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The K_d of a protein-protein interaction may be determined with Alpha assays using one of two approaches: saturation curves or competition assays. Of these, competition assays are applicable to a wider range of assay conditions.

Saturation curves for determination of Kd

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In limited situations, saturation curve assays can be performed to determine the affinity constant (Kd) for the protein-protein interaction in Alpha format. In a saturation assay, one binding protein is titrated across a range of concentrations to generate a saturation curve. The Kd can be derived from the data as the protein concentration at which half maximal signal is reached. Saturation curves can be used to determine Kd only if the assay meets the following criteria:

1. The Kd for the protein-protein interaction is far enough below the binding capacity of each bead so that all protein concentrations used to derive the Kd (usually up to 5X Kd) fall below the bead binding capacities. (This typically means that the Kd needs to be in the sub-nanomolar range, though some beads have a binding capacity up to ~300 nM – refer to Table below.)
2. There is an excess of the binding partner that will be varied in comparison to the concentration of the fixed binding partner. For example, if you are varying the concentration of Protein Y in the saturation curve, Protein Y should be in at least 10X excess (molar concentration) compared to Protein X. Otherwise, there is a ligand-depletion (protein-depletion), meaning that the percentage of “bound” protein can be above 10%. In this case, the amount of free ligand (protein) cannot be estimated as being equal to total ligand (protein) for the curve fitting equation.

If the expected Kd is not below the binding capacity of the beads used in the assay, a competition binding assay must be used to determine the Kd for the protein-protein interaction. The reason for this is that the bead system will become saturated when the binding capacity is reached, and two competing equilibria will be occurring: excess protein will be dissociating the interaction between the two beads, decreasing signal (the hooking effect), while the excess protein may simultaneously be driving the interaction between the two proteins, increasing signal. The curve generated will be a composite of these two equilibria, once the binding capacity has been reached. This composite curve may appear to reach saturation, may appear to begin to hook (decrease) slightly, or may continue increasing without reaching saturation (depending on the actual Kd, the concentrations of proteins being tested, and the binding capacities of the beads used in the assay).

Symptoms that a saturation curve cannot be used to accurately predict the Kd:

1. Underestimated Kd in Alpha assay. If the Alpha data is giving a Kd that is below what is expected for the protein-protein interaction, it is possible that bead saturation is skewing the data. A competition binding curve should be tested for Kd determination.
2. Kd is calculated to be ~5 nM when using streptavidin beads. Because the streptavidin-biotin interaction is a relatively tight interaction, the binding capacity of these beads is fairly predictable. If the calculated Kd is between 5 and 10 nM and streptavidin beads are being used, it is likely the binding capacity of the beads has been exceeded. A competition binding curve should be tested for determination of Kd.

Example data:
An excellent example of the use of saturation curves to determine Kd in an Alpha assay format is in a paper by Cassel et al. (2010). In this work, the Kd of the interaction between TAR DNA binding protein 43 (TDP-43) and biotinylated single-stranded TAR DNA and 6 TG repeats was determined to be 0.75 nM and 0.63 nM, respectively. Association and dissociation rates were also calculated and used to derive Kd values. In both cases, the Kd derived was consistent with previous reports using other methods.

In the example below, saturation curves were used to determine the Kd for the interaction between biotin-murine EGF and Fc-fusion human EGFR (Figure 1). Streptavidin Donor beads and Protein A AlphaLISA Acceptor beads were used in the assay. The expected Kd is ~2.8 nM as determined by a radioligand binding assay (Lax, I. et al., 1988). In the protocol for the data below, a 3-step assay was performed as follows. 1) biotinylated EGF and EGFR-Fc addition, 60 minute incubation. 2) Protein A AlphaLISA Acceptor bead addition, 60 minute incubation. 3) Streptavidin Donor bead addition, 30 minute incubation followed by reading the plate. The streptavidin Donor beads were added last (after the second incubation) to prevent the multi-biotinylated EGF from bridging two streptavidin Donor beads before other interactions could occur.

Figure 1. Saturation curve used to determine Kd of the interaction between biotinylated EGF and EGFR-Fc in Alpha format. View full protocol here. The expected Kd for this interaction is ~2.8 nM. This approach is generally suitable for low (sub-nanomolar) Kd values.

Example data where Kd cannot be determined by a saturation curve: In the data below, the expected Kd of the interaction between HDM2 and p53 peptide is ~ 0.3 μM. This is well above the expected binding capacity of the beads used in the Alpha assay, which is an indication that the saturation method should not be used to determine Kd; instead, a competition binding assay should be used. Based on the data below, the Kd would be incorrectly derived to be ~ 2 nM. (10 nM biotinylated-p53 peptide was used in the assay.)

