The concepts of stoichiometric and site binding constants

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The interaction between a monovalent ligand L and a multivalent receptor R involves the presence of various species, including the complex of R fully saturated with a number of ligands, and intermediate complexes of R partially saturated. This scenario can be described in terms of reaction schemes following two approaches:


  1. Based on equilibria between existing stoichiometric species (Stoichiometric approach).
  2. Based on equilibria between L and specific interaction sites of R (independent sites approach).
For a better understanding, let´s consider a particular case where L binds to a bivalent receptor:

1. Stoichiometric approach

This approach uses reaction schemes based on equilibria between stoichiometric species and yields stoichiometric binding constants. A model based on stoichiometric equilibria is valid to fit data of both independent and non-independent events and therefore, it is of wider applicability.

Here, the reaction scheme includes a first equilibrium between the free species and the intermediate RL and the second equilibrium between RL + L and RL2 (Fig. 1). The corresponding binding constants, K1 and K2, are denominated stoichiometric binding constants since they refer to equilibria between stoichiometric species.

2. Independent site approach

This approach uses a reaction scheme based on the binding of the ligand to individual sites present in the receptor and considering that all the sites are independent; thus, it supplies site binding constants.

In this case, the reaction scheme considers the presence of two sites in the bivalent receptor and two intermediate complexes (R, L and RL) formed when the ligand binds to s1 or s2 and consequently, the existence of a total of 4 equilibria (Fig. 2). The corresponding binding constants, Ks1, Ks2, Ks1s2 and Ks2s1, are denominated site binding constants since they refer to equilibria between L each specific site of R.

If you want to know more about how to get the stoichiometry (number of sites) and site binding constants with the independent sites approach you can click on the following button:


AFFINImeter binding models for Nuclear Magnetic Resonance

AFFINImeter is already well known in ITC binding data analysis for providing the possibility to use tailored binding models created by the user. The models are generated with the tool “model builder” that includes a letter code “M-A-B” to describe titrate (M), titrant (A) and if necessary, the presence of a third species (B) (Figure 1).


Fig.1 Example of a competitive binding model created in AFFINImeter where the titrant in syringe “A” binds to the titrate in cell “M” to form a 1:1 complex “MA” and a second ligand “B” mixed in the cell with “M” forms the complex “MB” and thus competes with “A”.


Following the same approach, the binding models available for the software AFFINImeter for Nuclear Magnetic Resonance are generated with the model builder and based on the “MAB” code. But there are significant differences between ITC and NMR data analysis when the time comes to select a binding model from AFFINImeter, which have an origin in the inherent characteristics of each technique and in the different experimental design. In chemical shift perturbation (CSP) NMR titration experiments, the observed parameter used to monitor the progress of the binding event is the chemical shift of titrate resonance signals. Hence, the models used for NMR data analysis require the presence of compound “M” (titrate) as it is the species from which changes associated with the binding process are monitored. Conversely, in ITC the observed parameter is the heat change upon interaction and this parameter is not necessarily linked to a particular species “M”, “A” or “B”.

An illustrative example is the evaluation of a monomer-dimer self-association process using NMR or ITC. In NMR, the standard experimental setup would consist in the incremental dilution of the compound sample at high concentration in the NMR tube, to monitor dimer dissociation (Figure 2a). In ITC the standard experimental setup would consist in a titration of the compound sample at high concentration in the syringe (species “A” according to the AFFINImeter code) into the calorimetric cell filled up with solvent (Figure 2b).


Fig.2 Representation of experimental setup for a) NMR dilution experiment and b) ITC dilution experiments. The corresponding schemes of AFFINImeter binding models for data analysis are shown.



Would you like to know more about AFFINImeter for Nuclear Magnetic Resonance? Press the button below:



The Model Builder is a versatile tool to translate binding interactions into mathematical models

The Model Builder is one of the novel features of AFFINImeter.  Through the model builder AFFINImeter offers an unlimited amount of thermodynamic models for ITC data analysis. The overall binding equilibria within the species involved in the experiments is easily drawn by the user directly in chemical language. Then AFFINImeter translates the resulting reaction scheme into robust  binding  models to be used to isotherm ITC simulation or to perform Isothermal Titration Calorimetry curve fitting.

The model builder is a versatile tool, it allows to design models involving up to three different species (i.e. the case of two ligands that compete with each other to bind a macromolecule) and has the advantage to selectively place them in the  syringe cell and/or in the calorimetric cell. 

Binding Reaction Scheme of a competitive interaction
Reaction Scheme of a Competitive Binding Interaction

It also allows the design of models for dissociation, ranging from simple homodimers to higher-order oligomers. During the model construction no mathematical equations are required, once the whole set of binding interactions is defined by the user in the reaction builder, AFFINImeter internally generates the system of equations that define the reaction scheme proposed. The new model (reaction scheme and equations) is saved  internally by AFFINImeter and listed in the user’s database so that can be utilized anytime so simulate or fit data.

AFFINImeter Reaction Builder
Competitive binding model builded with the AFFINImeter tool

AFFINImeter-ITC offers an exclusive unlimited amount of personalized model families including

  • Unrestricted Competitive Sequential Binding with no limitation in the stoichiometry of the binding model.
  • Competitive Multiple and Independent Sets of Identical and Independent Sites.
  • Dissociation of any chemical species including homogeneous n-mers, heterogeneous complexes and even micelles.

With this extensive offer of model families the user will be able to perform the thermodynamic characterization of a vast variety of biological and physicochemical processes from ITC measurements. A few examples of classical and new applications of ITC experiments that you can analyze with AFFINImeter are:

  • Protein-ligand or host-guest complex formation with unlimited stoichiometries
  • Competition of different molecules to occupy a given binding site even for high order complexes
  • Binding between ligands and polymers or large macromolecules with any number of (independent) sets and/or sites
  • Dissociation/aggregation of supramolecular heterogeneous species including protein oligomers
  • Structural and thermodynamic information of large aggregates, including micelles: aggregation number, enthalpy of formation, Gibbs energy and dilution heat of monomers and aggregates