Section: 7 | Apparent Equilibrium Thermodynamics of Protein-Ligand Binding Reactions |
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John R. Rumble, ed., CRC Handbook of Chemistry and Physics, 103rd Edition (Internet Version 2022), CRC Press/Taylor & Francis, Boca Raton, FL.
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Mark A. Williams

These tables contain values of the observed thermodynamics properties of the binding reactions of selected proteins with chemically related series of small molecule ligands at a specified temperature (T) and pH.

The standard Gibbs free energy change, ΔbG´°, upon a ligand, L, binding a protein, P, determines the relative populations of protein, ligand and protein:ligand complex (P:L) at equilibrium. The apparent association constant (Kb´) for the binding equilibrium is defined by

Kb´ = [P:L] / [P][L]

and the Gibbs energy determined from Kb´ via

ΔbG´° = -RT ln(Kb´)

where the molar gas constant R = 8.3144598 J K-1 mol-1, and c° is the standard state concentration of unit molarity (1 mol dm-3). The standard enthalpy change of the binding reaction (ΔbH´°) is the heat released (negative) or taken up (positive) upon forming the complex. All reactions reported here are carried out at a constant 1 atmosphere pressure (0.1 MPa). Under these conditions, the standard entropy change, ΔbS´°, associated with a reaction is determined by the Gibbs-Helmholtz relation,

ΔbG´° = ΔbH´° – T ΔbS´°

All experimental data reported here are obtained by isothermal titration microcalorimetry (ITC); a method that takes advantage of the fact that almost all binding reactions are accompanied by a measurable exchange of heat with their environment. An ITC experiment determines both the Gibbs energy and enthalpy change of a reaction by analysis of a single titration. In the most common experimental arrangement, a titration of ligand against protein is performed in a series of small increments. At each increment, the ligand:protein ratio is increased, and the net heat change arising from the shift in the binding equilibrium is measured. As the binding site of the protein becomes saturated, the incremental heat change diminishes to zero. ΔbH´° is determined from the sum total heat change at saturation and the known concentrations of reactants. ΔbG´° is determined from the dependence of the incremental heat (which corresponds to the fractional saturation) on the ligand:protein concentration ratio according to the analysis described in Ref. 1. For very high affinity interactions, almost all added ligand binds at each increment and the protein will abruptly saturate at a 1:1 concentration ratio making the data difficult to analyze to obtain accurate values for ΔbG´°. In such circumstances, the binding affinity of the ligand of interest is artefactually diminished in experiments by competition with a saturating excess of a lower affinity ligand that binds to the same site on the protein. The ligand of interest is titrated to displace the competitor, and the observed thermodynamics are then corrected for the known thermodynamics of the competitor binding according to procedures in Ref. 2. Those reactions carried out in this competitive manner are indicated in the tables. Column definitions for the table are as follows.

Column heading Definition
Sequence modification Protein system that binds to the ligand; includes species name as well as standard translated gene sequence code from the UNIPROT database (see text for further description of the protein systems)
Ligand Common name of binding ligand
ΔbG Gibbs energy of protein:ligand binding, in units kJ mol-1
ΔbH Enthalpy change of protein:ligand binding, in units kJ mol-1
-TΔbS Entropy change at specified temperature T (next column right) of protein:ligand binding, in units kJ mol-1
T Temperature of binding interaction, in K
Ref. Reference
Buffer composition Chemical composition of buffer in which binding interaction was measured
Alternative systematic ligand name Systematic name for ligand, when given

Biochemical binding reactions may be complex events. An idealized scenario of two rigid, chemically distinct, molecular species simply coming into close proximity is rarely the case. The idealized binding event is frequently accompanied by changes in other conformational or chemical equilibria involving the protein or ligand, e.g., due to only one conformation being able to bind or due to altered interactions with other solution components between the bound and free states. The apparent binding thermodynamics reported is for the total of all processes that necessarily accompany the binding. Here we also report the buffer composition in which the reactions were carried out as it is possible that altered interactions with these components affect the observations. Within each selected protein-ligand series, protein and ligands have similar bound conformations and experiments have been carried out under identical or very similar conditions meaning that, in so far as possible, differences in the thermodynamic properties between compounds in a series reflect differences between the ligands and in their interactions with the protein only and are more amenable to structural interpretation (Ref. 20).

