Explicit formulation of titration models for isothermal titration calorimetry

Isothermal titration calorimetry (ITC) produces a differential heat signal with respect to the total titrant concentration. This feature gives ITC excellent sensitivity for studying the thermodynamics of complex biomolecular interactions in solution. Currently, numerical methods for data fitting are based primarily on indirect approaches rooted in the usual practice of formulating biochemical models in terms of integrated variables. Here, a direct approach is presented wherein ITC models are formulated and solved as numerical initial value problems for data fitting and simulation purposes. To do so, the ITC signal is cast explicitly as a first-order ordinary differential equation (ODE) with total titrant concentration as independent variable and the concentration of a bound or free ligand species as dependent variable. This approach was applied to four ligand-receptor binding and homotropic dissociation models. Qualitative analysis of the explicit ODEs offers insights into the behavior of the models that would be inaccessible to indirect methods of analysis. Numerical ODEs are also highly compatible with regression analysis. Since solutions to numerical initial value problems are straightforward to implement on common computing platforms in the biochemical laboratory, this method is expected to facilitate the development of ITC models tailored to any experimental system of interest.     

A study of statistical error in isothermal titration calorimetry

In isothermal titration calorimetry (ITC), the two main sources of random (statistical) error are associated with the extraction of the heat q from the measured temperature changes and with the delivery of metered volumes of titrant. The former leads to uncertainty that is approximately constant and the latter to uncertainty that is proportional to q. The role of these errors in the analysis of ITC data by nonlinear least squares is examined for the case of 1:1 binding, M+X right arrow over left arrow MX. The standard errors in the key parameters-the equilibrium constant Ko and the enthalpy DeltaHo-are assessed from the variance-covariance matrix computed for exactly fitting data. Monte Carlo calculations confirm that these "exact" estimates will normally suffice and show further that neglect of weights in the nonlinear fitting can result in significant loss of efficiency. The effects of the titrant volume error are strongly dependent on assumptions about the nature of this error: If it is random in the integral volume instead of the differential volume, correlated least-squares is required for proper analysis, and the parameter standard errors decrease with increasing number of titration steps rather than increase.     

Calibration in isothermal titration calorimetry: heat and cell volume from heat of dilution of NaCl(aq)

An isothermal titration calorimeter of the perfusion type (MicroCal model VP-ITC) is calibrated using the heat of dilution of NaCl in water. The relative apparent molar enthalpy function (L(phi)) for NaCl(aq) varies strongly and nonlinearly with concentration in the low-concentration region (<0.2M) that is sampled easily and extensively in a single program of injections of NaCl solution into water. This nonlinearity makes it possible to calibrate with respect to two quantities: the measured heat and the active cell volume. The heat factor is determined with typical standard error 0.003; its value in the current case is 0.987. The cell volume factor is 0.93 but is quite sensitive to possible systematic errors in the temperature and in the literature values for L(phi). Both correction factors are closely tied to the delivered volume from the injection syringe, which required a correction factor of 0.973, attributed to an instrumental gear ratio error. Temperature calibration of the instrument showed a small offset of 0.12K at the temperature 25 degrees C of the experiments, but the error increased to more than 1K at 46 degrees C. The experiments were not able to distinguish clearly between mixing algorithms that assume instantaneous mixing on injection and those that assume instantaneous injection followed by mixing; however, examination of these algorithms has revealed an error in a program widely used to analyze isothermal titration calorimetry data.     

Applications of isothermal titration calorimetry in protein science

During the past decade, isothermal titration calorimetry (ITC) has developed from a specialist method for understanding molecular interactions and other biological processes within cells to a more robust, widely used method. Nowadays, ITC is used to investigate all types of protein interactions, including protein-protein interactions, protein-DNA/RNA interactions, protein-small molecule interactions and enzyme kinetics; it provides a direct route to the complete thermodynamic characterization of protein interactions. This review concentrates on the new applications of ITC in protein folding and misfolding, its traditional application in protein interactions, and an overview of what can be achieved in the field of protein science using this method and what developments are likely to occur in the near future. Also, this review discusses some new developments of ITC method in protein science, such as the reverse titration of ITC and the displacement method of ITC.     

