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

Calibrating ITC instruments: Problems with weak base neutralization

Modern isothermal titration calorimetry instruments give great precision, but for comparable accuracy they require chemical calibration. For the heat factor, one recommended process is HCl into the weak base TRIS. In studying this reaction with a VP-ITC and two Nano-ITCs, we have encountered some problems, most importantly a titrant volume shortfall Δv ≈ 0.3 μL, which we attribute to diffusive loss of HCl in the syringe tip. This interpretation is supported by a mathematical treatment of the diffusion problem. The effect was discovered through a variable-v protocol, which thus should be used to properly allow for it in any reaction that similarly approaches completion. We also find that the effects from carbonate contamination and from OH- from weak base hydrolysis can be more significant that previously thought. To facilitate proper weighting in the least-squares fitting of data, we have estimated data variance functions from replicate data. All three instruments have low-signal precision of σ ≈ 1 μJ; titrant volume uncertainty is a factor of ∼2 larger for the Nano-ITCs than for the VP-ITC. The final heat factors remain uncertain by more than the ∼1 % precision of the instruments and are unduly sensitive to the HCl concentration.

Combating DC-SIGN-mediated SARS-CoV-2 dissemination by glycan-mimicking polymers

Many viruses exploit the human C-type lectin receptor dendritic cell-specific ICAM-3 grabbing nonintegrin (DC-SIGN) for cell entry and virus dissemination. An inhibition of DC-SIGN-mediated virus attachment by glycan-derived ligands has, thus, emerged as a promising strategy toward broad-spectrum antiviral therapeutics. In this contribution, several cognate fragments of oligomannose- and complex-type glycans grafted onto a poly-l-lysine scaffold are evaluated as polyvalent DC-SIGN ligands. The range of selected carbohydrate epitopes encompasses linear (α- d-Man-(1→2)-α- d-Man, α- d-Man-(1→2)-α- d-Man-(1→2)-α- d-Man-(1→3)-α- d-Man) and branched (α- d-Man-(1→6)-[α- d-Man-(1→3)]-α- d-Man) oligomannosides, as well as α- l-Fuc. The thermodynamics of binding are investigated on a mono- and multivalent level to shed light on the molecular details of the interactions with the tetravalent receptor. Cellular models of virus attachment and DC-SIGN-mediated virus dissemination reveal a high potency of the presented glycopolymers in the low pico- and nanomolar ranges, respectively. The high activity of oligomannose epitopes in combination with the biocompatible properties of the poly- l-lysine scaffold highlights the potential for further preclinical development of polyvalent DC-SIGN ligands.

Fundamental Determinants of the Accuracy of Equilibrium Constants for Affinity Complexes

The equilibrium constant of a chemical reaction is arguably the key thermodynamic parameter in chemistry; we naturally expect that equilibrium constants are determined accurately. The majority of equilibrium constants determined today are those of binding reactions that form affinity complexes, such as protein-protein, protein-DNA, and protein-small molecule. There is growing awareness that the determination of equilibrium constants for highly stable affinity complexes may be very inaccurate. However, fundamental (i.e., method-independent) determinants of accuracy are poorly understood. Here, we present a study that explicitly shows what the accuracy of equilibrium constants of affinity complexes depends on. This study reveals the critical importance of the choice of concentration of interacting components and creates a theoretical foundation for improving the accuracy of the equilibrium constants. The predicted influence of concentrations on accuracy was confirmed experimentally. The results of this fundamental study provide instructive guidance for experimentalists independently on the method they use.

