(Extra)thermodynamics of the drug-receptor interaction.

A core concept in pharmacology is drug-receptor affinity, i.e., the tendency of a drug molecule to bind to one or more receptors due to the collective influence of multiple molecular forces. The estimation of affinity as a dissociation constant (reciprocal of the equilibrium constant) is extraordinarily valuable. However, elucidation of the nature of the underlying concept--i.e., what accounts for affinity--is not achievable using such a static measure. Observing how the system responds to a perturbation (e.g., to a change in temperature) reveals more fundamental information. The present review summarizes the general concepts of thermodynamic analysis applied to drug-receptor interactions and discusses 'extrathermodynamic' phenomena, such as enthalpy-entropy 'compensation'. Together, these concepts may provide insight into the nature of drug-receptor interactions, begin to elucidate the forces that underlie such interactions--and begin to define and refine more nebulous terms such as affinity.     

The thermodynamics of interaction between Sephadex and penetrating solutes

1. We have measured the partition coefficients of bovine serum albumin with Sephadex grades G-100, G-150 and G-200, and of a dextran ([unk]_n 19700) and a polyethylene glycol ([unk]_n 8000) with Sephadex G-200. We have also measured the effects of these solutes on the inner volumes of the grades of Sephadex. 2. The results can be described with fair consistency by means of a simple thermodynamic treatment that makes use of the virial coefficients of Sephadex and of the solute, and of a coefficient that expresses their interaction. This coefficient is related to the `exclusion volume' of Sephadex for the solutes. 3. The Sephadex G-200–polyethylene glycol system shows anomalies of behaviour that are ascribed to the occurrence of `incompatible' phase separation within the Sephadex beads.     

Lipoplex thermodynamics: determination of DNA-cationic lipoid interaction energies

An experimental study of the cationic lipid-DNA binding affinity is presented. The binding free energy was determined by monitoring lipoplex dissociation under conditions of increasing salt concentration. The primary procedure was based on the extent of quenching by energy transfer of fluorophores on DNA molecules by fluorophore on a lipid as these molecules came into close association in the lipoplex. Titration calorimetry on the Dickerson dodecamer was also done, with results that were in agreement with the fluorescence data. Measurements on short oligonucleotides allowed estimation of the binding energy per nucleotide. The binding free energy is approximately 0.6 kcal/mole nucleotide for the Dickerson dodecamer and declines for longer oligonucleotides. The entropy gained upon complex formation is approximately 1 entropy unit per released counterion. The method was applied to long DNA molecules (herring and lambda-phage DNA) and revealed that complete dissociation occurs at 750 mM NaCl. Likely contributions of macromolecular desolvation and DNA flexibility to the binding energy are discussed.     

Kinetics and thermodynamics of the interaction of 5-fluoro-2'-deoxyuridylate with thymidylate synthase

Thymidylate synthase (TS), 5-fluorodeoxyuridylate (FdUMP), and 5,10-methylenetetrahydrofolate (CH2-H4folate) form a covalent complex in which a Cys thiol of TS is attached to the 6-position of FdUMP and the one-carbon unit of the cofactor is attached to the 5-position. The kinetics of formation of this covalent complex have been determined at several temperatures by semirapid quench methods. Together with previously reported data the results permit calculation of every rate and equilibrium constant in the interaction. Conversion of the noncovalent ternary complex to the corresponding covalent complex proceeds at a rate of 0.6 s-1 at 25 degrees C, and the dissociation constant for loss of CH2-H4folate from the noncovalent ternary complex is approximately 1 microM. Activation parameters for the formation of the covalent complex were shown to be Ea = 20 kcal/mol, delta G+ = 17.9 kcal/mol, delta H+ = 19.3 kcal/mol, and delta S+ = 0.005 kcal/(mol.deg). The equilibrium constant between the noncovalent and covalent ternary complexes is approximately 2 X 10(4), and the overall dissociation constant of CH2-H4folate from the covalent complex is approximately 10(-11) M. The conversion of the noncovalent ternary complex to the covalent adduct is about 12-fold slower than kcat in the normal enzymic reaction. However, because the dissociation constant for CH2-H4folate from the noncovalent ternary complex is about 10-fold lower than that from the TS-dUMP-CH2-H4folate Michaelis complex, the terms corresponding to kcat/Km are nearly equal. We propose that some of the intrinsic binding energy of CH2-H4folate may be used to facilitate formation of a 5-iminium ion intermediate.(ABSTRACT TRUNCATED AT 250 WORDS)     

