Simultaneous determination of equilibrium constants and enthalpy changes by titration calorimetry: Methods, instruments, and uncertainties

Reaction of KHP with excess NaOH or TRIS as standard reactions for calibration of titration calorimeters from 0 to 60 °C

Calibration of titration calorimeters is an ongoing problem, particularly with calorimeters with reaction vessel volumes < 10 mL in which an electrical calibration heater is positioned outside the calorimetric vessel. Consequently, a chemical reaction with a known enthalpy change must be used to accurately calibrate these calorimeters. This work proposes the use of standard solutions of potassium acid phthalate (KHP) titrated into solutions of excess sodium hydroxide (NaOH) or excess tris(hydroxymethyl)aminomethane (TRIS) as standard reactions to determine the collective accuracy of the relevant variables in a determination of the molar enthalpy change for a reaction. KHP is readily available in high purity, weighable for easy preparation of solutions with accurately known concentrations, stable in solution, not compromised by side reactions with common contaminants such as atmospheric CO2, and non-corrosive to materials used in calorimeter construction. Molar enthalpy changes for these reactions were calculated from 0 to 60 °C from reliable literature data for the pKa of KHP, the molar enthalpy change for protonation of TRIS, and the molar enthalpy change for ionization of water. The feasibility of using these reactions as enthalpic standards was tested in several calorimeters; a 50 mL CSC 4300, a 185 μL NanoITC, a 1.4 mL VP-ITC, and a TAM III with 1 mL reaction vessels. The results from the 50 mL CSC 4300, which was accurately calibrated with an electric heater, verified the accuracy of the calculated standard values for the molar enthalpy changes of the proposed reactions.

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.

Isothermal titration calorimetry and molecular modeling study of the complex formation of daclatasvir by γ-cyclodextrin and trimethyl-β-cyclodextrin

The complex formation between daclatasvir and γ-CD or heptakis(2,3,6-tri-O-methyl)-β-CD (TM-β-CD) was studied by isothermal titration calorimetry and molecular modeling. Both techniques supported the predominant formation of a 2:1 complex in case of γ-CD although a 1:1 complex may be formed to a much lower extent as well. In case of TM-β-CD the stoichiometry of the complex was exclusively 1:1. Complex formation with γ-CD did not require dissociation of the daclatasvir dimer, which is present in solution, and resulted in a complex with a binding constant of 1.67·10⁷ M^-2. In contrast, formation of the weak TM-β-CD complex (K = 371 M^-1) required dissociation of the daclatasvir dimer. This is in line with the observation that the complex formation in case of γ-CD is enthalpy-driven, while the process is entropy-driven in case of TM-β-CD. It is concluded that the plateau observed in capillary electrophoresis is primarily based on the slow dissociation of the daclatasvir-CD complexes caused by steric constrains due to the folded terminal amino acid moieties of daclatasvir exerting a clip effect. In case γ-CD the thermodynamic stability might contribute to the overall slow dissociation.

Complexation of Lignin Dimers with β-Cyclodextrin and Binding Stability Analysis by ESI-MS, Isothermal Titration Calorimetry, and Molecular Dynamics Simulations

Lignin derived from lignocellulosic biomass is the largest source of renewable bioaromatics present on earth and requires environmentally sustainable separation strategies to selectively obtain high-value degradation products. Applications of supramolecular interactions have the potential to isolate lignin compounds from biomass degradation fractions by the formation of variable inclusion complexes with cyclodextrins (CDs). CDs are commonly used as selective adsorbents for many applications and can capture guest molecules in their internal hydrophobic cavity. The strength of supramolecular interactions between CDs and lignin model compounds that represent potential lignocellulosic biomass degradation products can be characterized by assessing the thermodynamics of binding stability. Consequently, the inclusion interactions of β-CD and lignin model compounds G-(β-O-4')-G, G-(β-O-4')-truncG (guaiacylglycerol-β-guaiacyl ether), and G-(β-β')-G (pinoresinol) were investigated empirically by electrospray ionization mass spectrometry and isothermal titration calorimetry, complemented by molecular dynamics (MD) simulations. Empirical results indicate that there are substantial differences in binding stability dependent on the linkage type. The lignin model β-β' dimer showed more potential bound states including 1:1, 2:1, and 1:2 (guest:host) complexation and, based on binding stability determinations, was consistently the most energetically favorable guest. Empirical results are supported by MD simulations that reveal that the capture of G-(β-β')-G by β-CD is promising with a 66% probability of being bound for G-(β-O-4')-truncG compared to 88% for G-(β-β')-G (unbiased distance trajectory and explicit counting of bound states). These outcomes indicate CDs as a promising material to assist in separations of lignin oligomers from heterogeneous mixtures for the development of environmentally sustainable isolations of lignin compounds from biomass fractions.

Thermodynamics of nanocrystal–ligand binding through isothermal titration calorimetry

Manipulations of nanocrystal (NC) surfaces have propelled the applications of colloidal NCs across various fields such as bioimaging, catalysis, electronics, and sensing applications.

