The slope factor or Hill slope

If the labeled and unlabeled ligands compete for a single class of binding site, the competitive binding curve will have a shape determined by the law of mass action. In this case, the curve will descend from 90% specific binding to 10% specific binding over an 81-fold increase in the concentration of the unlabeled drug. More simply, virtually the entire curve will cover two log units (100-fold change in concentration).

To quantify the steepness of a competitive binding curve, fit the data to the built-in equation "Sigmoid dose-response (variable slope)". Prism will fit the top and bottom plateaus, the IC50, and the slope factor (also called Hill slope). A standard competitive binding curve that follows the law of mass action has a slope of -1.0. If the slope is shallower, the slope factor will be a negative fraction, perhaps -0.85 or -0.60.

The slope factor describes the steepness of a curve. In most situations, there is no way to interpret the value in terms of chemistry or biology. If the slope factor is far from 1.0, then the binding does not follow the law of mass action with a single site.

Some investigators transform the data to create a linear Hill plot. The slope of this plot equals the slope factor. There is no advantage to determining the Hill slope this way - it is more difficult and less accurate.

Explanations for shallow binding

Explanations for shallow binding curves include:

A well studied example of agonist binding is the interaction of agonists with receptors linked to G proteins. This is studied by comparing the competition of agonists with radiolabeled antagonist binding in the presence and absence of GTP (or its analogues). These experiments are done in membrane preparations to wash away endogenous GTP. Without added GTP, the competitive binding curves tend to be shallow. When GTP or an analog is added, the competitive binding curve is of normal steepness. This figure shows an idealized experiment.

The extended ternary complex model, shown in the figure below, can partially account for these findings (and others). In this model, receptors can exist in two states, R and R*. The R* state has a high affinity for agonist and preferentially associates with G proteins. Although some receptor may exist in the R* state in the absence of agonist, the binding of agonist fosters the transition from R to R* and thus promotes interaction of the receptor with G protein. The extended ternary complex model is shown on the right. Even this extended ternary complex model may be too simple, as it does not allow for receptors in the R state to interact with G. A cubic ternary complex model adds these additional equilibria. For details, see Kenakin, Pharmacologic Analysis of Drug-Receptor Interaction, 3rd edition, Lippincott-Raven, 1997.

The agonist binding curve is shallow (showing high and low affinity components) in the absence of GTP because some receptors interact with G proteins and others do not. The receptors that interact with G proteins bind agonist with high affinity, while those the receptors that don't interact with G proteins bind agonist with low affinity. Why don't all receptors bind to G proteins? The simplest answer is that there are fewer G proteins than receptors, but biochemical evidence disputes this idea. Other possible explanations include heterogeneous receptors and membrane compartmentation (so some receptors are sequestered from G proteins). For a review of these issues, see RR Neubig, Faseb J. 8:939-946, 1994.

If all the receptors could interact with G proteins, you'd expect to see an entirely high affinity binding curve in the absence of GTP. In the presence of GTP (or an analog) the HR*G complex is not stable, the G protein dissociates into its aGTP and bg subunits, and the receptor is uncoupled from G.  With GTP present, only a tiny fraction of receptors are coupled to G at any given time, so the agonist competition curves are of low affinity and normal steepness, as if only R was present and not RG.

Although the extended ternary complex model is very useful conceptually, it is not very useful when analyzing data. There are simply too many variables! The simpler ternary complex model shown in the middle of the figure has fewer variables, but still too many to reliably fit with nonlinear regression. For routine analyses, most investigators fit data to the much simpler two-state model shown on the left of the figure. This model allows for receptors to exist in two affinity states (R and RG), but does not allow conversion between R and RG. It is easy to fit data to this simpler model using a two-site competition curve model. Since we know the model is too simple, the high and low affinity dissociation constants derived from the model should be treated merely as empirical descriptions of the data, and not as true molecular equilibrium constants.