The thermodynamics of protein-ligand interaction and solvation: insights for ligand design

Isothermal titration calorimetry is able to provide accurate information on the thermodynamic contributions of enthalpy and entropy changes to free energies of binding. The Structure/Calorimetry of Reported Protein Interactions Online database of published isothermal titration calorimetry studies and structural information on the interactions between proteins and small-molecule ligands is used here to reveal general thermodynamic properties of protein-ligand interactions and to investigate correlations with changes in solvation. The overwhelming majority of interactions are found to be enthalpically favoured. Synthetic inhibitors and biological ligands form two distinct subpopulations in the data, with the former having greater average affinity due to more favourable entropy changes on binding. The greatest correlation is found between the binding free energy and apolar surface burial upon complex formation. However, the free-energy contribution per unit area buried is only 30-50% of that expected from earlier studies of transfer free energies of small molecules. A simple probability-based estimator for the maximal affinity of a binding site in terms of its apolar surface area is proposed. Polar surface area burial also contributes substantially to affinity but is difficult to express in terms of unit area due to the small variation in the amount of polar surface buried and a tendency for cancellation of its enthalpic and entropic contributions. Conventionally, the contribution of apolar desolvation to affinity is attributed to gain of entropy due to solvent release. Although data presented here are supportive of this notion, because the correlation of entropy change with apolar surface burial is relatively weak, it cannot, on present evidence, be confidently considered to be correct. Further, thermodynamic changes arising from small differences between ligands binding to individual proteins are relatively large and, in general, uncorrelated with changes in solvation, suggesting that trends identified across widely differing proteins are of limited use in explaining or predicting the effects of ligand modifications.     

Structure, stability, and thermodynamics of lamellar DNA-lipid complexes.

We develop a statistical thermodynamic model for the phase evolution of DNA-cationic lipid complexes in aqueous solution, as a function of the ratios of charged to neutral lipid and charged lipid to DNA. The complexes consist of parallel strands of DNA intercalated in the water layers of lamellar stacks of mixed lipid bilayers, as determined by recent synchrotron x-ray measurements. Elastic deformations of the DNA and the lipid bilayers are neglected, but DNA-induced spatial inhomogeneities in the bilayer charge densities are included. The relevant nonlinear Poisson-Boltzmann equation is solved numerically, including self-consistent treatment of the boundary conditions at the polarized membrane surfaces. For a wide range of lipid compositions, the phase evolution is characterized by three regions of lipid to DNA charge ratio, rho: 1) for low rho, the complexes coexist with excess DNA, and the DNA-DNA spacing in the complex, d, is constant; 2) for intermediate rho, including the isoelectric point rho = 1, all of the lipid and DNA in solution is incorporated into the complex, whose inter-DNA distance d increases linearly with rho; and 3) for high rho, the complexes coexist with excess liposomes (whose lipid composition is different from that in the complex), and their spacing d is nearly, but not completely, independent of rho. These results can be understood in terms of a simple charging model that reflects the competition between counterion entropy and inter-DNA (rho < 1) and interbilayer (rho > 1) repulsions. Finally, our approach and conclusions are compared with theoretical work by others, and with relevant experiments.     