Co-Loading of Temozolomide and Curcumin into a Calix[4]arene-Based Nanocontainer for Potential Combined Chemotherapy: Binding Features, Enhanced Drug Solubility and Stability in Aqueous Medium

The co-delivery of anticancer drugs into tumor cells by a nanocarrier may provide a new paradigm in chemotherapy. Temozolomide and curcumin are anticancer drugs with a synergistic effect in the treatment of multiform glioblastoma. In this study, the entrapment and co-entrapment of temozolomide and curcumin in a p-sulfonato-calix[4]arene nanoparticle was investigated by NMR spectroscopy, UV-vis spectrophotometry, isothermal titration calorimetry, and dynamic light scattering. Critical micellar concentration, nanoparticle size, zeta potential, drug loading percentage, and thermodynamic parameters were all consistent with a drug delivery system. Our data showed that temozolomide is hosted in the cavity of the calix[4]arene building blocks while curcumin is entrapped within the nanoparticle. Isothermal titration calorimetry evidenced that drug complexation and entrapment are entropy driven processes. The loading in the calixarene-based nanocontainer enhanced the solubility and half-life of both drugs, whose medicinal efficacy is affected by low solubility and rapid degradation. The calixarene-based nanocontainer appears to be a promising new candidate for nanocarrier-based drug combination therapy for glioblastoma.

A multi-laboratory benchmark study of isothermal titration calorimetry (ITC) using Ca2+ and Mg2+ binding to EDTA

A small-scale ITC benchmarking study was performed involving 9 biophysics laboratories/facilities, to evaluate inter-laboratory and intra-laboratory basal levels of uncertainty. Our prime goal was to assess a number of important factors that can influence both the data gathered by this technique and the thermodynamic parameter values derived therefrom. In its first part, the study involved 5 laboratories and 13 different instruments, working with centrally prepared samples and the same experimental protocol. The second part involved 4 additional laboratories and 6 more instruments, where the users prepared their own samples according to provided instructions and did the experiments following the same protocol as in the first part. The study design comprised: (1) selecting a minimal set of laboratories; (2) providing very stable samples; (3) providing samples not requiring preparation or manipulation; and (4) providing a well-defined and detailed experimental protocol. Thus, we were able to assess: (i) the variability due to instrument and data analysis performed by each user on centrally prepared samples; (ii) the comparability of data retrieved when using 4 different software packages to analyze the same data, besides the data analysis carried out by the different users on their own experimental results; and (iii) the variability due to local sample preparation (second part of the study). Individual values, as well as averages and standard deviations for the binding parameters for EDTA-cation interaction, were used as metrics for comparing the equilibrium association constant (logK), enthalpy of interaction (ΔH), and the so-called "stoichiometry" (n), a concentration-correction factor.

Isothermal titration calorimetry (ITC): a standard operating procedure (SOP)

Isothermal titration calorimetry (ITC) is currently widely used in many applied areas of research, spanning protein-ligand binding, metal-ligand interactions, DNA/DNA or protein/DNA interactions, partition to membranes, and polymer surfactant interactions, to mention just a few. This is due to the availability of commercial instruments, and thus the production and spread of an accepted and widely followed SOP is felt by most users, in an effort to produce results that are scientifically correct and comparable. Therefore, within the efforts of Working Group 4 of the ARBRE-MOBIEU COST Action (CA15126), this ITC SOP was generated, alongside SOPs for several other biophysical techniques. Here, we discuss the factors that are fundamental for good experimental design and that need to be carefully considered, as well as machine calibration, in particular chemical calibration, linked to another outcome of Working Group 4 on ITC benchmarking, to be also published in this Special Issue.

Phage-Display-Derived Peptide Specific to Carbamylated Protein

Protein carbamylation has been linked with diseases commonly associated with patients with reduced kidney function. Carbamylated human serum albumin (cHSA), which has been proven to be nephrotoxic and associated with heart failure for chronic kidney disease (CKD) patients, was chosen for our study. Through phage display against cHSA, one specific peptide sequence (cH2-p1) was identified with higher selectivity toward cHSA over native HSA. The cH2-p1 peptide was synthesized, and its target binding was analyzed through isothermal titration calorimetry (ITC). The result showed that cH2-p1 was able to bind cHSA of different levels of carbamylation with a similar dissociation constant of ∼1.0 × 10^-4 M. This peptide also showed a binding specificity to carbamylated fibrinogen (cFgn), while not binding to native Fgn at all. For better understanding of the binding mechanism of cH2-p1, competitive binding of cH2-p1 and anti-homocitrulline to cHSA was performed, and the result revealed that cH2-p1 may bind to homocitrulline residues in a similar manner to the antibody. A molecular docking study was further performed to investigate the favored binding conformation of homocitrulline residue to cH2-p1. This work demonstrates the potential of peptides as a specific binding element to carbamylated proteins.

