ITC analysis of polydisperse systems: Unravelling the impact of sample heterogeneity.

Binding interactions often involve heterogeneous samples displaying a distribution of binding sites that vary in affinity and binding enthalpy. Examples include biological samples like proteins and chemically produced samples like modified cyclodextrins. Experimental studies often ignore sample heterogeneity and treat the system as an interaction of two homogeneous species, i.e. a chemically well-defined ligand binding to one type of site. The present study explores, by simulations and experiments, the impact of heterogeneity in isothermal titration calorimetry (ITC) setups where one of the binding components is heterogeneous. It is found that the standard single-site model, based on the assumption of two homogeneous binding components, provides excellent fits to simulated ITC data when the binding free energy is normally distributed and all sites have similar binding enthalpies. In such cases, heterogeneity can easily go undetected but leads to underestimated binding constants. Heterogeneity in the binding enthalpy is a bigger problem and may result in enthalpograms of increased complexity that are likely to be misinterpreted as two-site binding or other complex binding models. Finally, it is shown that heterogeneity can account for previously observed experimental anomalies. All simulations are accessible in Google Colab for readers to experiment with the simulation parameters.

pH-Responsive templates modulate the dynamic enzymatic synthesis of cyclodextrins.

Product selection in the dynamic enzymatic synthesis of cyclodextrins can be controlled by changing the pH. Using cyclodextrin glucanotransferase to make labile the glycosidic linkages in cyclodextrins (CDs), we generate a dynamic combinatorial library of interconverting linear and cyclic α-1,4-glucans. Templates can be employed to favour the selective production of specific CDs and, herein, we show that by using ionisable templates, the synthesis of α-CD or ß-CD can be favoured by simply changing the pH. Using 4-nitrophenol as the template, ß-CD is the preferred product at low pH, while α-CD is the preferred product at high pH. Furthermore, a new methodology is described for the simulation of product distributions in dynamic combinatorial libraries with ionisable templates at any given pH.

Specific Buffers Affect the Stability of a Charged Cyclodextrin Complex Via Competitive Binding and Ionic Strength.

The effect of 11 buffers as well as the effect of ionic strength were investigated on the binding between the bile salt taurochenodeoxycholate and the ionic sulfobutylether-ß-cyclodextrin. The investigations showed that both ionic strength and competitive binding affected the stability constant. The stability constant for the sulfobutylether-ß-cyclodextrin complex increased from 34,400 M-1 to 114,000 M-1 as the ionic strength of the solution increased to 0.15 M. Keeping the ionic strength constant, the stability constant for the complex depended on the buffer in the solution, with citric and succinic acid reducing the stability constant. The reduction in the stability constant by buffers was related to a competitive mechanism. The results showed that, when accounting for the variation in ionic strength between the buffers, three groupings of buffers existed. All carboxylic acid buffers decreased the stability constant of the sulfobutylether-ß-cyclodextrin complex, relative to the effect observed by altering the ionic strength, whereas the other buffers only affected the stability constant in terms of the changes in ionic strength. Both buffer species and ionic strength impacted the stability of ionic cyclodextrin complexes, hence, it is important to be aware of these effects when working with, comparing and reporting stability constants.

Certain carboxylic acid buffers can destabilize ß-cyclodextrin complexes by competitive interaction.

Thirteen buffers were investigated for their effect on the binding of adamantanol to ß-cyclodextrin and hydroxypropyl-ß-cyclodextrin. Stability constants for the ß-cyclodextrin complex ranged from 14,800 to 46,000 M-1, and the binding enthalpies were between -23.2 and -10.4 kJ/mole. Compared to water, the stability constant in seven carboxylic acid buffers (citric acid, maleic acid, fumaric acid, succinic acid, malonic acid, malic acid and tartaric acid) was reduced. All seven buffers exhibited a competitive mechanism. Binding constants for the interaction between ß-cyclodextrin and buffers ranged from 4 to 44 M-1, and binding enthalpies were in the range -19 to -11 kJ/mole. There was a relation between the chemical structures of the buffers and their ability to bind to cyclodextrin. All seven buffers had a carbon chain consisting of more than three carbons in the backbone. Hydroxyl groups on the carbon chain decreased the binding affinity. 1H and ROESY NMR spectroscopy supported inclusion of the citric acid into the cyclodextrin cavity, although the results for succinic and maleic acids were ambiguous. The results demonstrated that some buffers can interact with cyclodextrin complexes, and careful considerations are necessary when choosing a buffer for cyclodextrin research.