Kinetics and thermodynamics of RRF, EF-G, and thiostrepton interaction on the Escherichia coli ribosome

Ribosome recycling factor (RRF) and elongation factor-G (EF-G) are jointly essential for recycling bacterial ribosomes following termination of protein synthesis. Here we present equilibrium and rapid kinetic measurements permitting formulation of a minimal kinetic scheme that accounts quantitatively for RRF and EF-G interaction on the Escherichia coli ribosome. RRF and EF-G (a) each form a binary complex on binding to a bare ribosome which undergoes isomerization to a more stable complex, (b) form mixed ternary complexes on the ribosome in which the affinity for each factor is considerably lower than its affinity for binding to a bare ribosome, and (c) each bind to two sites per ribosome, with EF-G having considerably higher second-site affinity than RRF. Addition of EF-G to the ribosome-RRF complex induces rapid RRF dissociation, at a rate compatible with the rate of ribosome recycling in vivo, but added RRF does not increase the lability of ribosome-bound EF-G. Added thiostrepton slows the initial binding of EF-G, and prevents both formation of the more stable EF-G complex and EF-G-induced RRF dissociation. These findings are relevant for the mechanism of post-termination complex disassembly.     

Structure and thermodynamics of the extraordinarily stable molten globule state of canine milk lysozyme

Here, we show that an unfolded intermediate of canine milk lysozyme is extraordinarily stable compared with that of the other members of the lysozyme-alpha-lactalbumin superfamily, which has been studied previously. The stability of the intermediate of this protein was investigated using calorimetry, CD spectroscopy, and NMR spectroscopy, and the results were interpreted in terms of the structure revealed by X-ray crystallography at a resolution of 1.85 A to an R-factor of 17.8%. On the basis of the results of the thermal unfolding, this protein unfolds in two clear cooperative stages, and the melting temperature from the intermediate to the unfolded states is about 20 degrees C higher than that of equine milk lysozyme. Furthermore, the (1)H NMR spectra of canine milk lysozyme at 60 degrees C, essentially 100% of which exists in the intermediate, showed that small resonance peaks that arise from ring-current shifts of aliphatic protons are still present in the upfield region from 0 to -1 ppm. The protein at this temperature (60 degrees C) and pH 4.5 has been found to bind 1-anilino-naphthalene-8-sulfonate (ANS) with enhancement of the fluorescence intensity compared with that of native and thermally unfolded states. We interpret that the extraordinarily stable intermediate is a molten globule state, and the extraordinary stabilization of the molten globule state comes from stronger protection around the C- and D-helix of the aromatic cluster region due to the His-21 residue. The conclusion helps to explain how the molten globule state acquires its structure and stability.     

Structure/thermodynamics relationships of lectin-saccharide complexes: the Erythrina corallodendron case.

Molecular dynamics (MD) simulations of Erythrina corallodendron lectin binding to a monosaccharide, alpha-galactose, and a disaccharide, N-acetyl lactosamine, have been performed in order to investigate the relationship between structure and thermodynamics. A simulated annealing protocol has been used to generate ensembles of structures for the two complexes, from which both qualitative and quantitative information on binding dynamics have been extracted. The ensembled averaged lectin-saccharide interaction enthalpy is equivalent for both sugars, whereas the calculation based on the X-ray structures does show a difference. Within large statistical errors, the calculated 'binding enthalpy' is also the same for the two systems. These errors arise largely from terms involving solvent and are a typical limitation of current MD simulations. Significant qualitative differences in binding between the two complexes are, however, observed over the ensembles. These could be important for unraveling the structure/thermodynamic relationship. Stated simply, there are a greater number of binding options available to the disaccharide compared to the monosaccharide. The implications of alternative binding states on thermodynamic parameters and the 'breaking of enthalpy-entropy compensation' are discussed. The role of solvent in lectin-saccharide complex formation is suggested to be significant.     

The pH dependence of the thermodynamics of the interaction of 3'-cytidine monophosphate with ribonuclease A.