Figure 2. Saturation curve for interaction between GST-HDM2 and biotinylated p53. The expected Kd for this interaction is ~ 0.3 μM (reference). Because the expected Kd is above the estimated binding capacity of the anti-GST-coated Acceptor beads and the streptavidin-coated Donor beads, a saturation curve should not be used to determine Kd.

When performing a saturation curve to derive Kd, it is important to choose protein concentrations above, below, and centered around the expected Kd. If possible, at least eight protein concentrations should be chosen, ranging from 10X Kd to 0.1X Kd. The concentration of only one binding partner (protein) should be varied – the other protein should be held at a constant concentration that is below the binding capacity of its associating bead and at least 10X below the highest concentration of the varied protein.

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Competition binding assays for determination of Kd

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In many cases, a competition binding assay will need to be used to determine the Kd in Alpha format. This is because many protein-protein interactions have dissociation constants that are above the binding capacity of the beads. In the competitive binding assay, increasing concentrations of the untagged version of Protein X or Protein Y are used to displace the tagged reagent from the assay, disrupting the association between the beads (competition). The Kd value can then be calculated from the IC₅₀ value based on a method introduced by Cheng and Prusoff:

Cheng-Prusoff equation
The information above is written from the point-of-view of a receptor-radioligand binding assay. In an Alpha protein-protein interaction assay, the “target” becomes one of the tagged proteins being caught to the bead, and the “tracer” becomes the second tagged protein binding to the other bead. If the Kd is significantly higher than the concentration of either protein, the value for [L]/Kd in the Cheng & Prusoff equation approaches zero. The full equation then becomes Kd = IC₅₀/(1+0), and the Kd approximates the IC₅₀ in the competition binding assay.

In order to derive a Kd in this type of assay, a few criteria need to be met:

1. The Kd needs to be at least 10X higher than the concentration of either tagged protein used in the optimized assay. These protein concentrations should be chosen from the first cross-titration experiment, keeping in mind that it is not necessary to pick the concentrations that give the highest signal-to-background. As long as the assay window is acceptable, lower concentrations may be chosen.
2. The concentrations of each tagged protein used in the assay need to be below the binding capacity of their respective bead (refer to Table below for guidance).
3. The concentration of one labeled protein (“target”) should be at least 10X below the concentration of the other labeled protein (“tracer”). If you are using tagged Protein Y, untagged Protein Y, and tagged Protein X in the competition assay, tagged Protein X is the target and tagged Protein Y is the tracer.

Essentially, a displacement assay will be used. However, it will be important to choose concentrations of the untagged protein that are centered around the expected Kd, in order to derive an accurate IC₅₀. Ideally, a range of concentrations of untagged protein ranging from 0.01X to 100X the Kd would be used. If the expected Kd is not known, it may be necessary to perform two experiments – one using a very broad range of untagged protein concentrations, then once this data has been evaluated, a second experiment can be set up using a narrower concentration of untagged protein. Additionally, it is advisable to test the assay with two or more different concentrations of tagged proteins (that still adhere to the two criteria above) to see if the IC₅₀ changes significantly, depending on the tagged protein concentration. If the IC₅₀ does vary dramatically between the two concentrations tested, it is likely the lower concentration is more accurate – the assay may need to be re-run with still lower concentrations of tagged protein.

Sample data:

Figure 3. Competition binding assay to determine Kd for a biotinylated murine EGF/human EGFR-Fc protein-protein interaction. Streptavidin Donor beads and Protein A AlphaLISA Acceptor beads were used in this assay. Untagged EGF was titrated from 0.1 pM to 1 μM. The expected Kd is ~2.8 nM as determined by a radioligand binding assay (Lax, I. et al. 1988). Based on the data, the calculated IC₅₀ is 2.4 nM. View protocol for assay here.
Figure 4. Competition binding assay to determine Kd for a biotinylated p53/GST-HDM2 protein-protein interaction. Streptavidin Donor beads and anti-GST AlphaScreen Acceptor beads were used in this assay. A few concentrations of tagged protein (GST-HDM2) were tested, and the IC₅₀ values derived were fairly consistent. Untagged p53 was titrated from 30 nM to 100 μM. Concentration of biotinylated p53 used in the assay was 10 nM. The expected Kd for this interaction is ~ 0.3 μM (Dawson, R. et al., 2003). Compare to Figure 2, where data derived from a saturation curve erroneously gave a Kd of ~2 nM.

An excellent example of the use competition binding curves to determine affinity in an Alpha assay format is in a paper by Lazar et al., (2006). The IC₅₀ of the interaction between three Fc variant antibodies and Fcgamma receptor was determined to be 380 nM, 60.3 nM, and 7.94 nM, respectively. These IC₅₀s were in close agreement with SPR (surface plasmon resonance)-derived Kd values (252 nM, 30 nM, and 2 nM, respectively).

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Table

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