Binding Affinity and Driving Forces for the Interaction of Calixarene-Based Micellar Aggregates With Model Antibiotics in Neutral Aqueous Solution

The search for novel surfactants or drug delivery systems able to improve the performance of old-generation antibiotics is a topic of great interest. Self-assembling amphiphilic calix[4]arene derivatives provide well-defined nanostructured systems that exhibit promising features for antibiotics delivery. In this work, we investigated the capability of two micellar polycationic calix[4]arene derivatives to recognize and host ofloxacin, chloramphenicol, or tetracycline in neutral aqueous solution. The formation of the nanoaggregates and the host–guest equilibria were examined by nano-isothermal titration calorimetry, dynamic light scattering, and mono- and bi-dimensional NMR. The thermodynamic characterization revealed that the calix[4]arene-based micellar aggregates are able to effectively entrap the model antibiotics and enabled the determination of both the species and the driving forces for the molecular recognition process. Indeed, the formation of the chloramphenicol–micelle adduct was found to be enthalpy driven, whereas entropy drives the formation of the adducts with both ofloxacin and tetracycline. NMR spectra corroborated ITC data about the positioning of the antibiotics in the calixarene nanoaggregates.

Estimation of non-constant variance in isothermal titration calorimetry using an ITC measurement model

Isothermal titration calorimetry (ITC) is the gold standard for accurate measurement of thermodynamic parameters in solution reactions. In the data processing of ITC, the non-constant variance of the heat requires special consideration. The variance function approach has been successfully applied in previous studies, but is found to fail under certain conditions in this work. Here, an explicit ITC measurement model consisting of main thermal effects and error components has been proposed to quantitatively evaluate and predict the non-constant variance of the heat data under various conditions. Monte Carlo simulation shows that the ITC measurement model provides higher accuracy and flexibility than variance function in high c-value reactions or with additional error components, for example, originated from the fluctuation of the concentrations or other properties of the solutions. The experimental design of basic error evaluation is optimized accordingly and verified by both Monte Carlo simulation and experiments. An easy-to-run Python source code is provided to illustrate the establishment of the ITC measurement model and the estimation of heat variances. The accurate and reliable non-constant variance of heat is helpful to the application of weighted least squares regression, the proper evaluation or selection of the reaction model.

Associative structures formed from cellulose nanofibrils and nanochitins are pH-responsive and exhibit tunable rheology

HYPOTHESIS

Nanocellulose and nanochitin are both biobased materials with complementary structures and properties. Both exhibit pH-dependent surface charges which are opposite in sign. Hence, it should be possible to manipulate them to form complexed structures via ionic bond formation at prescribed pH conditions.

EXPERIMENT

Nanocellulose and nanochitin were mixed after exposure to acidic or neutral conditions to influence their ionization state. The heat of interaction during the introduction of nanochitin to nanocellulose was monitored via isothermal titration calorimetry. The strength and gel properties of the resulting structures were characterized via rheological measurement.

FINDINGS

The resultant gel properties in the designed hybrid systems were found to depend directly on the charge state of the starting materials, which was dictated by pH adjustment. Different interparticle interactions including ionic attraction, hydrophobic associations, and physical entanglement were identified in the systems and the influence of each was elucidated for different conditions of pH, concentration, and ratio of nanochitin to nanocellulose. Hydrophobic associations between neutralized nanochitin particles were found to contribute strongly to increased elastic modulus values. Ionic complex formation was found to provide enhanced stability under broader pH conditions, while physical entanglement of cellulose nanofibers was a substantial thickening mechanism in all systems.

Simultaneous determination of thermodynamic and kinetic data by isothermal titration calorimetry

BACKGROUND

Thermodynamic and binding kinetic data increasingly support and guide the drug optimization process.

METHODS

Because ITC thermograms contain binding thermodynamic and kinetic information, an efficient protocol for the simultaneous extraction of thermodynamic and kinetic data for 1:1 protein ligand reactions from AFFINImeter kinITC in one single experiment are presented.

RESULTS

The effort to apply this protocol requires the same time as for the standard protocol but increases the precision of both thermodynamic and kinetic data.

CONCLUSIONS

The protocol enables reliable extraction of both thermodynamic and kinetic data for 1:1 protein-ligand binding reactions with improved precision compared to the 'standard protocol'.

GENERAL SIGNIFICANCE

Thermodynamic and kinetic data are recorded under exactly the same conditions in solution without any labeling or immobilization from a protein sample that is not 100% active and would otherwise render the extraction of kinetic parameters impossible.

Complexation of As(III) by phosphonate ligands in aqueous fluids: Thermodynamic behavior, chemical binding forms and sequestering abilities

In recent years, the contamination of water by arsenic reached alarming levels in many countries of the world, attracting the interest of many researchers engaged in testing methodologies able to remove this harmful pollutant. An important aspect that must be taken into consideration is the possibility to find arsenic in different chemical forms which could require different approaches for its removal. At this aim, a speciation analysis appears to be crucial for better understanding the behavior of arsenic species in aqueous solutions, especially in presence of compounds with marked chelating properties. Phosphonates can be identified as good sequestering agents and, at this purpose, this manuscript intends to investigate the interaction of As(III) with three phosphonic acids derived from nitrilotriacetic acid (NTA) by replacements of one (N-(Phosphonomethyl) iminodiacetic acid, NTAP), two (N,N-Bis-(phosphonomethyl) glycine, NTA2P) and three (Nitrilotri(methylphosphonic acid), NTA3P) carboxylic groups with the same number of phosphonate groups. An in-depth potentiometric and calorimetric investigation allowed to determine speciation models featured by simple ML, MLH_i and ML(OH) species. A complete thermodynamic characterization of the systems is reported together with the definition of coordination mode by mass spectrometry measurements. On the light of the speciation models, the possibility of using these ligands in arsenic removal techniques was assessed by determining the pL_0.5 (the concentration of ligand able to remove the 50% of metal ion present in trace). All ligands show a good sequestering ability, in particular under the conditions of fresh water, following the trend NTA3P > NTA2P > NTAP.