The apparent free energy (deltaGapp) and enthalpy changes (deltaHB) associated with the interaction of 3'-cytosine monophosphate (3'-CMP) and ribonuclease A (RNase) are reported for the pH range 4--9, T = 25 degrees, mu = 0.05. The pH dependence of deltaGapp and deltaHB has been interpreted in terms of coupled ionization of histidine residues 12, 48, and 119, assuming that only the dianionic form of the inhibitor is bound. The results of this analysis are consistent with the calorimetric and potentiometric titration results for the free enzyme and its 3'-CMP complex reported in the previous paper (M. Flogel and R. L. Biltonen ((1975), Biochemistry, preceding paper in this issue). This analysis allows the calculation of the thermodynamic quantities associated with hypothetical but clearly defined reactions (e.g., the reaction of the dianionic inhibitor with the completely protonated enzyme). It is concluded that the primary thermodynamic driving forces for the reaction are van der Waals interactions between the riboside moiety and the protein fabric and electrostatic interaction between the negatively charged phosphate group of the inhibitor and the positively charged histidine residues at the binding locus. It is also suggested that the binding reaction is weakly coupled (approximately to 0.5 kcal/mol) with a conformational change of the protein associated with protonation of residue 48. These results are consistent with the model originally proposed by G. G. Hammes ((1968), Adv. Protein Chem. 23, 1) and lend additional quantitative detail to the nature of the reaction.     

Ion transport in a model gramicidin channel. Structure and thermodynamics.

The potential of mean force for Na+ and K+ ions as a function of position in the interior of a periodic poly(L,D)-alanine model for the gramicidin beta-helix is calculated with a detailed atomic model and realistic interactions. The calculated free energy barriers are 4.5 kcal/mol for Na+ and 1.0 kcal/mol for K+. A decomposition of the free energy demonstrates that the water molecules make a significant contribution to the free energy of activation. There is an increase in entropy at the transition state associated with greater fluctuations. Analysis reveals that the free energy profile of ions in the periodic channel is controlled not by the large interaction energy involving the ion but rather by the weaker water-water, water-peptide and peptide-peptide hydrogen bond interactions. The interior of the channel retains much of the solvation properties of a liquid in its interactions with the cations. Of particular importance is the flexibility of the helix, which permits it to respond to the presence of an ion in a fluidlike manner. The distortion of the helix is local (limited to a few carbonyls) because the structure is too flexible to transmit a perturbation to large distances. The plasticity of the structure (i.e., the property to deform without generating a large energy stress) appears to be an essential factor in the transport of ions, suggesting that a rigid helix model would be inappropriate.     

Separating the role of protein restraints and local metal-site interaction chemistry in the thermodynamics of a zinc finger protein

We express the effective Hamiltonian of an ion-binding site in a protein as a combination of the Hamiltonian of the ion-bound site in vacuum and the restraints of the protein on the site. The protein restraints are described by the quadratic elastic network model. The Hamiltonian of the ion-bound site in vacuum is approximated as a generalized Hessian around the minimum energy configuration. The resultant of the two quadratic Hamiltonians is cast into a pure quadratic form. In the canonical ensemble, the quadratic nature of the resultant Hamiltonian allows us to express analytically the excess free energy, enthalpy, and entropy of ion binding to the protein. The analytical expressions allow us to separate the roles of the dynamic restraints imposed by the protein on the binding site and the temperature-independent chemical effects in metal-ligand coordination. For the consensus zinc-finger peptide, relative to the aqueous phase, the calculated free energy of exchanging Zn²⁺ with Fe²⁺, Co²⁺, Ni²⁺, and Cd²⁺ are in agreement with experiments. The predicted excess enthalpy of ion exchange between Zn²⁺ and Co²⁺ also agrees with the available experimental estimate. The free energy of applying the protein restraints reveals that relative to Zn²⁺, the Co²⁺, and Cd²⁺-site clusters are more destabilized by the protein restraints. This leads to an experimentally testable hypothesis that a tetrahedral metal binding site with minimal protein restraints will be less selective for Zn²⁺ over Co²⁺ and Cd²⁺ compared to a zinc finger peptide. No appreciable change is expected for Fe²⁺ and Ni²⁺. The framework presented here may prove useful in protein engineering to tune metal selectivity.     

