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Heat capacity of hydrogen-bonded networks: an alternative view of protein folding thermodynamics.

Large changes in heat capacity (deltaCp) have long been regarded as the characteristic thermodynamic signature of hydrophobic interactions. However, similar effects arise quite generally in order-disorder transitions in homogeneous systems, particularly those comprising hydrogen-bonded networks, and this may have significance for our understanding of protein folding and other biomolecular processes. The positive deltaCp associated with unfolding of globular proteins in water, thought to be due to hydrophobic interactions, is also typical of the values found for the melting of crystalline solids, where the effect is greatest for the melting of polar compounds, including pure water. This suggests an alternative model of protein folding based on the thermodynamics of phase transitions in hydrogen-bonded networks. Folded proteins may be viewed as islands of cooperatively-ordered hydrogen-bonded structure, floating in an aqueous network of less-well-ordered H-bonds in which the degree of hydrogen bonding decreases with increasing temperature. The enthalpy of melting of the protein consequently increases with temperature. A simple algebraic model, based on the overall number of protein and solvent hydrogen bonds in folded and unfolded states, shows how deltaCp from this source could match the hydrophobic contribution. This confirms the growing view that the thermodynamics of protein folding, and other interactions in aqueous systems, are best described in terms of a mixture of polar and non-polar effects in which no one contribution is necessarily dominant.

Algorithms↗

A simple chemical example of hierarchical thermodynamic interactions: the protonation equilibria of inorganic polyprotic acids.

A general method for formulating complex thermodynamic systems in terms of hierarchical interactions has been developed, and has been applied in a previous analysis to hemoglobin oxygen binding data. Polyprotic acids can be considered a simple chemical model of thermodynamic interaction between ligand binding events. To further illustrate the hierarchical interaction approach it is applied to the analysis of the thermodynamic interactions between proton binding events in inorganic polyprotic acids. pK values for arsenate, carbonate, chromate, phosphate, phosphite, selenite, sulfide and sulfite were recast into hierarchical interaction terms. The intrinsic K(d,h) for protonation ranged from 8.8 x 10(-13) (M) for phosphate to 1.3 x 10(-6) (M) for chromate. Pairwise interactions (K(d,hh)) between protonation events ranged from 1.3 x 10(4) for phosphite to 9.4 x 10(5) for carbonate. Third order interactions (K(d,hhh)) were 0.91 and 0.51 for arsenate and phosphate, respectively, values relatively close to the no interaction value of 1. A principle feature of systems described by hierarchical interactions is that higher order interactions, representing more complex interactions, are less likely to be significant than lower order interactions, and this is further illustrated by these observations from polyprotic acids. The set of significant hierarchical interaction values can be used to predict values for as yet unobserved events, and projected pK values are made for all the polyprotic acids included in this study. Finally, application of this method to the protonation equilibria of water demonstrates a profound pairwise interaction between protonation events (K(d,hh) = 1.3 x 10(17)), which is attributed to oxygen's small size and lack of polarizability.

Acids↗

Thermodynamics of the hydrophobic effect. III. Condensation and aggregation of alkanes, alcohols, and alkylamines.

Knowledge of the energetics of the low solubility of non-polar compounds in water is critical for the understanding of such phenomena as protein folding and biomembrane formation. Solubility in water can be considered as one leg of the three-part thermodynamic cycle - vaporization from the pure liquid, hydration of the vapor in aqueous solution, and aggregation of the substance back into initial pure form as an immiscible phase. Previous studies on the model compounds n-alkanes, 1-alcohols, and 1-aminoalkanes have noted that the thermodynamic parameters (Gibbs free energy, DeltaG; enthalpy, DeltaH; entropy, DeltaS; and heat capacity, DeltaC(p)) associated with these three processes are generally linear functions of the number of carbons in the alkyl chains. Here we assess the accuracy and limitations of the assumption of additivity of CH(2) group contributions to the thermodynamic parameters for vaporization, hydration, and aggregation. Processes of condensation from pure gas to liquid and aqueous solution to aggregate are compared. Hydroxy, amino, and methyl headgroup contributions are estimated, liquid and solid aggregates are distinguished. Most data in the literature were obtained for compounds with short aliphatic hydrocarbon tails. Here we emphasize long aliphatic chain behavior and include our recent experimental data on long chain alkylamine aggregation in aqueous solution obtained by titration calorimetry and van't Hoff analysis. Contrary to what is observed for short compounds, long aliphatic compound aggregation has a large exothermic enthalpy and negative entropy.

