Occupancy and quantification of receptor blockade

The main measure used to estimate the strength of an antagonist is the dissociation equilibrium constant K_d, also called the dissociation constant. This is the ratio between the rate constant of association and that of dissociation. It corresponds to the concentration that will occupy 50% of receptors at equilibrium.

D₂ occupancy in treating schizophrenia

Key in understanding treatment of schizophrenia are the concentrations (or doses) needed to reach sufficient levels of blockade of the D₂/D₃ receptors so that psychotic symptoms are controlled. The different stages of schizophrenia – first episode, chronic-relapsing and stable with maintenance treatment – require different levels of occupancy that result from different drug concentrations, which can be expressed as multiples of the dissociation constant K_d (Table 1). This might be the consequence of dopamine release increasing and decreasing in the course of the illness; other factors, such as changes in receptor numbers, would complicate the calculation.

TABLE 1 Clinical stage, required occupancy of D₂/D₃ dopamine receptors by antagonist antipsychotic, and concentration (or dose) expressed as multiples of the dissociation constant

P, the proportion of receptors occupied (receptor occupancy); [B], concentration of the drug; K_d, dissociation constant.

a The reference level of 1 gives an occupancy or P of 50%. Doubling the reference level blocks about 66% of the receptors, and trebling blocks about 75%.

Receptor occupancy and dose

The relationship between dose and receptor occupancy is determined by the affinity of the drug for the receptor and can be predicted over a wide range of doses by the ‘law of mass action’, according to an equation describing a rectangular hyperbola:

$${\rm P} = 100[ {\rm B} ] /( {{\rm K}_{\rm d} + [ {\rm B} ] } ) $$

where P is the proportion of receptors occupied; [B] is concentration of the drug; and K_d is the dissociation constant of the drug at that receptor (Lazareno Reference Lazareno and Birdsall1993). This signifies that when the concentration is the same as the K_d, the occupancy is 50%.

For efficacy in an acute relapse of schizophrenia in adults, occupancy of up to 80% of receptors is required (Farde Reference Farde, Nordstrom and Wiesel1992). This would correspond to a concentration up to four times the K_d (Table 1). Importantly, with older antipsychotics the onset of Parkinsonian side-effects in young adults has been shown to occur with occupancies above 80% (Table 1). Only 65% occupancy is observed in some patients in the long-term maintenance phase of schizophrenia (Ozawa Reference Ozawa, Bies and Pillai2019) and in people with a first episode (Kapur Reference Kapur, Zipursky and Jones2000).

Replacing concentrations with doses

In practice, the dose of an antipsychotic is known but the concentration is usually unknown. It is therefore helpful to know the dose of drug that will produce a concentration leading to 50% occupancy at steady state blood levels. We call that dose the DssOcc50 (the dose producing 50% occupancy at steady state blood levels), and it can be derived from positron emission tomography (PET) scans. Nyberg & Farde (Reference Nyberg and Farde2000) called this measure K_i, but to be unambiguous we use DssOcc50 here.

The formula above can use doses in place of concentrations, provided that the K_d value is substituted by DssOcc50. But there are complications in the relationship between dose and blood level (Box 1). These complications mean that the relationship between concentration and occupancy is more robust than that between dose and occupancy. The latter shows more variation between individuals due, for example, to genetic differences in drug metabolism or transport.

The formula tells us that the concentration or dose required to produce extrapyramidal side-effects is twice the dose needed to treat a first episode but not always higher than the dose needed for an acute relapse.

An additional complication is that a blood–brain barrier exists whereby drugs are extruded from the brain and the efficiency of this extrusion varies between drugs and with age, with corresponding differences in brain/plasma concentration ratios.

Example converting blood level from mg/ml to nM/L

The following data are from Mamo et al (Reference Mamo, Graff and Mizrahi2007).

The mean blood level on aripiprazole 10 mg/day was 126 ng/ml. Aripiprazole has a molar mass of 448.385 g/mol:

$$126/448.385 = 0.281\,\,{\rm nM/ml\ or\ }281\,\,{\rm nm/L} $$

The protein binding of aripiprazole is 99.36%, giving a free aripiprazole level of 0.64% or 1.8 nM/L

