Differential binding models for isothermal titration calorimetry: moving beyond the Wiseman isotherm

Mixing Order Asymmetry in Nanoparticle-Polymer Complexation and Precipitation Revealed by Isothermal Titration Calorimetry

In recent years, there has been a renewed interest in complex coacervation, driven by concerted efforts to offer novel experimental and theoretical insights into electrostatic charge-induced association. While previous studies have primarily focused on polyelectrolytes, proteins, or surfactants, our work explores the potential of using cerium (CeO2) and iron (γ-Fe2O3) oxide nanoparticles (NPs) to develop innovative nanomaterials. By combining various charged species, such as polyelectrolytes, charged neutral block copolymers, and coated NPs, we study a wide variety of complexation patterns and compare them using isothermal titration calorimetry, light scattering, and microscopy. These techniques confirm that the titration of oppositely charged species occurs in two steps: the formation of polyelectrolyte complexes and subsequent phase (or microphase) separation, depending on the system studied. Across all examined cases, the entropic contribution to the total free energy surpasses the enthalpic contribution, in agreement with counterion release mechanisms. Furthermore, our investigation reveals a consistent asymmetry in the reaction enthalpy associated with the secondary process, with exothermic profiles observed upon the addition of cationic species to anionic ones and endothermic profiles in the reverse case.

Thermodynamic Characterization of the Interaction of Biofunctionalized Gold Nanoclusters with Serum Albumin Using Two- and Three-Dimensional Methods

Fluorescent gold nanoclusters have been successfully used as fluorescent markers for imaging of cells and tissues, and their potential role in drug delivery monitoring is coming to the fore. In addition, the development of biosensors using structure-tunable fluorescent nanoclusters is also a prominent research field. In the case of these sensor applications, the typical goal is the selective identification of, e.g., metal ions, small molecules having neuroactive or antioxidant effects, or proteins. During these application-oriented developments, in general, there is not enough time to systematically examine the interaction between nanoclusters and relevant biomolecules/proteins from a thermodynamic viewpoint. In this way, the primary motivation of this article is to carry out a series of tests to partially fill this scientific gap. Besides the well-known fluorescent probes, the mentioned interactions were investigated using such unique measurement methods as surface plasmon resonance (SPR) and isothermal titration calorimetry (ITC). These two-dimensional (at the solid/liquid interface) and three-dimensional (in the bulk phase) measuring techniques provide a unique opportunity for the thermodynamic characterization of the interaction between different gold nanoclusters containing various surface functionalizing ligands and bovine serum albumin (BSA).

Extracellular polymeric substances and mineral interfacial reactions control the simultaneous immobilization and reduction of arsenic (As(V))

Extracellular polymeric substances (EPS) play a crucial role in controlling the mobility and bioavailability of heavy metal(loid)s in water, soils, and sediments. The formation of EPS-mineral complex changes the reactivity of the end-member materials. However, little is known about the adsorption and redox mechanisms of arsenate (As(V)) in EPS and EPS-mineral complexes. Here we examined the reaction sites, valence state, thermodynamic parameters and distribution of As in the complexes using potentiometric titration, isothermal titration calorimetry (ITC), FTIR, XPS, and SEM-EDS. The results showed that ∼54% of As(V) was reduced to As(III) by EPS, potentially driven by an enthalpy change (ΔH) of - 24.95 kJ/mol. The EPS coating on minerals clearly affected the reactivity to As(V). The strong masking of functional sites between EPS and goethite inhibited both the adsorption and reduction of As. In contrast, the weak binding of EPS onto montmorillonite retained more reactive sites for the reaction with As. Meanwhile, montmorillonite facilitated the immobilization of As to EPS through the formation of As-organic bounds. Our findings deepen the understanding of EPS-mineral interfacial reactions in controlling the redox and mobility of As, and the knowledge is important for predicting the behavior of As in natural environments.

