in systems as thin as 8 layers across, but below this the transition cannot be detected. The shift of the transition temperature from its bulk value approaches the expected asymptotic linear dependence on inverse thickness, but significant deviations from this are seen for films of 10 layers thickness and less. These results enable an accurate estimate to be made of the bulk phase transition temperature in the thermodynamic limit, and the result is consistent with that extrapolated from systems with full periodic boundaries.     

Effect of hydration on the stability of the collagen-like triple-helical structure of [4(R)-hydroxyprolyl-4(R)-hydroxyprolylglycine]10

X-ray analysis has been carried out on a crystal of the collagen model peptide (Hyp(R)-Hyp(R)-Gly)10 [where Hyp(R) is 4(R)-hydroxyproline] with 1.5 A resolution. The triple-helical structure of (Hyp(R)-Hyp(R)-Gly)10 has the same helical parameters and Rich and Crick II hydrogen bond patterns as those of other collagen model peptides. However, our full-length crystal structure revealed that almost all consecutive Hyp(R) residues take the up-up pucker in contrast to putative down-up puckering propensities of other collagen model peptides. The unique feature of thermodynamic parameters associated with the conformational transition of this peptide from triple helix to single coil is that both enthalpy and entropy changes of the transition are much smaller than those of other model peptides such as (Pro-Pro-Gly)10 and (Pro-Hyp(R)-Gly)10. To corroborate the precise structural information including main- and side-chain dihedral angles and intra- and interwater bridge networks, we estimated the degrees of hydration by comparing molecular volumes observed experimentally in solution to those calculated ones from the crystal structure. The results showed that the degree of hydration of (Hyp(R)-Hyp(R)-Gly)10 is comparable to that of (Pro-Hyp(R)-Gly)10 in the triple-helical state, but the former was more highly hydrated than (Pro-Hyp(R)-Gly)10 in the single-coil state. Because hydration reduces the enthalpy due to the formation of a hydrogen bond with a water molecule and diminishes the entropy due to the restriction of water molecules surrounding a peptide molecule, we concluded that the high thermal stability of (Hyp(R)-Hyp(R)-Gly)10 is able to be described by its high hydration in the single-coil state.     

Solid model compounds and the thermodynamics of protein unfolding.

Analysis of thermodynamic data on the dissolution of solid cyclic dipeptides into water in terms of group additivity provides a rationale for the enthalpy and entropy convergence temperatures observed for small globular protein denaturation and the dissolution of model compounds into water. Convergence temperatures are temperatures at which the extrapolated enthalpy or entropy changes for a series of related compounds take on a common value. At these temperatures (TH* and TS*) the apolar contributions to the corresponding thermodynamic values (delta H degrees and delta S degrees) are shown to be zero. Other contributions such as hydrogen bonding and configurational effects can then be evaluated and their quantitative effects on the stability of globular proteins assessed. It is shown that the denaturational heat capacity is composed of a large positive contribution from the exposure of apolar groups and a significant negative contribution from the exposure of polar groups in agreement with previous results. The large apolar contribution suggests that a liquid hydrocarbon model of the hydrophobic effect does not accurately represent the apolar contribution to delta H degrees of denaturation. Rather, significant enthalpic stabilizing contributions are found to arise from peptide groups (hydrogen bonding). Combining the average structural features of globular proteins (i.e. number of residues, fraction of buried apolar groups and fraction of hydrogen bonds) with their specific group contributions permits a first-order prediction of the thermodynamic properties of proteins. The predicted values compare well with literature values for cytochrome c, myoglobin, ribonuclease A and lysozyme. The major thermodynamic features are described by the number of peptide and apolar groups in a given protein.     

Differential scanning calorimetry of thermotropic phase transitions in vitaminylated lipids: aqueous dispersions of N-biotinyl phosphatidylethanolamines.

