Competition Between Full and Partial Agonists

Why Competition Can Lower a Response

A partial agonist can activate a receptor, but it produces less response than a full agonist in the same system at sufficiently high concentrations. If both drugs compete for the same receptor population, increasing the partial agonist can displace some full agonist. The resulting response depends on both occupancy and efficacy: displacement lowers response only when the partial agonist’s contribution is less than the response it replaces.

The calculations below use a shared-receptor equilibrium model with an operational transducer. This makes the distinction between who occupies receptors and how strongly each occupied receptor contributes to response explicit. It also accounts for a nonlinear relationship between receptor stimulus and measured response.

The ratios \(x\) and \(y\) are dimensionless. A ligand’s concentration relative to its own \(K\) determines its contribution to occupancy: for example, \([A]=K_A\) gives \(x=1\). The two ligands need not have the same affinity; their concentrations enter the competition through separate ratios.

From Occupancy to Response

Let \(\tau_A\) and \(\tau_B\) denote the operational efficacy parameters of the two agonists in the system. They summarize ligand efficacy together with features of the receptor system, such as receptor abundance. For a partial agonist, \(0<\tau_B<\tau_A\) in the system being modeled. The combined stimulus \(S\) is the efficacy-weighted sum of the occupied fractions:

Assume the common operational transducer maps stimulus to response as \(E=E_0+E_{\max}S/(1+S)\), where \(E_0\) is the response with no agonist and \(E_{\max}\) is the system’s response scale. The normalized response above baseline is therefore \(S/(1+S)\). Because this mapping increases with \(S\), comparisons of responses can be made by comparing stimuli.

This response model is not the claim that response is always proportional to occupancy. A receptor system with amplification or reserve can respond nonlinearly to stimulus. If the response is known to be linear in stimulus over the range studied, a linear stimulus-to-response mapping may be more appropriate; the occupancy calculation remains the same, but the response calculation changes.

When Does Adding the Partial Agonist Reduce Response?

At a fixed full-agonist concentration, the stimulus with no partial agonist is \(S_A=\tau_Ax/(1+x)\). To determine what happens as \(y\) increases, differentiate the combined stimulus with respect to \(y\):

The denominator is positive, as is \(1+x\). Thus the sign of the derivative is the sign of \(\tau_B-S_A\). If \(S_A>\tau_B\), increasing partial-agonist concentration lowers stimulus and therefore lowers response. If \(S_A<\tau_B\), it raises stimulus and response. If \(S_A=\tau_B\), stimulus is unchanged as \(y\) varies. This result follows because the competing ligand shifts occupancy toward a ligand whose operational efficacy is either below or above the stimulus level it replaces.

As \(y\) becomes very large, nearly all receptors are occupied by \(B\), so \(S\) approaches \(\tau_B\) and the normalized response approaches \(\tau_B/(1+\tau_B)\). This limit does not mean that every addition of \(B\) must lower response: if the full agonist’s initial stimulus is below \(\tau_B\), the response rises toward the partial agonist’s single-ligand limit instead.

Solving for a Concentration That Gives a Target Response

The model can also be rearranged to find the partial-agonist concentration associated with a target response. First convert the target normalized response \(r\) to stimulus using \(S=r/(1-r)\). Then solve the stimulus equation for \(y\):

This solution is meaningful only if it gives \(y\geq 0\), and the target must be compatible with the range of stimulus attainable by varying \(B\) at the fixed \(A\) concentration. In particular, when \(S=\tau_B\), the rearrangement has a zero denominator: that stimulus is the limiting value as \(y\) grows without bound, unless the response is already constant at that value.

Assumptions, Diagnostics, and Alternatives

The calculations are useful only to the extent that the assumptions match the experiment. Equilibrium may be doubtful if the assay is read before binding has stabilized. The use of free concentrations may be inappropriate if ligand depletion is substantial. A single shared receptor population may be inadequate if the data show clearly distinct response phases or different binding behavior. These concerns call for checking the experimental design and model fit rather than treating a calculated occupancy as directly observed.

A practical diagnostic is to compare observed responses over a concentration matrix that varies both agonists. Systematic residual patterns across combinations of \([A]\) and \([B]\) can indicate that the shared transducer or binding assumptions are inadequate. It is also useful to compare the predicted limiting responses when either ligand is present alone with the observed single-ligand concentration-response data. A model that reproduces one agonist alone but consistently misses mixtures may have an incorrect efficacy-weighted competition structure.

The main alternatives differ in what they assume about response generation. A linear occupancy-response model makes response proportional to efficacy-weighted occupancy; it can be suitable over a range where transduction is approximately linear. The operational transducer used here allows a nonlinear response to stimulus. A simple sum of the two drugs’ responses is generally not an appropriate mixture calculation under shared-site competition, because the drugs cannot each occupy the same receptor at once. A competitive antagonist is a different limiting case: it has no activating efficacy in this model, whereas a partial agonist has \(\tau_B>0\).

A common mistake is to assume that a partial agonist must always lower response because it is less efficacious than a full agonist. That reasoning compares the ligands’ efficacy parameters but ignores the initial stimulus. The correct comparison at fixed \(A\) is \(S_A\) versus \(\tau_B\): adding \(B\) lowers response when \(S_A>\tau_B\), and raises it when \(S_A<\tau_B\). The phrase “partial agonist” describes its efficacy relative to the full agonist in the system; it does not determine the direction of every mixture response.