Assessing the Contribution of the Neutral Blocks in DNA/Block-Copolymer Polyplexes: Poly(acrylamide) vs. Poly(ethylene Oxide)

The interaction of DNA with different block copolymers, namely poly (trimethylammonium chloride methacryloyoxy)ethyl)-block-poly(acrylamide), i.e., (PTEA)-b-(PAm), and poly (trimethylammonium chloride methacryloyoxy)ethyl)-block-poly(ethylene oxide), i.e., (PTEA)-b-(PEO), was studied. The nature of the cationic block was maintained fixed (PTEA), whereas the neutral blocks contained varying amounts of acrylamide or (ethylene oxide) units. According to results from isothermal titration microcalorimetry measurements, the copolymers interaction with DNA is endothermic with an enthalpy around 4.0 kJ mol−1 of charges for (PTEA)-b-(PAm) and 5.5 kJ mol−1 of charges for (PTEA)-b-(PEO). The hydrodynamic diameters of (PTEA)-b-(PEO)/DNA and (PTEA)-b-(PAm)/DNA polyplexes prepared by titration were around 200 nm at charge ratio (Z+/−) < 1. At Z+/− close and above 1, the (PTEA)50-b-(PAm)50/DNA and (PTEA)50-b-(PAm)200/DNA polyplexes precipitated. Interestingly, (PTEA)50-b-(PAm)1000/DNA polyplexes remained with a size of around 300 nm even after charge neutralization, probably due to the size of the neutral block. Conversely, for (PTEA)96-b-(PEO)100/DNA polyplexes, the size distribution was broad, indicating a more heterogeneous system. Polyplexes were also prepared by direct mixture at Z+/− of 2.0, and they displayed diameters around 120−150 nm, remaining stable for more than 10 days. Direct and reverse titration experiments showed that the order of addition affects both the size and charge of the resulting polyplexes.

Isothermal Titration Calorimetry Analysis of a Cooperative Riboswitch Using an Interdependent-Sites Binding Model

Isothermal titration calorimetry (ITC) is a powerful biophysical tool to characterize energetic profiles of biomacromolecular interactions without any alteration of the underlying chemical structures. In this protocol, we describe procedures for performing, analyzing, and interpreting ITC data obtained from a cooperative riboswitch-ligand interaction.

Structural and Biophysical Analysis of the Phytochelatin-Synthase-Like Enzyme from Nostoc sp. Shows That Its Protease Activity is Sensitive to the Redox State of the Substrate

Phytochelatins (PCs) are nonribosomal thiol-rich oligopeptides synthetized from glutathione (GSH) in a γ-glutamylcysteinyl transpeptidation reaction catalyzed by PC synthases (PCSs). Ubiquitous in plant and present in some invertebrates, PCSs are involved in metal detoxification and homeostasis. The PCS-like enzyme from the cyanobacterium Nostoc sp. (NsPCS) is considered to be an evolutionary precursor enzyme of genuine PCSs because it shows sufficient sequence similarity for homology to the catalytic domain of the eukaryotic PCSs and shares the peptidase activity consisting in the deglycination of GSH. In this work, we investigate the catalytic mechanism of NsPCS by combining structural, spectroscopic, thermodynamic, and theoretical techniques. We report several crystal structures of NsPCS capturing different states of the catalyzed chemical reaction: (i) the structure of the wild-type enzyme (wt-NsPCS); (ii) the high-resolution structure of the γ-glutamyl-cysteine acyl-enzyme intermediate (acyl-NsPCS); and (iii) the structure of an inactive variant of NsPCS, with the catalytic cysteine mutated into serine (C70S-NsPCS). We characterize NsPCS as a relatively slow enzyme whose activity is sensitive to the redox state of the substrate. Namely, NsPCS is active with reduced glutathione (GSH), but is inhibited by oxidized glutathione (GSSG) because the cleavage product is not released from the enzyme. Our biophysical analysis led us to suggest that the biological function of NsPCS is being a part of a redox sensing system. In addition, we propose a mechanism how PCS-like enzymes may have evolved toward genuine PCS enzymes.