Alcohols↗

Generalized derivation of an exact relationship linking different coefficients that characterize thermodynamic effects of preferential interactions.

In solutions consisting of solvent water (component '1') and two solute components ('2' and '3'), various thermodynamic effects of differences between solute-solute and solute-solvent interactions are quantitatively characterized by state functions commonly called 'preferential interaction coefficients': gamma(mu(1),mu(3)) triple bond (delta(m3)/delta(m2))(T,mu(1),mu(3)) and gamma(mu(k)) triple bond (delta(m3)/delta(m2))(T,P,mu(k)), where k = 1,2 or 3. These different derivatives are not all directly accessible to experimental determination, nor are they entirely equivalent for analyses and interpretations of thermodynamic and molecular effects of preferential interactions. Consequently, various practical and theoretical considerations arise when, for a given system, different kinds of preferential interaction coefficients have significantly different numerical values. Previously we derived the exact relationship linking all three coefficients of the type gamma(mu(k), and hence identified the physical origins of the differences between gamma(mu(1)) and gamma(mu(3)) that have been experimentally determined for each of various common biochemical solutes interacting with a protein [J. Phys. Chem. B, 106 (2002) 418-433]. Continuing our investigation of exact thermodynamic linkages among different types of preferential interaction coefficients, we present here a generalized derivation of the relationship linking gamma(mu(1),mu(3)), gamma(mu(3)) and gamma(mu(1)), with no restrictions on m(2), m(3) or any physical characteristic of either solute component (such as partial molar volume). Hence, we show that (gamma(mu(1),mu(3)) - gamma(mu(3))) is related directly to (gamma(mu(3)) - gamma(mu(1))), for which the physical determinants have been considered in detail previously, and to a factor dependent on the ratio of the partial molar volumes V3/V1. Our generalized expression also provides a basis for calculating gamma(mu(1),mu(3)), even in situations where preferential interactions could not be investigated by equilibrium dialysis. To demonstrate this applicability, we analyze isopiestic distillation data for aqueous solutions containing urea and NaCl, two small solute components that cannot be selectively dialyzed.

Thermodynamics↗

Thermodynamic binding and site occupancy in the light of the Schellman exchange concept.

An analysis of Schellman's treatment of preferential interactions is presented, as viewed by a laboratory practitioner of the art. Starting with an intuitive description of what binding is in terms of the distribution of molecules of water and of a weakly interacting ligand (co-solvent), Schellman proceeded to a rigorous thermodynamic definition in which he showed that classical, dialysis equilibrium, binding is a purely thermodynamic quantity. Putting water and the co-solvent on an equivalent footing, he showed that the classical binding treatment is inadequate for weakly interacting systems, in which the replacement of water by ligand and exclusion of co-solvent are symmetrical concepts. Analyzing specifically the simple model of a single independent site, Schellman demonstrated how a positive binding constant can give rise to a measured negative binding stoichiometry. He showed that the origin of the complicated binding isotherms is the non-idealities of water and co-solvent, and went further to analyze critically the effect of site heterogeneity on the ligand concentration dependencies of site occupancy, preferential binding and the thermodynamic quantities, enthalpy, entropy and Gibbs free energy. This exposition of the Schellman treatment is accompanied by illustrations drawn from the experimental results obtained in this author's laboratory.

Binding Sites↗

Thermodynamics of protein folding: a microscopic view.