Cyclodextrin binding constants as a function of pH for compounds with multiple pKa values.

Complex formation between cyclodextrins and ionizable guest molecules depends on pH. In general, the neutral species of an ionizable guest molecule has the highest affinity for the cyclodextrin cavity, but ionized species will also be able to form complexes with cyclodextrins. This work presents a theoretical expression for the relationship between the stability constant and pH for interaction between neutral cyclodextrins and ionizable guest molecules with multiple pKa values. Input parameters for the theoretical expression are pKa values of the guest molecule and stability constants for the complex at specific pH values. The pH profile of the stability constant for a complex depends on the acid-base properties of the guest and the closeness of the pKa values, and examples of pH profiles for polyprotic acids, bases and amphoteric guests are shown. Empirical data sets from the literature were used to confirm the accuracy of the theoretical expression, and Monte Carlo simulations were used to validate that the theoretical expression yield a good fit to empirical data. Lastly, an experimental protocol was suggested, and a freely available graphical user interface was presented to facilitate easy use of the theoretical expression.

Determination of acidity constants for weak acids and bases by isothermal titration calorimetry.

The advantage of isothermal titration calorimetry (ITC) to determine the acid dissociation constant (pKa value) is the simultaneous determination of the binding constant and binding enthalpy, as well as being precise and easy to use. The pKa can be calculated from the binding constant, and the temperature dependency of the pKa can be calculated from the binding enthalpy. The use of ITC to study protonation reactions is less common compared to its more conventional use of studying macromolecules and ligands. Water will influence the equilibrium due to autoionization, meaning that both the conjugate base and acid will exist in the sample cell at the beginning of the experiment. These differences are accounted for by optimizing the theoretical model used to estimate the binding constant and binding enthalpy. Through simulations and experimental measurements, we show that ITC can be used to determine the pKa for ibuprofen, ascorbic acid, 2-morpholin-4-ylethanesulfonic acid and paracetamol. The pKa values were consistent with potentiometric or spectrophotometric determinations as well as literature values. Optimizing the theoretical model does not lead to an improved determination, so the "one set of sites" model is adequate for the determination of pKa values.

Complexation Kinetics of Cyclodextrins with Bile Salt Anions: Energy Barriers for the Threading of Ionic Groups.

Binding constants for thousands of cyclodextrin complexes have been reported in the literature, but much less is known about the kinetics of these host-guest complexes. In the present study, inclusion complexes of bile salts with ß-cyclodextrin, γ-cyclodextrin, and a methylated ß-cyclodextrin were studied by nuclear magnetic resonance (NMR) lineshape analysis to explore the structural factors that govern the complexation kinetics. For complexes with ß-cyclodextrin, the association rate constants ranged from 2 × 106 to 2 × 107 M-1 s-1 while the dissociation rate constants ranged from 12 to 6000 s-1 at 25 °C. The kinetics were thus significantly slower than for any other ß-cyclodextrin complex reported in the literature, due to the large energy barrier for threading the ionic sidechains of the bile salt anions. Bile salts with taurine and glycine sidechains had identical binding affinities, but the kinetics differed by a factor of 10. Introduction of a single hydroxyl group at the binding site of the bile salts reduced the lifetimes and binding constants of the complexes by more than 50 times. The strong temperature dependence of the rate constants revealed that the large activation energies were mainly enthalpic with a small contribution from entropy. The larger γ-cyclodextrin was threaded by the nonionic end of the bile salts, and the kinetics were too fast to be accurately determined. The study demonstrates that ionic groups on guest molecules constitute significant energy barriers for the threading and dethreading of ß-cyclodextrin hosts.

