Systematic errors in isothermal titration calorimetry: concentrations and baselines

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.

In situ characterization techniques of protein corona around nanomaterials

Nanoparticles (NPs) inevitably interact with proteins upon exposure to biological fluids, leading to the formation of an adsorption layer known as the "protein corona". This corona imparts NPs with a new biological identity, directly influencing their interactions with living systems and dictating their fates in vivo. Thus, gaining a comprehensive understanding of the dynamic interplay between NPs and proteins in biological fluids is crucial for predicting therapeutic effects and advancing the clinical translation of nanomedicines. Numerous methods have been established to decode the protein corona fingerprints. However, these methods primarily rely on prior isolation of NP-protein complex from the surrounding medium by centrifugation, resulting in the loss of outer-layer proteins that directly interact with the biological system and determine the in vivo fate of NPs. We discuss here separation techniques as well as in situ characterization methods tailored for comprehensively unraveling the inherent complexities of NP-protein interactions, highlighting the challenges of in situ protein corona characterization and its significance for nanomedicine development and clinical translation.

Preparation and characterization of iron(III) nitrilotriacetate complex in aqueous solutions for quantitative protein binding experiments

Various preparations of iron(III) nitrilotriacetate (FeNTA) solution reported in the literature lack a comprehensive method for accurate determination of FeNTA concentration and often result in unstable solutions. A detailed procedure for the preparation of FeNTA solution is presented that includes the standardization of both components of the chelate. The standardization of the components allowed the accurate determination of the molar absorption coefficients for the calculation of the FeNTA concentration in two different buffers at pH 5.6 and 7.4. The variation of pH in this range or ionic strength in the range from 0 M to 3 M (KCl) has little effect on the value of the molar absorption coefficient. The precise concentrations of all species involved in the equilibria between Fe and NTA were determined in the pH range 2-12 using the Jenkins-Traub algorithm to solve the 5th-order polynomial in Microsoft Excel. In view of the experimental observations and the calculated distribution of species, the stability of FeNTA solutions may be affected by the Fe : NTA ratio and the total concentrations, with dilute solutions and those with an excess of NTA over Fe showing higher stability.

Target-ligand binding affinity from single point enthalpy calculation and elemental composition

Reliable target-ligand binding thermodynamics data are essential for successful drug design and molecular engineering projects. Besides experimental methods, a number of theoretical approaches have been introduced for the generation of binding thermodynamics data. However, available approaches often neglect electronic effects or explicit water molecules influencing target-ligand interactions. To handle electronic effects within a reasonable time frame, we introduce a fast calculator QMH-L using a single target-ligand complex structure pre-optimized at the molecular mechanics level. QMH-L is composed of the semi-empirical quantum mechanics calculation of binding enthalpy with predicted explicit water molecules at the complex interface, and a simple descriptor based on the elemental composition of the ligand. QMH-L estimates the target-ligand binding free energy with a root mean square error (RMSE) of 0.94 kcal mol-1. The calculations also provide binding enthalpy values and they were compared with experimental binding thermodynamics data collected from the most reliable isothermal titration calorimetry studies of systems including various protein targets and challenging, large peptide ligands with a molecular weight of up to 2-3 thousand. The single point enthalpy calculations of QMH-L require modest computational resources and are based on short runs with open source and/or free software like Gromacs, Mopac, MobyWat, and Fragmenter. QMH-L can be applied for fast, automated scoring of drug candidates during a virtual screen, enthalpic engineering of new ligands or thermodynamic explanation of complex interactions.