Design of Gallic Acid-Glutamine Conjugate and Chemical Implications for Its Potency Against Alzheimer's Amyloid-β Fibrillogenesis

Epigallocatechin-3-gallate (EGCG) has been widely recognized as a potent inhibitor of Alzheimer's amyloid-β (Aβ) fibrillogenesis. We found that gallic acid (GA) has superior inhibitory effects over EGCG at the same mass concentrations and assumed the pivotal role of the carboxyl group in GA. Therefore, we designed five GA-derivatives to investigate the significance of carboxyl groups in modulating Aβ fibrillogenesis, including carboxyl-amidated GA (GA-NH₂), GA-glutamic acid conjugate (GA-E), and GA-E derivatives with amidated either of the two carboxyl groups (GA-Q and GA-E-NH₂) or with two amidated-carboxyl groups (GA-Q-NH₂). Intriguingly, only GA-Q shows significantly stronger potency than GA and extends the life span of the AD transgenic nematode by over 30%. Thermodynamic studies reveal that GA-Q has a strong binding affinity for Aβ₄₂ with two binding sites, one stronger (site 1, K_a1 = 3.1 × 10⁶ M^-1) and the other weaker (site 2, K_a2 = 0.8 × 10⁶ M^-1). In site 1, hydrogen bonding, electrostatic interactions, and hydrophobic interactions all have contributions, while in site 2, only hydrogen bonding and electrostatic interactions work. The two sites are confirmed by molecular simulations, and the computations specified the key residues. GA-Q has strong binding to Asp23, Gly33, Gly38, Ala30, Ile31, and Leu34 via hydrogen bonding and electrostatic interactions, while it interacts with Phe19, Ala21 Gly25, and Asn27 via hydrophobic interactions. Consequently, GA-Q destroys Asp23-Lys28 salt bridges and restricts β-sheet/bridge structures. The thermodynamic and molecular insight into the GA-Q functions on inhibiting Aβ fibrillogenesis would pave a new way to the design of potent molecules against Alzheimer's amyloid.

Development of the Sequential Binding Model and Application for Anticooperative Protein Adsorption onto Charged Dendrimers

The Langmuir binding model provides one of the simplest and elegant methods for characterizing an adsorption process. Despite its wide-ranging applications, enormous effort has been spent to further integrate complexity onto the standard Langmuir isotherm to incorporate a wide breadth of binding kinetics with the heterogeneity and cooperative effect among ligands and receptors. Here, we use statistical mechanics as a convenient theoretical framework to depict several adsorption processes on a Langmuir-like description. With regard to the system with a two-component mixture of macromolecular binders, we have derived the two-group sequential binding isotherm as an important extension of the original sequential model with more applications, including systems of non-identical binders. Via comparison of the Langmuir equilibrium with the Boltzmann equilibrium, for the first time the binding free energy defined in the Langmuir-like models can be meaningfully compared with simulations. In a practical example of the adsorption between the lysozyme protein and charged dendrimer, we have demonstrated how the calorimetry data of this system could be interpreted by the binding models described above, with an accurate description of the adsorption process, including the cooperative effect and dendrimer heterogeneity. Using the computer simulation as a benchmark, we also reveal and discuss the strengths and limitations of the proposed binding models. The entire analysis serves as a starting point for extending the standard Langmuir model to access more complicated binding processes.

Isothermal Titration Calorimetry Directly Measures the Selective Swelling of Block Copolymer Vesicles in the Presence of Organic Acid