Statistical thermodynamics provides a powerful theoretical framework for analyzing, understanding and predicting the conformational properties of biomolecules. The central quantity is the potential of mean force or effective energy as a function of conformation, which consists of the intramolecular energy and the solvation free energy. The intramolecular energy can be reasonably described by molecular mechanics-type functions. While the solvation free energy is more difficult to model, useful results can be obtained with simple approximations. Such functions have been used to estimate the intramolecular energy contribution to protein stability and obtain insights into the origin of thermodynamic functions of protein folding, such as the heat capacity. With reasonable decompositions of the various energy terms, one can obtain meaningful values for the contribution of one type of interaction or one chemical group to stability. Future developments will allow the thermodynamic characterization of ever more complex biological processes.

Algorithms↗

Practical limitations on the use of thermodynamic data from isothermal processes.

Enthalpy, entropy and volume data obtained for processes studied in aqueous solvents generally have been assumed to apply to the solute process without consideration of the coupling between the process and the two-state equilibrium of water. Walrafen's confirmation of the latter in 1983 shows that long-debated model to be correct so the enthalpy and entropy contributions to a free-energy change to give unambiguous information must be corrected for the water contribution. The situation is further complicated by differential chemical interaction of amphiphilic solutes with the two water species since experimental complications make correction difficult or impossible. A more general source of error in isothermal experiments is the linkage to the thermal-equilibrium device. That thermal problem discovered only in 1967 is not yet treated in textbooks although it is always a complication in isothermal processes and responsible for a hierarchy of thermodynamic quantities with different levels of reliability. Major consequences for several familiar thermodynamic and extra-thermodynamic methods are examined in terms of relative reliability. In most cases the thermal corrections are restricted by changes in phase state on cooling.

Entropy↗

Thermodynamics of the binding of ligands by macromolecules.

The thermodynamics of the binding of ligands by proteins and other biological macromolecules has been treated by Wyman and others on the basis of the binding polynomial and the binding potential. However, the thermodynamics of the binding of ligands by small molecules and the effects of ligands on the apparent equilibrium constants of biochemical reactions has been developed on the basis of Legendre transformed Gibbs energies of formation. This article brings these seemingly disparate approaches together by considering simple systems and the binding of oxygen by hemoglobin. When the ligand is H+, examples involving small molecules show that the standard transformed Gibbs energy of formation of a reactant at a specified pH is equal to the negative of the binding potential plus a term related to the standard thermodynamic properties of the elements. The standard transformed Gibbs energies of formation of eight forms of deoxygenated and oxygenated hemoglobin are calculated here for a specific set of conditions. This is the most efficient way to store the information from the seven independent apparent equilibrium constants involved. In a second step, a Legendre transform is used to introduce the concentration of molecular oxygen as a natural variable and calculate the apparent equilibrium constant K" for 2TotD = TotT at specified values of [O2], where TotD is the sum of the concentrations of the dimer and its oxygenated forms and TotT is the sum of the concentrations of the tetramer and its oxygenated forms.

Chemical Phenomena↗

Structure and thermodynamics of nonideal solutions of colloidal particles: investigation of salt-free solutions of human serum albumin by using small-angle neutron scattering and Monte Carlo simulation.

The understanding of the structural and thermodynamic properties of moderately or highly concentrated solutions is fundamental, e.g., in medicine and biology and also in many technical processes. In this work, we have used the small-angle neutron scattering method (SANS), in combination with Monte Carlo simulation, to study salt-free solutions of human serum albumin (HSA) in the concentration range up to 0.26 g ml-1. The model calculations of the theoretical SANS intensities are quite general, thus avoiding the approximation that the relative positions and orientations of the particles are independent of each other. The computation of the theoretical intensities also includes the calculation of a "thermodynamic' intensity scattered at zero angle, which is obtained via the nonideal part of the chemical potential. The latter quantity is obtained by applying the test particle method during the Monte Carlo simulations. It is found that the SANS data can be explained by a model where the HSA molecules behave as hard ellipsoids of revolution with semiaxes a = 6.8 nm, b = c = 1.9 nm. In addition to the hard core interaction, the particles are also surrounded by a soft, repulsive rectangular-shaped potential which is spherically oriented around the particles. The combination of SANS and statistical thermodynamics also allows a determination of the nonideal part of the chemical potential and the activity coefficient of HSA. As expected the activity coefficient deviates strongly from the value one (several powers of ten) already at fairly low concentrations: the effects are comparable to, or even larger than, for instance hydrophobic or van der Waals interaction.

