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.     

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.     

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.     

Open-ITC: an alternate computational approach to analyze the isothermal titration calorimetry data of complex binding mechanisms

Isothermal titration calorimetry (ITC) is an important technique used in quantitatively analyzing the global mechanism of protein-protein or protein-ligand interactions through thermodynamic measurements. Among different binding mechanisms, the parallel and ligand induced protein oligomerization mechanisms are technically difficult to analyze compared with a sequential binding mechanism. Here, we present a methodology implemented as a program "Open-ITC" that eliminates the need for exact analytical expressions for free ligand concentrations [L] and mole fractions of bound ligand θ that are required for the thermogram analysis. Adopting a genetic algorithm-based optimization, the thermodynamic parameters are determined, and its standard error is evaluated at the global minimum by calculating the Jacobian matrix. This approach yielded a statistically consistent result for a single-site and a two-site binding protein-ligand system. Further, a comparative simulation of a two-step sequential, a parallel, and a ligand induced oligomerization model revealed that their mechanistic differences are discernable in ITC thermograms, only if the first binding step is weaker compared with the second binding step (K(1) 相似文献   

A universal method for fishing target proteins from mixtures of biomolecules using isothermal titration calorimetry

The most challenging tasks in biology include the identification of (1) the orphan receptor for a ligand, (2) the ligand for an orphan receptor protein, and (3) the target protein(s) for a given drug or a lead compound that are critical for the pharmacological or side effects. At present, several approaches are available, including cell- or animal-based assays, affinity labeling, solid-phase binding assays, surface plasmon resonance, and nuclear magnetic resonance. Most of these techniques are not easy to apply when the target protein is unknown and the compound is not amenable to labeling, chemical modification, or immobilization. Here we demonstrate a new universal method for fishing orphan target proteins from a complex mixture of biomolecules using isothermal titration calorimetry (ITC) as a tracking tool. We took snake venom, a crude mixture of several hundred proteins/peptides, as a model to demonstrate our proposed ITC method in tracking the isolation and purification of two distinct target proteins, a major component and a minor component. Identities of fished out target proteins were confirmed by amino acid sequencing and inhibition assays. This method has the potential to make a significant advancement in the area of identifying orphan target proteins and inhibitor screening in drug discovery and characterization.     

Explicit formulation of titration models for isothermal titration calorimetry

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

Using nonlinear least squares to assess relative expression and its uncertainty in real-time qPCR studies

Relative expression ratios are commonly estimated in real-time qPCR studies by comparing the quantification cycle for the target gene with that for a reference gene in the treatment samples, normalized to the same quantities determined for a control sample. For the “standard curve” design, where data are obtained for all four of these at several dilutions, nonlinear least squares can be used to assess the amplification efficiencies (AE) and the adjusted ΔΔC_q and its uncertainty, with automatic inclusion of the effect of uncertainty in the AEs. An algorithm is illustrated for the KaleidaGraph program.     

Survey of the year 2008: applications of isothermal titration calorimetry

Isothermal titration calorimetry (ITC) is a fast, accurate and label‐free method for measuring the thermodynamics and binding affinities of molecular associations in solution. Because the method will measure any reaction that results in a heat change, it is applicable to many different fields of research from biomolecular science, to drug design and materials engineering, and can be used to measure binding events between essentially any type of biological or chemical ligand. ITC is the only method that can directly measure binding energetics including Gibbs free energy, enthalpy, entropy and heat capacity changes. Not only binding thermodynamics but also catalytic reactions, conformational rearrangements, changes in protonation and molecular dissociations can be readily quantified by performing only a small number of ITC experiments. In this review, we highlight some of the particularly interesting reports from 2008 employing ITC, with a particular focus on protein interactions with other proteins, nucleic acids, lipids and drugs. As is tradition in these reviews we have not attempted a comprehensive analysis of all 500 papers using ITC, but emphasize those reports that particularly captured our interest and that included more thorough discussions we consider exemplify the power of the technique and might serve to inspire other users. Copyright © 2010 John Wiley & Sons, Ltd.     

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

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

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

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

Applications of isothermal titration calorimetry in protein science

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

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.     

Adsorption of RNase A on cationic polyelectrolyte brushes: a study by isothermal titration calorimetry

We present a study of the adsorption of a positively charged protein to a positively charged spherical polyelectrolyte brush (SPB) by isothermal titration calorimetry (ITC). ITC is used to determine the adsorption isotherm as a function of temperature and of salt concentration (at physiological pH 7.2). At low ionic strength, RNase A is strongly adsorbed by the SPB particles despite the fact that both the SPB particles and the protein are positively charged. Virtually no adsorption takes place when the ionic strength is raised through added salt. This is strong evidence for counterion release as the primary driving force for protein adsorption. We calculated that ~2 counterions were released upon RNase A binding. The adsorption of RNase A into like-charged SPB particles is entropy-driven, and protein protonation was not significant. Temperature-dependent measurements showed a disagreement between the enthalpy derived via the van't Hoff equation and the calorimetric enthalpy. Further analysis shows that van't Hoff analysis leads to the correct enthalpy of adsorption. The additional contributions to the measured enthalpy are potentially sourced from unlinked equilibria such as conformational changes that do not contribute to the binding equilibrium.     