The maximal and current accuracy of rigorous protein-ligand binding free energy calculations

Computational techniques can speed up the identification of hits and accelerate the development of candidate molecules for drug discovery. Among techniques for predicting relative binding affinities, the most consistently accurate is free energy perturbation (FEP), a class of rigorous physics-based methods. However, uncertainty remains about how accurate FEP is and can ever be. Here, we present what we believe to be the largest publicly available dataset of proteins and congeneric series of small molecules, and assess the accuracy of the leading FEP workflow. To ascertain the limit of achievable accuracy, we also survey the reproducibility of experimental relative affinity measurements. We find a wide variability in experimental accuracy and a correspondence between binding and functional assays. When careful preparation of protein and ligand structures is undertaken, FEP can achieve accuracy comparable to experimental reproducibility. Throughout, we highlight reliable protocols that can help maximize the accuracy of FEP in prospective studies.

Quantifying cooperative multisite binding in the hub protein LC8 through Bayesian inference

Multistep protein-protein interactions underlie most biological processes, but their characterization through methods such as isothermal titration calorimetry (ITC) is largely confined to simple models that provide little information on the intermediate, individual steps. In this study, we primarily examine the essential hub protein LC8, a small dimer that binds disordered regions of 100+ client proteins in two symmetrical grooves at the dimer interface. Mechanistic details of LC8 binding have remained elusive, hampered in part by ITC data analyses employing simple models that treat bivalent binding as a single event with a single binding affinity. We build on existing Bayesian ITC approaches to quantify thermodynamic parameters for multi-site binding interactions impacted by significant uncertainty in protein concentration. Using a two-site binding model, we identify positive cooperativity with high confidence for LC8 binding to multiple client peptides. In contrast, application of an identical model to the two-site binding between the coiled-coil NudE dimer and the intermediate chain of dynein reveals little evidence of cooperativity. We propose that cooperativity in the LC8 system drives the formation of saturated induced-dimer structures, the functional units of most LC8 complexes. In addition to these system-specific findings, our work advances general ITC analysis in two ways. First, we describe a previously unrecognized mathematical ambiguity in concentrations in standard binding models and clarify how it impacts the precision with which binding parameters are determinable in cases of high uncertainty in analyte concentrations. Second, building on observations in the LC8 system, we develop a system-agnostic heat map of practical parameter identifiability calculated from synthetic data which demonstrates that the ability to determine microscopic binding parameters is strongly dependent on both the parameters themselves and experimental conditions. The work serves as a foundation for determination of multi-step binding interactions, and we outline best practices for Bayesian analysis of ITC experiments.

Bayesian regression and model selection for isothermal titration calorimetry with enantiomeric mixtures

Bayesian regression is performed to infer parameters of thermodynamic binding models from isothermal titration calorimetry measurements in which the titrant is an enantiomeric mixture. For some measurements the posterior density is multimodal, indicating that additional data with a different protocol are required to uniquely determine the parameters. Models of increasing complexity-two-component binding, racemic mixture, and enantiomeric mixture-are compared using model selection criteria. To precisely estimate one of these criteria, the Bayes factor, a variation of bridge sampling is developed.

Evaluating the use of absolute binding free energy in the fragment optimisation process

Key to the fragment optimisation process within drug design is the need to accurately capture the changes in affinity that are associated with a given set of chemical modifications. Due to the weakly binding nature of fragments, this has proven to be a challenging task, despite recent advancements in leveraging experimental and computational methods. In this work, we evaluate the use of Absolute Binding Free Energy (ABFE) calculations in guiding fragment optimisation decisions, retrospectively calculating binding free energies for 59 ligands across 4 fragment elaboration campaigns. We first demonstrate that ABFEs can be used to accurately rank fragment-sized binders with an overall Spearman's r of 0.89 and a Kendall τ of 0.67, although often deviating from experiment in absolute free energy values with an RMSE of 2.75 kcal/mol. We then also show that in several cases, retrospective fragment optimisation decisions can be supported by the ABFE calculations. Comparing against cheaper endpoint methods, namely Nwat-MM/GBSA, we find that ABFEs offer better ranking power and correlation metrics. Our results indicate that ABFE calculations can usefully guide fragment elaborations to maximise affinity.

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.

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.