Analysis of Protein-DNA Interactions Using Isothermal Titration Calorimetry: Successes and Failures

Isothermal titration calorimetry (ITC) is a golden standard for the characterization of protein-DNA binding affinities and allows direct assessment of the accompanying thermodynamic driving forces. Their interpretation can give insight into role of electrostatics, specificity of the DNA recognition, contribution of protein folding upon DNA binding and help to distinguish between minor and major groove binders. The main advantages of ITC are that the binding is measured in solution, and it requires no labeling of the samples, however, the method is not well suited for high-performance studies. Here we describe the sample preparation, a procedure to perform a typical ITC experiment, data analysis, and lastly discuss how to interpret the obtained thermodynamic parameters. In conclusion, we show examples of several unsuccessful ITC experiments and identify the underlying reasons for failed experiments. In most cases with a proper adjustment of the experimental setup, it was possible to obtain data appropriate for further analysis.

A discussion on the affecting factors of the fitting procedures' reliability in isothermal titration calorimetry analysis

The standard isothermal titration calorimetry (ITC) curve, characterized as a typical sigmoid is strictly confined by the so-called c value, which is a ratio of titrand concentration to K_D. The proper c value with a range from 5 to 500 is commonly recommended as a standard protocol in routine detection process for acquiring the reliable fitting results in 1:1 binding mode. However, if the c value is less than "1" due to the weak binding or low concentration of analyte, fitting precision gets unstable and susceptible to the data noise. Herein, we first got a deep discussion into the reliability of the fitting procedure for 1:1 binding mode by data simulation, then quantized the effect of several affecting factors on the precision of parameters estimation through mathematical analysis. Finally, we proposed the value of 2~4 times K_D for final ligand concentration is optimal for the ITC titration in low c system (c < 1). All the theoretical derivations were further verified by a practical experiment of Magnesium-EDTA binding test.

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.

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.

Isothermal Titration Calorimetry

Calorimetry is a classical biophysical method that by definition measures heat. In isothermal titration calorimetry (ITC), the heat is the result of titrating interacting components together and allows direct determination of the thermodynamics for this process. The measured heat reflects the enthalpy change (ΔH), and the prospect of determining this in biological systems where high-resolution structural information is available has led to the possibility of rational thermodynamics-guided design of ligands. Although there are limitations to this approach due to the participation of solvent in the thermodynamics, ITC has become an established technique in many labs providing a valuable tool with which to quantify protein-protein interactions. With careful use, ITC can also provide additional insights into the binding process or be used in increasingly complex systems and where interaction is coupled to other molecular events.

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.

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.

Biophysical approaches for the study of metal-protein interactions

Protein-protein interactions play important roles for a variety of cell functions, often involving metal ions; in fact, metal-ion binding mediates and regulates the activity of a wide range of biomolecules. Enlightening all of the specific features of metal-protein and metal-mediated protein-protein interactions can be a very challenging task; a detailed knowledge of the thermodynamic and spectroscopic parameters and the structural changes of the protein is normally required. For this purpose, many experimental techniques are employed, embracing all fields of Analytical and Bioinorganic Chemistry. In addition, the use of peptide models, reproducing the primary sequence of the metal-binding sites, is also proved to be useful. In this paper, a review of the most useful techniques for studying ligand-protein interactions with a special emphasis on metal-protein interactions is provided, with a critical summary of their strengths and limitations.

Critique of methods for estimating heats in isothermal titration calorimetry

Isothermal titration calorimetry data recorded on a MicroCal/Malvern VP-ITC instrument for water-water blanks and for dilution of aqueous solutions of BaCl₂ and Ba(NO₃)₂ are analyzed using Origin software, the freeware NITPIC program, and in-house algorithms, to compare precisions for estimating the heat per injection q. The data cover temperatures 6-47 °C, injection volumes 4-40 μL, and average heats 0-200 μcal. For water-water blanks, where baseline noise limits precision, NITPIC and the in-house algorithm achieve precisions of 0.05 μcal, which is better than Origin by a factor of 4. The precision differences decrease with increasing |q|, becoming insignificant for |q| > 200 μcal. In its default mode, NITPIC underestimates |q| for peaks with incomplete return to baseline, but the shortfall can be largely corrected by overriding the default injection time parameter. The variance estimates from 26 dilution experiments are used to assess the data variance function. The results determine the conditions under which weighted least squares should be used to estimate thermodynamic parameters from ITC data.

