Turn On, Tune In, Turnover! Target Biology Impacts In Vivo Potency, Efficacy, and Clearance

1. Age vs. Target Turnover

It is well known that aging impacts drug dosing and responses (Tumer et al., 1992; Turnheim, 2003; Andres et al., 2019; Thürmann, 2020) (Table 1). The inevitable gradual decay of bodily function from adulthood to older age results in altered PK (Rowland and Tozer, 2011) but also PD characteristics. Age-related changes in drug uptake, distribution, metabolism, and elimination processes thus often necessitate adjustments relative to standard prescription dosages (Andres et al., 2019). Several age-elicited physiologic function modifications likewise contribute to this (Tumer et al., 1992). However, less is known regarding shifts in target/transduction, circuit, and system homeostatic properties that may also influence the pharmacological treatment outcome in older as compared with younger adults (Levy, 1998).

Studies using irreversible target inactivation strategies in the rat and mouse suggest that turnover rates for receptor proteins normally become slower with age across targets and tissues alike (the possible exception is hippocampal 5-HT1A sites) (Keck and Lakoski, 1996a, 2000), tentatively due to decreasing plasticity (e.g., (Dorszewska, 2013; Mateos-Aparicio and Rodriguez-Moreno, 2019) in older compared with young subjects (Table 1). Thus, for example, following the annihilation of dopamine D2 receptors (D2R), the recovery rate is roughly 70% slower in senescent/aged as compared with young and mature rats (Leff et al., 1984; Norman et al., 1987; Kula et al., 1992); likewise, recovery half-life of striatal D1 receptors (D1R) after EEDQ was approximately65% slower in senescent than in mature rats (Battaglia et al., 1988). In fact, the rat cerebral D1R and D2R appear to follow an almost identical log-linear correlation trajectory between age and turnover rate, with gradually slower rates from young to senescent animals (Fig. 4). Similar observations have also been reported from rat studies of α- and β-adrenoceptor subtypes in heart, lung, and brain tissue regions (Pitha et al., 1982; Zhou et al., 1984) and of 5-HT2 (Battaglia et al., 1987) and mouse GABAA receptors (Miller et al., 1991a) in different brain subregions. This is in accord with the key role of altered protein synthesis and degradation with age and senescence (Ryazanov and Nefsky, 2002) and may also be in line with a common, albeit not universal, increase in pharmacodynamic sensitivity seen in the elderly, which agrees with a lowering of k_deg and therefore a subsequent increase in in vivo potency EC₅₀ (in vivo EC₅₀ numerically lower) (Wanwimolruk and Levy, 1987; Bowie and Slattum, 2007; Trifiro and Spina, 2011). While changes in membrane receptor number and turnover thus represent an obvious underlying possibility here, modifications of intracellular transduction efficiency processes in old age may also contribute.

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Fig. 4

Age vs. dopamine D1 (filled triangles) and D2 (filled circles) receptor turnover in rat striatum expressed in log-linear plot of data from Table 1; joint (D1/D2) line correlation and corresponding coefficient (R²; inset) also shown.

Consequently, it might be further predicted that depending on the afflicted organ (or subregion thereof), PD alteration-dependent drug-dosing adjustments may be required for the optimization of therapeutic benefit in elderly patients. For example, the EC₅₀ for the benzodiazepine GABAA enhancing agent midazolam to induce sedation/hypnosis was reported to be at least 50% lower in elderly compared with younger individuals despite similar PK parameters in both groups (Jacobs et al., 1995; Albrecht et al., 1999), thus warranting a dose reduction. Although there may, of course, be a number of different explanations, it is interesting to note in this context the nearly three times slower turnover of the benzodiazepine GABAA receptors in brain tissue of older compared with younger mice (Table 1) (Miller et al., 1991a), a feature that if translatable may also contribute to the observations in humans. Obviously, the chain of ligand-induced events for any biologic response—from target and transduction processes, via circuit and tissue, to the whole-organism level—implicates multiple proteins. Thus, even if literature examples are sparse, it is highly likely that changes in protein turnover at one or more sites along the ligand–target response chain may underlie a requirement for age-adjusted drug dosing (either jointly or in the absence of concurrent PK alterations). For agents engaging multiple targets in their mechanism of action, the overall pharmacodynamic impact on function would be expected to vary in relation not only to the affinities for the sites in question but also to the corresponding relative target turnover rates, in turn, possibly leading to altered drug profile expressions in older compared with younger subjects. Within the context of drug research and development, it is therefore evident that consideration of age as a factor in the intended clinical treatment population may affect the projection from in vitro target data toward adequate (efficacious as well as safe) in vivo exposures for desired pharmacodynamic responses in humans. Since the fractional turnover rate k_deg of a target is a term in the in vivo potency EC₅₀ expression of both reversible and irreversible systems, it becomes evident how changes with size (body weight) in k_deg also impact in vivo EC₅₀.