Stirring rate affects thermodynamics and unfolding kinetics in isothermal titration calorimetry

Isothermal titration calorimetry (ITC) directly provides thermodynamic parameters depicting the energetics of intermolecular interactions in solution. During ITC experiments, a titration syringe with a paddle is continuously rotating to promote a homogeneous mixing. Here, we clarified that the shape of the paddles (flat, corkscrew and small-pitched corkscrew) and the stirring rates influence on the thermodynamic parameters of protein-ligand interaction. Stirring with the flat paddle at lower and higher rate both yielded a lower exothermic heat due to different reasons. The complete reaction with no incompetent fractions was achieved only when the stirring was performed at 500 or 750 rpm using the small-pitched corkscrew paddle. The evaluation of the protein solution after 1,500 rpm stirring indicated that proteins in the soluble fraction decreased to 94% of the initial amount, among which 6% was at an unfolded state. In addition, a significant increase of micron aggregates was confirmed. Furthermore, a new approach for the determination of the unfolding kinetics based on the time dependence of the total reaction heat was developed. This study demonstrates that a proper stirring rate and paddle shape are essential for the reliable estimation of thermodynamic parameters in ITC experiments.

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 (pK_a value) is the simultaneous determination of the binding constant and binding enthalpy, as well as being precise and easy to use. The pK_a can be calculated from the binding constant, and the temperature dependency of the pK_a 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 pK_a for ibuprofen, ascorbic acid, 2-morpholin-4-ylethanesulfonic acid and paracetamol. The pK_a 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 pK_a values.

Halogenated and di-substituted benzenesulfonamides as selective inhibitors of carbonic anhydrase isoforms

By applying an approach of a "ring with two tails", a series of novel inhibitors possessing high-affinity and significant selectivity towards selected carbonic anhydrase (CA) isoforms has been designed. The "ring" consists of 2-chloro/bromo-benzenesulfonamide, where the sulfonamide group is as an anchor coordinating the Zn(II) in the active site of CAs, and halogen atom orients the ring affecting the affinity and selectivity. First "tail" is a substituent containing carbonyl, carboxyl, hydroxyl, ether groups or hydrophilic amide linkage. The second "tail" contains aryl- or alkyl-substituents attached through a sulfanyl or sulfonyl group. Both "tails" are connected to the benzene ring and play a crucial role in selectivity. Varying the substituents, we designed compounds selective for CA VII, CA IX, CA XII, or CA XIV. Since due to binding-linked protonation reactions the binding-ready fractions of the compound and protein are much lower than one, the "intrinsic" affinities were calculated that should be used to study correlations between crystal structures and the thermodynamics of binding for rational drug design. The "intrinsic" affinities together with the intrinsic enthalpies and entropies of binding together with co-crystal structures were used demonstrate structural factors determining major contributions for compound affinity and selectivity.

Obtaining precise and accurate results by ITC

Acquisition of precise and accurate results by isothermal titration calorimetry (ITC) can be achieved through thoughtful experimental design and modeling and careful experimental operations. Large reported errors in ITC results in determinations of stoichiometries, equilibrium constants and enthalpy changes for ligand binding to proteins are the consequence of poor experiment design, failure to properly calibrate and test instruments and protocols, lack of controls, errors in solution preparation, and incorrect data analyses. Analysis of a recent report that claimed to have determined the "repeatability, precision, and accuracy of the enthalpies and Gibbs energies of a protein-ligand binding reaction" by ITC is used to illustrate how to improve ITC operations and results. The analysis shows that the reported results are misleading because calorimeters were not calibrated, operating parameters were not optimized, errors were made in solution preparations, and data analysis was not optimized. As a consequence, the results do not provide a valid comparison of the capabilities of the calorimeters included in the study. A proposal that reaction of acetazolamide with carbonic anhydrase II be used as a comparison standard for testing ITCs and procedures is problematic because the binding constant is too large and for several other reasons discussed in the paper. Requirements for obtaining precise and accurate results by ITC are discussed and experimental results are presented to illustrate the precision and accuracy attainable with low volume ITCs. The problem of the blank correction is identified as the limiting factor in obtaining accurate results by ITC.

Zn2+ Interaction with Amyloid-Β: Affinity and Speciation

Conflicting values, obtained by different techniques and often under different experimental conditions have been reported on the affinity of Zn²⁺ for amyloid-β, that is recognized as the major interaction responsible for Alzheimer’s disease. Here, we compare the approaches employed so far, i.e., the evaluation of K_d and the determination of the stability constants to quantitatively express the affinity of Zn²⁺ for the amyloid-β peptide, evidencing the pros and cons of the two approaches. We also comment on the different techniques and conditions employed that may lead to divergent data. Through the analysis of the species distribution obtained for two selected examples, we show the implications that the speciation, based on stoichiometric constants rather than on K_d, may have on data interpretation. The paper also demonstrates that the problem is further complicated by the occurrence of multiple equilibria over a relatively narrow pH range.