Defining substrate interactions with calreticulin: an isothermal titration calorimetric study

Calreticulin (CRT) is a soluble, lectin chaperone found in the endoplasmic reticulum of eukaryotes. It binds the N-glycosylated polypeptides via the glycan intermediate Glc₁Man_5–9GlcNAc₂, present on the target glycoproteins. Earlier we have studied interactions of substrate with CRT by isothermal titration calorimetry (ITC) and molecular modeling, to establish that CRT recognizes the Glcα1–3 linkage and forms contacts with each saccharide moiety of the oligosaccharide Glcα1–3Manα1–2Manα1–2Man. We also delineated the amino acid residues in the sugar binding pocket of CRT that play a crucial role in sugar–CRT binding. Here, we have used mono-deoxy analogues of the trisaccharide unit Glcα1–3Manα1–2Man to determine the role of various hydroxyl groups of the sugar substrate in sugar–CRT interactions. Using the thermodynamic data obtained by ITC with these analogues we demonstrate that the 3-OH group of Glc1 plays an important role in sugar–CRT binding, whereas the 6-OH group does not. Also, the 4-OH, 6-OH of Man2 and 3-OH, 4-OH of Man3 in the trisaccharide are involved in binding, of which 6-OH of Man2 and 4-OH of Man3 have a more significant role to play. This study sheds light further on the interactions between the substrate sugar of glycoproteins and the lectin chaperone CRT.     

Beta-D-glucosidase reaction kinetics from isothermal titration microcalorimetry

The cellobiase activities of nine thermal stable mutants of Thermobifida fusca BglC were assayed by isothermal titration microcalorimetry (ITC). The mutations were previously generated using random mutagenesis and identified by high-temperature screening as imparting improved thermal stability to the beta-D-glucosidase enzyme. Analysis of the substrate-saturation curves obtained by ITC for the wild-type enzyme and the nine thermally stabilized mutants revealed that the wild type and all the mutants were subject to binding of a second substrate molecule. Furthermore, the "inhibited" enzyme-substrate complexes were shown to retain catalytic activity. In the case of three of the BglC mutants (N178I, N317Y/L444F, and N317Y/L444F/A433V), binding of a second substrate molecule resulted in improved cellobiose turnover rates at lower substrate concentrations. No correlation between denaturation temperatures of the mutants and activity on cellobiose at 25 degrees C was evident. However, one particular mutant, BglC S319C, was significantly improved in both thermal tolerance and cellobiase activity with respect to those of the wild-type BglC. The triple mutant, N317Y/L444F/A433V, had a 5 degrees C increase in denaturation temperature while maintaining activity levels similar to that of the wild type at higher substrate concentrations. ITC provided a highly sensitive and nondestructive means to continuously monitor the reaction of BglC with cellobiose, resulting in abundant data sets that could be rigorously analyzed by fitting to known enzyme kinetics models. One distinct advantage of using data from the ITC was the empirical validation of the pseudo steady state assumption, a necessary condition for obtaining solutions to the proposed mechanisms.     

Analytical error in stable isotope ecology

The increasing popularity of stable isotope analysis (SIA) as an ecological research tool and the ease of automated analysis have created a knowledge gap between ecologists using SIA and the operators of isotope ratio mass spectrometry (IRMS) equipment. This has led to deterioration in the understanding of IRMS methodology and its proper dissemination in the ecological literature. Of 330 ecological research papers surveyed, 63 (19%) failed to report any form of analytical error associated with IRMS. Of the 267 papers that reported analytical error, there was considerable variation both in the terminology and approach used to quantify and describe error. Internal laboratory standards were often used to determine the analytical error associated with IRMS, so chosen because they are homogenous and have isotopic signatures that do not vary over time. We argue that true ecological samples collected in the field are complex bulk mixtures and often fail to adhere to these two criteria. Hence the analytical error associated with samples is potentially greater than that of standards. A set of standard data run over time with a precision typically reported in the ecological literature (1 standard deviation: 1SD=0.26‰) was simulated to determine the likelihood of spurious treatment effects depending on timing of analysis. There was a 90% likelihood of detecting a significant difference in the stable nitrogen ratio of a single sample (homogenized bovine liver) run in two time periods when n>30. Minor protocol adjustments, including the submission of blind replicates by researchers, random assignment of sample repeats within a run by analytical labs, and reporting 1SD of a single sample analyzed both within and between runs, will only serve to strengthen the interpretation of true ecological processes by both researchers and reviewers.     

