Characterization of sites of different thermodynamic affinities on the same metal center via isothermal titration calorimetry

Direct Determination of High-Affinity Binding Constants by Continuous Injection Isothermal Titration Calorimetry

Isothermal titration calorimetry (ITC) is a method to determine thermodynamic values (ΔG, ΔH, and ΔS) for ligand-receptor binding in biological and abiological systems. It is challenging to directly determine subnanomolar dissociation constants using a standard incremental injection approach ITC (IIA-ITC) measurement. We recently demonstrated a continuous injection approach ITC (CIA-ITC) [ J. Phys. Chem. B 2021, 125, 8075-8087]enables the estimation of thermodynamic parameters in situ. In this work, we demonstrate a label-free and surface modification-free CIA-ITC to determine the complete binding thermodynamics of a ligand with a subnanomolar dissociation constant KD. The KD for desthiobiotin (DTB)-avidin binding was determined to be 6.5 pM with respect to the ligand by CIA-ITC, a quantity unsuccessfully measured with IIA-ITC and surface plasmon resonance spectroscopy (SPR). This value compares well with literature-reported spectroscopic determination of DTB-avidin binding. Criteria with respect to the concentration of the ligand and receptor and flow rate for obtaining true equilibrium dissociation constants without displacement titration are presented.

Continuous Injection Isothermal Titration Calorimetry for In Situ Evaluation of Thermodynamic Binding Properties of Ligand-Receptor Binding Models

We utilize a continuous injection approach (CIA) rather than the traditional incremental injection approach (IIA) to deliver ligand (or receptor) to the calorimeter cell to evaluate thermodynamic binding parameters for three common ligand-receptor binding models-single independent, competitive, and two independent binding sites-using isothermal titration calorimetry (ITC). A general mathematical expression for the binding isotherm for any binding stoichiometry under continuous delivery of ligand (or receptor) resulting in an analytical solution for the thermodynamic binding parameters is presented. The advantages of CIA include reduction in experimental time, estimation of thermodynamic binding parameter values, and automation of the experiment since thermodynamic parameters are estimated in situ. We demonstrate the inherent advantages of CIA over IIA for the three binding models. For the single independent site model, we utilized the binding of Ba²⁺ ions to ethylenediaminetetraacetic acid (EDTA), while competitive binding was captured by titration of Ca²⁺ ions into a buffered solution of Ba²⁺ and EDTA. We experimentally simulated a two independent binding site system by injecting Ca²⁺ into a solution of EDTA and 1,3-diaminopropane-N,N,N',N'-tetraacetic acid (DPTA). The results demonstrate estimation of thermodynamic parameters with greater confidence and simultaneous reduction in the experimental time of 83% and titrating reagent of 50%, as compared to IIA.

Solvent manipulation of the pre-reduction metal-ligand complex and particle-ligand binding for controlled synthesis of Pd nanoparticles

Understanding how to control the nucleation and growth rates is crucial for designing nanoparticles with specific sizes and shapes. In this study, we show that the nucleation and growth rates are correlated with the thermodynamics of metal-ligand/solvent binding for the pre-reduction complex and the surface of the nanoparticle, respectively. To obtain these correlations, we measured the nucleation and growth rates by in situ small angle X-ray scattering during the synthesis of colloidal Pd nanoparticles in the presence of trioctylphosphine in solvents of varying coordinating ability. The results show that the nucleation rate decreased, while the growth rate increased in the following order, toluene, piperidine, 3,4-lutidine and pyridine, leading to a large increase in the final nanoparticle size (from 1.4 nm in toluene to 5.0 nm in pyridine). Using density functional theory (DFT), complemented by 31P nuclear magnetic resonance and X-ray absorption spectroscopy, we calculated the reduction Gibbs free energies of the solvent-dependent dominant pre-reduction complex and the solvent-nanoparticle binding energy. The results indicate that lower nucleation rates originate from solvent coordination which stabilizes the pre-reduction complex and increases its reduction free energy. At the same time, DFT calculations suggest that the solvent coordination affects the effective capping of the surface where stronger binding solvents slow the nanoparticle growth by lowering the number of active sites (not already bound by trioctylphosphine). The findings represent a promising advancement towards understanding the microscopic connection between the metal-ligand thermodynamic interactions and the kinetics of nucleation and growth to control the size of colloidal metal nanoparticles.

Thermochemical Measurements of Cation Exchange in CdSe Nanocrystals Using Isothermal Titration Calorimetry

Among the various reported post synthetic modifications of colloidal nanocrystals, cation exchange (CE) is one of the most promising and versatile approaches for the synthesis of nanostructures that cannot be directly synthesized from their constitutive precursors. Numerous studies have reported on the qualitative analysis of these reactions, but rigorous quantitative study of the thermodynamics of CE in colloidal nanoparticles is still lacking. We demonstrate using isothermal titration calorimetry (ITC), the thermodynamics of the CE between cadmium selenide (CdSe) nanocrystals and silver in solution can be quantified. We survey the influence of CdSe nanocrystal diameter, capping ligands and temperature on the thermodynamics of the exchange reaction. Results obtained from ITC provide a detailed description of overall thermodynamic parameters-equilibrium constant ( K _eq), enthalpy (Δ H), entropy (Δ S) and stoichiometry ( n)-of the exchange reaction. We compared the free energy change of reaction (Δ G) between CdSe and Ag⁺ obtained directly from ITC for both CdSe bulk and nanoparticles with values calculated from previously reported methods. While the calculated value is closer to the experimentally obtained Δ G _rxn for bulk particles, nanocrystals show an additional Gibbs free energy stabilization of ∼-14 kJ/mol Se. We discuss a thermochemical cycle elucidating the steps involved in the overall cation exchange process. This work demonstrates the application of ITC to probe the thermochemistry of nanoscale transformations under relevant solution conditions.

Colloidal nanoparticle size control: experimental and kinetic modeling investigation of the ligand-metal binding role in controlling the nucleation and growth kinetics

Despite the major advancements in colloidal metal nanoparticles synthesis, a quantitative mechanistic treatment of the ligand's role in controlling their size remains elusive. We report a methodology that combines in situ small angle X-ray scattering (SAXS) and kinetic modeling to quantitatively capture the role of ligand-metal binding (with the metal precursor and the nanoparticle surface) in controlling the synthesis kinetics. We demonstrate that accurate extraction of the kinetic rate constants requires using both, the size and number of particles obtained from in situ SAXS to decouple the contributions of particle nucleation and growth to the total metal reduction. Using Pd acetate and trioctylphosphine in different solvents, our results reveal that the binding of ligands with both the metal precursor and nanoparticle surface play a key role in controlling the rates of nucleation and growth and consequently the final size. We show that the solvent can affect the metal-ligand binding and consequently ligand coverage on the nanoparticles surface which has a strong effect on the growth rate and final size (1.4 nm in toluene and 4.3 nm in pyridine). The proposed kinetic model quantitatively predicts the effects of varying the metal concentration and ligand/metal ratio on nanoparticle size for our work and literature reports. More importantly, we demonstrate that the final size is exclusively determined by the nucleation and growth kinetics at early times and not how they change with time. Specifically, the nanoparticle size in this work and many literature reports can be predicted using a single, model independent kinetic descriptor, (growth-to-nucleation rate ratio)^1/3, despite the different metals and synthetic conditions. The proposed model and kinetic descriptor could serve as powerful tools for the design of colloidal nanoparticles with specific sizes.