8.7. Methods for the experimental determination of the binding constant

Understanding the molecular mechanisms and interactions that govern various processes and reactions in living systems is a central issue in molecular biology, biochemistry, medicine and in the new fields of proteomics and genomics. To reach this goal, it is indispensable to identify the interacting partners and characterise their interactions. A variety of techniques are available for screening and measuring protein-ligand interactions. Methods include affinity chromatography, cross-linking, gel filtration, co-localisation, two-hybrid methods, spectroscopic methods, 3D structure determination, equilibrium dialysis, radioactive labelling, sedimentation velocity measurements, isothermal titration calorimetry, surface plasmon resonance, microarray, immunoblotting and ELISA.

Below we discuss some of the frequently used methods. The radioimmunoassay (RIA) is suitable for the determination of the concentration of various antigens, hormones and drugs in different body fluids such as the human blood. During the experiment, a known amount of a radioactively-labelled antigen is mixed into the solution of its corresponding antibody. Usually, gamma-radiating isotopes such as tyrosine-bound iodine are used. Subsequently, the unlabeled (“cold”) antigen sample is added to the solution and the liberation of the labelled antigen is measured. The unlabelled material competes with the labelled one and may “chase it off” from the antibody, depending on the concentrations. The material bound in complex is separated from the free antigen. This is a technique with high sensitivity; however, the handling of radioactive material needs special care. Nowadays, the ELISA technique is more popular, which measures the antigen-antibody interactions by applying colour reactions.

In ELISA (enzyme-linked immunosorbent assay), the antigen is bound to a surface and then recognised by a specific antibody. Subsequently, a second antibody is applied that is specific to the first one and usually carries a covalently-bound enzyme molecule. By the addition of the substrate of the enzyme, a colourful and/or fluorescent product will form. This way, the presence of the antigen—or even its concentration—can be determined. A more sophisticated variant of ELISA is the “sandwich” ELISA. In this case, a “capture” antibody is immobilised on the membrane to which the antigen binds in the second step. Then a second antibody is added that also binds the antigen but—similarly to the above procedure—it carries a covalently-bound enzyme. Thus a “sandwich” is being formed, and then detection is carried out by adding substrate. The sandwich ELISA is much more sensitive than the common ELISA technique. Pregnancy tests are usually based on this method.

In the following, we provide an introduction to modern methods for the detailed characterisation of protein-ligand interactions, including surface plasmon resonance (SPR), isothermal titration calorimetry and fluorescence depolarisation.

8.7.1. Surface plasmon resonance (SPR)

During a surface plasmon resonance experiment, one of the interacting partners is immobilised onto the surface of a chip and then a solution containing the other partner (analyte) is flown over the surface. The association and dissociation rate constants (kon and koff) can be determined in the system described in detail below. The instrument measures the material (mass) bound to the surface upon the binding reaction by a spectroscopic phenomenon, the surface plasmon resonance. The chip is a glass slide whose surface is covered by a thin layer of metal, usually gold. Over this surface, micro-flow channels are constructed, making possible the controlled flow of solutions containing the interacting partners over the surface. Usually, the golden layer is covered with one or more further layers (such as dextran) to ensure the immobilisation of one of the partners, which usually occurs via covalent linkage. After successful immobilisation, the other component is applied in the solution flowing over the surface and can bind to the immobilised partner on the surface, forming the complex. Figure 8.9 depicts an SPR system. The chip is placed on a prism. During the measurement, the chip is irradiated from the bottom with a beam of a wide angle range within that of total internal reflection. The beam is reflected from the glass surface holding the golden layer and projected onto a detector. It is a known physical phenomenon that, during total internal reflection, the incident electromagnetic wave penetrates to the other side by an intensity exponentially decreasing with distance. This is the so-called evanescent field, which is localised in the metal layer and a narrow range above it. Importantly, it is sensitive to the material bound to the surface. The incident light at a certain angle interacts with the free electrons in the metal layer and their electromagnetic field, exciting them, leading to the phenomenon of surface plasmon resonance. The light at the resonance angle will be absorbed, thus the intensity is decreased. The detector will determine the angle of the intensity decrease. Upon binding of any material to the surface, the local refractive index will change and, through the evanescent field, it will have an effect on the plasmon waves, which results in the shift of the resonance angle. This shift is linearly proportional to the amount (mass) of the material bound to the surface. Its value is given in angle change or, in the case of some SPR instruments, in resonance units (RU). 1 RU = 1 pg/mm2—in other words, it is a 1-pg mass deposited per 1-mm2 surface. An angle shift of 1 millidegree equals ~6 RU.