New insights into tau-microtubules interaction revealed by isothermal titration calorimetry

Microtubule dynamic instability is tightly regulated by coordinated action of stabilizing and destabilizing microtubule associated proteins. Among the stabilizing proteins, tau plays a pivotal role in both physiological and pathological processes. Nevertheless, the detailed mechanism of tau-tubulin interaction is still subject to controversy. In this report, we studied for the first time tau binding to tubulin by a direct thermodynamic method in the absence of any tubulin polymerization cofactors that could influence this process. Isothermal titration calorimetry enabled us to evidence two types of tau-tubulin binding modes: one corresponding to a high affinity binding site with a tau:tubulin stoichiometry of 0.2 and the other one to a low affinity binding site with a stoichiometry of 0.8. The same stoichiometries were obtained at all temperatures tested (10-37°C), indicating that the mechanism of interaction does not depend on the type of tubulin polymer triggered upon tau binding. These findings allowed us to get new insights into the topology of tau on microtubules.     

Kinetics of trypsin-catalyzed hydrolysis determined by isothermal titration calorimetry

Isothermal titration calorimetry (ITC) was applied to determine enzymatic activity and inhibition. We measured the Michaelis–Menten kinetics for trypsin-catalyzed hydrolysis of two substrates, casein (an insoluble macromolecule substrate) and Nα-benzoyl-dl-arginine β-naphthylamide (a small substrate), and estimated the thermodynamic parameters in the temperature range from 20 to 37 °C. The inhibitory activities of reversible (small molecule benzamidine) and irreversible (small molecule phenylmethanesulfonyl fluoride and macromolecule α1-antitrypsin) inhibitors of trypsin were also determined. We showed the usefulness of ITC for fast and direct measurement of inhibition constants and half-maximal inhibitory concentrations and for predictions of the mechanism of inhibition. ITC kinetic assays could be an easy and straightforward way to estimate Michaelis–Menten constants and the effectiveness of inhibitors as well as to predict the inhibition mechanism. ITC efficiency was found to be similar to that of classical spectrophotometric enzymatic assays.     

Misuse of thermodynamics in the interpretation of isothermal titration calorimetry data for ligand binding to proteins

Isothermal titration calorimetry (ITC) has given a mass of data on the binding of small molecules to proteins and other biopolymers, with particular interest in drug binding to proteins chosen as therapeutic indicators. Interpretation of the enthalpy data usually follows an unsound protocol that uses thermodynamic relations in circumstances where they do not apply. Errors of interpretation include incomplete definitions of ligand binding and equilibrium constants and neglect of the non-ideality of the solutions under study, leading to unreliable estimates of standard free energies and entropies of binding. The mass of reported thermodynamic functions for ligand binding to proteins estimated from ITC enthalpies alone is consequently of uncertain thermodynamic significance and utility. ITC and related experiments to test the protocol assumptions are indicated. A thermodynamic procedure avoiding equilibrium constants or other reaction models and not requiring protein activities is given. The discussion draws attention to the fundamental but neglected relation between the thermodynamic activity and bioactivity of drugs and to the generally unknown thermodynamic status of ligand solutions, which for drugs relates directly to effective therapeutic dosimetry.     