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.

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.

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.

Modulation of the HIV nucleocapsid dynamics finely tunes its RNA-binding properties during virion genesis

During HIV-1 assembly and budding, Gag protein, in particular the C-terminal domain containing the nucleocapsid domain (NCd), p1 and p6, is the site of numerous interactions with viral and cellular factors. Most in vitro studies of Gag have used constructs lacking p1 and p6. Here, using NMR spectroscopy, we show that the p1-p6 region of Gag (NCp15) is largely disordered, but interacts transiently with the NCd. These interactions modify the dynamic properties of the NCd. Indeed, using isothermal titration calorimetry (ITC), we have measured a higher entropic penalty to RNA-binding for the NCd precursor, NCp15, than for the mature form, NCp7, which lacks p1 and p6. We propose that during assembly and budding of virions, concomitant with Gag oligomerization, transient interactions between NCd and p1-p6 become salient and responsible for (i) a higher level of structuration of p6, which favours recruitment of budding partners; and (ii) a higher entropic penalty to RNA-binding at specific sites that favours non-specific binding of NCd at multiple sites on the genomic RNA (gRNA). The contributions of p6 and p1 are sequentially removed via proteolysis during Gag maturation such that the RNA-binding specificity of the mature protein is governed by the properties of NCd.

Bisubstrate analogues as structural tools to investigate m6A methyltransferase active sites

RNA methyltransferases (MTases) catalyse the transfer of a methyl group to their RNA substrates using most-often S-adenosyl-L-methionine (SAM) as cofactor. Only few RNA-bound MTases structures are currently available due to the difficulties in crystallising RNA:protein complexes. The lack of complex structures results in poorly understood RNA recognition patterns and methylation reaction mechanisms. On the contrary, many cofactor-bound MTase structures are available, resulting in well-understood protein:cofactor recognition, that can guide the design of bisubstrate analogues that mimic the state at which both the substrate and the cofactor is bound. Such bisubstrate analogues were recently synthesized for proteins monomethylating the N6-atom of adenine (m6A). These proteins include, amongst others, RlmJ in E. coli and METLL3:METT14 and METTL16 in human. As a proof-of-concept, we here test the ability of the bisubstrate analogues to mimic the substrate:cofactor bound state during catalysis by studying their binding to RlmJ using differential scanning fluorimetry, isothermal titration calorimetry and X-ray crystallography. We find that the methylated adenine base binds in the correct pocket, and thus these analogues could potentially be used broadly to study the RNA recognition and catalytic mechanism of m6A MTases. Two bisubstrate analogues bind RlmJ with micro-molar affinity, and could serve as starting scaffolds for inhibitor design against m6A RNA MTases. The same analogues cause changes in the melting temperature of the m1A RNA MTase, TrmK, indicating non-selective protein:compound complex formation. Thus, optimization of these molecular scaffolds for m6A RNA MTase inhibition should aim to increase selectivity, as well as affinity.

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.

Bayesian analysis of isothermal titration calorimetry for binding thermodynamics

Isothermal titration calorimetry (ITC) is the only technique able to determine both the enthalpy and entropy of noncovalent association in a single experiment. The standard data analysis method based on nonlinear regression, however, provides unrealistically small uncertainty estimates due to its neglect of dominant sources of error. Here, we present a Bayesian framework for sampling from the posterior distribution of all thermodynamic parameters and other quantities of interest from one or more ITC experiments, allowing uncertainties and correlations to be quantitatively assessed. For a series of ITC measurements on metal:chelator and protein:ligand systems, the Bayesian approach yields uncertainties which represent the variability from experiment to experiment more accurately than the standard data analysis. In some datasets, the median enthalpy of binding is shifted by as much as 1.5 kcal/mol. A Python implementation suitable for analysis of data generated by MicroCal instruments (and adaptable to other calorimeters) is freely available online.

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.