Sequence-Defined Introduction of Hydrophobic Motifs and Effects in Lectin Binding of Precision Glycomacromolecules

This study investigates the influence of an increasingly hydrophobic backbone of multivalent glycomimetics based on sequence-defined oligo(amidoamines) on their resulting affinity toward bacterial lectins. Glycomacromolecules are obtained by stepwise assembly of tailor-made building blocks on solid support, using both hydrophobic aliphatic and aromatic building blocks to enable a gradual change in hydrophobicity of the backbone. Their binding behavior toward model lectin Concanavalin A (ConA) is evaluated using isothermal titration calorimetry (ITC) and surface plasmon resonance (SPR) showing higher affinities for glycomacromolecules with higher content of hydrophobic and aromatic moieties in the backbone. Finally, glycomacromolecules are tested in a bacterial adhesion inhibition study against Escherichia coli where more hydrophobic backbones yield higher inhibitory potentials most likely due to additional secondary interactions with hydrophobic regions of the protein receptor as well as a change in conformation exposing carbohydrate ligands for increased binding. Overall, the results highlight the influence and thereby importance of the polymer backbone itself on the resulting properties of polymeric biomimetics.

Characterization of Cyclodextrin/Volatile Inclusion Complexes: A Review

Cyclodextrins (CDs) are a family of cyclic oligosaccharides that constitute one of the most widely used molecular hosts in supramolecular chemistry. Encapsulation in the hydrophobic cavity of CDs positively affects the physical and chemical characteristics of the guests upon the formation of inclusion complexes. Such a property is interestingly employed to retain volatile guests and reduce their volatility. Within this scope, the starting crucial point for a suitable and careful characterization of an inclusion complex is to assess the value of the formation constant (K_f), also called stability or binding constant. This task requires the application of the appropriate analytical method and technique. Thus, the aim of the present paper is to give a general overview of the main analytical tools used for the determination of K_f values for CD/volatile inclusion complexes. This review emphasizes on the advantages, inconvenients and limits of each applied method. A special attention is also dedicated to the improvement of the current methods and to the development of new techniques. Further, the applicability of each technique is illustrated by a summary of data obtained from the literature.

Chromis-1, a Ratiometric Fluorescent Probe Optimized for Two-Photon Microscopy Reveals Dynamic Changes in Labile Zn(II) in Differentiating Oligodendrocytes

Despite the significant advantages of two-photon excitation microscopy (TPEM) over traditional confocal fluorescence microscopy in live-cell imaging applications, including reduced phototoxicity and photobleaching, increased depth penetration, and minimized autofluorescence, only a few metal ion-selective fluorescent probes have been designed and optimized specifically for this technique. Building upon a donor-acceptor fluorophore architecture, we developed a membrane-permeant, Zn(II)-selective fluorescent probe, chromis-1, that exhibits a balanced two-photon cross section between its free and Zn(II)-bound form and responds with a large spectral shift suitable for emission-ratiometric imaging. With a Kd of 1.5 nM and wide dynamic range, the probe is well suited for visualizing temporal changes in buffered Zn(II) levels in live cells as demonstrated with mouse fibroblast cell cultures. Moreover, given the importance of zinc in the physiology and pathophysiology of the brain, we employed chromis-1 to monitor cytoplasmic concentrations of labile Zn(II) in oligodendrocytes, an important cellular constituent of the brain, at different stages of development in cell culture. These studies revealed a decrease in probe saturation upon differentiation to mature oligodendrocytes, implying significant changes to cellular zinc homeostasis during maturation with an overall reduction in cellular zinc availability. Optimized for TPEM, chromis-1 is especially well-suited for exploring the role of labile zinc pools in live cells under a broad range of physiological and pathological conditions.

Ubiquitin Associates with the N-Terminal Domain of Nerve Growth Factor: The Role of Copper(II) Ions

Many biochemical pathways involving nerve growth factor (NGF), a neurotrophin with copper(II) binding abilities, are regulated by the ubiquitin (Ub) proteasome system. However, whether NGF binds Ub and the role played by copper(II) ions in modulating their interactions have not yet been investigated. Herein NMR spectroscopy, circular dichroism, ESI-MS, and titration calorimetry are employed to characterize the interactions of NGF with Ub. NGF_1-14 , which is a short model peptide encompassing the first 14 N-terminal residues of NGF, binds the copper-binding regions of Ub (K_D =8.6 10^-5  m). Moreover, the peptide undergoes a random coil-polyproline type II helix structural conversion upon binding to Ub. Notably, copper(II) ions inhibit NGF_1-14 /Ub interactions. Further experiments performed with the full-length NGF confirmed the existence of a copper(II)-dependent association between Ub and NGF and indicated that the N-terminal domain of NGF was a valuable paradigm that recapitulated many traits of the full-length protein.