Block copolymer (BCP) vesicles loaded with drug molecules may have a nonidentical swelling behavior due to the strong interactions between BCP vesicles and loaded molecules. A thermodynamic study of the swelling for such a system is of great importance in clarifying their pH-gated drug delivery behavior. In this study, the selective swelling of polystyrene-block-poly(2-vinylpyridine) (PS-b-P2VP) vesicles in the presence of different acids was compared using dynamic light scattering, zeta-potential, and isothermal titration calorimetry (ITC) measurements. Transmission electron microscopy observation verified that these PS-b-P2VP vesicles were mainly multilamellar. Importantly, using the ITC measurement, we first compared the thermodynamic parameters, including ΔH, ΔG, and ΔS, association binding sites (N), and binding association constants (K _a) in the selective swelling of the PS-b-P2VP vesicles in low pH (pH ∼3.5), with or without a hydrogen bonding interaction. We observed that the existence of a hydrogen bonding interaction between tartaric acid/malic acid and PS-b-P2VP generates a limitation to the selective swelling of PS-b-P2VP vesicles, in which conditions will depend on the molecular structures of the organic acids and PS-b-P2VP. This work first provides a quantitative insight on the swelling of BCP vesicles in the presence of hydrogen bonding and highlights the power of ITC measurements for investigating the structural transformation of polymer nanostructures.

Counterintuitive Electrostatics upon Metal Ion Coordination to a Receptor with Two Homotopic Binding Sites

The consecutive binding of two potassium ions to a bis(18-crown-6) analogue of Tröger’s base (BCETB) in water was studied by isothermal titration calorimetry using four different salts, KCl, KI, KSCN, and K₂SO₄. A counterintuitive result was observed: the enthalpy change associated with the binding of the second ion is more negative than that of the first (ΔH_bind,2^° < ΔH_bind,1^°). This remarkable finding is supported by continuum electrostatic theory as well as by atomic scale replica exchange molecular dynamics simulations, where the latter robustly reproduces experimental trends for all simulated salts, KCl, KI, and KSCN, using multiple force fields. While an enthalpic K⁺–K⁺attraction in water poses a small, but fundamentally important, contribution to the overall interaction, the probability of the collapsed conformation (COL) of BCETB, where both crown ether moieties (CEs) of BCETB are bent in toward the cavity, was found to increase successively upon binding of the first and second potassium ions. The promotion of the COL conformation reveals favorable intrinsic interactions between the potassium coordinated CEs, which further contribute to the observation that ΔH_bind,2^° < ΔH_bind,1^°. While the observed trend is independent of the counterion, the origin of the significantly larger magnitude of the difference ΔH_bind,2^° – ΔH_bind,1^° observed experimentally for KSCN was studied in light of the weaker hydration of the thiocyanate anion, resulting in an enrichment of thiocyanate ions close to BCETB compared to the other studied counterions.

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

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

Mucoadhesive properties of nanogels based on stimuli-sensitive glycosaminoglycan-graft-pNIPAAm copolymers

Mucoadhesive formulations capable of situ gelation are promising for improving ocular drug delivery. Here we investigated two types of nanogels based on anionic glycosaminoglycans with grafted thermo-responsive poly(N-isopropylacrylamide) chains. One type of nanogels were formed by thermo-induced gelling of heparin-graft-poly(N-isopropylacrylamide) and chondroitin sulfate-graft-poly(N-isopropylacrylamide) copolymers. Another type of nanogels was based on the same copolymers, but terminal groups of thermosensitive macromolecular chains were modified to form covalent disulfide cross-links. All types of nanogels were studied towards their ability to encapsulate and release model drug - dexamethasone. Mucoadhesivity of both thermo-gelled and covalently cross-linked polymeric systems, as well as their ability to interact with dexamethasone, was assessed by microscale thermophoresis (MST). Mucoadhesion properties were also evaluated by isothermal titration calorimetry (ITC), which were in good correlation with MST data. The presence of disulfide linkages and thiol groups were shown to favor improved binding of cross-linked nanogels to mucin. Moreover, in vivo intraocular pressure studies showed that presence of polymers in solution can alter the ocular absorption of carbonic anhydrase inhibitor from eyedrops. The pharmacological effect was in line with mucoadhesive properties of these copolymers.

