Thermodynamics of the hydrophobic effect. I. Coupling of aggregation and pK(a) shifts in solutions of aliphatic amines

Long aliphatic hydrocarbon chains aggregate in aqueous solution due to the hydrophobic effect, forming structures such as micelles and membranes, while amino groups titrate at basic pH. These two biologically important behaviors are linked in alkylamines, in which the pK(a) of the amino group is shifted downward by aggregation. In this paper we study the thermodynamics of these coupled processes, following aggregation by observing alkylamine pH titration behavior. The magnitude of the shift depended on the aliphatic chain length and on the concentration of alkylamine: longer chains and higher concentrations lowered the pK(a) to a greater extent. Gibbs free energies of protonation and aggregation were calculated from the pK(a) shifts. Enthalpies, entropies, and heat capacities were estimated by van't Hoff analysis from the pK(a) shift dependencies on temperature. However, the results were less precise than the calorimetrically measured values, as described in the following article. A model to calculate titration curves, pK(a) shifts, and aggregation of uncharged alkylamines as a function of aliphatic chain length, concentration, and temperature is presented.     

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.     

Significant discrepancies between van't Hoff and calorimetric enthalpies. II.

Isothermal calorimetric titration of 18-crown-6 ether with BaCl2 in pure aqueous solution over the temperature range 7-40 degrees C gives precise binding constants and enthalpy changes. Nonlinear least-squares fitting of the binding constants to the integrated van't Hoff equation, including a temperature-independent change in heat capacity, leads to van't Hoff enthalpies that differ significantly from the observed calorimetric enthalpies. This perplexing discrepancy appears at present to be very widely occurring.     

Calorimetric vs. van't Hoff binding enthalpies from isothermal titration calorimetry: Ba2+-crown ether complexation

The 1:1 complexation reaction between Ba(2+) and 18-crown-6 ether is re-examined using isothermal titration calorimetry (ITC), with the goal of clarifying previously reported discrepancies between reaction enthalpies estimated directly (calorimetric) and indirectly, from the temperature dependence of the reaction equilibrium constant K (van't Hoff). The ITC thermograms are analyzed using three different non-linear fit models based on different assumptions about the data error: constant, proportional to the heat and proportional but correlated. The statistics of the fitting indicate a preference for the proportional error model, in agreement with expectations for the conditions of the experiment, where uncertainties in the delivered titrant volume should dominate. With attention to proper procedures for propagating statistical error in the van't Hoff analysis, the differences between Delta H(cal) and Delta H(vH) are deemed statistically significant. In addition, statistically significant differences are observed for the Delta H(cal) estimates obtained for two different sources of Ba(2+), BaCl(2) and Ba(NO(3))(2). The effects are tentatively attributed to deficiencies in the standard procedure in ITC of subtracting a blank obtained for pure titrant from the thermogram obtained for the sample.     

A Thermodynamic Characterization of the Binding of Thrombin Inhibitors to Human Thrombin, Combining Biosensor Technology, Stopped-Flow Spectrophotometry, and Microcalorimetry

The binding of a series of low-molecular-mass, active-site-directed thrombin inhibitors (399-575 Da) to human alpha-thrombin was investigated by surface plasmon resonance technology (BIACORE), stopped-flow spectrophotometry, and isothermal titration microcalorimetry (ITC). The equilibrium constants K(D) (nM to microM range) at 25 degrees C obtained from the BIACORE analysis correlated well with the inhibition constants K(i) in a chromogenic inhibition assay. The interactions between thrombin and three potent inhibitors, melagatran, inogatran, and CH-248, were further investigated at temperatures between 278 and 310K. A one-to-one binding stoichiometry found with ITC was supported by BIACORE data. K(i) and K(D) values increased with the temperature, mainly due to higher values for dissociation rate constants. The changes in enthalpy, DeltaH, and entropy, DeltaS, determined from the linear van't Hoff plots (R coefficient > 0.99), were linearly correlated by chemical compensation. Both techniques indicated clear differences in DeltaS for the three inhibitors, with a strong correlation to the number of rotational bonds. Immobilization of thrombin increased the binding stability at higher temperature and reduced the DeltaH by 20 kJ mol(-1). DeltaH values obtained from the inhibition kinetics and BIACORE were thus not identical, but correlated well with ITC data obtained at 37 degrees C. The two thermodynamic techniques allowed further differentiation between compounds of similar affinity; furthermore, kinetic analysis, hence analysis of the transition state, is complementary to ITC. A direct BIACORE binding assay might be a useful alternative to more elaborate inhibition studies.     