Stabilization of Cu(I) for binding and calorimetric measurements in aqueous solution

Conditions have been developed for the comproportionation reaction of Cu(2+) and copper metal to prepare aqueous solutions of Cu(+) that are stabilized from disproportionation by MeCN and other Cu(+)-stabilizing ligands. These solutions were then used in ITC measurements to quantify the thermodynamics of formation of a set of Cu(+) complexes (Cu(I)(MeCN)3(+), Cu(I)Me6Trien(+), Cu(I)(BCA)2(3-), Cu(I)(BCS)2(3-)), which have stabilities ranging over 15 orders of magnitude, for their use in binding and calorimetric measurements of Cu(+) interaction with proteins and other biological macromolecules. These complexes were then used to determine the stability and thermodynamics of formation of a 1 : 1 complex of Cu(+) with the biologically important tri-peptide glutathione, GSH. These results identify Me6Trien as an attractive Cu(+)-stabilizing ligand for calorimetric experiments, and suggest that caution should be used with MeCN to stabilize Cu(+) due to its potential for participating in unquantifiable ternary interactions.

Applications of isothermal titration calorimetry - the research and technical developments from 2011 to 2015

Isothermal titration calorimetry is a widely used biophysical technique for studying the formation or dissociation of molecular complexes. Over the last 5 years, much work has been published on the interpretation of isothermal titration calorimetry (ITC) data for single binding and multiple binding sites. As over 80% of ITC papers are on macromolecules of biological origin, this interpretation is challenging. Some researchers have attempted to link the thermodynamics constants to events at the molecular level. This review highlights work carried out using binding sites characterized using x-ray crystallography techniques that allow speculation about individual bond formation and the displacement of individual water molecules during ligand binding and link these events to the thermodynamic constants for binding. The review also considers research conducted with synthetic binding partners where specific binding events like anion-π and π-π interactions were studied. The revival of assays that enable both thermodynamic and kinetic information to be collected from ITC data is highlighted. Lastly, published criticism of ITC research from a physical chemistry perspective is appraised and practical advice provided for researchers unfamiliar with thermodynamics and its interpretation. Copyright © 2016 John Wiley & Sons, Ltd.

Differential Binding Models for Direct and Reverse Isothermal Titration Calorimetry

Isothermal titration calorimetry (ITC) is a technique to measure the stoichiometry and thermodynamics from binding experiments. Identifying an appropriate mathematical model to evaluate titration curves of receptors with multiple sites is challenging, particularly when the stoichiometry or binding mechanism is not available. In a recent theoretical study, we presented a differential binding model (DBM) to study calorimetry titrations independently of the interaction among the binding sites (Herrera, I.; Winnik, M. A. J. Phys. Chem. B 2013, 117, 8659-8672). Here, we build upon our DBM and show its practical application to evaluate calorimetry titrations of receptors with multiple sites independently of the titration direction. Specifically, we present a set of ordinary differential equations (ODEs) with the general form d[S]/dV that can be integrated numerically to calculate the equilibrium concentrations of free and bound species S at every injection step and, subsequently, to evaluate the volume-normalized heat signal (δQ(V) = δq/dV) of direct and reverse calorimetry titrations. Additionally, we identify factors that influence the shape of the titration curve and can be used to optimize the initial concentrations of titrant and analyte. We demonstrate the flexibility of our updated DBM by applying these differentials and a global regression analysis to direct and reverse calorimetric titrations of gadolinium ions with multidentate ligands of increasing denticity, namely, diglycolic acid (DGA), citric acid (CIT), and nitrilotriacetic acid (NTA), and use statistical tests to validate the stoichiometries for the metal-ligand pairs studied.

Determination of thermodynamic potentials and the aggregation number for micelles with the mass-action model by isothermal titration calorimetry: A case study on bile salts

The aggregation number (n), thermodynamic potentials (ΔG, ΔH, ΔS) and critical micelle concentration (CMC) for 6 natural bile salts were determined on the basis of both original and previously published isothermal titration calorimetry (ITC) data. Different procedures to estimate parameters of micelles with ITC were compared to a mass-action model (MAM) of reaction type: n⋅S⇌Mn. This analysis can provide guidelines for future ITC studies of systems behaving in accordance with this model such as micelles and proteins that undergo self-association to oligomers. Micelles with small aggregation numbers, as those of bile salts, are interesting because such small aggregates cannot be characterized as a separate macroscopic phase and the widely applied pseudo-phase model (PPM) is inaccurate. In the present work it was demonstrated that the aggregation number of micelles was constant at low concentrations enabling determination of the thermodynamic potentials by the MAM. A correlation between the aggregation number and the heat capacity was found, which implies that the dehydrated surface area of bile salts increases with the aggregation number. This is in accordance with Tanford's principles of opposing forces where neighbouring molecules in the aggregate are better able to shield from the surrounding hydrophilic environment when the aggregation number increases.

Dissecting ITC data of metal ions binding to ligands and proteins

BACKGROUND

ITC is a powerful technique that can reliably assess the thermodynamic underpinnings of a wide range of binding events. When metal ions are involved, complications arise in evaluating the data due to unavoidable solution chemistry that includes metal speciation and a variety of linked equilibria.

SCOPE OF REVIEW

This paper identifies these concerns, provides recommendations to avoid common mistakes, and guides the reader through the mathematical treatment of ITC data to arrive at a set of thermodynamic state functions that describe identical chemical events and, ideally, are independent of solution conditions. Further, common metal chromophores used in biological metal sensing studies are proposed as a robust system to determine unknown solution competition.