Correlation between the stability constant and pH for ß-cyclodextrin complexes.

In drug formulations, cyclodextrins are used to increase aqueous solubility and chemical stability of drugs via formation of inclusion complexes. For ionizable drug molecules, the complexation strength depends on pH. Increased ionization leads to a more soluble drug, but also results in destabilization of cyclodextrin complexes. Therefore, formulation scientists aim to find a balance between increased drug solubility and high complexation strength. In this work, a theoretical expression for the dependency between the stability constant and pH is presented, allowing the accurate prediction of the stability constant at any pH. The theoretical expression requires three out of four input parameters; the pKa of the free guest molecule, the pKa of the complex, and the stability constants for the neutral and fully ionized complex. Stability constants for ß-cyclodextrin and ibuprofen complexes were determined by isothermal titration calorimetry at seven pH values (2.5-5.5) and four temperatures (15-55 °C). All these measured stability constants complied with the theoretical expression. Ten additional data sets from the literature comprising eight different drug molecules and three different cyclodextrins confirmed the ability of the theoretical expression to account for the observed pH-dependence of stability constants.

Exploring the Origins of Enthalpy-Entropy Compensation by Calorimetric Studies of Cyclodextrin Complexes.

Cyclodextrin complexes were used as simple model systems to explore the enthalpy-entropy compensation phenomenon, which is often observed in biomolecular processes, e.g., in protein-ligand binding. The complexation thermodynamics for the binding of a series of adamantane derivatives to several cyclodextrin hosts were determined by isothermal titration calorimetry in the temperature range 10-55 °C. As for other cyclodextrin complexes, the thermodynamic parameters depended systematically on the structural modifications of the cyclodextrins. Hydroxypropyl chains at the rims of the cyclodextrin hosts changed the thermodynamic fingerprint of binding to all guests by inducing significant increases in the complexation enthalpies and entropies. Similarly, the heat capacity changes upon complexation also showed a linear dependence on the number of hydroxypropyl chains. The altered complexation thermodynamics was ascribed to the increased dehydration of polar groups on the guest by the hydroxypropyl chains on the host. This unfavorable interaction destabilized the complexes as the enthalpic penalty was only partially compensated by the gain in entropy. The degree of enthalpy-entropy compensation depended on the guest molecule and seems to be related to the hydrophilicity/hydrophobicity of the desolvated molecular surface.

Buffer solutions in drug formulation and processing: How pKa values depend on temperature, pressure and ionic strength.

Solution pH is an important factor during drug formulation and processing. Changes in pH present challenges. Regulation of pH is typically managed by using a buffer system, which must have a suitable pKa. The pKa of buffers depends on temperature, pressure and ionic strength. In addition, the pKa can also be affected by the polarity of the solvent, e.g., by the addition of a co-solvent. Theoretical considerations and accessible experimental data were used to understand how the pKa values of pharmaceutically relevant buffers depend on these factors. Changes in temperature also affect the buffer pKa. Carboxylic acid moieties were least affected by changes in temperature. Buffers containing amino groups were most affected by changes in temperature, and the pKa decreased as temperature was increased. It was possible to predict accurately how buffer pKa varies with temperature, based on changes in enthalpy and heat capacity for the ionization reactions. Changes in pressure had a limited effect on buffer pKa for pressures <100 MPa. At higher pressures, buffer pKa varied by up to 0.5 pH units. Altering the ionic strength or polarity of the solvent influenced buffer pKa slightly. However, it is possible to keep both the ionic strength and the polarity of the solvent constant during drug formulation and processing.

Drug Solubilization by Mixtures of Cyclodextrins: Additive and Synergistic Effects.

