Volume errors in isothermal titration calorimetry

Isothermal titration calorimetry in the single-injection mode with imperfect mixing

Isothermal titration calorimetry (ITC) is now a method of choice to obtain thermodynamic information about the interaction between two molecular partners. Most often, the method in use is the so-called multiple-injection method (MIM) consisting in distinct short-time injections of the titrant separated by sufficient delay to reach equilibrium before each new injection. However, an alternative single-injection method (SIM) exists. It consists in a unique continuous injection and, despite the fact that it is quite simple and generally faster than MIM, it is very little used. The goal of this work is to reconsider its theoretical basis. A new equation taking into account the effect of dilution resulting from the continuous titration process is obtained. It allows to consider efficiently the continuum of possibilities from perfect to imperfect mixing of the cell content. It is shown that, to good approximation, imperfect mixing can be accounted for by considering the cell volume as an adjustable parameter. Most likely, this should lead to an artificial increase of it, although one cannot reject the possibility of a decrease. The processing of experimental data on the interaction of Ba⁺⁺ with 18-crown-6 from led to an increase by 6.9%, which resulted in a much better fit of the titration curve and improved results on the association constant Ka and enthalpy variation ∆H. A criterion is also obtained on the maximum injection rate to be used for maintaining quasi-equilibrium during the whole titration for the association-dissociation mechanism [Formula: see text].

A (partial) resolution of binding enthalpy discrepancies in ITC studies of Ba2+crown ether complexation: The importance of calibration

By conducting binding experiments at a range of temperatures T using isothermal titration calorimetry (ITC), one can obtain two estimates of the binding enthalpy - calorimetric (ΔH°_cal) from the experiments at each T, and van't Hoff (ΔH°_vH) from the T dependence of the binding constant K°. From thermodynamics it is clear that these two must be identical, but early efforts to demonstrate this for ITC data indicated significant inconsistency. In an extensive 2004 study of the Ba²⁺ + 18-crown-6 ether complexation used in prior comparisons, Mizoue and Tellinghuisen found modest (10-20%) but statistically significant differences, which were tentatively attributed to problems converting the calorimetric estimates to their standard state values, as implied by the superscript ° in the notation. In the present work the 2004 results are reanalyzed using results obtained since then from temperature, heat, and volume calibration of the instrument and a better determination of the data variance function required for the weighted least-squares fitting of the data. The new results show consistency for temperatures 5-30 °C but persistent statistically significant differences from 35-46 °C. Several possible explanations for the remaining discrepancies are examined, with methods that include fitting the K and ΔH_cal data together.

Quantitative FRET (qFRET) Technology for the Determination of Protein-Protein Interaction Affinity in Solution

Protein-protein interactions play pivotal roles in life, and the protein interaction affinity confers specific protein interaction events in physiology or pathology. Förster resonance energy transfer (FRET) has been widely used in biological and biomedical research to detect molecular interactions in vitro and in vivo. The FRET assay provides very high sensitivity and efficiency. Several attempts have been made to develop the FRET assay into a quantitative measurement for protein-protein interaction affinity in the past. However, the progress has been slow due to complicated procedures or because of challenges in differentiating the FRET signal from other direct emission signals from donor and receptor. This review focuses on recent developments of the quantitative FRET analysis and its application in the determination of protein-protein interaction affinity (K_D), either through FRET acceptor emission or donor quenching methods. This paper mainly reviews novel theatrical developments and experimental procedures rather than specific experimental results. The FRET-based approach for protein interaction affinity determination provides several advantages, including high sensitivity, high accuracy, low cost, and high-throughput assay. The FRET-based methodology holds excellent potential for those difficult-to-be expressed proteins and for protein interactions in living cells.

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.

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.

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.

Optimizing isothermal titration calorimetry protocols for the study of 1:1 binding: Keeping it simple

BACKGROUND

Successful ITC experiments require conversion of cell reagent (titrand M) to product and production or consumption of heat. These conditions are quantified for 1:1 binding, M+X ⇔ MX.

METHODS

Nonlinear least squares is used in error-propagation mode to predict the precisions with which the key quantities - binding constant K, reaction enthalpy ΔH°, and stoichiometry number n - can be estimated over a wide range of the dimensionless quantity that governs isotherm shape, c=K[M]0. The measurement precision σq is estimated from analysis of water-water blanks.

RESULTS

When the product conversion exceeds 90%, the parameter relative standard errors are proportional to σq/qtot, where the total heat qtot ≈ ΔH° [M]0V0. Specifically, σK/K×qtot/σq ≈ 25 for c=10(-3)-10, ≈ 11 c(1/3) for c=10-10(4). For c>1, n and ΔH° are more precise than K; this holds also at smaller c for the product n×ΔH° and for ΔH° when n can be held fixed. Use of as few as 10 titrant injections can outperform the customary 20-40 while also improving productivity.

CONCLUSION

These principles are illustrated in experiment design using the program ITC-PLANNER15.

GENERAL SIGNIFICANCE

Simple quantitative guidelines replace the "c rules" that have dominated the literature for decades.

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.

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.

Systematic errors in isothermal titration calorimetry: concentrations and baselines

In the study of 1:1 binding by isothermal titration calorimetry, reagent concentration errors are fully absorbed in the data analysis, giving incorrect values for the key parameters--K, ΔH, and n--with no effect on the least-squares statistics. Reanalysis of results from an interlaboratory study of a selected biochemical process demonstrates that concentration errors are likely responsible for most of the overall statistical error in these parameters. The concentration errors are approximately 10%, greatly exceeding expected levels. Furthermore, examination of selected data sets reveals a surprising sensitivity to the baseline, suggesting a need for great care in treating dilution heats.