Enthalpy and heat capacity changes for formation of an oligomeric DNA duplex: interpretation in terms of coupled processes of formation and association of single-stranded helices.

The thermodynamics of self-assembly of a 14 base pair DNA double helix from complementary strands have been investigated by titration (ITC) and differential scanning (DSC) calorimetry, in conjunction with van't Hoff analysis of UV thermal scans of individual strands. These studies demonstrate that thermodynamic characterization of the temperature-dependent contributions of coupled conformational equilibria in the individual "denatured" strands and in the duplex is essential to understand the origins of duplex stability and to derive stability prediction schemes of general applicability. ITC studies of strand association at 293 K and 120 mM Na+ yield an enthalpy change of -73 +/- 2 kcal (mol of duplex)-1. ITC studies between 282 and 312 K at 20, 50, and 120 mM Na+ show that the enthalpy of duplex formation is only weakly salt concentration-dependent but is very strongly temperature-dependent, decreasing approximately linearly with increasing temperature with a heat capacity change (282-312 K) of -1.3 +/- 0.1 kcal K-1 (mol of duplex)-1. From DSC denaturation studies in 120 mM Na+, we obtain an enthalpy of duplex formation of -120 +/- 5 kcal (mol of duplex)-1 and an estimate of the corresponding heat capacity change of -0.8 +/- 0.4 kcal K-1 (mol of duplex)-1 at the Tm of 339 K. van't Hoff analysis of UV thermal scans on the individual strands indicates that single helix formation is noncooperative with a temperature-independent enthalpy change of -5.5 +/- 0.5 kcal at 120 mM Na+. From these observed enthalpy and heat capacity changes, we obtain the corresponding thermodynamic quantities for two fundamental processes: (i) formation of single helices from disordered strands, involving only intrastrand (vertical) interactions between neighboring bases; and (ii) formation of double helices by association (docking) of single helical strands, involving interstrand (horizontal and vertical) interactions. At 293 K and 120 mM Na+, we calculate that the enthalpy change for association of single helical strands is approximately -64 kcal (mol of duplex)-1 as compared to -210 kcal (mol of duplex)-1 calculated for duplex formation from completely unstructured single strands and to the experimental ITC value of -73 kcal (mol of duplex)-1. The intrinsic heat capacity change for association of single helical strands to form the duplex is found to be small and positive [ approximately 0.1 kcal K-1 (mol of duplex)-1], in agreement with the result of a surface area analysis, which also predicts an undetectably small heat capacity change for single helix formation.     

Adsorption of RNase A on cationic polyelectrolyte brushes: a study by isothermal titration calorimetry

We present a study of the adsorption of a positively charged protein to a positively charged spherical polyelectrolyte brush (SPB) by isothermal titration calorimetry (ITC). ITC is used to determine the adsorption isotherm as a function of temperature and of salt concentration (at physiological pH 7.2). At low ionic strength, RNase A is strongly adsorbed by the SPB particles despite the fact that both the SPB particles and the protein are positively charged. Virtually no adsorption takes place when the ionic strength is raised through added salt. This is strong evidence for counterion release as the primary driving force for protein adsorption. We calculated that ~2 counterions were released upon RNase A binding. The adsorption of RNase A into like-charged SPB particles is entropy-driven, and protein protonation was not significant. Temperature-dependent measurements showed a disagreement between the enthalpy derived via the van't Hoff equation and the calorimetric enthalpy. Further analysis shows that van't Hoff analysis leads to the correct enthalpy of adsorption. The additional contributions to the measured enthalpy are potentially sourced from unlinked equilibria such as conformational changes that do not contribute to the binding equilibrium.     