Combination of isothermal titration calorimetry and time-resolved luminescence for high affinity antibody-ligand interaction thermodynamics and kinetics

For experiments using synthetic ligands as probes for biological experiments, it is useful to determine the specificity and affinity of the ligands for their receptors. As ligands with higher affinities are developed (K(A)>10(8)M(-1); K(D)<10(-8)M), a new challenge arises: to measure these values accurately. Isothermal titration calorimetry measures heat produced or consumed during ligand binding, and also provides the equilibrium binding constant. However, as normally practiced, its range is limited. Displacement titration, where a competing weaker ligand is used to lower the apparent affinity of the stronger ligand, can be used to determine the binding affinity as well as the complete thermodynamic data for ligand-antibody complexes with very high affinity. These equilibrium data have been combined with kinetic measurements to yield the rate constants as well. We describe this methodology, using as an example antibody 2D12.5, which captures yttrium S-2-(4-aminobenzyl)-1, 4, 7, 10-tetraazacyclododecanetetraacetate.     

Thallium-205 NMR determination of the thermodynamics of the interaction between the thallous ion and gramicidin dimers incorporated into micelles

A study has been made of the thermodynamics of the interaction between the thallous ion and gramicidin dimers incorporated into micelles using thallium-205 NMR spectroscopy. The chemical shift data obtained are interpreted interms of a model in which the dimer has only one tight binding site. The variation of the binding constant over the temperature range 303-323 K is used to determine the changes in enthalpy and entropy of binding giving values of -11.3 kcal/mole and -16 e.u. at 303 K, respectively.     

Small changes in the primary structure of transportan 10 alter the thermodynamics and kinetics of its interaction with phospholipid vesicles

The kinetics and thermodynamics of binding of transportan 10 (tp10) and four of its variants to phospholipid vesicles, and the kinetics of peptide-induced dye efflux, were compared. Tp10 is a 21-residue, amphipathic, cationic, cell-penetrating peptide similar to helical antimicrobial peptides. The tp10 variants examined include amidated and free peptides, and replacements of tyrosine by tryptophan. Carboxy-terminal amidation or substitution of tryptophan for tyrosine enhance binding and activity. The Gibbs energies of peptide binding to membranes determined experimentally and calculated from the interfacial hydrophobicity scale are in good agreement. The Gibbs energy for insertion into the bilayer core was calculated using hydrophobicity scales of residue transfer from water to octanol and to the membrane/water interface. Peptide-induced efflux becomes faster as the Gibbs energies for binding and insertion of the tp10 variants decrease. If anionic lipids are included, binding and efflux rate increase, as expected because all tp10 variants are cationic and an electrostatic component is added. Whether the most important effect of peptide amidation is the change in charge or an enhancement of helical structure, however, still needs to be established. Nevertheless, it is clear that the changes in efflux rate reflect the differences in the thermodynamics of binding and insertion of the free and amidated peptide groups.     

The relationship between ligand-binding thermodynamics and protein-ligand interaction forces measured by atomic force microscopy.

The interaction forces between biotin and a set of streptavidin site-directed mutants with altered biotin-binding equilibrium and activation thermodynamics have been measured by atomic force microscopy. The AFM technique readily discriminates differences in interaction force between the site-directed (Trp to Phe or Ala) mutants. The interaction force is poorly correlated with both the equilibrium free energy of biotin binding and the activation free energy barrier to dissociation of the biotin-streptavidin complex. The interaction force is generally well correlated with the equilibrium biotin-binding enthalpy as well as the enthalpic activation barrier, but in the one mutant where these two parameters are altered in opposite directions, the interaction force is clearly correlated with the activation enthalpy of dissociation. These results suggest that the AFM force measurements directly probe the enthalpic activation barrier to ligand dissociation.     

From irreversible thermodynamics to network thermodynamics

Whenever the subject of the thermodynamics of irreversible processes TIP is brought up among biologists, there seems to be a very polarized reaction: some have found it a useful tool, others reject it utterly, and for some reason which I do not understand, even fervently. For the present school, Professor Aharon Katchalsky had suggested that we try together to point out some ways in which TIP has been useful, to discuss limitations and shortcomings, and, finally, to show the direction and first results of present efforts, mainly in network thermodynamics¹. It would have been my task to show you the darker side of the coin, but now Aharon is not with us to show you the shining side in his unique way, to carry you along with his enthusiasm. I believe it is in Aharon's spirit that I do not attempt to evaluate or commemorate his contributions and achievements, but just talk science and try to convey a little of what was at the center of his interest during the last years.