Cyclodextrins are popular drug solubilizers, but the use of the natural cyclodextrins is hampered by their tendency to coprecipitate with the drug. To understand and overcome such problems, we have studied the solubility of dexamethasone in the presence of natural ß-cyclodextrin and γ-cyclodextrin, individually and in various combinations. Equilibrium models of the phase-solubility diagrams with individual cyclodextrins revealed that dexamethasone was solubilized as 1:1 complexes, but formation of insoluble higher-order complexes set an upper limit to the concentration of solubilized dexamethasone. This limit could be raised from 8 to 17 mM by using combinations of the two cyclodextrins, as their solubilizing properties were additive in some regions of the phase-solubility diagram and synergistic in other regions. The additive effects arise from the additivity of solubilities-the same phenomenon contributes to the good solubilizing properties of many modified cyclodextrins. The synergistic effects, however, could not be explained. The results open up for an increased use of the natural cyclodextrins as an improved alternative to modified cyclodextrins.

Extracavity Effect in Cyclodextrin/Surfactant Complexation.

Cyclodextrin (CD) complexation is a convenient method to sequester surfactants in a controllable way, for example, during membrane-protein reconstitution. Interestingly, the equilibrium stability of CD/surfactant inclusion complexes increases with the length of the nonpolar surfactant chain even beyond the point where all hydrophobic contacts within the canonical CD cavity are saturated. To rationalize this observation, we have dissected the inclusion complexation equilibria of a structurally well-defined CD, that is, heptakis(2,6-di- O-methyl)-ß-CD (DIMEB), and a homologous series of surfactants, namely, n-alkyl- N, N-dimethyl-3-ammonio-1-propanesulfonates (SB3- x) with chain lengths ranging from x = 8 to 14. Thermodynamic parameters obtained by isothermal titration calorimetry and structural insights derived from nuclear magnetic resonance spectroscopy and molecular dynamics simulations revealed that, upon inclusion, long-chain surfactants with x = ≥10 extend beyond the canonical CD cavity. This enables the formation of hydrophobic contacts between long surfactant chains and the extracavity parts of DIMEB, which make additional favorable contributions to the stability of the inclusion complex. These results explain the finding that the stability of CD/surfactant inclusion complexes monotonously increases with the surfactant chain length even for long chains that completely fill the canonical CD cavity.

Charge Determines Guest Orientation: A Combined NMR and Molecular Dynamics Study of ß-Cyclodextrins and Adamantane Derivatives.

The strong binding of the adamantyl moiety to the cavity of ß-cyclodextrin makes it a common binding motif in supramolecular chemistry and a common model system. Despite the attention, there are still unresolved questions regarding the orientation of the adamantane derivatives in the inclusion complexes-do they protrude from the wide or narrow opening of the cyclodextrin hosts? A combined analysis of ROESY NMR and molecular dynamics simulations allows the conclusion that positively charged adamantane derivatives are oriented with the hydrophilic group protruding from the wider opening of the cyclodextrin, while negatively charged adamantane derivatives form two coexisting types of complexes where the hydrophilic group respectively protrudes from the wide and narrow opening. Interestingly, structural modifications of the cyclodextrin host only have a slight impact on the guest orientation.

Soluble 1:1 complexes and insoluble 3:2 complexes - Understanding the phase-solubility diagram of hydrocortisone and γ-cyclodextrin.

The molecular mechanisms underlying the drug-solubilizing properties of γ-cyclodextrin were explored using hydrocortisone as a model drug. The BS-type phase-solubility diagram of hydrocortisone with γ-cyclodextrin was thoroughly characterized by measuring the concentrations of hydrocortisone and γ-cyclodextrin in solution and the solid phase. The drug-solubilizer interaction was also studied by isothermal titration calorimetry from which a precise value of the 1:1 binding constant (K11=4.01mM-1 at 20°C) was obtained. The formation of water-soluble 1:1 complexes is responsible for the initial increase in hydrocortisone solubility while the precipitation of entities with a 3:2 ratio of γ-cyclodextrin:hydrocortisone is responsible for the plateau and the ensuing strong decrease in solubility once all solid hydrocortisone is used up. The complete phase-solubility diagram is well accounted for by a model employing the 1:1 binding constant and the solubility product of the precipitating 3:2 entity (K32S=5.51 mM5). For such systems, a small surplus of γ-cyclodextrin above the optimum concentration may result in a significant decrease in drug solubility, and the implications for drug formulations are briefly discussed.

Apomorphine and its esters: Differences in Caco-2 cell permeability and chylomicron affinity.