The thermotropic phase behavior of a homologous series of saturated diacyl phosphatidylethanolamines in which the headgroup is N-derivatized with biotin has been investigated by differential scanning calorimetry. In 1 M NaCl, derivatives with acyl chainlengths from C(12:0) to C(20:0) all exhibit sharp chain-melting phase transitions, which are reversible with a hysteresis of 1.5 degrees or less, except for the C(12:0) lipid which has a transition temperature below 0 degree C. The transition enthalpy and the transition entropy depend approximately linearly on the lipid chainlength, with incremental values per CH2 group that are very similar to those obtained for the corresponding underivatized phosphatidylethanolamines in aqueous dispersion. The chainlength-independent contribution to the transition enthalpy is significantly smaller than that for the underivatized phosphatidylethanolamines, and that for the transition entropy is much smaller; the latter suggesting that the N-biotinylated phosphatidylethanolamine headgroups are differently hydrated from those of the underivatized lipids. The gel-to-fluid phase transition temperatures of the N-biotinylated lipids are lower than those of the parent phosphatidylethanolamines, and their chainlength dependence conforms well with that predicted by assuming that the transition enthalpy and entropy are linearly dependent on chainlength. Although the chain-melting phase behavior is generally similar to that of the parent phosphatidylethanolamines, the gel phases (and the fluid phases in the case of chainlengths C(12:0) to C(16:0)) have a different lyotropic structure in the two cases, and this is reflected in the chainlength-independent contributions to the thermodynamic parameters. In the absence of salt, the thermotropic phase behavior of aqueous dispersions of the N-biotinyl phosphatidylethanolamines is considerably more complex.(ABSTRACT TRUNCATED AT 250 WORDS)     

Thermodynamics of the acid transition in blue copper proteins

The thermodynamic parameters of the conformational transition occurring at low pH (acid transition, AT) in blue copper proteins, involving protonation and detachment from the Cu(I) ion of one histidine ligand, have been determined electrochemically for spinach and cucumber plastocyanins, Rhus vernicifera stellacyanin, cucumber basic protein (CBP), and Paracoccus versutus amicyanin. These data were obtained from direct protein electrochemistry experiments carried out at varying pH and temperature. For all species but CBP, the overall conformational change turns out to be exothermic. The entropy change is remarkably species-dependent. In particular, we found that (i) the balance of bond breaking/formation favors the acid transition in plastocyanins, which show remarkably negative DeltaH degrees '(AT) values, and (ii) the transition enthalpy turns out to be much less negative (or even positive) for the two phytocyanins (stellacyanin and CBP): for these species, the transition turns out to be observable thanks to the favorable (positive) entropy change. Thus, it is apparent that the thermodynamic "driving force" for this transition is enthalpic for the plastocyanins and entropic for the phytocyanins. Amicyanin is an intermediate case in which both enthalpic and entropic terms favor the transition. Under the assumption that the transition entropy originates from solvent reorganization effects, which are known to involve compensative enthalpy and entropy changes, the free energy change of the transition would also correspond to the enthalpy change due to bond breaking/formation in the first coordination sphere of the metal and in its immediate environment. Indeed, this term turns out to be very similar for the proteins investigated, in line with the conservation of the Cu(I)-His bond strengths in these species, except for amicyanin, for which the greater exothermicity of the transition can be ascribed to peculiar features of the active site.     

Thermodynamic Parameters of Frog Brain κ-Opioid Receptors

Abstract: The thermodynamic parameters for [³H]-ethylketocyclazocine binding in frog ( Rana esculenta ) brain membranes have been examined. Computer-based nonlinear regression analysis of the untransformed equilibrium displacement data showed that this ligand bound to two sites with different affinities and capacities in this tissue. K _A values derived from equilibrium displacement curves have been used for calculating the changes in the standard Gibbs energy, enthalpy, and entropy during the binding process. Van't Hoff plots are bipartite, with transitions occurring at 18°C for both the high- and the low-affinity sites. For the high-affinity site, the reaction appears to be associated with a decrease in enthalpy below the transition temperature and a significant gain in entropy above this temperature. The reverse appears to be true for the low-affinity site. We conclude that this profile fairly approximates the mixed agonist-antagonist nature of this ligand and surmise that thermodynamic analysis could be a very useful tool for characterization of the nature of cloned opioid receptors in vitro.     