The Molecular Origin of Enthalpy/Entropy Compensation in Biomolecular Recognition

Biomolecular recognition can be stubborn; changes in the structures of associating molecules, or the environments in which they associate, often yield compensating changes in enthalpies and entropies of binding and no net change in affinities. This phenomenon—termed enthalpy/entropy (H/S) compensation—hinders efforts in biomolecular design, and its incidence—often a surprise to experimentalists—makes interactions between biomolecules difficult to predict. Although characterizing H/S compensation requires experimental care, it is unquestionably a real phenomenon that has, from an engineering perspective, useful physical origins. Studying H/S compensation can help illuminate the still-murky roles of water and dynamics in biomolecular recognition and self-assembly. This review summarizes known sources of H/ S compensation (real and perceived) and lays out a conceptual framework for understanding and dissecting—and, perhaps, avoiding or exploiting—this phenomenon in biophysical systems.

Calorimetry Methods to Study Membrane Interactions and Perturbations Induced by Antimicrobial Host Defense Peptides

Biological membranes play an important role in determining the activity and selectivity of antimicrobial host defense peptides (AMPs). Several biophysical methods have been developed to study the interactions of AMPs with biological membranes. Isothermal titration calorimetry and differential scanning calorimetry (ITC and DSC, respectively) are powerful techniques as they provide a unique label-free approach. ITC allows for a complete thermodynamic characterization of the interactions between AMPs and membranes. DSC allows one to study the effects of peptide binding on the packing of the phospholipids in the membrane. Used in combination with mimetic models of biological membranes, such as phospholipid vesicles, the role of different phospholipid headgroups and distinct acyl chains can be characterized. In these protocols the use of ITC and DSC methods for the study of peptide-membrane interactions will be presented, highlighting the importance of membrane model systems selected to represent bacterial and mammalian cells. These studies provide valuable insights into the mechanisms involved in the membrane binding and perturbation properties of AMPs.

Accounting for apparent deviations between calorimetric and van't Hoff enthalpies

BACKGROUND

In theory, binding enthalpies directly obtained from calorimetry (such as ITC) and the temperature dependence of the binding free energy (van't Hoff method) should agree. However, previous studies have often found them to be discrepant.

METHODS

Experimental binding enthalpies (both calorimetric and van't Hoff) are obtained for two host-guest pairs using ITC, and the discrepancy between the two enthalpies is examined. Modeling of artificial ITC data is also used to examine how different sources of error propagate to both types of binding enthalpies.

RESULTS

For the host-guest pairs examined here, good agreement, to within about 0.4kcal/mol, is obtained between the two enthalpies. Additionally, using artificial data, we find that different sources of error propagate to either enthalpy uniquely, with concentration error and heat error propagating primarily to calorimetric and van't Hoff enthalpies, respectively.

CONCLUSIONS

With modern calorimeters, good agreement between van't Hoff and calorimetric enthalpies should be achievable, barring issues due to non-ideality or unanticipated measurement pathologies. Indeed, disagreement between the two can serve as a flag for error-prone datasets. A review of the underlying theory supports the expectation that these two quantities should be in agreement.

GENERAL SIGNIFICANCE

We address and arguably resolve long-standing questions regarding the relationship between calorimetric and van't Hoff enthalpies. In addition, we show that comparison of these two quantities can be used as an internal consistency check of a calorimetry study.

Interaction of human serum albumin with uremic toxins: a thermodynamic study

Interaction of uremic toxins with HSA is studied by ITC and understood in terms of thermodynamic driving forces.

Evaluation and Minimization of Uncertainty in ITC Binding Measurements: Heat Error, Concentration Error, Saturation, and Stoichiometry

BACKGROUND

Isothermal titration calorimetry (ITC) is uniquely useful for characterizing binding thermodynamics, because it straightforwardly provides both the binding enthalpy and free energy. However, the precision of the results depends on the experimental setup and how thermodynamic results are obtained from the raw data.

