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PubMed2001

Heat does not come in different colours: entropy-enthalpy compensation, free energy windows, quantum confinement, pressure perturbation calorimetry, solvation and the multiple causes of heat capacity effects in biomolecular interactions.

Modern techniques in microcalorimetry allow us to measure directly the heat changes and associated thermodynamics for biomolecular processes in aqueous solution at reasonable concentrations. All these processes involve changes in solvation/hydration, and it is natural to assume that the heats for these processes should reflect, in some way, such changes in solvation. However, the interpretation of data is still somewhat ambiguous, since different non-covalent interactions may have similar thermodynamic signatures, and analysis is frustrated by large entropy-enthalpy compensation effects. Changes in heat capacity (Delta C(p)) have been related to changes in hydrophobic hydration and non-polar accessible surface areas, but more recent empirical and theoretical work has shown how this need not always be the case. Entropy-enthalpy compensation is a natural consequence of finite Delta C(p) values and, more generally, can arise as a result of quantum confinement effects, multiple weak interactions, and limited free energy windows, giving rise to thermodynamic homeostasis that may be of evolutionary and functional advantage. The new technique of pressure perturbation calorimetry (PPC) has enormous potential here as a means of probing solvation-related volumetric changes in biomolecules at modest pressures, as illustrated with preliminary data for a simple protein-inhibitor complex.

Calorimetry↗

PubMed2000

Entropy measurements and the kinetic method: a statistically meaningful approach

In the literature, data obtained using the kinetic method have been analyzed to provide both ion affinities and relative entropies for the competitive dissociations involved. In this work, the procedure used to extract this information is shown to be statistically flawed. Using more rigorous statistical procedures, we outline alternative methods of acquiring the same information, including straightforward means of analyzing the uncertainties in the thermodynamic quantities obtained. Fortunately, it is expected that the central values reported in previous work need not be changed, but the uncertainties are much larger than has been previously detailed. The validity of the assumptions involved in the extraction of entropy effects is discussed in some detail.

Journal Article↗

PubMed2000

Determination of the proton affinities of bromo- and iodoacetonitrile using the kinetic method with full entropy analysis

The proton affinities bromo- and iodoacetonitrile are determined using a full implementation of the kinetic method, which includes calculation of the entropies. Branching ratios for dissociation of proton-bound dimers are measured for collision energies ranging from approximately 2 to 5 eV. Using a rigorously correct statistical approach, the proton affinities of bromo- and iodoacetonitrile are calculated to be 179.8 +/- 1.7 and 182.9 +/- 1.6 kcal/mol, respectively. It is shown that neglecting the entropy contributions for these systems leads to proton affinities that are too high by approximately 0.6 kcal/mol.

Journal Article↗

PubMed1999

Quality control of polysomnographic sleep data by histogram and entropy analysis.

OBJECTIVE AND METHODS: Sixteen polysomnographic recordings from 8 European sleep laboratories were analyzed. The histogram analysis was used to introduce quality control of all-night EEG recordings. RESULTS: It was found that the header information does not always provide the real saturation values of the recording equipment. The entropy measure was used for the quantitative analysis of the dynamic range of routinely used polysomnographic recorders. It was found that the recording equipment provides EEG data with entropy in the range of 8-11 bits. CONCLUSION: In the all-night sleep EEG were observed non-linearities. It is recommended that the equipment provide the saturation values in order to apply automated overflow detection.

Humans↗

PubMed2002

Thermodynamic interpretation of retention equilibrium in reversed-phase liquid chromatography based on enthalpy-entropy compensation.

The fundamentals of the retention equilibrium in reversed-phase liquid chromatography (RPLC) are studied on the basis of enthalpy-entropy compensation (EEC). First, retention data were acquired and the influence of the nature of the compounds, organic solvent modifier, and temperature on these data was assessed. Then, the data were analyzed according to the four different methods proposed by Krug et al., and an EEC was formally established. Linear correlations were observed between the logarithm of the adsorption equilibrium constants under the different RPLC conditions, suggesting linear free energy relationships (LFERs). Finally, the variations of the retentions with the experimental conditions are shown to be quantitatively explained by a new model based on EEC. This model affords a comprehensive interpretation of the variations of retention originating from changes of either one parameter alone or several simultaneously. The slope and intercept of the LFER that relates two equilibrium systems are accounted for by the new model. The parameters of this model are the changes of enthalpy and entropy associated with the retention, the compensation temperatures, and the experimental conditions.