Theoretical and Experimental Design of Heavy Metal-Mopping Magnetic Nanoparticles

Herein, we show a comprehensive experimental, theoretical, and computational study aimed at designing macromolecules able to adsorb a cargo at the nanoscale. Specifically, we focus on the adsorption properties of star diblock copolymers, i.e., macromolecules made by a number f of H-T diblock copolymer arms tethered on a central core; the H monomeric heads, which are closer to the tethering point, are attractive toward a specific target, while the T monomeric tails are neutral to the cargo. Experimentally, we exploited the adaptability of poly(2-oxazoline)s (POxs) to realize block copolymer-coated nanoparticles with a proper functionalization able to interact with heavy metals and show or exhibit a thermoresponsive behavior in aqueous solution. We here present the synthesis and analysis of the properties of a high molecular mass block copolymer featured by (i) a polar side chain, capable of exploiting electrostatic and hydrophilic interaction with a predetermined cargo, and (ii) a thermoresponsive scaffold, able to change the interaction with the media by tuning the temperature. Afterward, the obtained polymers were grafted onto iron oxide nanoparticles and the thermoresponsive properties were investigated. Through isothermal titration calorimetry, we then analyzed the adsorption properties of the synthesized superparamagnetic nanoparticles for heavy metal ions in aqueous solution. Additionally, we use a combination of scaling theories and simulations to link equilibrium properties of the system to a prediction of the loading properties as a function of size ratio and effective interactions between the considered species. The comparison between experimental results on adsorption and theoretical prediction validates the whole design process.

Compaction and condensation of DNA mediated by the C-terminal domain of Hfq

Hfq is a bacterial protein that is involved in several aspects of nucleic acids metabolism. It has been described as one of the nucleoid associated proteins shaping the bacterial chromosome, although it is better known to influence translation and turnover of cellular RNAs. Here, we explore the role of Escherichia coli Hfq's C-terminal domain in the compaction of double stranded DNA. Various experimental methodologies, including fluorescence microscopy imaging of single DNA molecules confined inside nanofluidic channels, atomic force microscopy, isothermal titration microcalorimetry and electrophoretic mobility assays have been used to follow the assembly of the C-terminal and N-terminal regions of Hfq on DNA. Results highlight the role of Hfq's C-terminal arms in DNA binding, change in mechanical properties of the double helix and compaction of DNA into a condensed form. The propensity for bridging and compaction of DNA by the C-terminal domain might be related to aggregation of bound protein and may have implications for protein binding related gene regulation.

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.

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.

Integration and global analysis of isothermal titration calorimetry data for studying macromolecular interactions

Isothermal titration calorimetry (ITC) is a powerful and widely used method to measure the energetics of macromolecular interactions by recording a thermogram of differential heating power during a titration. However, traditional ITC analysis is limited by stochastic thermogram noise and by the limited information content of a single titration experiment. Here we present a protocol for bias-free thermogram integration based on automated shape analysis of the injection peaks, followed by combination of isotherms from different calorimetric titration experiments into a global analysis, statistical analysis of binding parameters and graphical presentation of the results. This is performed using the integrated public-domain software packages NITPIC, SEDPHAT and GUSSI. The recently developed low-noise thermogram integration approach and global analysis allow for more precise parameter estimates and more reliable quantification of multisite and multicomponent cooperative and competitive interactions. Titration experiments typically take 1-2.5 h each, and global analysis usually takes 10-20 min.

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.

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.

Use of isothermal titration calorimetry to study surfactant aggregation in colloidal systems

BACKGROUND

Isothermal titration calorimetry (ITC) is a general technique that allows for precise and highly sensitive measurements. These measurements may provide a complete and accurate thermodynamic description of association processes in complex systems such as colloidal mixtures.

SCOPE OF THE REVIEW

This review will address uses of ITC for studies of surfactant aggregation to form micelles, with emphasis on the thermodynamic studies of homologous surfactant series. We will also review studies on surfactant association with polymers of different molecular characteristics and with colloidal particles.