Thermal Activity in Affinity Separation Techniques Such as Liquid-Liquid Extraction Analyzed by Isothermal Titration Calorimetry and Accuracy Analysis of the Technique in the Molar Concentration Domain

The applicability and accuracy of isothermal titration calorimetry (ITC) to investigate intermolecular interactions in a high concentration domain applicable to liquid–liquid extraction (LLX) was studied for acid–base interactions. More accurate fits can be obtained using a sequential binding mechanism compared to a single reaction model, at the risk of finding a local minimum. Experiments with 0.24 M tri-n-octylamine (TOA) resulted in a residue of fit of 4.3% for the single reaction model, with a standard deviation σ of 1.6% in the stoichiometry parameter n, 12% in the complexation constant K_n,1, and 2.5% in the enthalpy ΔH_n,1. For the sequential model, σ was higher: 11% in K_1,1, 26% in K_n+1,1, and 12% in ΔH_n+1,1. This study clearly showed that, at higher concentrations (order of moles per liter), accurate parameter estimation is possible and parameter values are concentration dependent. It is thus important to do ITC at the application concentration.

Can you trust the parametric standard errors in nonlinear least squares? Yes, with provisos

BACKGROUND

Questions about the reliability of parametric standard errors (SEs) from nonlinear least squares (LS) algorithms have led to a general mistrust of these precision estimators that is often unwarranted.

METHODS

The importance of non-Gaussian parameter distributions is illustrated by converting linear models to nonlinear by substituting e^A, ln A, and 1/A for a linear parameter a. Monte Carlo (MC) simulations characterize parameter distributions in more complex cases, including when data have varying uncertainty and should be weighted, but weights are neglected. This situation leads to loss of precision and erroneous parametric SEs, as is illustrated for the Lineweaver-Burk analysis of enzyme kinetics data and the analysis of isothermal titration calorimetry data.

RESULTS

Non-Gaussian parameter distributions are generally asymmetric and biased. However, when the parametric SE is <10% of the magnitude of the parameter, both the bias and the asymmetry can usually be ignored. Sometimes nonlinear estimators can be redefined to give more normal distributions and better convergence properties.

CONCLUSION

Variable data uncertainty, or heteroscedasticity, can sometimes be handled by data transforms but more generally requires weighted LS, which in turn require knowledge of the data variance.

GENERAL SIGNIFICANCE

Parametric SEs are rigorously correct in linear LS under the usual assumptions, and are a trustworthy approximation in nonlinear LS provided they are sufficiently small - a condition favored by the abundant, precise data routinely collected in many modern instrumental methods.

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.

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.

Preparation To Minimize Buffer Mismatch in Isothermal Titration Calorimetry Experiments

There is a growing need to study ligand binding to proteins in native or complex solution using isothermal titration calorimetry (ITC). For example, it is desirable to measure ligand binding to membrane proteins in more native lipid-like environments such as bicelles, where ligands can access both sides of the membrane in a homogeneous environment. A critical step to obtain high signal-to-noise is matching the reaction chamber solution to the ligand solution, typically through a final dialysis or gel filtration step. However, to obtain reproducible bicelles, the lipid concentrations must be carefully controlled which eliminates the use of dialysis that can disrupt these parameters. Here, we report and validate a rapid preparation ITC (RP-ITC) approach to measure ligand binding without the need for a dialysis step. This general approach is used to quantify ion binding to a K(+) channel embedded in bicelles and can be applied to complex, less defined systems.

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.

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.