Proteins and many ligands contain a variety of titratable acidic and basic groups, and the fractional protonation state of those groups may change upon binding if the protonated state of each group is stabilized or destabilized by interactions between the ligand and protein. Such direct effects of binding are a necessary consequence of the interaction and are appropriately included in the apparent thermodynamic properties. However, any net change in protonation of protein and ligand is coupled to change in protonation of the buffer that introduces an artefactual buffer-dependent heat of ionization (see "Thermodynamic Quantities for the Ionization Reactions of Buffers in Water" in this section). Heats of reaction are consequently corrected for buffer ionization where appropriate.

The amino acid residue sequence of the protein is given by reference to the standard translated gene sequence found in the UNIPROT database, Ref. 3. Any differences from the standard sequence are noted.

  1. Wiseman, T., Williston, S., Brandts, J. F., and Lin, L. N., Anal. Biochem., 179, 131, 1989. []
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  11. Malham, R., Johnstone, S., Bingham, R. J., Barratt, E., Phillips, S. E. V., Laughton, C. A., and Homans, S. W., J. Am. Chem. Soc., 127, 17061, 2005. []
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Description of Protein Systems

In the table following this section, thermodynamic data for a set of widely studied proteins binding to a variety of ligands are presented. Below are given more detailed descriptions of the proteins as well as structural and interaction details.

Enterococcus faecalis Aminoglycoside 3'-phosphotransferase
Uniprot ID: P0A3Y5

Aminoglycoside 3'-phosphotransferase is able to phosphorylate many aminoglycoside antibiotics rendering them inactive. The reaction proceeds by transferring a phosphate from ATP bound in a neighboring site to the antibiotic, e.g., ATP + kanamycin = ADP + kanamycin 3'-phosphate. The reaction is dependent on Mg2+. Replacing magnesium with calcium ions leads to formation of the ternary ATP:aminoglycoside:enzyme complex, but no product is formed. The enzyme is monomeric, and crystallographic analysis shows that it undergoes only local structural change on ATP and/or aminoglycoside binding. The thermodynamics of formation of the binary complex by titration of aminoglycoside to enzyme and the ternary complex by titration of aminoglycoside into enzyme in the presence of Ca2+ and ATP have been measured. Data below are corrected for coupled protonation of the buffer according to procedures described in Ref. 4.

Homo sapiens Aurora A kinase
Uniprot ID: O14965

Aurora A kinase transfers phosphate from ATP to serine and threonine residues in other proteins in the context of specific amino acid sequences. Aurora A activity regulates processes in normal cell division. Increased concentrations, and thus activity, of Aurora A in cells leads to aberrant cell division and cancer. Consequently, inhibitors of its action may be useful as anticancer drugs. The series of (bis)anilinopyrimidine inhibitors has a common binding mode that prevents a conformational change required for enzyme activity.

Thermotoga maritima β-glucosidase A
Uniprot ID: Q08638

Glycoside hydrolases are a large family of related enzymes that act to degrade oligosaccharides in a variety of extracellular digestive and intracellular metabolic processes. Several members of the family are implicated in diseases. β-glucosidases attack the β-1-4 linkage of nonreducing (acetal) β-D-glucosyl residues releasing β-D-glucose. β-glucosidase A is an experimentally tractable and stable member of the family that is used to study the binding of a series of inhibitors that mimic the transition state of the reaction. At the pH of these experiments, the binding of 1-deoxynojirimycin and isofagomine are associated with the net release of a single proton upon binding (Ref. 6). This protonation event is thought to be associated with interaction with the glutamic acid, which acts as the general base in the catalytic mechanism. Given the high degree of structural similarity between the ligand complexes (Ref. 7), it is assumed all of the compounds in the series below undergo this same net protonation. Consequently, all of the enthalpies in this series are corrected here by -3.38 kJ mol-1 to account for the small heat of ionization of the citrate buffer.