Oral delivery of apomorphine via prodrug principle may be a potential treatment for Parkinson's disease. The purpose of this study was to investigate the transport and stability of apomorphine and its esters across Caco-2 cell monolayer and their affinity towards chylomicrons. Apomorphine, monolauroyl apomorphine (MLA) and dilauroyl apomorphine (DLA) were subjected to apical to basolateral (A-B) and basolateral to apical (B-A) transport across Caco-2 cell monolayer. The stability of these compounds was also assessed by incubation at intestinal pH and physiological pH with and without Caco-2 cells. Molecular dynamics (MD) simulations were performed to understand the stability of the esters on a molecular level. The affinity of the compounds towards plasma derived chylomicrons was assessed. The A-B transport of intact DLA was about 150 times lower than the transport of apomorphine. In contrast, MLA was highly unstable in the aqueous media leading to apomorphine appearance basolaterally. MD simulations possibly explained the differences in hydrolysis susceptibilities of DLA and MLA. The affinity of apomorphine diesters towards plasma derived chylomicrons provided an understanding of their potential lymphatic transport. The intact DLA transport is not favorable; therefore, the conversion of DLA to MLA is an important step for intestinal apomorphine absorption.

Hydration Differences Explain the Large Variations in the Complexation Thermodynamics of Modified γ-Cyclodextrins with Bile Salts.

The structure and thermodynamics of inclusion complexes of seven different γ-cyclodextrins (γCDs) and three biologically relevant bile salts (BS) were investigated in the present study. Natural γCD and six modified γCDs [two methyl-γCDs, one sulfobutyl ether-γCD (SBEγCD), and three 2-hydroxypropyl-γCDs (HPγCD)] and their complexes with BS were investigated by isothermal titration calorimetry, NMR, and molecular dynamics simulations. With the exception of the fully methylated γCD, which did not bind the BSs investigated, all of the γCDs formed 1:1 complexes with the BS, and the structures were similar to those with natural γCD; i.e., the modifications of the γCD had limited structural impact on the formation of complexes. Isothermal titration calorimetry was carried out over in the temperature interval 5-55 °C to enable the calculation of the stability constant (K) and the thermodynamic parameters enthalpy (ΔH°), entropy (ΔS°), and heat capacity (ΔCp°). The stability constants decreased with an increased degree of substitution (DS), with methyl substituents having a lower effect on the stability constant than the sulfobutyl ether and hydroxypropyl substituents on the stability constants. Enthalpy-entropy compensation was observed, since both enthalpy and entropy increased with the degree of substitution, which may reflect dehydration of the hydrophobic surface on both CD and BS. Calculations based on ΔCp° data suggested that each of the substituents dehydrated 10-20 (hydroxypropyl), 22-33 (sulfobutyl ether), and 10-15 Å(2) (methyl) of the BS surface area, in reasonable agreement with estimates from the molecular dynamics simulations. Combined with earlier investigations on modified ßCDs, these results indicate general trends of the substituents on the thermodynamics of complex formation.

Solvent effects and driving forces in pillararene inclusion complexes.

Pillararenes, a recently discovered class of aromatic macrocycles, form inclusion complexes with a large number of guest molecules, but not much is known about the driving forces of complexation, including the role of the solvent. We have measured the binding thermodynamics for a small number of model complexes in several solvents and used computational chemistry to rationalize the obtained results and identify the driving forces of complexation. Favorable electrostatic interactions between the host and guest are obtained when the charge distribution in the guest matches the negative electrostatic potential in the cavity of the pillararene. Polar guests, however, also interact strongly with polar solvents, thereby shifting the complexation equilibrium away from the complex. The shape of the solvent molecules is another important factor as some solvents are sterically hindered from entering the pillararene cavity. By changing solvent from acetonitrile to o-xylene the binding constant in one case increased more than 4 orders of magnitude. Even electrostatically similar solvents such as o-xylene and p-xylene have very different impacts on the binding constants due to their different abilities to fit into the cavity. The study illustrates the importance of taking into account the interactions between the solvent and the complexing species in the investigation and design of molecular host:guest systems.