Structural Basis for a Unique ATP Synthase Core Complex from Nanoarcheaum equitans

ATP synthesis is a critical and universal life process carried out by ATP synthases. Whereas eukaryotic and prokaryotic ATP synthases are well characterized, archaeal ATP synthases are relatively poorly understood. The hyperthermophilic archaeal parasite, Nanoarcheaum equitans, lacks several subunits of the ATP synthase and is suspected to be energetically dependent on its host, Ignicoccus hospitalis. This suggests that this ATP synthase might be a rudimentary machine. Here, we report the crystal structures and biophysical studies of the regulatory subunit, NeqB, the apo-NeqAB, and NeqAB in complex with nucleotides, ADP, and adenylyl-imidodiphosphate (non-hydrolysable analog of ATP). NeqB is ∼20 amino acids shorter at its C terminus than its homologs, but this does not impede its binding with NeqA to form the complex. The heterodimeric NeqAB complex assumes a closed, rigid conformation irrespective of nucleotide binding; this differs from its homologs, which require conformational changes for catalytic activity. Thus, although N. equitans possesses an ATP synthase core A3B3 hexameric complex, it might not function as a bona fide ATP synthase.

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.

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.

SEDPHAT--a platform for global ITC analysis and global multi-method analysis of molecular interactions

Isothermal titration calorimetry experiments can provide significantly more detailed information about molecular interactions when combined in global analysis. For example, global analysis can improve the precision of binding affinity and enthalpy, and of possible linkage parameters, even for simple bimolecular interactions, and greatly facilitate the study of multi-site and multi-component systems with competition or cooperativity. A pre-requisite for global analysis is the departure from the traditional binding model, including an 'n'-value describing unphysical, non-integral numbers of sites. Instead, concentration correction factors can be introduced to account for either errors in the concentration determination or for the presence of inactive fractions of material. SEDPHAT is a computer program that embeds these ideas and provides a graphical user interface for the seamless combination of biophysical experiments to be globally modeled with a large number of different binding models. It offers statistical tools for the rigorous determination of parameter errors, correlations, as well as advanced statistical functions for global ITC (gITC) and global multi-method analysis (GMMA). SEDPHAT will also take full advantage of error bars of individual titration data points determined with the unbiased integration software NITPIC. The present communication reviews principles and strategies of global analysis for ITC and its extension to GMMA in SEDPHAT. We will also introduce a new graphical tool for aiding experimental design by surveying the concentration space and generating simulated data sets, which can be subsequently statistically examined for their information content. This procedure can replace the 'c'-value as an experimental design parameter, which ceases to be helpful for multi-site systems and in the context of gITC.

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.

Plasmonic nanosensors for simultaneous quantification of multiple protein-protein binding affinities

Most of current techniques used for the quantification of protein-protein interactions require the analysis of one pair of binding partners at a time. Herein we present a label-free, simple, fast, and cost-effective route to characterize binding affinities between multiple macromolecular partners simultaneously, using optical dark-field spectroscopy and individual protein-functionalized gold nanorods as sensing elements. Our NanoSPR method could easily become a simple and standard tool in biological, biochemical, and medical laboratories.

Experimental support for a desolvation energy term in governing equations for binding equilibria

This study introduces a new thermodynamic framework for aqueous reaction equilibria that treats water as a coreactant in the development of a general binding equation. The approach features an explicit consideration for the change in hydration that occurs when two solvated surfaces come into contact. As an outcome of this framework, the standard-state free energy of binding is defined by the summation of two terms: the traditional term (-RT ln Ki) plus a desolvation free-energy term that is weighted by the number of complexes formed at equilibrium. The new formalism suggests that the equilibrium ratio, Ki, is not a constant and that the observed concentration dependence of Ki may be used to obtain the molar desolvation energy and the standard-state free energy at infinite dilution. The governing equation is supported by results from isothermal titration calorimetry using the chelation of calcium(II) by EDTA as a model binding reaction. This work may have far-reaching implications for solution thermodynamics, including an explanation for the oft-noted discrepancy between the enthalpy values obtained by calorimetry and those from the van't Hoff approach.

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.