Application and use of isothermal calorimetry in pharmaceutical development

There are many steps involved in developing a drug candidate into a formulated medicine and many involve analysis of chemical interaction or physical change. Calorimetry is particularly suited to such analyses as it offers the capacity to observe and quantify both chemical and physical changes in virtually any sample. Differential scanning calorimetry (DSC) is ubiquitous in pharmaceutical development, but the related technique of isothermal calorimetry (IC) is complementary and can be used to investigate a range of processes not amenable to analysis by DSC. Typically, IC is used for longer-term stability indicating or excipient compatibility assays because both the temperature and relative humidity (RH) in the sample ampoule can be controlled. However, instrument design and configuration, such as titration, gas perfusion or ampoule-breaking (solution) calorimetry, allow quantification of more specific values, such as binding enthalpies, heats of solution and quantification of amorphous content. As ever, instrument selection, experiment design and sample preparation are critical to ensuring the relevance of any data recorded. This article reviews the use of isothermal, titration, gas-perfusion and solution calorimetry in the context of pharmaceutical development, with a focus on instrument and experimental design factors, highlighted with examples from the recent literature.

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

Calorimetric methods have been used to determine equilibrium constants since 1937, but no comprehensive review of the various calorimeters and methods has been done previously. This article reports methods for quantitative comparison of the capabilities of calorimeters for simultaneous determination of equilibrium constants and enthalpy changes, for determining optimal experimental conditions, and for assessing the effects of systematic and random errors on the accuracy and precision of equilibrium constants and enthalpy changes determined by this method.

From biochemistry to physiology: the calorimetry connection

This article provides guidelines for selecting optimal calorimetric instrumentation for applications in biochemistry and biophysics. Applications include determining thermodynamics of interactions in non-covalently bonded structures, and determining function through measurements of enzyme kinetics and metabolic rates. Specific examples illustrating current capabilities and methods in biological calorimetry are provided. Commercially available calorimeters are categorized by application and by instrument characteristics (isothermal or temperature-scanning, reaction vessel volume, heat rate detection limit, fixed or removable reaction vessels, etc.). Advantages and limitations of commercially available calorimeters are listed for each application in biochemistry, biophysics, and physiology.

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.

Hydration changes in the association of Hoechst 33258 with DNA

The role of water in the interaction of Hoechst 33258 with the minor groove binding site of the (AATT)2 sequence was investigated using calorimetric and equilibrium constant measurements. Using isothermal titration calorimetry measurements, the heat capacity change for the reaction is -256 +/- 10 cal/(K mol of Hoechst). Comparison with the heat capacity changes based on area models supports the expulsion of water from the interface of the Hoechst-DNA complex. To further consider the role of water, the osmotic stress method was used to determine if the Hoechst association with DNA was coupled with hydration changes. Using four osmolytes with varying molecular weights and chemical properties, the Hoechst affinity for DNA decreases with increasing osmolyte concentration. From the dependence of the equilibrium constant on the solution osmolality, 60 +/- 13 waters are acquired in the complex relative to the reactants. It is proposed that the osmotic stress technique is measuring weakly bound waters that are not measured via the heat capacity changes.

Measurements of binding thermodynamics in drug discovery

Thermodynamics governs the process of biomolecular recognition. The steps of characterizing, understanding and exploiting binding thermodynamics have the potential to contribute to an improved rational drug design process that is more robust and reliable. It is only relatively recently that instrumentation capable of direct and full thermodynamic characterization has been improved, giving impetus to the application of thermodynamic measurements in drug discovery. This review highlights current instruments and methods that can be employed to measure binding thermodynamics and their use in studies of biomolecular recognition and drug discovery.

Optimizing Experimental Parameters in Isothermal Titration Calorimetry

In isothermal titration calorimetry, the statistical precisions with which the equilibrium constant (K) and reaction enthalpy (DeltaH degrees ) can be estimated from data for 1:1 binding depend on a number of quantities, key among them being the products c identical with K[M](0) and h identical with DeltaH degrees [M](0), the stoichiometry range (R(m)(), ratio of total titrant X to total titrate M after the last injection), and the number of injections of titrant. A study of the statistical errors as functions of these quantities leads to the following prescription for optimizing throughput and precision: (1) Make 10 injections of titrant. (2) Set the concentrations in accord with the empirical equation R(m)() = 6.4/c(0.2) + 13/c (but no smaller than 1.1). (3) Make the starting concentration [M](0) as large as possible within the large-signal limits of the instrumentation but limited to c < 10(3) for estimating K. With this procedure, both K and [M](0) are predicted to have relative standard errors <1% over large ranges of K. Systematic errors in the concentrations, [X](0) and [M](0), are fully compensated by the "site number" or stoichiometry parameter (n). On the other hand, altering and freezing any of the fit parameters leads to a deterioration of the fit quality and to predictable changes in the other parameters. Fit divergence at very small c is avoidable through a simple redefinition of the fit parameters; however, unless n can be fixed from other information, DeltaH degrees may be statistically ill-defined in this region.

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.

Survey of the year 2004: literature on applications of isothermal titration calorimetry

The market for commercially available isothermal titration calorimeters continues to grow as new applications and methodologies are developed. Concomitantly the number of users (and abusers) increases dramatically, resulting in a steady increase in the number of publications in which isothermal titration calorimetry (ITC) plays a role. In the present review, we will focus on areas where ITC is making a significant contribution and will highlight some interesting applications of the technique. This overview of papers published in 2004 also discusses current issues of interest in the development of ITC as a tool of choice in the determination of the thermodynamics of molecular recognition and interaction.