Computational investigation of enthalpy-entropy compensation in complexation of glycoconjugated bile salts with ß-cyclodextrin and analogs.

The inclusion complexes of glycoconjugated bile salts with ß-cyclodextrin (ß-CD) and 2-hydroxypropyl-ß-cyclodextrins (HP-ß-CD) in aqueous solution were investigated by molecular dynamics simulations to provide a molecular explanation of the experimentally observed destabilizing effect of the HP substituents. Good agreement with experimental data was found with respect to penetration depths of CDs. An increased degree of HP substitution (DS) resulted in an increased probability of blocking the cavity opening, thereby hindering the bile salt from entering CD. Further, the residence time of water molecules in the cavity increased with the DS. Release of water from the cavity resulted in a positive enthalpy change, which correlates qualitatively with the experimentally determined increase in complexation enthalpy and contributes to the enthalpy-entropy compensation. The positive change in complexation entropy with DS was not able to compensate for this unfavorable change in enthalpy induced by the HP substituents, resulting in a destabilizing effect. This was found to originate from fixation of the HP substituents and decreased free rotation of the bile salts within the CD cavities.

Complexation thermodynamics of modified cyclodextrins: extended cavities and distorted structures.

Inclusion complexes between two bile salts and a range of differently methylated ß-cyclodextrins were studied in an attempt to rationalize the complexation thermodynamics of modified cyclodextrins. Calorimetric titrations at a range of temperatures provided precise values of the enthalpies (ΔH°), entropies (ΔS°), and heat capacities (ΔCp) of complexation, while molecular dynamics simulations assisted the interpretation of the obtained thermodynamic parameters. As previously observed for several types of modified cyclodextrins, the substituents at the rims of the cyclodextrin induced large changes in ΔH° and ΔS°, but due to enthalpy-entropy compensation the changes in Gibbs free energy, and the binding constant, were much smaller. For the methylated ß-cyclodextrins, the substituent-induced increments in ΔH° and ΔS° were nonmonotonic with an initial strong increase in both ΔH° and ΔS° and then a strong decrease when the degree of substitution exceeded some threshold. Exactly the same trend was observed for ΔCp. The dehydration of nonpolar surface, as quantified by the simulations, can to a large extent explain the variation in the thermodynamic parameters. The methyl substituents form additional hydrophobic contacts with the bile salt, but at high degrees of methylation they also cause significant distortion of the otherwise circular cyclodextrin structure. These two opposing contributions to the dehydration are the major causes for the observed variations in the thermodynamic functions. The structural effects are not expected to be specific for methylated cyclodextrins but should be observed for most modified cyclodextrins. An even more general conclusion is that variations in the extent of hydration are an important underlying reason for the commonly observed phenomenon termed enthalpy-entropy compensation and also for the less frequent reports of entropy convergence around 110 °C.

Higher order inclusion complexes and secondary interactions studied by global analysis of calorimetric titrations.

This paper investigates the use of isothermal titration calorimetry (ITC) as a tool for studying molecular systems in which weaker secondary interactions are present in addition to a dominant primary interaction. Such systems are challenging since the signal pertaining to the stronger primary interaction tends to overshadow the signal from the secondary interaction. The methodology presented here enables a complete and precise thermodynamic characterization of both the primary and the weaker secondary interaction, exemplified by the binding of ß-cyclodextrin to the primary and secondary binding sites of the bile salt glycodeoxycholate. Global regression analysis of calorimetric experiments at various concentrations and temperatures provide a precise determination of ΔH, ΔG°, and ΔC(p) for both binding sites in glycodeoxycholate (K1 = 5.67 ± 0.05 × 10(3) M(-1), K2 = 0.31 ± 0.02 × 10(3) M(-1)). The results are validated by a (13)C NMR titration and negative controls with a bile salt with no secondary binding site (glycocholate) (K = 2.96 ± 0.01 × 10(3) M(-1)). The method proved useful for detailed analysis of ITC data and may strengthen its use as a tool for studying molecular systems by advanced binding models.