The method of surface plasmon resonance

Figure 8.9. The method of surface plasmon resonance

The kon association rate constant of binding can be determined by the kinetics of the SPR signal change. The koff dissociation constant can be measured after binding, by washing the surface with ligand-free buffer. The ratio of the two will give the KA equilibrium association constant i.e., the binding affinity, and through this, ΔG°. Figure 8.10 shows the steps of an SPR measurement.

Representation of an SPR measurement

Figure 8.10. Representation of an SPR measurement

During immobilisation, the ligand is usually bound to the surface of the chip. The covalent link is very stable and usually does not require the modification of the ligand before attachment. However, the ligand must contain some reactive groups (such as –NH2, –SH, –COOH), and its binding orientation is not well-defined. Most often, thiol and amino groups are used for immobilisation; however, the streptavidin-biotin linkage is also popular. First, the dextran surface is activated by modifying its carboxyl groups with N-hydroxysuccinimide (NHS) and 1-[3-(dimethylamino)propyl]-3-ethylcarbodiimid hydrochloride (EDC). Subsequently, the ligand can be linked to the surface in the required concentration. Finally, the remaining free reactive surface can be blocked by injecting ethanolamine. The advantage of the SPR technique is that it does not require the modification or labelling of the molecules of interest, keeping their properties unchanged. The binding kinetics can be followed in real time, and the parameters of the interaction can be determined. A further advantage of the method is that it requires a low amount of material. Moreover, the chip can be regenerated with the bound ligand and can be reused several times, enabling the measurement of different binding partners. The turbidity of the solution does not interfere with the measurement. Although the partners do not need to be modified or labelled for the SPR measurement, the immobilisation can interfere with the binding reaction by orienting the binding region towards the chip surface or if the immobilisation occurs through the same groups as those involved in ligand interaction. This disadvantage of the technique may be a serious issue in some cases. To avoid such a problem, a longer linker molecule can be used for immobilisation. Another problem might arise from the condition that the binding interaction occurs on a surface instead of the solution phase. In the case of strong binding or high concentration of immobilised molecules, the dissociated binding partners will be present in an increased local concentration and may rebind immediately after dissociation. In this case, an artificially increased binding affinity will be observed. In case of multiple binding sites, the interpretation of the results might become complicated. It is worth noting that molecules with sizes of Mw < 300-500 might be too small for a quantitative measurement.

8.7.2. Isothermal titration calorimetry (ITC)

Protein-ligand interactions can be measured by ITC in solution phase without the need of any immobilisation or modification. The number of binding sites, the equilibrium constant (Ka), and the thermodynamic parameters including enthalpy, free enthalpy, entropy and the partial specific heat capacity (ΔH, ΔG°, ΔS°, ΔCp) can be determined directly via the measurement of the reaction heat. (As far as the thermodynamic parameters are concerned, all other methods, such as the spectroscopic methods, are indirect: calculations are based on spectral or other differences between the complex and the free ligand.) In the ITC measurement, the turbidity and the absorption of the solution are indifferent. Another advantage of the technique is its cheap maintenance cost. The evaluation of the data is simple and computer-controlled. Compared to SPR, the disadvantage of ITC is that it needs a higher amount of material and, sometimes, solubility problems make it difficult to establish suitable experimental conditions.

The calorimeter has two cells: a reference and a sample cell. The reference cell is filled with water. The sample cell contains the protein or ligand solution, which is titrated stepwise with its binding partner through a computer-controlled injector. During the experiment, the reference cell is heated with a small power, which does not increase the temperature of the cell significantly during the measurement. The essence of the measurement is that the temperature of the sample cell is kept the same as that of the reference cell with high accuracy. For this purpose, a variable heating power should be introduced on the sample cell, driven by feedback depending on the studied reaction. In the absence of reaction, the sample cell needs to be heated with a power similar to that of the reference cell. In the case of an endothermic reaction that consumes heat, the sample cell needs to be heated with higher power than the reference. When the reaction is exothermic, less heating power is needed to keep the temperature constant. Small aliquots of the titrant are injected into the cell at defined time intervals, and the reaction heat is measured. The reaction heat is proportional to the bound fraction of the injected molecules. At the beginning, a larger fraction of is bound, whereas no binding occurs upon injection when the binding sites have become saturated at the end of the titration.