Regrettably, very little turnover data are available for nonadults. However, intuitively, it seems likely that such states would be decidedly much more variable and dynamic across stages (embryonic, fetal, infant, child/adolescent) overall compared with adult and even aging conditions. Even if far more drugs are aimed at/used to treat adult (vs. nonadult) diseases and disorders, further detailed insights into the particular target dynamic properties of the nonadult periods remain important tasks for future study also from a drug developmental and treatment perspective.

2. Species and Tissues vs. Turnover

Any attempt to use target turnover information for drug response translation purposes inevitably needs to account for interspecies differences. While allometric predictions (for a review of allometry principles, see Boxenbaum, 1982; Boxenbaum and Ronfeld, 1983) of PK variables are commonly based on the correlation of body mass to metabolic rate (Kleiber’s law) (Kleiber, 1947), it is less clear how the translation of drug PD indices relates to species-dependent target turnover properties (Table 2). In this regard, it is notable that Swovick et al. (Swovick et al., 2018) found a negative correlation of median fractional turnover rate k_deg values for the global proteome with maximal lifespan (i.e., faster protein degradation with shorter lifespan) but not with the adult body mass of eight rodent species (approximately 20g ≥ approximately 20 kg). These authors also noticed that whereas there were clearcut species differences in the turnover across much of the proteome, turnover remained conserved for some proteins regardless of (rodent) species. Spector (Spector, 1974) further reported that there is a negative correlation between plasma protein turnover rates and animal longevity, including rodents, ruminants, and humans. The general applicability of these findings across target proteins and mammalian species remains to be established. Interestingly, and possibly concurring with the aforementioned (Spector, 1974; Swovick et al., 2018), the literature data for cerebral MAO-B protein turnover half-life (days) for five different mammalian species (Table 2) seemed to correlate better versus lifespan than versus adult body (or brain; not shown) mass (Fig. 5).

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Fig. 5

Brain MAO B turnover for five mammalian species (Table 1) vs. lifespan (left) and adult body mass (right), expressed in log–log diagrams [line correlations and corresponding coefficients (R²) shown as insets]. MAO B data were aken from references in Table 2; max lifespan potential data were taken from Boxenbaum (Boxenbaum, 1982) and AnAge [The Animal Aging & Longevity database (https://genomics.senescence.info/species/)].

Further, even though the very same target protein may be present in several different tissues throughout the body, turnover rates can vary significantly between locations, even within the same organ or tissue (Table 2). The half-life also varies between subcategories of receptor proteins responding to the same transmitter (e.g., 5-HT1B vs. 5-HT2A) (Table 2). Although data from the same laboratory comparing rates between different organ tissues are scarce, the turnover of rat α1-adrenoceptors was reported to be approximately three to four times slower in rat and rabbit brain than in submaxillary gland and spleen, respectively (McKernan and Campbell, 1982; Sladeczek and Bockaert, 1983; Hamilton and Reid, 1985). Similarly, the half-life of MAO-B in rat brain may be approximately two to four times slower than in liver, salivary glands, and small intestinal tissue (Goridis and Neff, 1971; Planz et al., 1972a,b). It is relevant in this context that whereas cell types in the body differ in their dividing pace, the turnover of central nervous system (CNS) neuronal cells is generally slow and sustained (Savage et al., 2007) although, depending on function, the cells express a wide range of rates across the various cell constituents (e.g., vesicular vs. receptor target proteins) (Dorrbaum et al., 2018). As a likely overarching principle, the functions of the specific target protein and dynamics of the associated complexes may determine the rate of turnover. Overall, data cited in the previous discussion are consistent with the observation that target half-lives in peripheral organs and tissues are often faster than in brain (Price et al., 2010), but also that turnover rates may vary among subregions and proteins within the brain and peripheral tissue (see Table 2 for examples). Notably, Price et al. (Price et al., 2010) point out that turnover rates as determined in vitro versus in vivo correlate poorly, possibly at least partly related to more rapid proliferation and less regulatory control in cultured cell lines compared to in a living organism. This further emphasizes the importance of knowledge of in vivo target turnover rates toward drug response predictions and translation efforts. Since the fractional turnover rate k_deg of a target is present in the in vivo potency EC₅₀ expression of both reversible and irreversible systems, it becomes evident from the compiled literature how species differences in k_deg also impact in vivo EC₅₀.