MAJOR CONCLUSIONS

Metal ions present several complications in ITC experiments. This review presents strategies to avoid these pitfalls and proposes and experimentally validates mathematical approaches to deconvolute complex equilibria that exist in these systems.

GENERAL SIGNIFICANCE

This review discusses the wide range of complications that exists in metal-based ITC experiments. It provides a starting point for scientists new to this field and articulates concerns that will help experienced researchers troubleshoot experiments.

Improving ITC studies of cyclodextrin inclusion compounds by global analysis of conventional and non-conventional experiments

The study of 1:1 cyclodextrin inclusion compounds by isothermal titration calorimetry was explored in a theoretical and experimental point of view to compare the efficiency of conventional and non-conventional experiments. All direct and competitive protocols were described and evaluated in terms of accuracy on both binding constant and inclusion enthalpy. Significant improvement in the calorimetric characterization may be obtained by means of the global analysis of non-conventional experiments coupled to the standard titration protocol. While the titration-release approach proved to be the most accurate strategy for classical complexations, the valuable contribution of other non-conventional experiments was demonstrated for issues concerning weak stability, enthalpy, or solubility.

An integrated study of the affinities of the Aβ16 peptide for Cu(i) and Cu(ii): implications for the catalytic production of reactive oxygen species

Affinities of Aβ16 peptide and several selected variants for Cu(i) and Cu(ii) were determined with new probes and correlated to their binding modes and abilities in promoting ROS generation.

Robust affinity standards for Cu(I) biochemistry

The measurement of reliable Cu(I) protein binding affinities requires competing reference ligands with similar binding strengths; however, the literature on such reference ligands is not only sparse but often conflicting. To address this deficiency, we have created and characterized a series of water-soluble monovalent copper ligands, MCL-1, MCL-2, and MCL-3, that form well-defined, air-stable, and colorless complexes with Cu(I) in aqueous solution. X-ray structural data, electrochemical measurements, and an extensive network of equilibrium titrations showed that all three ligands form discrete Cu(I) complexes with 1:1 stoichiometry and are capable of buffering Cu(I) concentrations between 10(-10) and 10(-17) M. As most Cu(I) protein affinities have been obtained from competition experiments with bathocuproine disulfonate or 2,2'-bicinchoninic acid, we further calibrated their Cu(I) stability constants against the MCL series. To demonstrate the application of these reagents, we determined the Cu(I) binding affinity of CusF (log K = 14.3 ± 0.1), a periplasmic metalloprotein required for the detoxification of elevated copper levels in Escherichia coli . Altogether, this interconnected set of affinity standards establishes a reliable foundation that will facilitate the precise determination of Cu(I) binding affinities of proteins and small-molecule ligands.

Differential binding models for isothermal titration calorimetry: moving beyond the Wiseman isotherm

We present a set of model-independent differential equations to analyze isothermal titration calorimetry (ITC) experiments. In contrast with previous approaches that begin with specific assumptions about the number of binding sites and the interactions among them (e.g., sequential, independent, cooperative), our derivation makes more general assumptions, such that a receptor with multiple sites for one type of ligand species (homotropic binding) can be studied with the same analytical expression. Our approach is based on the binding polynomial formalism, and the resulting analytical expressions can be extended to account for any number of binding sites and any type of binding interaction among them. We refer to the set of model-independent differential equations to study ITC experiments as a differential binding model (DBM). To demonstrate the flexibility of our DBM, we present the analytical expressions to study receptors with one or two binding sites. The DBM for a receptor with one site is equivalent to the Wiseman isotherm but with a more intuitive representation that depends on the binding polynomial and the dimensionless parameter c = K·MT, where K is the binding constant and MT the total receptor concentration. In addition, we show how to constrain the general DBM for a receptor with two sites to represent sequential, independent, or cooperative binding interactions between the sites. We use the sequential binding model to study the binding interaction between Gd(III) and citrate anions. In addition, we simulate calorimetry titrations of receptors with positive, negative, and noncooperative interactions between the two binding sites. Finally, we derive a DBM for titrations of receptors with n-independent binding sites.

Entropy-enthalpy compensation: role and ramifications in biomolecular ligand recognition and design

Recent calorimetric studies of interactions between small molecules and biomolecular targets have generated renewed interest in the phenomenon of entropy-enthalpy compensation. In these studies, entropic and enthalpic contributions to binding are observed to vary substantially and in an opposing manner as the ligand or protein is modified, whereas the binding free energy varies little. In severe examples, engineered enthalpic gains can lead to completely compensating entropic penalties, frustrating ligand design. Here, we examine the evidence for compensation, as well as its potential origins, prevalence, severity, and ramifications for ligand engineering. We find the evidence for severe compensation to be weak in light of the large magnitude of and correlation between errors in experimental measurements of entropic and enthalpic contributions to binding, though a limited form of compensation may be common. Given the difficulty of predicting or measuring entropic and enthalpic changes to useful precision, or using this information in design, we recommend ligand engineering efforts instead focus on computational and experimental methodologies to directly assess changes in binding free energy.

