In the following, I will refer to the two interacting proteins A and B as analyte and ligand. Based on SPR terminology, the analyte describes the protein that is free in solution and available in varying concentrations. The ligand describes the protein that is available in limited and stable amounts and depending on the experimental method used, is sometimes fixed on a surface.
The information given in the following paragraphs has been mainly taken from [129], otherwise specified. The determination of the dissociation constant KD of an interac-tion between two proteins (often protein fragments) can be readily obtained if the con-centrations of the free proteins and the complex are known (see equation 4.1). In most experiments, the concentration of one protein in its free form is unknown necessitating titration experiments and data fitting for KD estimation. In titration experiments, the ligand is usually titrated with different analyte concentrations. Another possibility consists of titrating with constant analyte concentrations. Here, increases in analyte concentration are obtained by using the sample of the previous injection for the next injection. This latter approach, however, is less accurate because dilution of the ligand concentration after each injection has to be taken into account forKD determination.
For both approaches, a signal is recorded after each injection that is directly propor-tional to the concentration of the formed complex. The (relative) concentration of the complex can be plotted as a function of the total analyte concentration (see Figure 4.1 and 4.2 for logarithmic scale). This data can be fit to mathematical equations derived from chemico-biological models to obtain an estimation of the KD.
Signal that is proportional to concentration of formed complex
Total analyte concentration
Figure 4.1. Typical diagram obtained during experimental determination of binding affini-ties. Signals obtained at equilibrium for different analyte concentrations are displayed for three interactions of different binding strengths. Saturation in the binding signal for increasing analyte concentrations is necessary for reliable KD determination (figure has been modified from [130]).
Numerous methods exist that allowKDdetermination. Which of these methods is a good one to choose for a particular setting depends on the strength of the interaction in question and the sensitivity of the method. It appears that it is generally more difficult to reliably determine weak binding affinities between proteins as this
prereq-uisites high concentrations of ligands and/or analytes in order to observe a saturation.
Highly concentrated, monomeric protein samples are not always possible to obtain and often bear the risk to form (soluble) aggregates or to precipitate. In the follow-ing, I summarise the main characteristics of four methods for dissociation constant determination that have been extensively applied in domain–linear motif biology.
4.2.1. Isothermal titration calorimetry (ITC)
When two proteins form a complex, the free energy, enthalpy, and entropy of the sys-tem change (see equation 4.2), and these changes can be measured by highly sensitive calorimetry. Isothermal titration calorimetry (ITC) is special in comparison to other methods presented in this section because analyte concentrations have to be kept con-stant. The ligand is in solution in a calorimetric cell, and is titrated with consecutive injections of the same analyte concentration. The heat that is released (exothermic reaction) or absorbed (endothermic reaction) upon complex formation is measured.
The level of heat of reaction change directly depends on the concentration of free lig-and binding sites. Plotting the changes in heat versus the ratio of total analyte lig-and ligand concentration allows an estimation of the KD. ITC has several advantages:
both molecules are in solution, and in addition to the KD, the enthalpic and entropic contributions to the binding affinity can be directly determined.
4.2.2. Nuclear magnetic resonance (NMR)
The chemical environment of atoms that are part of the binding interface between two molecules change upon complex formation. These changes are visible in changes of chemical shifts that can be observed with NMR. The higher the concentration of one protein, the more complex formed, the stronger the chemical shift perturbations measured by NMR. Differences in chemical shifts for an atom can be plotted versus the varying total analyte concentrations to estimate the KD. As for ITC, NMR has the advantage that both proteins are in solution but what makes NMR a unique method is the potential to look at the responses of individual atoms upon binding, even allowing to detect site-specific binding constants [131]. In addition, NMR is well suited for determination of very weak binding affinities (e.g. KD >200µM). The disadvantage is that the ligand has to be highly concentrated in order to obtain significant signals, and thus, a high affinity KD (i.e. better than 20 µM) cannot be directly determined (but indirectly via competition experiments for example).