METHODS

Experiments and Monte Carlo analysis are used to study how uncertainties in injection heat and concentration propagate to binding enthalpies in various scenarios. We identify regimes in which it is preferable to fix the stoichiometry parameter, N, and evaluate the reliability of uncertainties provided by the least squares method.

RESULTS

The noise in the injection heat is mainly proportional in character, with ~1% and ~3% uncertainty at 27C and 65C, respectively; concentration errors are ~1%. Simulations of experiments based on these uncertainties delineate how experimental design and curve fitting methods influence the uncertainty in the final results.

CONCLUSIONS

In most cases, experimental uncertainty is minimized by using more injections and by fixing N at its known value. With appropriate technique, the uncertainty in measured binding enthalpies can be kept below ~2% under many conditions, including low C values.

GENERAL SIGNIFICANCE

We quantify uncertainties in ITC data due to heat and concentration error, and identify practices to minimize these uncertainties. The resulting guidelines are important when ITC data are used quantitatively, such as to test computer simulations of binding. Reproducibility and further study are supported by free distribution of the new software developed here.

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.

Recent Advances in Computational Models for the Study of Protein-Peptide Interactions

We review computational models and software tools in current use for the study of protein-peptide interactions. Peptides and peptide derivatives are growing in interest as therapeutic agents to target protein-protein interactions. Protein-protein interactions are pervasive in biological systems and are responsible for the regulation of critical functions within the cell. Mutations or dysregulation of expression can alter the network of interactions among proteins and cause diseases such as cancer. Protein-protein binding interfaces, which are often large, shallow, and relatively feature-less, are difficult to target with small-molecule inhibitors. Peptide derivatives based on the binding motifs present in the target protein complex are increasingly drawing interest as superior alternatives to conventional small-molecule inhibitors. However, the design of peptide-based inhibitors also presents novel challenges. Peptides are more complex and more flexible than standard medicinal compounds. They also tend to form more extended and more complex interactions with their protein targets. Computational modeling is increasingly being employed to supplement synthetic and biochemical work to offer guidance and energetic and structural insights. In this review, we discuss recent in silico structure-based and physics-based approaches currently employed to model protein-peptide interactions with a few examples of their applications.

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.

Application of isothermal titration calorimetry as a tool to study natural product interactions

The study of molecular interactions of natural products by isothermal titration calorimetry (ITC) is a potent tool to get new insights of the underpinning driving forces.

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.

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.

Rational Re-engineering of a Transcriptional Silencing PreQ1 Riboswitch

Re-engineered riboswitches that no longer respond to cellular metabolites, but that instead can be controlled by synthetic molecules, are potentially useful gene regulatory tools for use in synthetic biology and biotechnology fields. Previously, extensive genetic selection and screening approaches were employed to re-engineer a natural adenine riboswitch to create orthogonal ON-switches, enabling translational control of target gene expression in response to synthetic ligands. Here, we describe how a rational targeted approach was used to re-engineer the PreQ1 riboswitch from Bacillus subtilis into an orthogonal OFF-switch. In this case, the evaluation of just six synthetic compounds with seven riboswitch mutants led to the identification of an orthogonal riboswitch-ligand pairing that effectively repressed the transcription of selected genes in B. subtilis. The streamlining of the re-engineering approach, and its extension to a second class of riboswitches, provides a methodological platform for the creation of new orthogonal regulatory components for biotechnological applications including gene functional analysis and antimicrobial target validation and screening.

Isothermal titration calorimetry of ion-coupled membrane transporters

Binding of ligands, ranging from proteins to ions, to membrane proteins is associated with absorption or release of heat that can be detected by isothermal titration calorimetry (ITC). Such measurements not only provide binding affinities but also afford direct access to thermodynamic parameters of binding--enthalpy, entropy and heat capacity. These parameters can be interpreted in a structural context, allow discrimination between different binding mechanisms and guide drug design. In this review, we introduce advantages and limitations of ITC as a methodology to study molecular interactions of membrane proteins. We further describe case studies where ITC was used to analyze thermodynamic linkage between ions and substrates in ion-coupled transporters. Similar type of linkage analysis will likely be applicable to a wide range of transporters, channels, and receptors.