Most of the examples in Table 2 involve pharmacological challenge. It is, however, worth noting the correspondence to data obtained using the Leu-incorporation methodology (Planz et al., 1972b), arguing that the pharmacological perturbation per se may leave the turnover process relatively untouched.

3. Target Pool Turnover vs. Functional Recovery

For biologic responses to materialize, drugs or other ligands need to occupy molecular target proteins (e.g., GPCR, ion channels, enzymes, neurotransmitter transporters, polypeptides). However, there is a notable variation in the level of fractional occupancy (i.e., the proportion of targets occupied by a ligand) required for functional effect (Furchgott, 1966; Furchgott and Bursztyn, 1967; Grimwood and Hartig, 2009; Kenakin, 2016), and the level of receptor occupancy for a 50% response differs greatly for different agonists. What constitutes “adequate” occupancy not only differs between ligands and targets but may also vary across tissues for the same target and, depending on the type of downstream effector response assessed, even within the same tissue (Hoyer and Boddeke, 1993). In an open system context, occupancy is defined as in Table 3.

As most of the turnover data in Tables 1, 2, and 4 represent studies of agents acting at GPCRs, the discussion in the following section focuses on this therapeutically highly prevalent target class (Garland, 2013). The intrinsic activity or efficacy of a GPCR ligand describes its ability to trigger an intracellular transduction process via its target site (i.e., defining stimulus force) expressed relative to a defined full agonist (i.e., able to elicit 100% under the same experimental conditions) (Kenakin, 2013). For example, the neurotransmitter DA (by definition, a full D2 receptor agonist) and the full D2 agonist NPA (N-n-propyl-norapomorphine) inhibit cAMP generation—one of the G-protein-mediated, immediate transduction pathways linked to the site—to a much greater extent than do partial D2 agonists like, for example, aripiprazole (Jordan et al., 2007; Beaulieu and Gainetdinov, 2011). This outcome may be envisaged in terms of ligand-induced changes in conformational states as a result of target binding, whereby agonists prompt (intracellular) second messenger amplification cascades and onward signaling more effectively than partial agonists, and antagonists fail to do so at all (intrinsic activity/efficacy = zero). However, for full (high-efficacy) agonists, there is typically a nonlinear relationship between drug–target occupancy and effect on functional output, as low receptor occupancy levels (2–30%) may suffice to trigger adequate—even near-maximal—functional responding (Grimwood and Hartig, 2009; Kenakin, 2016). In this situation, a major proportion of available target sites therefore remain functional but temporarily idle/unoccupied, which reflects the high agonist sensitivity of the signaling pathway (a.k.a. receptor reserve or spare receptors) (Neubig et al., 2003; Kenakin, 2018). For comparison, low(er)-efficacy agonists require high levels of target binding to elicit biologic responses and are often unable to reach maximal functional responding even at target saturation in a defined assay system. Thus, the definition of efficacy for a drug along the agonist–antagonist spectrum is dynamic as it is expressly reliant on the size of the available receptor pool and transduction function (Charlton, 2009). Consequently, efficacy may differ markedly, for example, between tissues (receptor amounts) and responses measured, as well as alterations induced by disease states and chronic drug treatments. As ligand efficacy is thus in part system-dependent: any given agent may behave as a full agonist for one tissue or particular readout while showing up as a partial agonist under other conditions (Kenakin, 2013). The interrelation between drug properties and the number of receptor sites—and as a corollary, influences via target turnover (see eq. 4)—in any given situation is thus a central factor in determining response efficacy to an agent within a defined context.