Detection of conformational changes in immunoglobulin G using isothermal titration calorimetry with low-molecular-weight probes

Proteins for therapeutic use may contain small amounts of partially misfolded monomeric precursors to postproduction aggregation. To detect these misfolded proteins in the presence of an excess of properly folded protein, fluorescent probes such as 8-anilino-1-naphthalene sulfonate (ANS) are commonly used. We investigated the possibility of using isothermal titration calorimetry (ITC) to improve the detection of this type of conformational change using hydrophobic probes. As a case study, conformational changes in human polyclonal immunoglobulin G (IgG) were monitored by measuring the enthalpies of binding of ANS using ITC. Results were compared with those using fluorescence spectroscopy. IgG heated at 63 °C was used as a model system for “damaged” IgG. Heat-treated IgG can be detected already at levels below 5% with both ITC and fluorescence. However, ITC allows a much wider molar probe-to-protein ratio to be sampled. In particular, using reverse titration experiments (allowing high probe-to-protein ratios not available to fluorescence spectroscopy), an increase in the number of binding sites with a K_d > 10 mM was observed for heat-treated IgG, reflecting subtle changes in structure. Both ITC and fluorescence spectroscopy showed low background signals for native IgG. The nature of the background signals was not clear from the fluorescence measurements. However, further analysis of the ITC background signals shows that a fraction (8%) binds ANS with a dissociation constant of approximately 0.2 mM. Measurements were also carried out at pH 4.5. Precipitation of IgG was induced by ANS at concentrations above 0.5 mM, interfering with the ITC measurements. Instead, with the nonfluorescent probes 4-amino-1-naphthalene sulfonate and 1-naphthalene sulfonate, no precipitation is observed. These probes yield differences in the enthalpies of binding to heated and nonheated IgG similar to ANS. The data illustrate that ITC with low-molecular-weight probes is a versatile tool to monitor conformational changes in proteins with a wider application potential than fluorescence measurements.     

Analysis of the Escherichia coli glucosamine-6-phosphate synthase activity by isothermal titration calorimetry and differential scanning calorimetry

Glucosamine-6-phosphate synthase (GlmS) is responsible for the first and rate-limiting step in the hexosamine biosynthetic pathway. It catalyzes the conversion of D-fructose-6P (F6P) into D-glucosamine-6P (GlcN6P) using L-glutamine (Gln) as nitrogen donor (synthase activity) according to an ordered bi-bi process where F6P binds first. In the absence of F6P, the enzyme exhibits a weak hydrolyzing activity of Gln into Glu and ammonia (glutaminase activity), whereas the presence of F6P strongly stimulates it (hemi-synthase activity). Until now, these different activities were indirectly measured using either coupled enzyme or colorimetric methods. In this work, we have developed a direct assay monitoring the heat released by the reaction. Isothermal titration calorimetry and differential scanning calorimetry were used to determine kinetic and thermodynamic parameters of GlmS. The direct determination at 37 °C of kinetic parameters and affinity constants for both F6P and Gln demonstrated that part of the ammonia produced by Gln hydrolysis in the presence of both substrates is not used for the formation of the GlcN6P. The full characterization of this phenomenon allowed to identify experimental conditions where this leak of ammonia is negligible. Enthalpy measurements at 25 °C in buffers of various heats of protonation demonstrated that no proton exchange with the medium occurred during the enzyme-catalyzed glutaminase or synthase reaction suggesting for the first time that both products are released as a globally neutral pair composed by the Glu carboxylic side chain and the GlcN6P amine function. Finally we showed that the oligomerization state of GlmS is concentration-dependent.     

Partition of amphiphilic molecules to lipid bilayers by isothermal titration calorimetry

The partition of the amphiphile sodium dodecyl sulfate (SDS) between an aqueous solution and a 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) bilayer was followed by isothermal titration calorimetry (ITC) as a function of the total concentration of SDS. It was found that the obtained partition coefficient is strongly affected by the ligand concentration, even after correction for the charge imposed in the bilayer by the bound SDS. The partition coefficient decreased as the total concentration of SDS increased, with this effect being significant for local concentrations of SDS in the lipid bilayer above 5 molar%. At those high local concentrations, the properties of the lipid bilayer are strongly affected, leading to nonideal behavior and concentration-dependent apparent partition coefficients. It is shown that with the modern ITC instruments available, the concentrations of SDS can be drastically reduced while maintaining a good signal-to-noise ratio. The intrinsic parameters of the interaction with unperturbed membranes can be obtained from the asymptotic behavior of the apparent parameters as a function of the ligand concentration for both nonionic and ionic solutes. A detailed analysis is performed, and a spreadsheet is provided to obtain the interaction parameters with and without correction for electrostatics.     