Thermodynamics of binding of structurally similar ligands to histone deacetylase 8 sheds light on challenges in the rational design of potent and isozyme-selective inhibitors of the enzyme

Among the different histone deacetylase (HDAC) isozymes, HDAC8 is the most highly malleable enzyme, and it exhibits the potential to accommodate structurally diverse ligands (albeit with moderate binding affinities) in its active site pocket. To probe the molecular basis of this feature, we performed detailed thermodynamic studies of the binding of structurally similar ligands, which differed with respect to the “cap”, “linker”, and “metal-binding” regions of the suberoylanilide hydroxamic acid (SAHA) pharmacophore, to HDAC8. The experimental data revealed that although the enthalpic (ΔH°) and entropic (ΔS°) changes for the binding of individual SAHA analogues to HDAC8 were substantially different, their binding free energies (ΔG°) were markedly similar, conforming to a strong enthalpy–entropy compensation effect. This effect was further observed in the temperature-dependent thermodynamics of binding of all SAHA analogues to the enzyme. Notably, in contrast to other metalloenzymes, our isothermal titration calorimetry experiments (performed in different buffers of varying ionization enthalpies) suggest that depending on the ligand, its zinc-binding group may or may not be deprotonated upon the binding to HDAC8. Furthermore, the heat capacity changes (ΔC_p°) associated with the ligand binding to HDAC8 markedly differed from one SAHA analogue to the other, and such features could primarily be rationalized in light of the dynamic flexibility in the enzyme structure in conjunction with the reorganization of the active site resident water molecules. Arguments are presented that although the binding thermodynamic features described above would facilitate identification of weak to moderately tight-binding HDAC8 inhibitors (by a high-throughput and/or virtual screening of libraries of small molecules), they would pose major challenges for the structure-based rational design of highly potent and isozyme-selective inhibitors of human HDAC8.

Learning from our mistakes: the 'unknown knowns' in fragment screening

In the past 15 years, fragment-based lead discovery (FBLD) has been adopted widely throughout academia and industry. The approach entails discovering very small molecular fragments and growing, merging, or linking them to produce drug leads. Because the affinities of the initial fragments are often low, detection methods are pushed to their limits, leading to a variety of artifacts, false positives, and false negatives that too often go unrecognized. This Digest discusses some of these problems and offers suggestions to avoid them. Although the primary focus is on FBLD, many of the lessons also apply to more established approaches such as high-throughput screening.

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.

Entropy-enthalpy transduction caused by conformational shifts can obscure the forces driving protein-ligand binding

Molecular dynamics simulations of unprecedented duration now can provide new insights into biomolecular mechanisms. Analysis of a 1-ms molecular dynamics simulation of the small protein bovine pancreatic trypsin inhibitor reveals that its main conformations have different thermodynamic profiles and that perturbation of a single geometric variable, such as a torsion angle or interresidue distance, can select for occupancy of one or another conformational state. These results establish the basis for a mechanism that we term entropy-enthalpy transduction (EET), in which the thermodynamic character of a local perturbation, such as enthalpic binding of a small molecule, is camouflaged by the thermodynamics of a global conformational change induced by the perturbation, such as a switch into a high-entropy conformational state. It is noted that EET could occur in many systems, making measured entropies and enthalpies of folding and binding unreliable indicators of actual thermodynamic driving forces. The same mechanism might also account for the high experimental variance of measured enthalpies and entropies relative to free energies in some calorimetric studies. Finally, EET may be the physical mechanism underlying many cases of entropy-enthalpy compensation.

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.