Journal Article↗

PubMed1995

A positive entropy change for guanosine binding and for the chemical step in the Tetrahymena ribozyme reaction.

The ribozyme derived from the group I intron of Tetrahymena thermophila binds an exogenous guanosine nucleotide, which acts as the nucleophile in the sequence-specific cleavage of oligonucleotides. By examining the temperature dependence of the reaction under conditions where Km = Kd, we conclude the following: (1) Guanosine 5'-monophosphate (pG) binds to the closed ribozyme-oligonucleotide substrate complex with a positive entropy change (delta S degree' = +23 eu) and an enthalpy change (delta H degree') close to zero. This is contrary to the expectation that binding would cause increased order (negative delta S degree) and be driven by a negative delta H degree. (2) Inosine and 2-aminopurine riboside, each lacking two hydrogen-bonding moieties relative to guanosine, also bind with a positive entropy value and an unfavorable (positive) delta H degree'. From this result, we suggest that the hydrogen-bonding moieties make an enthalpic contribution to guanosine binding overcoming an intrinsic unfavorable delta H. (3) At 0 degree C, there is equally tight binding of pG in the presence and absence of oligonucleotide substrate bound to the ribozyme. Thus, energetic interactions responsible for the thermodynamic coupling between pG and oligonucleotide substrate binding seen at higher temperatures are indirect. (4) The activation barrier of the chemical step is stabilized by a positive delta S++ (+31 to 39 eu). This stabilization is seen in four reactions using substrates with two different leaving groups in the presence and absence of pG, suggesting that the entropic contribution is inherent to the active site. The positive delta S values for the chemical step and for the binding of pG can be explained by a conformational change or release of water. Thus, although hydrogen bonding contributes to binding of nucleotides to this RNA enzyme as previously thought, it is these other events which produce a positive delta S that provide the energetic driving force for binding.

Animals↗

PubMed1983

Enthalpy-entropy compensation and heat capacity changes for protein-ligand interactions: general thermodynamic models and data for the binding of nucleotides to ribonuclease A.

General thermodynamic models are presented that can account for the existence of heat capacity changes and compensation between the enthalpy and entropy changes in protein-ligand interactions. The models involve the coupling between some type of transition in the state of the protein (or ligand) and the binding process. The coupled transition may be a proton dissociation, the binding of a second ligand, a change in the degree of aggregation, or a conformational change in either the protein or ligand. Both mandatory coupling and nonmandatory coupling between the binding process and the transition are considered. The model is also extended to include a multistate transition of the protein. Computer simulations show that apparently linear compensation plots (plots of delta H degrees vs. delta S degrees) with a slope approximately equal to the experimental temperature are to be expected for the binding of a ligand to a protein when such coupled reactions exist. Also heat capacity changes, which may be either positive or negative, are to be expected to accompany the reaction. Experimental thermodynamic data for the binding of cytidine 3'-phosphate to ribonuclease A are presented. These data demonstrate apparent enthalpy-entropy compensation when pH and ionic strength are varied. A negative heat capacity change, ranging from -145 (at mu = 1.0 M) to -225 cal/(mol X deg) (at mu = 0.05 M), is also observed for this protein-ligand interaction. The apparent compensation and heat capacity change data are interpreted according to the models presented.

Computers↗

PubMed1986

Thermodynamic properties of oxidation-reduction reactions of bacterial, microsomal, and mitochondrial cytochromes P-450: an entropy-enthalpy compensation effect.

An optically transparent thin-layer electrode cell with a very small volume was used for determination of the formal reduction potentials of bacterial, microsomal, and mitochondrial cytochromes P-450. At an extrapolated zero concentration of dye, the bacterial cytochrome from Pseudomonas putida catalyzing the hydroxylation of camphor and the adrenal mitochondrial cytochrome catalyzing the cholesterol side-chain cleavage reaction had formal reduction potentials of -168 and -285 mV (pH 7.5 and 25 degrees C), respectively. The oxidation-reduction potentials for the rabbit liver microsomal cytochrome P-450 induced by 3-methylcholanthrene and the mitochondrial cytochrome for steroid 11 beta-hydroxylation were found as -360 and -286 mV, respectively. Potential measurements at different temperatures allowed documentation of the standard thermodynamic parameters for cytochrome P-450 reduction for the first time. All cytochromes tested were found to have a relatively large negative entropy change upon reduction. The extent of these changes is comparable to that observed for the ferric-ferrous couple of cytochrome c. An entropy-enthalpy compensation effect was observed among the four cytochromes P-450 examined although the correlation is weaker than that observed with cytochrome c isolated from various sources.