Statistical error in isothermal titration calorimetry: variance function estimation from generalized least squares

The method of generalized least squares (GLS) is used to assess the variance function for isothermal titration calorimetry (ITC) data collected for the 1:1 complexation of Ba(2+) with 18-crown-6 ether. In the GLS method, the least squares (LS) residuals from the data fit are themselves fitted to a variance function, with iterative adjustment of the weighting function in the data analysis to produce consistency. The data are treated in a pooled fashion, providing 321 fitted residuals from 35 data sets in the final analysis. Heteroscedasticity (nonconstant variance) is clearly indicated. Data error terms proportional to q(i) and q(i)/v are well defined statistically, where q(i) is the heat from the ith injection of titrant and v is the injected volume. The statistical significance of the variance function parameters is confirmed through Monte Carlo calculations that mimic the actual data set. For the data in question, which fall mostly in the range of q(i)=100-2000 microcal, the contributions to the data variance from the terms in q(i)(2) typically exceed the background constant term for q(i)>300 microcal and v<10 microl. Conversely, this means that in reactions with q(i) much less than this, heteroscedasticity is not a significant problem. Accordingly, in such cases the standard unweighted fitting procedures provide reliable results for the key parameters, K and DeltaH(degrees) and their statistical errors. These results also support an important earlier finding: in most ITC work on 1:1 binding processes, the optimal number of injections is 7-10, which is a factor of 3 smaller than the current norm. For high-q reactions, where weighting is needed for optimal LS analysis, tips are given for using the weighting option in the commercial software commonly employed to process ITC data.     

Predicting Ligand Binding Affinity with Alchemical Free Energy Methods in a Polar Model Binding Site

We present a combined experimental and modeling study of organic ligand molecules binding to a slightly polar engineered cavity site in T4 lysozyme (L99A/M102Q). For modeling, we computed alchemical absolute binding free energies. These were blind tests performed prospectively on 13 diverse, previously untested candidate ligand molecules. We predicted that eight compounds would bind to the cavity and five would not; 11 of 13 predictions were correct at this level. The RMS error to the measurable absolute binding energies was 1.8 kcal/mol. In addition, we computed “relative” binding free energies for six phenol derivatives starting from two known ligands: phenol and catechol. The average RMS error in the relative free energy prediction was 2.5 kcal/mol (phenol) and 1.1 kcal/mol (catechol). To understand these results at atomic resolution, we obtained x-ray co-complex structures for nine of the diverse ligands and for all six phenol analogs. The average RMSD of the predicted pose to the experiment was 2.0 Å (diverse set), 1.8 Å (phenol-derived predictions), and 1.2 Å (catechol-derived predictions). We found that predicting accurate affinities and rank-orderings required near-native starting orientations of the ligand in the binding site. Unanticipated binding modes, multiple ligand binding, and protein conformational change all proved challenging for the free energy methods. We believe that these results can help guide future improvements in physics-based absolute binding free energy methods.     

Isothermal titration calorimetry — A new method for the quantification of microbial degradation of trace pollutants

The environmental fate and, in particular, biodegradation rates of hydrophobic organic compounds (HOC) are of high interest due to the ubiquity, persistence, and potential health effects of these compounds. HOC tend to interact with bioreactor materials and sampling devices and are frequently volatile, so that conventionally derived degradation parameters are often biased. We report on the development and validation of a novel calorimetric approach that serves to gain real time information on the kinetics and the physiology of HOC bioconversion in aqueous systems while overcoming weaknesses of conventional biodegradation experiments. Soil bacteria Mycobacterium frederiksbergense LB501T, Rhodococcus erythropolis K2-3 and Pseudomonas putida G7 were exposed to pulsed titrations of dissolved anthracene, 4-(2,4-dichlorophenoxy)butyric acid or naphthalene, respectively, and the thermal responses were monitored. The combinations of strains and pollutants were selected as examples for complete and partial biodegradation and complete degradation with storage product formation, respectively. Heat production signals were interpreted thermodynamically and in terms of Michaelis-Menten kinetics. The half-saturation constant k_D and the degradation rate r_D^Max were derived. Comparison with conventional methods shows the suitability to extract kinetic degradation parameters of organic trace pollutants from simple ITC experiments, while thermodynamic interpretation provided further information about the metabolic fate of HOC compounds.     