Modeling complex equilibria in isothermal titration calorimetry experiments: thermodynamic parameters estimation for a three-binding-site model

Isothermal titration calorimetry (ITC) is a powerful technique that can be used to estimate a complete set of thermodynamic parameters (e.g., K(eq) (or ΔG), ΔH, ΔS, and n) for a ligand-binding interaction described by a thermodynamic model. Thermodynamic models are constructed by combining equilibrium constant, mass balance, and charge balance equations for the system under study. Commercial ITC instruments are supplied with software that includes a number of simple interaction models, for example, one binding site, two binding sites, sequential sites, and n-independent binding sites. More complex models, for example, three or more binding sites, one site with multiple binding mechanisms, linked equilibria, or equilibria involving macromolecular conformational selection through ligand binding, need to be developed on a case-by-case basis by the ITC user. In this paper we provide an algorithm (and a link to our MATLAB program) for the nonlinear regression analysis of a multiple-binding-site model with up to four overlapping binding equilibria. Error analysis demonstrates that fitting ITC data for multiple parameters (e.g., up to nine parameters in the three-binding-site model) yields thermodynamic parameters with acceptable accuracy.

Interest of designed cyclodextrin-tools in gene delivery

Cyclodextrins (CyDs) currently displays even today the image of a natural macrocyclic compound largely dominant in the formation of inclusion complexes with small hydrophobic molecules. During the past 10 years, advances in this field allowed to achieve more and more sophisticated CyDs derivatives opening a simple access in scale-up quantities to original and better CyD-based gene delivery systems. In addition, possibility to combine covalent and supramolecular approaches offers new venues for the design of tailor-made CyD-based nanovehicles to improve their transfection ability and gene transfer in cells. In this account, we describe our recent progress in the construction of a novel CyD-based G0 (generation number) core dendrimer, scalable to CyD oligomers by a strategy using protonable guanidine tethers and whose concept can be generalized for the assembly of CyD pre-coated dendrimers. The synthetic strategy based on an original Staudinger-Aza-Wittig tandem coupling reaction. We present an outline of the different analytical strategies to characterize CyD-ODN (cyclodextrin-oligodeoxynucleotide) complexes. Among them, Capillary electrophoresis (CE) was used to perfectly characterize our CyD-siRNA and CyD-DNA complexes and shown to be a very attractive method with advantages of low sample consumption, rapid analysis speed, and high efficiency that make this technology a major tool for association constant measurement. Finally, we present the different biological methods that can be used, in vitro, to study gene delivery, and more precisely ones we have performed to evaluate the capability of our original model bis-guanidinium-tetrakis-β-cyclodextrin dendrimeric tetrapod, to deliver efficiently DNA or siRNA in eukaryotic cells.

Designing isothermal titration calorimetry experiments for the study of 1:1 binding: problems with the "standard protocol"

Literature recommendations for designing isothermal titration calorimetry (ITC) experiments to study 1:1 binding, M+X -->/<-- MX, are not consistent and have persisted through time with little quantitative justification. In particular, the "standard protocol" employed by most workers involves 20 to 30 injections of titrant to a final titrant/titrand mole ratio (R(m)) of ~ 2-a scheme that can be far from optimal and can needlessly limit applicability of the ITC technique. These deficiencies are discussed here along with other misconceptions. Whether a specific binding process can be studied by ITC is determined less by c (the product of binding constant K and titrand concentration [M](0)) than by the total detectable heat q(tot) and the extent to which M can be converted to MX. As guidelines, with 90% conversion to MX, K can be estimated within 5% over the range 10 to 10(8)M(-1) when q(tot)/σ(q)≈700, where σ(q) is the standard deviation for estimation of q. This ratio drops to ~150 when the stoichiometry parameter n is treated as known. A computer application for modeling 1:1 binding yields realistic estimates of parameter standard errors for use in protocol design and feasibility assessment.

Isothermal titration calorimetry in nanoliter droplets with subsecond time constants

We reduced the reaction volume in microfabricated suspended-membrane titration calorimeters to nanoliter droplets and improved the sensitivities to below a nanowatt with time constants of around 100 ms. The device performance was characterized using exothermic acid-base neutralizations and a detailed numerical model. The finite element based numerical model allowed us to determine the sensitivities within 1% and the temporal dynamics of the temperature rise in neutralization reactions as a function of droplet size. The model was used to determine the optimum calorimeter design (membrane size and thickness, junction area, and thermopile thickness) and sensitivities for sample volumes of 1 nL for silicon nitride and polymer membranes. We obtained a maximum sensitivity of 153 pW/(Hz)(1/2) for a 1 μm SiN membrane and 79 pW/(Hz)(1/2) for a 1 μm polymer membrane. The time constant of the calorimeter system was determined experimentally using a pulsed laser to increase the temperature of nanoliter sample volumes. For a 2.5 nanoliter sample volume, we experimentally determined a noise equivalent power of 500 pW/(Hz)(1/2) and a 1/e time constant of 110 ms for a modified commercially available infrared sensor with a thin-film thermopile. Furthermore, we demonstrated detection of 1.4 nJ reaction energies from injection of 25 pL of 1 mM HCl into a 2.5 nL droplet of 1 mM NaOH.