Stoichiometry determination for carbon monoxide binding to Rhodospirillum molischianum cytochrome c'

The stoichiometry of CO ligation to the dimer heme protein Rhodospirillum molischianum cytochrome c' is determined. We have recently measured the enthalpy change of CO ligation to this molecule by the van't Hoff method and found the value of -10.7 +/- 1.2 kcal/mol CO (aqueous) (Doyle, M. L., Weber, P. C., and Gill, S. J. (1985) Biochemistry 24, 1987-1991). In the present paper the enthalpy change of CO ligation, measured directly by titration calorimetry, is found to be -9.5 +/- 0.2 kcal/mol heme. Since the van't Hoff method gives the heat value in units/mole of CO and the calorimetric method gives the heat value in units/mole of heme, the stoichiometry of the reaction is given by the ratio of the two values and found to be 0.9 +/- 0.1, or within experimental error, one CO molecule bound per heme.     

A survey of the year 2007 literature on applications of isothermal titration calorimetry

Elucidation of the energetic principles of binding affinity and specificity is a central task in many branches of current sciences: biology, medicine, pharmacology, chemistry, material sciences, etc. In biomedical research, integral approaches combining structural information with in-solution biophysical data have proved to be a powerful way toward understanding the physical basis of vital cellular phenomena. Isothermal titration calorimetry (ITC) is a valuable experimental tool facilitating quantification of the thermodynamic parameters that characterize recognition processes involving biomacromolecules. The method provides access to all relevant thermodynamic information by performing a few experiments. In particular, ITC experiments allow to by-pass tedious and (rarely precise) procedures aimed at determining the changes in enthalpy and entropy upon binding by van't Hoff analysis. Notwithstanding limitations, ITC has now the reputation of being the "gold standard" and ITC data are widely used to validate theoretical predictions of thermodynamic parameters, as well as to benchmark the results of novel binding assays. In this paper, we discuss several publications from 2007 reporting ITC results. The focus is on applications in biologically oriented fields. We do not intend a comprehensive coverage of all newly accumulated information. Rather, we emphasize work which has captured our attention with originality and far-reaching analysis, or else has provided ideas for expanding the potential of the method. Copyright (c) 2008 John Wiley & Sons, Ltd.     

Making cool drugs hot: isothermal titration calorimetry as a tool to study binding energetics

Characterization of the thermodynamics of binding interactions is important in improving our understanding of bimolecular recognition and forms an essential part of the rational drug design process. Isothermal titration calorimetry (ITC) is rapidly becoming established as the method of choice for undertaking such studies. The power of ITC lies in its unique ability to measure binding reactions by the detection of the heat change during the binding interaction. Since heat changes occur during many physicochemical processes, ITC has a broad application, ranging from chemical and biochemical binding studies to more complex processes involving enthalpy changes, such as enzyme kinetics. Several features of ITC have facilitated its preferential use compared to other techniques that estimate affinity. It is a sensitive, rapid, and direct method with no requirement for chemical modification or immobilization. It is the only technique that directly measures enthalpy of binding and so eliminates the need for van't Hoff analysis, which can be time consuming and prone to uncertainty in parameter values. Although ITC has facilitated the measurement of the thermodynamics governing binding reactions, interpretation of these parameters in structural terms is still a major challenge.     