The measured heat will be:


where V0 is the cell volume, ΔHb is the enthalpy change corresponding to the binding of one mole of ligand, [M]t is the total macromolecule concentration in the cell, Ka is the association constant, and [L] is the free ligand concentration. In the case of multiple binding sites, the equation is summed up for all binding sites.

The accurate determination of concentration is of high importance in ITC. After subtracting the baseline (which is the heating power with no reaction), the areas under the observed peaks give the enthalpy changes that belong to the reactions occurring upon injection steps. Figure 8.11 shows a schematic representation of the calorimeter and a characteristic titration profile with its evaluation. It is very important to have the protein and the injected ligand exactly in the same buffer solution at identical pH to avoid a large dilution and ionisation enthalpy. To account for such effects, control measurements should be carried out by injecting buffer to buffer, titrant to buffer, and buffer to the protein solution. The measured enthalpy effects can be used for correction.

Schematic representation of the isothermal titration calorimeter and a characteristic titration experiment with its evaluation

Figure 8.11. Schematic representation of the isothermal titration calorimeter (left) and a characteristic titration experiment (upper right) with its evaluation (lower right)

The sensitivity of the ITC instrument is extremely high: heat changes in the range of 10-8 W can be measured. Association constants can be determined accurately in the range of Ka = 102 – 109 M-1.

8.7.3. Fluorescence depolarisation to characterise protein-ligand binding interactions

In fluorescence depolarisation (FD) experiments, the sample is excited by a plane-polarised light, and the polarisation level of the emitted light is measured by recording the intensity in two polarisation planes: one parallel to that of the exciting light and the other being perpendicular (see also Chapter 4). Polarisation is defined by the measured intensities in the parallel and perpendicular polarisation planes:


The level of polarisation is often expressed in the form of another related parameter, the anisotropy:


When a fluorescent group is oriented and rigid, i.e. not moving, the emitted light will be polarised. In case the group is moving and/or rotating, the polarisation level of the emitted light is decreased.

The absorption of light by a chromophore occurs extremely rapidly in the order of 10-15 second (femtosecond). In contrast, fluorescence emission is a substantially slower process in the order of 10-8 second (10 nanoseconds). When the sample is excited by a plane-polarised light, the movement and rotation during absorption is negligible. During the longer time necessary for emission, the molecules might move and rotate—making the emitted light more depolarised. Large molecules move slower in solution; thus, they emit more polarised light, while small molecules and rapidly rotating fluorophores show higher degree of depolarisation.

The size and shape of the molecular complex formed in a protein-ligand interaction is different from that of the individual partners. Therefore, their diffusion and mobility will also differ. The local mobility of a fluorophore can be altered inside a molecule upon complexation if the packing of their environment is changed or they participate in interactions. All of these conditions affect the level of depolarisation, which can be a measured easily and thus used for the characterisation of protein-ligand binding.

The fluorescent groups or probes applied in FD measurements might be natural inner chromophores such as tryptophan and tyrosine, NADH and FAD. Synthetic molecules can be used to label, modify or substitute amino acid residues. External fluorescent probes exhibit fluorescence upon binding to target molecules.

Fluorescence depolarisation can be measured in steady-state or time-resolved modes. In steady-state measurements, the fluorescence intensities are measured in the parallel and perpendicular polarisation planes at constant excitation. In time-resolved mode, the fluorescence lifetime or anisotropy decay is measured after excitation with a short pulse. This is an accurate measurement to determine the translation and rotation of fluorophores.

Fluorescence depolarisation is a simple and rapid technique to measure protein interactions in solution phase. Using inner fluorophores, we can measure without modification of the protein molecules; however, we often need to use fluorescent labelling, which needs circumspection because it might change the properties of the system and can interfere with ligand binding. Site-specific information can be obtained by linking the fluorescent label to an appropriate group of the molecule.