Energetic basis of structural stability in the molten globule state: alpha-lactalbumin

The denatured states of alpha-lactalbumin, which have features of a molten globule state, have been studied to elucidate the energetics of the molten globule state and its contribution to the stability of the native conformation. Analysis of calorimetric and CD data shows that the heat capacity increment of alpha-lactalbumin denaturation highly correlates with the degree of disorder of the residual structure of the state. As a result, the denaturational transition of alpha-lactalbumin from the native to a highly ordered compact denatured state, and from the native to the disordered unfolded state are described by different thermodynamic functions. The enthalpy and entropy of the denaturation of alpha-lactalbumin to compact denatured state are always greater than the enthalpy and entropy of its unfolding. This difference represents the unfolding of the molten globule state. Calorimetric measurements of the heat effect associated with the unfolding of the molten globule state reveal that it is negative in sign over the temperature range of molten globule stability. This observation demonstrates the energetic specificity of the molten globule state, which, in contrast to a protein with unique tertiary structure, is stabilized by the dominance of negative entropy and enthalpy of hydration over the positive conformational entropy and enthalpy of internal interactions. It is concluded that at physiological temperatures the entropy of dehydration is the dominant factor providing stability for the compact intermediate state on the folding pathway, while for the stability of the native state, the conformational enthalpy is the dominant factor.     

Evaluation of the thermal coefficient of the resistance to fluorophore rotation in model membranes.

The thermal coefficient of the frictional resistance to fluorophore rotation (b), a parameter related to the change in the local viscosity with temperature, was determined for anthroyloxy-fatty acid probes in micelles and dimyristoyl lecithin (DMPC) and dioleoyl lecithin (DOPC) unilamellar and multilamellar vesicles. The value of b and the percent change in anisotropy with temperature (%dA/dT) remained constant with membrane depth and only depended on composition. These parameters were also the same when either in-plane, or in-plane and out-of-plane fluorophore motions were observed. This result indicates that the membranes expand isotropically. The magnitude of b was found to be primarily dependent on the packing of the hydrocarbon chains with higher b values relating to more closely-packed chains. b was responsive to the gel to liquid crystal phase transition of DMPC and the bilayer to hexagonal phase transition of egg-phosphatidylethanolamine. When the enthalpy values for the fluorophore transfer from one phase to another are calculated, the values are larger than those measured by calorimetry and reflect a discrepancy between the microscopic enthalpy experienced by the fluorophore due to a change in environment versus the macroscopic enthalpy of the system as a whole.     

Temperature-induced conformational changes in human tearlipids hydrocarbon chains

As a first step to characterize human meibum and tear lipids, infrared spectroscopy was applied to characterize the molecular structure/conformation and packing of hydrocarbon chains. Temperature-induced phase transitions were fit to a sigmoid equation and were experimentally reproducible and were similar for multiple samples collected from the same person. No hysteresis was observed. Hydration of polar tear lipids increased their phase transition cooperativity, enthalpy and entropy. Hydrophobic interactions in meibum lipid (ML) were stronger than in tear-fluid lipids (TL), as reflected by the higher entropy and enthalpy of the gel to liquid crystalline phase transition of ML. The results of this study provide further evidence of the differences in the composition and structure of ML and TL. The conformational changes observed in the hydrocarbon chains of ML with temperature suggest that the observed therapeutic increased delivery of ML with eye lid heating could be related to the increased disorder in the packing of the hydrocarbon tails. This work also highlights the power of infrared spectroscopy to characterize molecular structure/conformation, and packing of human tear lipids and provides a basis for future studies of tear film lipid composition-structure-function relationships and lipid-protein interactions in relation to age, sex, and dry eye symptoms.     

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.     

Effects of mutations on the thermodynamics of a protein folding reaction: implications for the mechanism of formation of the intermediate and transition states

We have measured changes in heat capacity, entropy, and enthalpy for each step in the folding reaction of CD2.d1 and evaluated the effects of core mutations on these properties. All wild-type and mutant forms fold through a rapidly formed intermediate state that precedes the rate-limiting transition state. Mutations have a pronounced effect on the enthalpy of both the intermediate and folded states, but in all cases a compensatory change in entropy results in a small net free-energy change. While the enthalpy change in the folded state can be attributed to a loss of van der Waals interactions, it has already been shown that changes in the stability of the intermediate are dominated by changes in secondary structure propensity [Lorch et al. (1999) Biochemistry 38, 1377-1385]. It follows that the thermodynamic basis of beta-propensity is enthalpic in origin. The effects of mutations on the enthalpy and entropy of the transition state are smaller than on the ground states. This relative insensitivity to mutation is discussed in the light of theories concerning the nature of the rate-limiting barrier in folding reactions.     