GENERAL SIGNIFICANCE

ITC studies on the association of different homologous series of surfactants provide quantitative information on independent contribution from their apolar hydrocarbon chains and polar headgroups to the different thermodynamic functions associated with micellization (Gibbs energy, enthalpy and entropy). Studies on surfactant association to polymers by ITC provide a comprehensive description of the association process, including examples in which particular features revealed by ITC were elucidated by using ancillary techniques such as light or X-ray scattering measurements. Examples of uses of ITC to follow surfactant association to biomolecules such as proteins or DNA, or nanoparticles are also highlighted. Finally, recent theoretical models that were proposed to analyze ITC data in terms of binding/association processes are discussed.

MAJOR CONCLUSIONS

This review stresses the importance of using direct calorimetric measurements to obtain and report accurate thermodynamic data, even in complex systems. These data, whenever possible, should be confirmed and associated with other ancillary techniques that allow elucidation of the nature of the transformations detected by calorimetric results, providing a complete description of the process under scrutiny.

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.

Evidence of a two-step process and pathway dependency in the thermodynamics of poly(diallyldimethylammonium chloride)/poly(sodium acrylate) complexation

Recent studies have pointed out the importance of polyelectrolyte assembly in the elaboration of innovative nanomaterials. Beyond their structures, many important questions on the thermodynamics of association remain unanswered. Here, we investigate the complexation between poly(diallyldimethylammonium chloride) (PDADMAC) and poly(sodium acrylate) (PANa) chains using a combination of three techniques: isothermal titration calorimetry (ITC), static and dynamic light scattering and electrophoresis. Upon addition of PDADMAC to PANa or vice-versa, the results obtained by the different techniques agree well with each other, and reveal a two-step process. The primary process is the formation of highly charged polyelectrolyte complexes of size 100 nm. The secondary process is the transition towards a coacervate phase made of rich and poor polymer droplets. The binding isotherms measured are accounted for using a phenomenological model that provides the thermodynamic parameters for each reaction. Small positive enthalpies and large positive entropies consistent with a counterion release scenario are found throughout this study. Furthermore, this work stresses the importance of the underestimated formulation pathway or mixing order in polyelectrolyte complexation.

A unified framework based on the binding polynomial for characterizing biological systems by isothermal titration calorimetry

Isothermal titration calorimetry (ITC) has become the gold-standard technique for studying binding processes due to its high precision and sensitivity, as well as its capability for the simultaneous determination of the association equilibrium constant, the binding enthalpy and the binding stoichiometry. The current widespread use of ITC for biological systems has been facilitated by technical advances and the availability of commercial calorimeters. However, the complexity of data analysis for non-standard models is one of the most significant drawbacks in ITC. Many models for studying macromolecular interactions can be found in the literature, but it looks like each biological system requires specific modeling and data analysis approaches. The aim of this article is to solve this lack of unity and provide a unified methodological framework for studying binding interactions by ITC that can be applied to any experimental system. The apparent complexity of this methodology, based on the binding polynomial, is overcome by its easy generalization to complex systems.

Lanthanide loading of luminescent multi-tridentate polymers under thermodynamic control

This work illustrates the use of basic statistical mechanics for rationalizing the loading of linear multitridentate polymers with trivalent lanthanides, Ln(III), and identifies the specific ionic sizes of europium and yttrium as promising candidates for the further design of organized heterometallic f–f′ materials. Using [Ln(hfac)3] (hfac = hexafluoroacetylacetonate) as lanthanide carriers, the thermodynamically controlled formation of Wolf type-II lanthanidopolymers [{Ln(hfac)3}m(L4)] is modeled with the help of two simple microscopic descriptors: (i) the intrinsic affinity of Ln(III) for the tridentate binding sites fN3(Ln) and (ii) the intermetallic interactions ΔE1–2(Ln,Ln) operating between two occupied adjacent sites. Selective complexation (fN3La << fN3Eu > fN3(Y)) modulated by anticooperative interactions (ΔE1–2(La,La) ≃ ΔE1–2(Eu,Eu) > ΔE1–2(Y,Y) ≈ 0) favors the fixation of Eu(III) in semiorganized lanthanidopolymers [{Eu(hfac)3}m(L4)] displaying exploitable light-downshifting.