New insights into the mechanism of dihydrodipicolinate synthase using isothermal titration calorimetry

Thermodynamic binding information, obtained via isothermal titration calorimetry (ITC), provides new insights into the binding of substrates, and of allosteric inhibitor interactions of dihydrodipicolinate synthase (DHDPS) from Escherichia coli. DHDPS catalyses the first committed step in (S)-lysine biosynthesis: the Schiff-base mediated aldol condensation of pyruvate with (S)-aspartate semi-aldehyde. Binding studies indicate that pyruvate is a weak binder (0.023 mM) but that (S)-ASA does not interact with the enzyme in the absence of a Schiff-base with pyruvate. These results support the assignment of a ping pong catalytic mechanism in which enthalpically driven Schiff-base formation (ΔH = −44.5 ± 0.1 kJ mol⁻¹) provides the thermodynamic impetus for pyruvate association. The second substrate, (S)-ASA, was observed to bind to a Schiff-base mimic (ΔH = −2.8 ± 0.1 kJ mol⁻¹) formed through the reduction of the intermediate pyruvyl–Schiff-base complex.     

Analysis of multitemperature isothermal titration calorimetry data at very low c: Global beats van't Hoff

Isothermal titration calorimetry data for very low c (≡K[M]₀) must normally be analyzed with the stoichiometry parameter n fixed — at its known value or at any reasonable value if the system is not well characterized. In the latter case, ΔH° (and hence n) can be estimated from the T-dependence of the binding constant K, using the van't Hoff (vH) relation. An alternative is global or simultaneous fitting of data at multiple temperatures. In this Note, global analysis of low-c data at two temperatures is shown to estimate ΔH° and n with double the precision of the vH method.     

Interaction of a designed interleukin-10 epitope mimic with an antibody studied by isothermal titration microcalorimetry

The mechanism of recognition of proteins and peptides by antibodies and the factors determining binding affinity and specificity are mediated by essentially the same features. However, additional effects of the usually unfolded and flexible solution structure of peptide ligands have to be considered. In an earlier study we designed and optimized six peptides (pepI to pepVI) mimicking the discontinuous binding site of interleukin-10 for the anti-interleukin-10 monoclonal antibody (mab) CB/RS/1. Three of them were selected for analysis of their solution conformation by circular dichroism measurements. The peptides differ in the content of alpha-helices and in the inducibility of helical secondary structures by trifluoroethanol. These properties, however, do not correlate with the binding affinity. PepVI, a 32-mer cyclic epitope mimic, has the highest affinity to mab CB/RS/1 identified to date. CD difference spectroscopy suggests an increase of the alpha-helix content of pepVI with complex formation. Binding of pepVI to mab CB/RS/1 is characterized by a large negative, favorable binding enthalpy and a smaller unfavorable loss of entropy (DeltaH degrees = -16.4 kcal x mol(-1), TDeltaS degrees = -6.9 kcal x mol(-1)) resulting in DeltaG degrees = -9.5 kcal x mol(-1) at 25 degrees C as determined by isothermal titration calorimetry. Binding of pepVI is enthalpically driven over the entire temperature range studied (10-35 degrees C). Complex formation is not accompanied by proton uptake or release. A negative heat capacity change DeltaC(p) of -0.354 kcal x mol(-1) x K(-1) was determined from the temperature dependence of DeltaH degrees. The selection of protein mimics with the observed thermodynamic properties is promoted by the applied identification and iterative optimization procedure.