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.

Recent trends and some applications of isothermal titration calorimetry in biotechnology

Isothermal titration calorimeters (ITCs) are thermodynamic instruments used for the determination of enthalpy changes in any physical/chemical reaction. This can be applied in various fields of biotechnology. This review explains ITC applications, especially in bioseparation, drug development and cell metabolism. In liquid chromatography, the separation/purification of specific proteins or polypeptides in a mixture is usually achieved by varying the adsorption affinities of the different proteins/polypeptides for the adsorbent under different mobile-phase conditions and temperatures. Using ITC analysis, the binding mechanism of proteins with adsorbent solid material is derived by elucidating enthalpy and entropy changes, which offer valuable guidelines for designing experimental conditions in chromatographic separation. The binding affinity of a drug with its target is studied by deriving binding enthalpy and binding entropy. To improve the binding affinity, suitable lead compounds for a drug can be identified and their affinity tested by ITC. Recently ITC has also been used in studying cell metabolism. The heat produced by animal cells in culture can be used as a primary indicator of the kinetics of cell metabolism, which provides key information for drug bioactivity and operation parameters for process cell culture.     

A survey of the year 2006 literature on applications of isothermal titration calorimetry

Isothermal titration calorimetry (ITC) is a fast and robust method to determine the energetics of association reactions in solution. The changes in enthalpy, entropy and heat capacity that accompany binding provide unique insights into the balance of forces driving association of molecular entities. ITC is used nowadays on a day-to-day basis in hundreds of laboratories. The method aids projects both in basic and practice-oriented research ranging from medicine and biochemistry to physical chemistry and material sciences. Not surprisingly, the range of studies utilizing ITC data is steadily expanding. In this review, we discuss selected results and ideas that have accumulated in the course of the year 2006, the focus being on biologically relevant systems. Theoretical developments, novel applications and studies that provide a deeper level of understanding of the energetic principles of biological function are primarily considered. Following the appearance of a new generation of titration calorimeters, recent papers provide instructive examples of the synergy between energetic and structural approaches in biomedical and biotechnological research.     

A survey of the year 2003 literature on applications of isothermal titration calorimetry

Over the last decade isothermal titration calorimetry (ITC) has developed from a specialist method which was largely restricted in its use to dedicated experts, to a major, commercially available tool in the arsenal directed at understanding molecular interactions. The number of those proficient in this field has multiplied dramatically, as has the range of experiments to which this method has been applied. This has led to an overwhelming amount of new data and novel applications to be assessed. With the increasing number of publications in this field comes a need to highlight works of interest and impact. In this overview of the literature we have attempted to draw attention to papers and issues for which both the experienced calorimetrist and the interested dilettante hopefully will share our enthusiasm.     

A survey of the year 2002 literature on applications of isothermal titration calorimetry

Isothermal titration calorimetry (ITC) is becoming widely accepted as a key instrument in any laboratory in which quantification of biomolecular interactions is a requisite. The method has matured with respect to general acceptance and application development over recent years. The number of publications on ITC has grown exponentially over the last 10 years, reflecting the general utility of the method. Here all the published works of the year 2002 in this area have been surveyed. We review the broad range of systems to which ITC is being directed and classify these into general areas highlighting key publications of interest. This provides an overview of what can be achieved using this method and what developments are likely to occur in the near future.     

A survey of the year 2007 literature on applications of isothermal titration calorimetry

Elucidation of the energetic principles of binding affinity and specificity is a central task in many branches of current sciences: biology, medicine, pharmacology, chemistry, material sciences, etc. In biomedical research, integral approaches combining structural information with in-solution biophysical data have proved to be a powerful way toward understanding the physical basis of vital cellular phenomena. Isothermal titration calorimetry (ITC) is a valuable experimental tool facilitating quantification of the thermodynamic parameters that characterize recognition processes involving biomacromolecules. The method provides access to all relevant thermodynamic information by performing a few experiments. In particular, ITC experiments allow to by-pass tedious and (rarely precise) procedures aimed at determining the changes in enthalpy and entropy upon binding by van't Hoff analysis. Notwithstanding limitations, ITC has now the reputation of being the "gold standard" and ITC data are widely used to validate theoretical predictions of thermodynamic parameters, as well as to benchmark the results of novel binding assays. In this paper, we discuss several publications from 2007 reporting ITC results. The focus is on applications in biologically oriented fields. We do not intend a comprehensive coverage of all newly accumulated information. Rather, we emphasize work which has captured our attention with originality and far-reaching analysis, or else has provided ideas for expanding the potential of the method. Copyright (c) 2008 John Wiley & Sons, Ltd.