Understanding occupancy with combinations of drugs

The consequence (in terms of receptor occupancy, Occ) of combining two antipsychotics depends on the concentration (or dose) and the dissociation constants (K_d values) of the two drugs. The formulae are:

$${\rm \% \;Occ\;drug\;}1 = \displaystyle{{100[ {{\rm B}_1} ] } \over {[ {{\rm B}_1} ] + {\rm K_{d1}}\left({1 + {\rm \;}\displaystyle{{[ {{\rm B}_2} ] } \over {{\rm K_{d2}}}}} \right)}} $$

$${\rm \% \;Occ\;drug\;}2 = {\rm \;}\displaystyle{{100[ {{\rm B}_2} ] } \over {[ {{\rm B}_2} ] + {\rm K_{d2}}\left({1 + {\rm \;}\displaystyle{{[ {{\rm B}_1} ] } \over {{\rm K_{d1}}}}} \right)}} $$

where B₁ is the concentration of drug 1; B₂ the concentration of drug 2; K_d1 the dissociation constant of drug 1; and K_d2 the dissociation constant of drug 2 (Salahudeen Reference Salahudeen and Nishtala2017).

Using dopamine receptor affinity and occupancy to compare doses

The main laboratory measure used to estimate the strength of a receptor antagonist is the dissociation constant K_d introduced above and this is the concentration that will occupy 50% of those receptors at equilibrium.

Since clinicians seldom have access to blood levels of antipsychotics (and their interpretation would be complicated by protein binding) it would be more clinically useful to know the proportion of receptors occupied when the drug has reached a steady state level on regular dosing.

Substituting dose for concentration and assuming they are linearly related:

$${\rm P} = 100 \times {\rm dose}/( {{\rm DssOcc}50 + {\rm dose}} ) $$

where DssOcc50 is the dose producing 50% occupancy at steady state.

Published data from PET scans using ligands that bind to D₂/D₃ receptors (particularly [¹¹C]raclopride) provide values for DssOcc50 for several antipsychotics: amisulpride (Sparshatt Reference Sparshatt, Taylor and Patel2009), haloperidol and risperidone (Nyberg Reference Nyberg and Farde2000), aripiprazole (Sparshatt Reference Sparshatt, Taylor and Patel2010) and olanzapine (Bishara Reference Bishara, Olofinjana and Sparshatt2013). The doses shown are averaged and there is a two-fold range in the dose between individuals in the cases of risperidone, haloperidol and amisulpride (Table 2). A very high occupancy is reported for zuclopenthixol acetate (used to control severe agitation in psychosis), where the DssOcc50 is less than 12.5 mg and the maximum recommended dose is 400 mg over 3 days (Nyberg Reference Nyberg, Farde and Bartfai1995).

TABLE 2 Doses of antipsychotics producing 50% occupancy of D₂/D₃ receptors in positron emission tomography scans at steady state (DssOcc50) compared with lowest doses for maximum efficacy

ED95, 95% of the effective dose, defined as the lowest dose that produces the maximum effect.

Source: Leucht et al (Reference Leucht, Crippa and Siafis2020).

For efficacy in an acute relapse of schizophrenia, occupancy by D₂/D₃ antagonists of up to 80% of receptors is required (Farde Reference Farde, Nordstrom and Wiesel1992). This would correspond to a concentration four times the K_d or a dose four times the DssOcc50.

Leucht et al (Reference Leucht, Crippa and Siafis2020) presented graphs of dose–response relationships for a range of antipsychotics in acute schizophrenia, to compare their relative potency. Their preferred measure of potency is the ED95, 95% of the effective dose or ‘maximal effective dose’, defined as the lowest dose that produces the maximum effect.

Furthermore, examination of the ED95 values calculated by Leucht et al (Reference Leucht, Crippa and Siafis2020) shows that they are similar to four times the DssOcc50. Notably, aripiprazole is an exception (Table 2).

We can therefore substitute DssOcc50 for K_d in formulae (c) and (d) above, as shown in Box 2.

BOX 2 Formulae to determine receptor occupancy for two drugs in combination

$${\rm \% \;Occupancy\;by\;drug\;}1 = {\rm \;}\displaystyle{{100[ {{\rm Dose\;ofdrug\;}1} ] } \over {[ {{\rm Dose\;of\;drug\;}1} ] {\rm \;} + {\rm \;DssOcc}50( {{\rm drug\;}1} ) \left({1 + {\rm \;}\displaystyle{{[ {{\rm Dose\;of\;drug\;}2} ] } \over {{\rm DssOcc}50( {{\rm drug\;}2} ) }}} \right)}}$$

$${\rm \% \;Occupancy\;by\;drug\;}2 = {\rm \;}\displaystyle{{100[ {{\rm Dose\;of\;drug\;}2} ] } \over {[ {{\rm Dose\;of\;drug\;}2} ] {\rm \;} + {\rm \;DssOcc}50( {{\rm drug\;}2} ) \left({1 + {\rm \;}\displaystyle{{[ {{\rm Dose\;of\;drug\;}1} ] } \over {{\rm DssOcc}50( {{\rm drug\;}1} ) }}} \right)}}$$

where DssOcc50(drug1) is the dose of drug 1 producing 50% occupancy of D₂/D₃ receptors (seen in positron emission tomography scans) at steady state blood levels.