Escherichia coli Dihydrodipicolinate reductase
Uniprot ID: P04036

Dihydrodipicolinate reductase catalyzes the cofactor-dependent reaction, NAD(P)H + dihydropicolinic acid = tetrahydropicolinic acid + NAD(P)+, and is an essential component of the biosynthetic pathway of L-lysine and meso-diaminopimelic acid in bacteria. Given the requirement for these amino acids in, respectively, protein synthesis and the formation of peptidoglycan in the bacterial cell wall, inhibition of this enzyme is considered to be a possible therapeutic strategy. The native enzyme is a homotetramer. There is no evidence for cooperativity of binding of the cofactor and thermodynamic data are analyzed assuming that the four sites are equivalent. The thermodynamics of binding of the cofactor(s) and several analogs have been determined in the absence of the dihydropicolinic acid substrate.

Mus musculus Major urinary protein
Uniprot ID: P02762

Mouse major urinary proteins are a family of monomeric sequence-similar proteins that bind pheromones that are released from the urine of male mice. These pheromones affect the sexual behavior of females. The pheromone binding site is a deep pocket lined with nonpolar amino acids and has consequently been used as an archetypal hydrophobic binding site to investigate factors influencing hydrophobic small-molecule binding.

Escherichia coli Periplasmic dipeptide binding protein DppA
Uniprot ID: P23847

DppA is a component of the dipeptide ATP-binding cassette transporter, a multiprotein complex that is responsible for transport of dipeptides across the cytoplasmic inner membrane of enteric bacteria.

Salmonella typhimurium/enterica Oligopeptide binding protein OppA
Uniprot ID: P06202

OppA is a component of the oligopeptide permease peptide transport system. It is evolutionarily related to the dipeptide binding proteins but has a larger binding pocket capable of binding peptides up to five amino acids long with high affinity.

Homo sapiens Thrombin (in complex Hirudo medicinalis Hirudin)
Uniprot ID: P00734 (thrombin ) & P01050 (hirudin)

Thrombin is a protease that is important in the coagulation of blood, in which process the protease specifically cleaves and activates fibrinogen, the clot-forming protein. Thrombin is a serine protease, in which the active site contains a serine-apartate-histidine catalytic triad, arranged such that the serine catalyzes hydrolysis of the peptide bond of a bound substrate protein or peptide. The structure of the active site is complementary to a limited number of peptide sequences. There is specificity for cleavage of peptides to the C-terminal side of a proline-arginine sequence. The series of ligands below contain or structurally mimic some of the features of this dipeptide sequence. The enzyme is inhibited by a peptide derived from the leech anticoagulant, hirudin and stabilized by Na+ binding. Both these binding events are remote from the active site and there is no direct interaction with the titrated ligands.

Homo sapiens Thrombin (in complex Hirudo medicinalis Hirudin 2)
Uniprot ID: P00734 (thrombin) & P09945 (hirudin2)

For the ligands in this set of data, titrations in different buffers show a fractional net change in protonation state of the protein and ligand. Enthalpy changes have been corrected for buffer ionization effects as reported in Ref. 17. The thermodynamics of the very high affinity benzylsulfonyl-containing compounds have been determined via competition with the other two ligands.