Isothermal acid-titration calorimetry for evaluating the pH dependence of protein stability

A new method, which can be called as isothermal acid-titration calorimetry (IATC), was proposed for evaluating the enthalpy of protein molecules as a function of pH using isothermal titration calorimetry (ITC). This measurement was used to analyze the acid-denaturation of bovine ribonuclease A. The enthalpy change by acid-denaturation of this protein was estimated as 310 kJ/mol at pH 2.8 and 40 degrees C. This value agreed well with the enthalpy change obtained by differential scanning calorimetry. The midpoint pH and proton binding-number difference observed by IATC agreed well with those of the acid transition of the three-dimensional structure monitored by circular dichroism spectrometry. The van't Hoff enthalpy of the transition was derived from the temperature dependence of the midpoint pH and the proton binding-number difference. It agreed well with the calorimetric enthalpy change directly observed by IATC, strongly indicating that there was no stable intermediate state during the acid transition of this protein.     

Isothermal titration calorimetry study of the polyelectrolyte complexation of xanthan and chitosan samples of different degree of polymerization

Mixing oppositely charged polyelectrolytes in aqueous solutions leads to the spontaneous formation of polyelectrolyte complexes. Here, we characterize the interaction between xanthan of two different chain lengths, a tri-glucosamine and a chitosan polymer by isothermal titration calorimetry (ITC). Analysis of the experimental thermodynamic data assuming a single set of identical sites indicated both enthalpic and entropic contributions to the overall interaction in the interaction between xanthan and tri-glucosamine. The relative contribution of entropy compared to enthalpy was found to be largest for the shortest chain length of xanthan. Using a chitosan polymer instead of tri-glucosamine gave rise to two different stages in the interaction process. A model where the first stage of the ITC curve represent an initial polyelectrolyte complexation stage followed by aggregation on further titration of chitosan to the xanthan is suggested. Ultrastructure images by applying atomic force microscopy at some selected extents of titration are consistent with the two-stage interpretation of the thermodynamic data.     

Substrate specificity of a long-chain alkylamine-degrading <Emphasis Type="Italic">Pseudomonas</Emphasis> sp isolated from activated sludge

A bacterium strain BERT, which utilizes primary long-chain alkylamines as nitrogen, carbon and energy source, was isolated from activated sludge. This rod-shaped motile, Gram-negative strain was identified as a Pseudomonas sp. The substrate spectrum of this Pseudomonas strain BERT includes primary alkylamines with alkyl chains ranging from C₃ to C₁₈, and dodecyl-1,3-diaminopropane. Amines with alkyl chains ranging from 8 to 14 carbons were the preferred substrates. Growth on dodecanal, dodecanoic acid and acetic acid and simultaneous adaptation studies indicated that this bacterium initiates degradation through a C_alkyl–N cleavage. The cleavage of alkylamines to the respective alkanals in Pseudomonas strain BERT is mediated by a PMS-dependent alkylamine dehydrogenase. This alkylamine dehydrogenase produces stoichiometric amounts of ammonium from octylamine. The PMS-dependent alkylamine was found to oxidize a broad range of long-chain alkylamines. PMS-dependent long-chain aldehyde dehydrogenase activity was also detected in cell-free extract of Pseudomonas strain BERT grown on octylamine. The proposed pathway for the oxidation of alkylamine in strain BERT proceeds from alkylamine to alkanal, and then to the fatty acid.     

Thermodynamics of the denaturation of lysozyme in alcohol--water mixtures.

The thermal denaturation of lysozyme was studied at pH 2 in aqueous mixtures of methanol, ethanol, and 1-propanol by high sensitivity differential scanning calorimetry (DSC). The most obvious effect of alcohols was the lowering of Td, the temperature of denaturation, increasingly with higher alcohol concentration and longer alkyl chain. Both the calorimetric and van't Hoff enthalpies of denaturation initially increased and then decreased with increasing alcohol concentration, the ratio of the two enthalpies being nearly unity, 1.007 +/- 0.011, indicating the validity of the two-state approximation for the unfolding of lysozyme in these solvent systems. The reversibility of the denaturation was demonstrated by the reversibility of the DSC curves and the complete recovery of enzymic activity on cooling. The changes in heat capacity on unfolding decreased with increasing alcohol concentration for each alcohol. Experimentally determined values of denaturation temperature and of entropy and heat capacity changes were used to derive the additional thermodynamic parameters delta G degrees and delta S degrees for denaturation as a function of temperature for each alcohol--water mixture. Comparison of the thermodynamic parameters with those reported [Pfeil, W., & Privalov, P.L. (1976) Biophys. Chem. 4, 23--50] in aqueous solution at various values of pH and guanidine hydrochloride concentration showed that these latter changes have no effect on the heat capacity changes, whereas the addition of alcohols causes a sharp decrease.     