Chemical Phenomena↗

An alternative approach in the structure-based predictions of the thermodynamics of protein unfolding.

A new approach for a first-order prediction of the thermodynamic properties of small globular proteins has been developed. The method put forward here has been shown to be successful in predicting, within acceptable margins of uncertainty, the denaturational heat capacity changes of a given protein if its amino acid composition is known. If compared with other models this method has the following advantages: (1) no details about the three-dimensional structure of the protein are required; (2) comparison with the thermodynamic properties of small model compounds is not necessary; (3) the temperature dependence of the denaturational heat capacity change is taken into account. Moreover, the equations developed have allowed us to point out the errors that can be made if the temperature-dependence of the denaturational heat capacity change is not taken into account in the calculation of the unfolding thermodynamic functions.

Amino Acids↗

A thermodynamic study on the formation and stability of DNA duplex at transcription site for DNA binding proteins GCN4.

Using isothermal titration calorimetry (ITC), we studied the thermodynamic parameters of the 15-mer duplex dsDNA [d(GAGATGACTCATCTC)].[d(GAGATGAGTCATCTC)] formation from its two complementary single strands (S1 and S2) over a range of temperatures. The two complementary single strands d(GAGATGACTCATCTC) (herein called S1) and d(GAGATGAGTCATCTC) (herein called S2) containing palindromic sequences may assume ordered structures at low temperatures, which made the duplex dsDNA formation rather complicated. The thermodynamic parameters for the duplex formation, such as the binding constants (Kb), the enthalpies (delta H0), the free energies (delta G0), the entropies (delta S0) are strongly temperature-dependent. The thermally-induced disruptions of the duplex and its two complementary single strands, S1 and S2, were measured using differential scanning calorimetry (DSC) and CD spectroscopy, the results demonstrate that the DNA duplex is very stable, and its component single strands have an ordered structure at low temperature. This 15-mer specific sequence DNA may act as recognition site for DNA binding proteins GCN4 and plays a key role in transcription regulation of gene expression. Our analyses of the thermodynamic data suggest that the duplex formation is a coupled process between conformational transitions in the two single strands and their binding to form duplex dsDNA.

Binding Sites↗

Thermodynamic analysis of compact formation; compaction, unloading, and ejection. II. Mechanical energy (work) and thermal energy (heat) determinations of compact unloading and ejection.

A compaction calorimeter, previously described (DeCrosta, M.T., Schwartz, J.B., Wigent, J.B., Marshall, K., 2000. Thermodynamic analysis of compact formation; compaction, unloading, and ejection. I. Design and development of a compaction calorimeter and mechanical and thermal energy determinations of powder compaction. Int. J. Pharm. 198, 113--134), was utilized to evaluate the thermodynamics of the unloading and ejection of compacts of Avicel pH102, Emcompress, Fast-Flo #316, Starch 1500, and acetaminophen (APAP). A constant strain waveform, applied by a compaction simulator, enabled the separate thermodynamic evaluation of unloading from compaction. The brittle materials, Fast-Flo #316 and Emcompress, displayed the most unloading work, and the plastic/self-lubricating materials, Avicel and Starch 1500, displayed the least. Unloading heat values were negative for all materials, except APAP. APAP's positive heat values indicated the breaking of bonds during unloading as a result of its highly elastic nature. Positive internal energy changes of unloading, which indicate the net breaking of bonds, were observed for APAP and Emcompress over the compaction forces tested. Negative energy changes for Starch 1500, Fast-Flo #316, and Avicel became positive with increasing compaction forces. Ejection work increased with increasing compaction force for the brittle materials, whereas smaller ejection work values for Avicel, Starch 1500, and APAP remained constant. Increasing negative heat values as a function of compaction force were observed for Fast-Flo #316 and Emcompress. Negative internal energy values for ejection were observed for Fast-Flo #316 and Emcompress, which indicates net bond formation as a result of high shear of the compact with the die wall. Internal energy changes for Starch 1500, Avicel, and APAP, were approximately zero, indicating the absence of net bonding or bond formation during the process.