Bos taurus Trypsin
Uniprot ID: P00760

Trypsin is a serine protease important in the digestion of proteins and also a useful model system due to it being readily purifiable from animal sources and its stability under laboratory conditions. Trypsin is evolutionarily related to thrombin and cleaves a similar but broader range of peptides, in this case preferentially to the C-terminal side of arginine or lysine residues. Benzamidine-based inhibitors mimic the arginine side-chain interactions. These inhibitors bind as the benzamidinium ion to the carboxylate side chain of an active-site aspartic acid. The enzyme is stabilized by Ca2+ ion binding, but this binding is remote from the active site with no direct interaction with substrates or inhibitors. Experiments with titrations in different buffers show no net change in protonation upon formation of the benzamadine complex at pH 8.0, although fractional protonation changes do occur at lower pH. Because of the chemical and structural similarity of this series of compounds, it is assumed that no protonation corrections are required for any of the compounds in the series.

Thermodynamic Data of Protein-Ligand Reactions

Sequence modificationLigandΔbG´°/kJ mol-1ΔbH´°/kJ mol-1-TΔbS´°/kJ mol-1T/KRef. Buffer compositionAlternative systematic ligand name
Continued on next page...
Enterococcus faecalis Aminoglycoside 3'-phosphotransferase (P0A3Y5)
Enterococcus faecalis Aminoglycolside 3'-phosphotransferase (P0A3Y5)NoneAmikacin-23.8-74.951.0310.15450 mM Tris, 100 mM KCl, pH 7.5
Kanamycin A-31.0-187.9156.9310.15450 mM Tris, 100 mM KCl, pH 7.5
Kanamycin B-38.5-172.8134.3310.15450 mM Tris, 100 mM KCl, pH 7.5
Lividomycin A-36.0-239.7203.8310.15450 mM Tris, 100 mM KCl, pH 7.5
Neomycin B-38.9-233.0194.1310.15450 mM Tris, 100 mM KCl, pH 7.5
Paramomycin I-37.7-183.7146.0310.15450 mM Tris, 100 mM KCl, pH 7.5
Ribostamycin-33.9-107.173.2310.15450 mM Tris, 100 mM KCl, pH 7.5
Tobramycin-36.4-196.6160.2310.15450 mM Tris, 100 mM KCl, pH 7.5
Amikacin-26.4-117.290.8310.15450 mM Tris, 100 mM KCl, 1.5 mM CaCl2, 1 mM ATP, pH 7.5
Kanamycin A-35.6-129.794.1310.15450 mM Tris, 100 mM KCl, 1.5 mM CaCl2, 1 mM ATP, pH 7.5
Kanamycin B-39.3-121.882.4310.15450 mM Tris, 100 mM KCl, 1.5 mM CaCl2, 1 mM ATP, pH 7.5
Lividomycin A-36.4-153.1116.7310.15450 mM Tris, 100 mM KCl, 1.5 mM CaCl2, 1 mM ATP, pH 7.5
Neomycin B-41.0-151.9110.9310.15450 mM Tris, 100 mM KCl, 1.5 mM CaCl2, 1 mM ATP, pH 7.5
Paramomycin I-40.6-116.776.1310.15450 mM Tris, 100 mM KCl, 1.5 mM CaCl2, 1 mM ATP, pH 7.5
Ribostamycin-38.9-60.721.8310.15450 mM Tris, 100 mM KCl, 1.5 mM CaCl2, 1 mM ATP, pH 7.5
Tobramycin-39.3-128.489.1310.15450 mM Tris, 100 mM KCl, 1.5 mM CaCl2, 1 mM ATP, pH 7.5
Homo sapiens Aurora A kinase (O14965)
Homo sapiens Aurora A kinase (O14965)Residues 123-390 of the full-length protein with a T287D mutation4-{[4-(Phenylamino)pyrimidin-2-yl]amino}benzoic acid-42.3-58.616.3298.155100 mM Na/K phosphate, pH 7.4
2-({2-[(4-Carboxyphenyl)amino]pyrimidin-4- yl}amino)benzoic acid-42.6-56.914.3298.155100 mM Na/K phosphate, pH 7.4
4-{[4-(Biphenyl2-ylamino)pyrimidin-2-yl]amino}benzoic acid-37.2-13.7-23.5298.155100 mM Na/K phosphate, pH 7.4

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