Other pharmacological mechanisms in antipsychotics

Many newer antipsychotics (e.g. olanzapine and risperidone) block serotonin at 5-HT_2A receptors and are thought to increase presynaptic dopamine release in motor areas of the basal ganglia (Dewey Reference Dewey, Smith and Logan1995). This is thought to contribute to the avoidance of extrapyramidal side-effects (EPSE). Such an increased release would require an increase in the concentration of drug to reach the level of D₂/D₃ receptor occupancy that would cause EPSE.

Antipsychotic effects can arise from mechanisms other than D₂/D₃ blockade – clozapine being a clear example involving other mechanisms.

Example: olanzapine combined with amisulpride

The COMBINE trial, a randomised controlled trial comparing olanzapine with amisulpride or a combination of the two in acutely ill people with schizophrenia, found that the combination of olanzapine and amisulpride brought greater improvement over 8 weeks than olanzapine alone, but not significantly greater than amisulpride alone (Schmidt-Kraepelin Reference Schmidt-Kraepelin, Feyerabend and Engelke2022). However, the authors noted higher dose equivalents in the combined treatment. The mean daily doses were olanzapine 14.1 mg, amisulpride 659 mg and the combination 14.4 mg olanzapine plus 567 mg amisulpride (Table 3). The equations imply occupancy levels of 80% for olanzapine alone, 81% for amisulpride alone and 88% for the combination. One possible explanation is that for some patients occupancy levels over 80% brought about greater improvement.

TABLE 3 Striatal dopamine D₂/D₃ occupancy in the COMBINE study (Schmidt-Kraepelin Reference Schmidt-Kraepelin, Feyerabend and Engelke2022) of olanzapine, amisulpride and their combination

DssOcc50, the dose that will produce a concentration leading to 50% occupancy at steady state blood levels.

Exploring the exceptional partial agonism of aripiprazole

Aripiprazole monotherapy

When a partial agonist occupies receptors it competes with the transmitter – to produce some blockade – but it has an important stimulating effect, which is also known as intrinsic activity.

Aripiprazole's intrinsic activity has been calculated to be about 25% (Cosi Reference Cosi, Carilla-Durand and Assié2006; Mace Reference Mace and Taylor2009). Therefore, to achieve 75% blockade, near complete (99%) receptor occupancy is necessary with aripiprazole. It should be emphasised that although intrinsic activity is a robust measure of individual receptor responses, differences can arise in whole tissues according to the number of receptors available and which second messenger is involved.

Interestingly, the maximum recommended clinical dose of 30 mg produces about 73% antagonistic occupancy or blockade (Table 4); this would avoid Parkinsonian side-effects and could be sufficient to treat a first episode of psychosis (Robinson Reference Robinson, Gallego and John2015; Pagsberg Reference Pagsberg, Jeppesen and Klauber2017).

TABLE 4 Doses of aripiprazole, total D₂/D₃ receptor occupancy and antagonistic occupancy based on P = 100[dose]/(DssOcc50 + [dose]), assuming DssOcc50 is 1 mg (Sparshatt Reference Sparshatt, Taylor and Patel2010)

P, the proportion of receptors occupied (receptor occupancy); DssOcc50, the dose that will produce a concentration leading to 50% occupancy at steady state blood levels.

However, it would not necessarily be sufficient to achieve remission in an acute relapse; there, the full antagonists amisulpride, risperidone and olanzapine have greater overall efficacy than aripiprazole (Huhn Reference Huhn, Nikolakopoulou and Schneider-Thoma2019). Aripiprazole has efficacy is preventing relapse in maintenance therapy of schizophrenia compared with placebo (Kane Reference Kane, Sanchez and Perry2012), but in a long-term study of effectiveness, aripiprazole was not as effective as most other antipsychotics for continuation or preventing re-admission to hospital (Zhao Reference Zhao, Lin, Teng, Khoo, Soh and Furukawa2016).