Adrenal Cortex↗

PubMed1989

Contribution of a single hydroxyl group to transition-state discrimination by adenosine deaminase: evidence for an "entropy trap" mechanism.

Adenosine deaminase was found to bind 6-hydroxy-1,6-dihydropurine ribonucleoside (II), formed by reversible addition of water to purine ribonucleoside (I) in a reaction analogous to formation of a tetrahedral intermediate in substrate deamination, with an apparent Ki value of 3 x 10(-13) M at 20 degrees C. 1,6-Dihydropurine ribonucleoside (IV), synthesized by photolysis of purine ribonucleoside in the presence of NaBH4, exhibited a Ki value of 5.4 x 10-6 M. After correction for differences between the relative free energies of solvation of II and IV, the 6-hydroxyl group of II was estimated to contribute more than 16 kcal to the free energy of binding, approaching the enthalapy of formation of a single hydrogen bond to charged group in the vapor phase. The relatively weak binding of IV and of substrate water suggests that entropic effects, arising from the cooperative action of binding determinants contained within these separate molecules, contribute more than 10 kcal/mol to the free energy of binding of II in which these binding determinants are contained within a single molecule. In free solution, the entropy of reversible hydration of I was evaluated by measuring the temperature dependence of equilibria of protonation of I and of pseudobase formation from I-methylpurinium ribonucleoside as -35 eu, comparable with the entropy of activation for the uncatalyzed hydrolysis of adenosine. In the active site of adenosine deaminase, this thermodynamic obstacle is evidently climbed spontaneously as a result of attractive interactions between the active site and the critical hydroxyl group at the 6-position.(ABSTRACT TRUNCATED AT 250 WORDS)

Adenosine Deaminase↗

PubMedDate not supplied

Differential Shannon Entropy as a sensitive measure of differences in database variability of molecular descriptors.

A method termed Differential Shannon Entropy (DSE) is introduced to compare differences in information content and variance of molecular descriptors between compound databases. The analysis is based on histograms recording the individual and grouped distributions of molecular descriptors and calculation of Shannon entropy (SE), a formalism originally applied to digital communication. We have recently shown that SE values reflect the nonparametric variability of descriptor settings. Now the analysis has been advanced to assess differences in information content of 143 molecular descriptors in databases containing synthetic compounds, natural products, or drug-like molecules. The DSE metric captures the degree to which descriptor distributions complement or duplicate information contained in molecular databases. In our analysis, we observe significant differences for a number of descriptors and rank them according to their associated DSE values. Using DSE calculations, relative information content of different types of descriptors can be quantified, even if differences are subtle.

Journal Article↗

PubMed2001

Entropy-controlled solvolytic dissociation kinetics of lanthanide(III) complexes with polyaminocarboxylates in aqueous solutions.

The factors involved in the formation of an inert complex in terms of solvolysis reaction have been studied for lanthanide(III)-acyclic polyaminocarboxylate complexes, as the basis for kinetically controlled selectivity used in analytical methodologies such as HPLC and HPCE. The rate constants for solvolysis and acid-assisted dissociation processes of the lanthanide complexes were determined in a batch system through metal- and ligand-exchange reactions. The reagents used were 8-amino-2-[(2-amino-5-methylphenoxy)methyl]-6-methoxyquinoline-N,N,N',N'-tetraacetic acid (Quin2) and O,O'-bis(2-aminophenyl)ethylene glycol-N,N,N',N'-tetraacetic acid (BAPTA) as octadentate ligands and trans-1,2-diaminocyclohexane-N,N,N',N'-tetraacetic acid (CyDTA) as a hexadentate ligand. It has been found that the rate constants for solvolysis vary from 5.7 x 10(-3) x s(-1) (La3+) to 1.7 x 10(-6) x s(-1) (Lu3+) depending on the ionic radii of Ln(III) ions for the Quin2 complexes, while no such monotonic dependence was observed for the BAPTA complexes. Among the parameters of activation, it is worth noting that there is a considerably large negative entropy of activation, of up to -250 J x mol(-1) x K(-1), and it is this which is responsible for the inertness of the Ln-polyaminocarboxylate complexes. Our data suggest that multiple ligation of the ligand in favor of the large coordination number of Ln(III) ions is of key importance for formation of the negative entropy of activation, in addition to the basicity of the ligand which also plays a significant role in the slow dissociation kinetics of the Ln(III) complexes.