Thermodynamics of oligosaccharide binding to a monoclonal antibody specific for a Salmonella O-antigen point to hydrophobic interactions in the binding site.

The thermodynamic characteristics of oligosaccharide binding to an antibody binding site that is dominated by aromatic amino acids suggest that the hydrophobic effect contributes substantially to complex formation as well as hydrogen bonding and van der Waals interactions. A detailed titration microcalorimetric study on the temperature dependence of the binding of a trisaccharide, representing the epitope of a Salmonella O-antigen, showed that its maximum binding to the monoclonal antibody Se155-4 occurs just below room temperature and both enthalpy and entropy changes are strongly dependent on temperature in a mutually compensating manner. The heat capacity change also shows an unusually strong temperature dependence being large and negative above room temperature and positive below. van't Hoff analysis of the temperature dependence of the binding constant yielded a biphasic curve with two apparent intrinsic enthalpy estimations (approximately -100 kJ mol-1 above 18 degrees C and approximately +100 kJ mol-1 below), each very different from the calorimetrically determined enthalpies (ranging from about -60 kJ mol-1 to -20 kJ mol-1). This was interpreted as being due to large enthalpy contributions from concomitant reactions, most notably changes in solvation. Linear plots, -delta H0 versus -T delta S0, observed for temperature-dependent measurements mirror the behavior seen for a series of functional group replacements, suggesting that the molecular and physical origin of these phenomena are closely related and linked to the role of water in complex formation. The thermodynamic results are compared to the mode of binding determined from a 2.05-A resolution structure of the Fab-oligosaccharide complex, and with literature data for the heat capacities of sugars in aqueous solution and for the thermodynamics of carbohydrate binding to transport proteins and lectins.     

Thermodynamic comparison of PNA/DNA and DNA/DNA hybridization reactions at ambient temperature

The thermodynamics of 13 hybridization reactions between 10 base DNA sequences of design 5'-ATGCXYATGC-3' with X, Y = A, C, G, T and their complementary PNA and DNA sequences were determined from isothermal titration calorimetry (ITC) measurements at ambient temperature. For the PNA/DNA hybridization reactions, the binding constants range from 1.8 x 10(6)M(-1)for PNA(TT)/DNA to 4.15 x 10(7)M(-1)for PNA(GA)/DNA and the binding enthalpies range from -194 kJ mol(-1)for PNA(CG)/DNA to -77 kJ mol(-1)for PNA(GT)/DNA. For the corresponding DNA/DNA binding reactions, the binding constants range from 2.9 x 10(5)M(-1)for DNA(GT)/DNA to 1.9 x 10(7)M(-1)for DNA(CC)/DNA and the binding enthalpies range from -223 kJ mol(-1)for DNA(CG)/DNA to -124 kJ mol(-1)for DNA(TT)/DNA. Most of the PNA sequences exhibited tighter binding affinities than their corresponding DNA sequences resulting from smaller entropy changes in the PNA/DNA hybridization reactions. van't Hoff enthalpies and extrapolated Delta G values determined from UV melting studies on the duplexes exhibited closer agreement with the ITC binding enthalpies and Delta G values for the DNA/DNA duplexes than for the PNA/DNA duplexes.     