4.2.3. Fluorescence polarisation (FP)
In FP, the ligand is labelled with a fluorophore, e.g. a green fluorescent protein (GFP), and is titrated with varying unlabelled analyte concentrations. The fluorophore will emit light upon stimulation with light. If the incoming light is polarised, the emitted light will be to a certain degree polarised as well. The degree to which the emitted light will be polarised depends on the rotational diffusion rates of the ligand, to which the fluorophore had been attached. The rotational diffusion rate of a molecule depends
primarily on its molecular weight and shape. The smaller the molecule, the higher the rotational diffusion rate, the lower the fluorescence polarisation. If an analyte binds to the labelled ligand, it will increase the overall molecular weight of the ligand (that is now in complex) leading to a decrease of the rotational diffusion rate of the formed complex and thus, increase the degree of polarisation. The degree of polarisation light emitted can be plotted against the total analyte concentration allowing the determina-tion of theKD. FP has several advantages. The analyte and the ligand are in solution and signals can be obtained under steady state conditions or (more difficult) in real time allowing for the determination of kinetic constants.
4.2.4. Surface plasmon resonance (SPR)
In SPR, the detection principle is based on changes of the optical properties of a sur-face due to changes in the overall mass of proteins that are bound to it. The ligand is attached to a surface and the analyte is flowed at various concentrations over the surface. In contrast to FP and NMR, SPR does not allow to work with constant an-alyte concentrations for KD determination. Depending on the analyte concentration and its binding affinity, a certain amount of analyte will bind to the attached ligands leading to a change of the overall mass on the surface. This change is detected with laser light under total reflection conditions and is translated into response units (RUs).
One RU is equivalent to the binding of approximately 1 pg of protein per mm2 of the SPR chip surface. The time-course of SPR signals are displayed in sensorgrams (see Figure 4.2). The RUs obtained at steady state can be plotted as a function of the total analyte concentration allowing the determination of the KD. SPR has the advantage of measuring in real time providing the possibility to determine the kinetics of the interaction. Problems can appear when using higher concentrations of analytes (e.g.
>50µM) that may lead to experimental artefacts (e.g. through blocked flow channels or mass transport effects).
Significant improvements in data quality can be achieved when performing ”double referencing“ [132]. The first correction consists of substracting non-specific binding signals obtained from analyte injections on a reference surface on which a negative control ligand had been attached. A second correction can be performed by sub-stracting non-specific binding signals obtained from a blank injection (only buffer) that had been flowed over the surface [132]. These two corrections take into account the non-specific contributions to the signal of the analyte and the solvent that are flowed over a surface. Different modes of ligand attachment to the surface exist that can be distinguished into reversible attachments (e.g. via a glutathione S-transferase (GST)-antibody system) and non-reversible attachments (e.g. via a streptavidin-biotin system).
0 200 400
-20 0 20 40 60 80
RU
time in sec.
strong interaction
0 25 50
-20 0 20 40 60 80 time in sec.
weak interaction
0 25 50
-20 0 20 40 60 80 time in sec.
no interaction
0.00.1 0.20.5 1.02.0 5.0 10.018.0 19.030.0 μM
0 200 400 600
0.01 0.1 1 10 100 1000
Req
total analyte [C]
0 20 40 60
0.01 0.1 1 10
Req
total analyte [C]
RURU
sensorgrams saturation curves
0 20 40 60
0.01 0.1 1 10
Req
total analyte [C]
Figure 4.2. Sensorgrams and corresponding saturation curves obtained from SPR experi-ments. A sensorgram shows the development of the binding signal over time as determined with SPR. Three representative sensorgrams (left) and corresponding saturation curves (right) for a strong (1 µM range), weak (50 - 100µM range), and no interaction are shown. Different colours represent different concentrations of the analyte that have been injected (see legend to the right).
Ideally, for binding affinity determination, RUs are extracted for each run at equilibrium (horizontal signal course). In saturation curves (here with logarithmic x-axis), these RUs at equilibrium (Req) are plotted versus the total analyte concentration. KDdetermination is more reliable if saturation of the signal courses can be observed as it is the case for the first saturation plot.