Amino Acids↗

PubMed1996

Thermolysis of Neopentylcobalamin Analogs Complexed to Haptocorrin: Side Chain Entropy and Activation of Organocobalamins for Carbon-Cobalt Bond Homolysis.

The kinetics of the thermal Co-C bond homolysis of the complexes of a vitamin B(12) binding protein (haptocorrin) with a series of analogs of neopentylcobalamin modified in side chain structure have been studied. The analogs include the C13 epimer in which the e propionamide side chain adopts an "upwardly" axial conformation and a series of c side chain-modified analogs, including the c-monocarboxylate, the c-N-methylamide, the c-N,N-dimethylamide, and the c-N-isopropylamide. Activation parameters for the thermal homolysis of these complexes show that the previously observed stabilization of alkylcobalamins by haptocorrin is due to both enthalpic and entropic factors. With the exception of that for the analog having the bulkiest c side chain substituent, neopentylcobalamin-c-N-isopropylamide, the enthalpies of activation are independent of analog structure, but the entropies of activation increase with the steric bulk of the c side chain and with the number of "upwardly" projecting side chains, as previously observed for protein-free neopentylcobalamin and its analogs. The results are discussed in terms of the solvent cage effect on Co-C bond homolysis and the importance of corrin ring side chain thermal motions to the entropy of activation for this reaction.

Journal Article↗

PubMed2001

Entropy control of the cross-reaction between carbon-centered and nitroxide radicals.

Absolute rate constants for the cross-coupling reaction of several carbon-centered radicals with various nitroxides and their temperature dependence have been determined in liquids by kinetic absorption spectroscopy. The rate constants range from <2 x 10(5) M(-)(1) s(-)(1) to 2.3 x 10(9) M(-)(1) s(-)(1) and depend strongly on the structure of the nitroxide and the carbon-centered radical. Grossly, they decrease with increasing rate constant of the cleavage of the corresponding alkoxyamine. In many cases, the temperature dependence shows a non-Arrhenius behavior. A model assuming a short-lived intermediate that is hindered to form the coupling product by an unfavorable activation entropy leads to a satisfactory analytic description. However, the behavior is more likely due to a barrierless single-step reaction with a low exothermicity where the free energy of activation is dominated by a large negative entropy term.

Journal Article↗

PubMed2001

Thermal reactions of anti- and syn-dispiro[5.0.5.2]tetradeca-1,8-dienes: stereomutation and fragmentation to 3-methylcyclohexenes. Entropy-dictated product ratios from diradical intermediates?

A series of cyclobutanes substituted 1,2- by polyenes of increasing radical-stabilizing power has been investigated to test the proposition that stabilization energies obtained independently from apposite, cis,trans geometric isomerizations can be successfully transferred to another system, in this paper, cyclobutanes. The first member of the series, 3-methylenecyclohexene (1), is photodimerized to anti- and syn-dispiro[5.0.5.2]tetradeca-1,8-dienes (anti-2 and syn-2), which undergo stereomutation (stereochemical interconversion) and cycloreversion (fragmentation) to 1 when heated in the range 72.1-118.2 degrees C: anti-2 --> syn-2, DeltaH() = 30.3 kcal mol(-)(1), DeltaS() = 0.2 cal mol(-)(1) K(-)(1); anti-2 --> 1, DeltaH() = 32.8 kcal mol(-)(1), DeltaS() = +8.0 cal mol(-)(1) K(-)(1). Agreement with an enthalpy of activation predicted by assuming full allylic stabilization in a hypothetical diradical intermediate is good. An example of further activation by a radical-stabilizing group is manifested by the approximately 20 000-fold acceleration in rate shown by the system 1-phenyl-3-methylenecyclohexene (3) and anti- and syn-2,9-diphenyldispiro[5.0.5.2]tetradeca-1,8-dienes (anti-4 and syn-4), measured, however, only at 43.6 degrees C. In both systems 2 and 4, volumes of activation for stereochemical interconversion and cycloreversion have been determined and found to be essentially identical within experimental uncertainties, DeltaV() = +10.2 +/- 1.0 and +12.6 +/- 1.4 cm(3) mol(-)(1), respectively (weighted means). These strongly positive values are consistent with the rate-determining step being the first bond-breaking, while the near identity of the volumes of activation argues against the indispensable second bond-breaking being a determining factor in fragmentation. These results are consistent with the theoretically based construct of Charles Doubleday for the paradigm, cyclobutane, in which the ratio between two channels of exit from a "generalized common biradical" is not controlled by enthalpy and entropy, as in the transition state model, but by entropy alone.

