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.

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

We present a set of model-independent differential equations to analyze isothermal titration calorimetry (ITC) experiments. In contrast with previous approaches that begin with specific assumptions about the number of binding sites and the interactions among them (e.g., sequential, independent, cooperative), our derivation makes more general assumptions, such that a receptor with multiple sites for one type of ligand species (homotropic binding) can be studied with the same analytical expression. Our approach is based on the binding polynomial formalism, and the resulting analytical expressions can be extended to account for any number of binding sites and any type of binding interaction among them. We refer to the set of model-independent differential equations to study ITC experiments as a differential binding model (DBM). To demonstrate the flexibility of our DBM, we present the analytical expressions to study receptors with one or two binding sites. The DBM for a receptor with one site is equivalent to the Wiseman isotherm but with a more intuitive representation that depends on the binding polynomial and the dimensionless parameter c = K·MT, where K is the binding constant and MT the total receptor concentration. In addition, we show how to constrain the general DBM for a receptor with two sites to represent sequential, independent, or cooperative binding interactions between the sites. We use the sequential binding model to study the binding interaction between Gd(III) and citrate anions. In addition, we simulate calorimetry titrations of receptors with positive, negative, and noncooperative interactions between the two binding sites. Finally, we derive a DBM for titrations of receptors with n-independent binding sites.

Metal-chelating polymers by anionic ring-opening polymerization and their use in quantitative mass cytometry.

Metal-chelating polymers (MCPs) are important reagents for multiplexed immunoassays based on mass cytometry. The role of the polymer is to carry multiple copies of individual metal isotopes, typically as lanthanide ions, and to provide a reactive functionality for convenient attachment to a monoclonal antibody (mAb). For this application, the optimum combination of chain length, backbone structure, end group, pendant groups, and synthesis strategy has yet to be determined. Here we describe the synthesis of a new type of MCP based on anionic ring-opening polymerization of an activated cyclopropane (the diallyl ester of 1,1-cyclopropane dicarboxylic acid) using a combination of 2-furanmethanethiol and a phosphazene base as the initiator. This reaction takes place with rigorous control over molecular weight, yielding a polymer with a narrow molecular weight distribution, reactive pendant groups for introducing a metal chelator, and a functional end group with orthogonal reactivity for attaching the polymer to the mAbs. Following the ring-opening polymerization, a two-step transformation introduced diethylenetriaminepentaacetic acid (DTPA) chelating groups on each pendant group. The polymers were characterized by NMR, size exclusion chromatography (SEC), and thermogravimetric analysis (TGA). The binding properties toward Gd(3+) as a prototypical lanthanide (Ln) ion were also studied by isothermal titration calorimetry (ITC). Attachment to a mAb involves a Diels-Alder reaction of the terminal furan with a bismaleimide, followed by a Michael addition of a thiol on the mAb, generated by mild reduction of a disulfide bond in the hinge region. Polymer samples with a number average degree of polymerization of 35, with a binding capacity of 49.5 ± 6 Ln(3+) ions per chain, were loaded with 10 different types of Ln ions and conjugated to 10 different mAbs. A suite of metal-tagged Abs was tested by mass cytometry in a 10-plex single cell analysis of human adult peripheral blood, allowing us to quantify the antibody binding capacity of 10 different cell surface antigens associated with specific cell types.

Synthesis of a functional metal-chelating polymer and steps toward quantitative mass cytometry bioassays.

We describe the synthesis and characterization of metal-chelating polymers with a degree of polymerization of 67 and 79, high diethylenetriaminepentaacetic acid (DTPA) functionality, M(w)/M(n) ≤ 1.17, and a maleimide as an orthogonal functional group for conjugation to antibodies. The polymeric disulfide form of the DP(n) = 79 DTPA polymer was analyzed by thermogravimetric analysis to determine moisture and sodium-ion content and by isothermal titration calorimetry (ITC) to determine the Gd(3+) binding capacity. These results showed each chain binds 68 ± 7 Gd(3+) per chain. Secondary goat antimouse IgG was covalently labeled with the maleimide form of the DTPA polymer (DP(n) = 79) carrying (159)Tb. Conventional ICPMS analysis of this conjugate showed each antibody carried an average of 161 ± 4 (159)Tb atoms. This result was combined with the ITC result to show there are an average of 2.4 ± 0.3 polymer chains attached to each antibody. Eleven monoclonal primary antibodies were labeled with different lanthanide isotopes using the same labeling methodology. Single cell analysis of whole umbilical cord blood stained with a mixture of 11 metal-tagged antibodies was performed by mass cytometry.

ICP-MS-based multiplex profiling of glycoproteins using lectins conjugated to lanthanide-chelating polymers.

Lectins have been increasingly important in the study of glycoproteins. Here, we report a glycoprofiling method based on the covalent attachment of metal-chelating polymers to lectins for use in an ICP-MS-based assay. The labeled lectins are able to distinguish between glycoproteins covalently attached to a microtiter plate and their binding can be directly quantified by ICP-MS. Since each conjugate contains a different lanthanide, the assays can be conducted in a single or multiplex fashion, and may be readily elaborated to many different assay formats.

Poiquilodermia atrofica vascular / Poikiloderma vascularis atrophicans

Se presenta el caso de una paciente con poiquilodermia atrófica vascular, entidad infrecuente que puede asociarse a otras enfermedades sistémicas. Se comentan algunos aspectos clínicos e histológicos (AU)