Algorithms↗

Thermodynamics of solutions. II. Flurbiprofen and diflunisal as models for studying solvation of drug substances.

Three independent methods (sublimation, solubility and solution calorimetry) were used to study the dissolution and solvation processes of diflunisal (DIF) and flurbiprofen (FBP). Thermodynamic functions for the sublimation of DIF and FBP were obtained. Concentrations of saturated solutions and standard solution enthalpies of DIF and FBP in aliphatic alcohols and individual organic solvents were measured. Correlation analysis between: (a) the thermodynamic functions for a substance in various solvents, and (b) the same functions for different compounds was carried out. The investigated substances can be arranged with increasing Gibbs energy of solvation as follows: benzoic acid<DIF<FBP. Enthalpy is found to be the major driving force of the solvation process for all the studied compounds. The ratio of specific and nonspecific solute-solvent interaction in terms of enthalpies (epsilon (H)) and in terms of entropies (epsilon (S)) was analyzed. Based on the experimental data, a compensation effect of thermodynamic solubility functions of the investigated substances both in alcohols and in organic solvents was found.

Alcohols↗

Thermodynamic quantitative structure-activity relationship analysis for enzyme-ligand interactions in aqueous phosphate buffer and organic solvent.

Thermodynamic quantitative structure-activity relationships (QSAR) for chymotrypsin-ligand binding is developed, and the results are compared for the effects of organic solvent on the substrate specificity of the enzymes to those in aqueous phosphate buffer. This is the first of such analysis utilizing thermodynamic QSAR. A possible explanation for the difference describing the effects of organic solvent for the binding of substituted phenyl esters of N-benzoyl L-alanine analogues [PhCONHCH(Me)COOC(6)H(4)-p-X, I] observed in both the classical and the thermodynamic QSAR is presented.

Alanine↗

The thermodynamics and evolution of complexity in biological systems.

Recent advances in nonequilibrium thermodynamics leads to the conclusion that similar processes, constrained by the second law of thermodynamics, give rise to the emergence of structure and process in a broad class of dissipative systems. The second law suggests that, in systems moved away from equilibrium, processes can emerge so that the system organizes in a way that reduces the effect of the applied gradient. If dynamic and or kinetic conditions permit, self organization processes can be expected. As biosystems grow and develop, they should increase their total dissipation, and develop more complex structures with more energy flow, increase their cycling activity, develop greater diversity and generate more hierarchical levels. As a corollary to this general statement, biosystems which do not increase their total dissipation, are organisms dedicated to death, like observed during the aging of any biosystem. Species which survive in ecosystems are those that funnel energy into their own production and reproduction and contribute to autocatalytic processes which increase the total dissipation of the ecosystem while at same time surviving within the constraints of their changing environment. In a broad class of biosystems, stress and aging have similar thermodynamic properties and suggests common underlying principles.

Aging↗

Role of H1 in chromatin folding. A thermodynamic study of chromatin reconstitution by differential scanning calorimetry.

In a series of related papers, we have recently presented the results of a thermodynamic approach to the conformational transitions of bulk chromatin induced in vitro by different structure-perturbing agents, such as the intercalating dye ethidium bromide or the ionic strength. In all these studies, we took advantage of the capability of differential scanning calorimetry to detect the changes in the melting behavior of the structural domains of chromatin (the linker and the core particle) associated with the order-disorder transitions. This technique also revealed that the higher-order structure undergoes a catastrophic decondensation process in the course of the transformation of rat hepatocytes as well as of cultured cells. Therefore, several questions arose concerning the biological function (if any) of the changes in the degree of condensation of bulk chromatin, as well as the mechanism of transition and the nature of the modulating agents. In this paper, we report a thermodynamic analysis of the reconstitution of H1-depleted calf thymus chromatin with the purpose of establishing (1) the binding mode of H1 and (2) the energetics and cooperativity of the transition from the unfolded to the condensed state. When H1 is progressively extracted from calf thymus nuclei by high-salt treatment, the endotherm at 107 degrees C, characteristic of the core particles interacting within condensed domains, converts into the thermal transition at 90 degrees C, resulting from the denaturation of noninteracting core particles. Binding of H1 fully restores the thermal profile of native chromatin. Analysis of H1 association shows that binding occurs at independent sites with KA = (3.67 +/- 0.60) x 10(4) M-1 and each site comprising 180 +/- 10 bp. The experimental dependence of the fraction of condensed chromatin on R, the moles of bound H1 per nucleosome mole, was compared with a simple thermodynamic model for the conformational change. This analysis yields a value of -5 kcal per nucleosome mole for the interaction free energy of nucleosomes within the ordered state. The process of condensation, is not, however, a highly cooperative (all-or-none) one, as expected from a consideration of the solenoidal model for the 30 nm fiber. Rather, nucleation of the helical state involves the face-to-face interaction between consecutive core particles, and the growth is largely determined by the mergence and rearrangement of neighboring clusters of helically arrayed nucleosomes.