Alkadienes↗

PubMed2003

Activation enthalpies and entropies for the microscopic rate constants of acetate-catalyzed isomerization of 5-androstene-3,17-dione.

Both acetic acid and acetate catalyze the isomerization of 5-androstene-3,17-dione (1) to its conjugated isomer, 4-androstene-3,17-dione (3), through a dienol(ate) intermediate. The temperature dependence of the overall isomerization rate constants and of the microscopic rate constants for this isomerization was determined, and the Arrhenius plots give the activation enthalpy and entropy for each step. The source of the activation energy for the overall isomerization and for each of the individual steps is predominantly enthalpic, with a moderate to low entropic penalty. Additionally, the entropy and enthalpy for the keto-enol equilibrium of 1 and dienol were determined; this equilibrium is entirely controlled by enthalpy with no entropic contribution. The relevance of these results to the mechanism of the isomerization of 1 catalyzed by the enzyme 3-oxo-Delta(5)-steroid isomerase is discussed.

Acetates↗

PubMed2005

Enthalpy-entropy compensation is not a general feature of weak association.

Relationships between the enthalpy and entropy changes resulting from perturbations of a system have been discussed in the literature for some time. Both positive correlations (compensation) and negative correlations (anti-compensation) between deltaH and DeltaS have been observed in various experimental contexts, including chemical reaction, physical association, solvation, and protein folding. Many examples have been demonstrated to be statistical artifacts, but some are genuine signatures of the perturbations in molecular characteristics. In particular, recent literature claims that compensation is a general feature of bimolecular associations arising from weak intermolecular interactions. We employ a statistical mechanical framework to predict the magnitude and direction of enthalpy-entropy correlation in bimolecular association. The theory links the macroscale thermodynamic correlation to the relationship between the intermolecular potential parameters. Using a harmonic approximation to the Lennard-Jones model and potential parameters taken from the literature, we show examples of both compensation and anti-compensation for gas-phase self-association among five homologous series. Furthermore, an aggregate presentation of data for 48 different chemical species shows no correlation in either direction, for the case of self-association in a dilute gas phase.

Journal Article↗

PubMed2002

Entropy-controlled diastereoselectivity in the photocyclization of rigid derivatives of o-allylaniline.

Two rigid derivatives of o-allylaniline, namely 8-allyl-2-phenyl-1,2,3,4-tetrahydroquinoline (1b) and 7-(trans-2-cinnamyl)-2-methylindoline (1c), have been chosen as suitable systems to study the potential stereoselectivity of the photocyclization process. Photolysis of 1b leads to a mixture of diastereomeric lilolidines 4 (trans/cis), while 1cproduces a mixture of 4 (trans/cis) and the tetrahydropyrrolo[3,2,1-hi]indole derivatives 5 (trans/cis). To disclose whether the diastereoselectivity could be entropy dependent, photolysis of 1b and 1c has been performed at several temperatures. In both cases, linear relationships have been observed when ln(k(t)/k(c)) (the relative reaction rate constants calculated from the diastereomeric excess) is plotted against the reciprocal temperatures. However, significant entropy-controlled diastereoselectivity has only been found for the photocyclization of 1c to 4. The fluorescence spectra of 1b,c show formation of intramolecular charge-transfer exciplexes, which is in agreement with the proposed excited-state electron-transfer mechanism for photocyclization.

Journal Article↗

PubMed2002

"Chiral perturbation factor" approach reveals importance of entropy term in stereocontrol of the 2,4-pentanediol-tethered reaction.

The stereocontrol mechanism of the 2,4-pentanediol (PD)-tethered reaction was studied in detail using a reaction system consisting of phenyl and rhodium carbenoid moieties. Different tethers were examined to analyze the effects of the methyl groups on the PD tether. Among the reactions with these tethers, the PD tether achieves an unmeasurably high stereoselectivity in a diastereomeric ratio of >500. Another tether showing a high but measurable stereoselectivity in a ratio of 41 is mostly controlled by the entropy term. To clarify the role of the methyl groups on the chiral tethers, which are the origin of the stereocontrol, the "chiral perturbation factor" is introduced. This parameter is defined as the rate of a chiral reaction relative to that of an achiral reference reaction. By analyzing the temperature dependence of the chiral perturbation factors for different chiral-tethered reactions, high potentials of the PD-tethered reaction in its stereocontrol are concluded to be due to the entropy term.

Journal Article↗