Temperature-induced conformational change at the catalytic site of Sulfolobus solfataricus alcohol dehydrogenase highlighted by Asn249Tyr substitution. A hydrogen/deuterium exchange, kinetic, and fluorescence quenching study

A combination of hydrogen/deuterium exchange, fluorescence quenching, and kinetic studies was used to acquire experimental evidence for the crystallographically hypothesized increase in local flexibility which occurs in thermophilic NAD(+)-dependent Sulfolobus solfataricus alcohol dehydrogenase (SsADH) upon substitution Asn249Tyr. The substitution, located at the adenine-binding site, proved to decrease the affinity for both coenzyme and substrate, rendering the mutant enzyme 6-fold more active when compared to the wild-type enzyme [Esposito et al. (2003) FEBS Lett. 539, 14-18]. The amide H/D exchange data show that the wild-type and mutant enzymes have similar global flexibility at 22 and 60 degrees C. However, the temperature dependence of the Stern-Volmer constant determined by acrylamide quenching shows that the increase in temperature affects the local flexibility differently, since the K(SV) increment is significantly higher for the wild-type than for the mutant enzyme over the range 18-45 degrees C. Interestingly, the corresponding van't Hoff plot (log K(SV) vs 1/T) proves nonlinear for the apo and holo wild-type and apo mutant enzymes, with a break at approximately 45 degrees C in all three cases due to a conformational change affecting the tryptophan microenvironment experienced by the quencher molecules. The Arrhenius and van't Hoff plots derived from the k(cat) and K(M) thermodependence measured with cyclohexanol and NAD(+) at different temperatures display an abrupt change of slope at 45-50 degrees C. This proves more pronounced in the case of the mutant enzyme compared to the wild-type enzyme due to a conformational change in the structure rather than to an overlapping of two or more rate-limiting reaction steps with different temperature dependencies of their rate constants. Three-dimensional analysis indicates that the observed conformational change induced by temperature is associated with the flexible loops directly involved in the substrate and coenzyme binding.     

Van't Hoff and calorimetric enthalpies from isothermal titration calorimetry: are there significant discrepancies?

The enthalpy of a reaction is most often determined through one of two means; it can be determined directly using calorimetry or indirectly by measuring the temperature dependence of the equilibrium constant (i.e., the van't Hoff method). Recently, discrepancies have been noted between the enthalpy measured by calorimetry, and the enthalpy determined by the van't Hoff method,. This has been suggested to indicate that the binding reaction is more complex than the simple one-to-one binding model used to describe the data. To better understand possible discrepancies between and, we have undertaken both experimental studies using isothermal titration calorimetry to measure the binding energetics of Ba(2+) binding 18-crown-6 ether and 2'-CMP binding RNase A, along with a simulation of a system involving a molecule in conformational equilibrium coupled with binding. We find that when experimental setup and analysis are correctly performed, no statistically significant discrepancies between and exist even for the linked system.     

Statistical aspects of van't Hoff analysis: a simulation study

The thermodynamics of biological interactions is frequently studied by the van't Hoff analysis whereby data on variation of the binding constant K(D) with temperature are used to obtain estimates of standard enthalpy (Delta H degrees ), entropy (Delta S degrees ), and heat capacity (Delta C degrees P) of complex formation. A Monte Carlo simulation demonstrates that the absolute error of the above parameters is proportional to the relative error of KD and independent of the actual values of KD and of the way they vary with temperature. The error of Delta H degrees is approximately the same as that of T Delta S degrees (within 14% in the temperature range 5-45 degrees C). The error depends both on the number of temperature points within the experimental temperature range and on the size of the range, but it is more sensitive to the latter. Using the linear form of the van't Hoff equation to fit data with non-zero Delta C degrees P gives erroneous Delta H degrees and DeltaS degrees estimates at standard temperature except for the case when the T points are placed symmetrically with respect to the standard temperature. With the range of Delta C degrees P values usual for protein-protein interactions, the KD error must be very low to confidently infer that Delta C degrees P is non-zero or to claim that two interactions have different Delta C degrees P.