Animals↗

Interaction of minor groove ligands to an AAATT/AATTT site: correlation of thermodynamic characterization and solution structure.

A combination of circular dichroism spectroscopy, titration calorimetry, and optical melting has been used to investigate the association of the minor groove ligands netropsin and distamycin to the central A3T2 binding site of the DNA duplex d(CGCAAATTGGC).d(GCCAATTTGCG). For the complex with netropsin at 20 degrees C, a ligand/duplex stoichiometry of 1:1 was obtained with Kb approximately 4.3 x 10(7) M-1, delta Hb approximately -7.5 kcal mol-1, delta Sb approximately 9.3 cal K-1 mol-1, and delta Cp approximately 0. Previous NMR studies characterized the distamycin complex with A3T2 at saturation as a dimeric side-by-side complex. Consistent with this result, we found a ligand/duplex stoichiometry of 2:1. In the current study, the relative thermodynamic contributions of the two distamycin ligands in the formation of this side-by-side complex (2:1 Dst.A3T2) were evaluated and compared with the thermodynamic characteristics of netropsin binding. The association of the first distamycin molecule of the 2:1 Dst.A3T2 complex yielded the following thermodynamic profile: Kb approximately 3.1 x 10(7) M-1, delta Hb = -12.3 kcal mol-1, delta Sb = -8 cal K-1 mol-1, and delta Cp = -42 cal K-1 mol-1. The binding of the second distamycin molecule occurs with a lower Kb of approximately 3.3 x 10(6) M-1, a more favorable delta Hb of -18.8 kcal mol-1, a more unfavorable delta Sb of -34 cal K-1 mol-1, and a higher delta Cp of -196 cal K-1 mol-1. The latter term indicates an ordering of electrostricted and structural water molecules by the complexes. These results correlate well with the NMR titrations and are discussed in context of the solution structure of the 2:1 Dst.A3T2 complex.

Base Sequence↗

Impact of phosphorothioate substitutions on the thermodynamic stability of an RNA GAAA tetraloop: an unexpected stabilization.

This study analyzes the impact of phosphorothioate substitutions on the thermodynamic stability of a 12-nt RNA hairpin containing a (5')GAAA(3') tetraloop. The thermodynamic consequences of stereospecific phosphorothioate substitutions 5' to each adenosine in the loop region are measured using optical melting and calorimetry experiments. Surprisingly, a single stereospecific phosphorothioate substitution 5' to the second adenosine of the tetraloop, R(p)-A7, results in a stabilization corresponding to a Delta(DeltaG(37)(degrees)(C)) of approximately -2.9 kcal mol(-1) (0.1 M NaCl) when compared with that of an unmodified sample. Five other phosphorothioate-substituted samples did not show significant thermodynamic differences in comparison with the unsubstituted samples. Addition of Mg(2+) to all of the hairpins studied results in increased t(m's) that are fit with a general electrostatic model to a dissociation constant of K(d)(Mg(2+)) approximately 2-3 mM (0.1 M NaCl). The R(p)-A7 phosphorothioate-substituted hairpin showed an unusual decrease in t(m) and apparent increase in enthalpy of unfolding upon addition of Cd(2+). These results may impact the interpretation of interference mapping experiments that use phosphorothioate substitutions to characterize RNAs in solution.

Cadmium↗