From the previous discussion, it follows that to reasonably gauge target turnover using functional in vivo output, an understanding of ligand efficacy in the system in question is vital (Grimwood and Hartig, 2009; Kenakin, 2017). To account for this element, the linear transduction factor ρ [the signal or stimulus triggered in the cell by the ligand–target complex; also known as the conversion of a chemical (complex concentration) or electrical (voltage) signal via amplification and/or feedback to a measurable in vivo pharmacological response (blood pressure, heart rate)] is included to separate full and partial agonists from each other and describe the efficacy parameter E_max (Choe and Lee, 2017). Hence, the in vivo efficacy parameter of a ligand, defined as the maximum drug-induced response by an individual ligand (E_max for stimulatory systems of agonists and antagonists or I_max for inhibitory systems such as with inverse agonism), derived from eqs. 1 and 2, becomes

The in vivo efficacy parameter of ligand, E_max (or I_max if derived from inverse agonism), is the maximum obtainable response, composed of maximum complex concentration (RL_max) derived from k_syn/k_e(RL) and the transduction factor ρ (strength of the ligand–target complex RL_max to elicit a pharmacological response; see the previous discussion) (the in vivo efficacy parameter E_max is observed in response–time data; maximum ligand–target complex concentration in vivo RL_max may be measurable in certain instances, which allows prediction of the transduction parameter ρ from E_max/RL_max). Practically, E_max is the parameter obtained by fitting the Hill function (eq. 5, bottom line) to concentration–response or response–time data where E_max is equivalent to the maximal drug-induced response as the ligand concentration approaches infinity (Choe and Lee, 2017; Gabrielsson and Weiner, 2016). Equation 4 suggests that target synthesis k_syn and the degradation of ligand–target complex k_e(RL) contribute to the overall capacity of the system (Gabrielsson and Peletier, 2017) rather than the ligand–target binding parameters per se (k_on, k_off). The elimination rate of complex k_e(RL) is a shared parameter among in vivo potency, and efficacy parameters and hence connects these two pharmacological properties. A logistic expression of transduction ρ may, in some cases, be considered, provided supplementary information in vivo data are available and possible to access/extract.

The implications of the transduction (encompassing all steps involved in the conversion from a target–ligand complex concentration to a measurable pharmacological response in vivo) factor ρ are illustrated not only in a host of literature aimed at establishing the number of temporarily idle or “spare” receptors (a.k.a. receptor reserve) but also in some of the target inactivation–recovery studies cited in Table 4. In this regard, it was reported (Agneter et al., 1993; Pineda et al., 1997) that the recovery of α2-adrenoceptor function was significantly faster than the regain of actual target protein molecules. This is in line with the view that high-efficacy agonists may produce a regain of function already by occupying relatively few receptors; that is, even low receptor–agonist ligand (RL) complex concentrations may elicit an adequate level of functional responding (Grimwood and Hartig, 2009). For comparison, the return of target protein and functionality after inactivation of the DA transporter parallel each other (Rego et al., 1999). These latter observations agree with the high target binding required for functional responding in this target class (see the previous discussion) (Grimwood and Hartig, 2009).

A special case is when k_e(RL) is equal to zero, which means that there is no irreversible loss of the complex as such via k_e(RL). The ligand–target complex hence only functions as a storage pool and can only be split into its principal parts L and R via dissociation, controlled by k_off. The free target concentration at steady-state R_ss returns to its baseline value R₀ since routes of production and loss of target are governed by k_syn and k_deg, respectively (Gabrielsson and Peletier, 2017; Gabrielsson et al., 2018a). This is a situation that may be observed as functional adaptation or “fading” of the pharmacological response (i.e., tolerance). If suppression of the levels of the free target (e.g., antigen–antibody complexing) is the main goal and proportional to pharmacologic effect, it will only be accomplished during a certain amount of time until the target has returned to its baseline level and the effect vanished. It is possible that the natural behavior of such a system might reflect a disequilibrium between ligand, target, and complex rather than an example of functional adaptation. Almquist et al. (Almquist et al., 2018) demonstrated the correspondence between in vitro (functional assays) and in vivo properties (EC₅₀ by means of modeling) for a series of antilipolytic compounds (Fig. 6).

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Fig. 6

In vitro lipolysis negative logarithm of unbound in vivo potency (pEC₅₀) vs. unbound in vivo potency (pEC₅₀) data redrawn from Almquist et al. (2018). The gray dashed line (lower diagonal) represents the line of unity, and the red (upper diagonal) line represents the regression of all data. For all prediction models, both in vitro and in vivo potency are expressed on a logarithmic scale normalized to 1 molar (1M), according to pEC₅₀ = -log₁₀(EC₅₀/1M). Note the pEC₅₀ scale, meaning that compounds become more potent toward the upper right corner. The endogenous ligand nicotinic acid NiAc is specifically identified in the graph.