A calorimetric study of the folding-unfolding of an alpha-helix with covalently closed N and C-terminal loops.

The thermal melting of a dicyclic 29-residue peptide, having helix-stabilizing side-chain to side-chain covalent links at each terminal, has been studied by circular dichroism spectropolarimetry (CD) and differential scanning calorimetry (DSC). The CD spectra for this dicyclic peptide indicate that it is monomeric, almost fully alpha-helical at -10 degrees C, and undergoes a reversible transition from the folded to the disordered state with increasing temperature. The temperature dependencies of the ellipticity at 222 nm and the excess heat capacity measured calorimetrically are well fit by a two-state model, which indicates a cooperative melting transition that is complete within the temperature ranges of these experiments (from -10 degrees C to 100 degrees C). This allows a complete analysis of the thermodynamics of helix formation. The helix unfolding is found to proceed with a small positive heat-capacity increment, consistent with the solvation of some non-polar groups upon helix unfolding. It follows that the hydrogen bonds are not the only factors responsible for the formation of the alpha-helix, and that hydrophobic interactions are also playing a role in its stabilization. At 30 degrees C, the calorimetric enthalpy and entropy values are estimated to be 650(+/-50) cal mol(-1)and 2.0(+/-0.2) cal K(-1)mole(-1), respectively, per residue of this peptide. Comparison with the thermodynamic characteristics obtained for the unfolding of double-stranded alpha-helical coiled-coils shows that at that temperature the enthalpic contribution of non-polar groups to the stabilization of the alpha-helix is insignificant and the estimated transition enthalpy can be assigned to the hydrogen bonds. With increasing temperature, the increasing magnitude of the negative enthalpy of hydration of the exposed polar groups should decrease the helix-stabilizing enthalpy of the backbone hydrogen bonds. However, the helix-stabilizing negative entropy of hydration of these groups should also increase in magnitude with increasing temperature, offsetting this effect.     

Physical properties of cholesteryl esters

Cholesteryl esters, the intracellular storage form and intravascular transport form of cholesterol, can exist in crystal, liquid crystal and liquid states. The physical state of cholesteryl esters at physiologic temperatures may be a determinant of their pathogenicity. This review has surveyed saturated aliphatic cholesteryl esters of chain length 1 to 24 carbons and a series of medium-chained unsaturated cholesteryl esters from chain lengths 14 to 24 carbons. A systematic study of transition temperatures by polarizing microscopy and enthalpies by differential scanning calorimetry has provided unifying concepts concerning the phase behavior as a function of chain length and unsaturation. Neat cholesteryl esters show chain-length dependence of transition temperature and enthalpy of both the crystal and liquid crystal transitions. Double bond position along the fatty acyl chain affected stability of the liquid crystal phases; a smectic phase was not observed for any cholesteryl ester with a double bond more proximal than delta 9. 13C NMR spectroscopy in the isotropic liquid phase has provided evidence suggesting a balance of ring-ring vs. chain-chain interactions as a determinant for isotropic liquid----cholesteric vs. isotropic liquid----smectic transitions. Specifically, anisotropic molecular motions of the steroid ring are greater for cholesteryl esters forming a cholesteric phase than a smectic phase from the melt. Chain-chain interactions apparently predominate in smectic phase formation. The X-ray diffraction patterns of cholesteryl esters as a function of chain length reveal several isostructural series and known single crystal data are presented. A chain length depending on the periodicity of the smectic phase is observed which may be different for saturated vs. unsaturated esters. In summary, the phase behavior of cholesteryl ester molecules is complex and cannot be determined a priori from the phase behavior of component cholesterol and fatty acid. The data presented here should provide insight into the biological behavior of this lipid class.