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Section5:Special Circumstances
From Assay Guidance Wiki
High Affinity Competitors
For high affinity competitors, the assumption related to inhibitor depletion may not be met and an alternative analysis method can be used.
When the assay is designed properly, ligand depletion should not be a problem. However, once competitors reach an activity 2 to 3 fold lower than the ligand, inhibitor depletion can be an issue. Assuming that the hill slope for these compounds is near 1, the Ki computed using the Cheng-Prusoff equation could be compared to the Ki found by fitting the tightly bound inhibitor model below.
The ligand concentration [L] and the Kd are exactly those that would be used in the Cheng-Prusoff equation. The inhibitor concentration, [I]t, is the concentration tested. The Ki and receptor concentration [R]t are obtained by fitting the model. In order to use this model, the response determined by the plate reader, which measure the amount of receptor ligand complex [RL], must be converted to the same concentration units that are used for the ligand [L] and inhibitor [I]t. This requires the specific activity of the label and a plate reader that is calibrated well.
Even though the T-B model looks much more complex than the sigmoid curve model or the one site competition model in GraphPad Prism, both the fitted curve and the Ki are virtually identical unless a substantial portion of the inhibitor is bound. This can be seen in the graph of the radioligand binding results from an assay with Kd≈100 and ligand concentration of 4 nM that is shown below. The ratio of the Ki determined by Cheng-Prusoff to the Ki determined using the T-B model is plotted against the Ki determined by the T-B model. Inhibitor depletion will always result in understating the true potency of the molecule. Hence, the ratios are always greater than one. Also, the Ki values are virtually identical unless the Ki is much lower than the Kd.
Hill Slope Deviations
A standard competitive binding curve that follows the law of mass action will descend from 90% specific binding to 10% specific binding over an 81-fold range of unlabeled drug concentrations. The steepness of the competition curve is given by a slope factor, called the Hill Slope. This parameter is determined from a nonlinear regression analysis of the competition data when using a four-parameter logistic equation. A standard competition curve that meets all assumptions would have a Hill Slope of -1.0. If the slope factor deviates from 1.0 significantly, then the binding may not follow the law of mass action and you may be dealing with a receptor with more than a single class of binding sites, solubility issues or an assay artifact.
There is no adequate way to interpret the absolute value of the Hill Slope. However, there are several possible explanations when a competition curve has a calculated Hill Slope that is significantly less than 1 (shallow curve):
- Experimental problems such as improper serial dilution of the compound
- Curve fitting problems due to undefined top and bottom plateaus or too few data points
- Negative cooperativity - binding on one ligand molecule reduces affinity of other binding sites
- Heterogeneous receptors - different populations of receptors with different affinities
- Assay variability
Although the Hill Slope for a compound may not be -1.0, repetitive determinations for the same compound should yield similar Hill Slopes each time. If this is not the case, further optimization of the receptor binding assay may be required.
Some compounds being tested may not be soluble in the standard solvent, DMSO. In addition, compounds at high concentrations may not be soluble. Both of these cases can affect the shape of competition curves (i.e. Hill Slope, top or bottom plateau, etc.) and the calculated parameters. Therefore, it is important to review each competition curve for the following features:
- Specific binding descends from 90% to 10% over an 81-fold concentration range
- The Hill Slope is at or near -1.00
- Top and bottom plateaus have been appropriately defined
- Data points are evenly spaced along the entire range of concentrations tested
The example below demonstrates a compound tested in Diluent 1 and Diluent 2. In Diluent 2, the compound appears to have limited solubility and exhibits a very shallow Hill Slope and poorly defined top and bottom plateaus. In Diluent 1, the compound competes with the radioligand in the expected manner.