An approximate estimate of the complex kinetics k_e(RL) term is obtained by regressing the data in Fig. 6 of the negative logarithm of in vivo potency (Y-axis) versus the negative logarithm of binding dissociation constant (X-axis) and inserting estimates of k_deg (denoted k_out) from Almquist et al. (Almquist et al., 2018). Unfortunately, plasma protein–binding differences across compounds were not considered in vivo, which might potentially have improved the consistency between in vitro and in vivo, as was shown for a series of opioids (Kalvass et al., 2007) in mice. Similar in vitro and in vivo correlation data have also been collected for in vitro (K_i) and in vivo potency (EC₅₀) of benzodiazepines (Visser et al., 2003). These three examples illustrate good correlations between in vitro binding properties and in vivo potency EC₅₀ for reversible systems, provided k_off is greater than k_e(RL) and that k_deg-to-k_e(RL) in eq. 2 of in vivo potency EC₅₀ is a constant term across compounds.

Predictions of exposure levels for repeated dosing in animals in vivo are typically based on target in vitro IC₅₀/EC₅₀ data, with the aim to attain a specific multiple of exposure above the in vitro potency. However, the required duration of exposure needed for a therapeutic pharmacological response can vary significantly, a point generally that receives very little attention. In fact, it is often implicit that predicted exposure coverage requires 24 h/day for meaningful in vivo drug effects. Thus, based on the particular pharmacokinetic profile of a test compound, a dosing rate (often involving multiple daily doses) may be set to ensure constant drug exposure at a prespecified level of target engagement. However, if the target half-life exceeds the plasma half-life of the drug with irreversible action (e.g., proton-pump inhibitors), the duration of response will rather depend on de novo synthesis and half-life of the target protein. Conversely, if the target half-life is shorter than the plasma half-life of the drug, the duration of response will be determined primarily by the presence of the drug at the target (vide infra).

The conventional notion of 24 h/day exposure above a target concentration was recently challenged in the nicotinic acid (NiAc) treatment context (Kroon et al., 2017), emphasizing the importance of target biology integration with drug PK and PD features. Thus, these authors found that

an intermittent but not continuous NiAc dosing strategy, succeeded in retaining NiAc’s ability to lower plasma FFA and improve insulin sensitivity. Furthermore, a well-defined NiAc exposure, timed to feeding-periods, but not fasting-periods, profoundly improves the metabolic phenotype of this animal model.

The discontinuous NiAc dosing approach hence minimized tolerance to the drug effect and lessened the impact with regard to counterbalancing feedback processes. Indeed, by incorporating biologic properties such as turnover of the NiAc target and of insulin, Andersson et al. (Andersson et al., 2019) succeeded in modeling and quantifying the interwoven behavior of NiAc with free fatty acid (FFA) and insulin. The target turnover aspects, as previously described, are therefore also an example of a property to be considered within the multifaceted field of chronopharmacology (for a review, see Dallmann et al., 2014).

4. Pharmacological Effect and Target Turnover: Dependency on Baseline States

In a typical closed in vitro system situation, the experimental setup determines the (static) size of the target pool (e.g., native tissue or induced expression of a target in a select cell preparation); whether the readout is affinity only or a functional (e.g., receptor binding or the magnitude of a particular biosignal, respectively); and, needless to say, disconnected from fluctuations in drug/ligand exposure across time.

From a modeling point of view, two principally different states may thus be envisaged: (i) when the baseline target occupancy and effect in vitro is zero or negligible (resting) and (ii) when the baseline activity is higher than the absolute zero, either as a consequence of endogenous ligand tone because the target is constitutively active in the absence of ligand or when there is baseline variability due to unknown factors. Compared with in vitro–controlled system assays (typically in non-native tissue or cells), the open, thermodynamically determined in vivo situation confers many more options (variable receptor conformations, temperature changes, cell and tissue nutritional fluctuations) for stimulating the receptor baseline behavior. Thus, the situations described in (ii) are more likely to be the case in vivo.

Fig. 7 shows schematically the relationship between different maximum complex concentrations and the efficacy parameter E_max, (Fig. 7, A) and ligand concentration L and in vivo effect, free target concentration R, and ligand–target complex Fig. 7, B, solid blue line, solid red line, and dashed red line, respectively). The pharmacological effect response is a function of the baseline effect E₀ and the nonlinear E_max function, where the efficacy parameter E_max and potency EC₅₀ are model parameters (eq. 5).

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Fig. 7

(A) Efficacy parameter E_max vs. different maximum complex concentrations RL_max (eq. 4). Upper row left: Agonism: the steepness of the slope (ρ) is a correlate of the efficacy of the agonist ligand–target complex to generate a cellular response [i.e., (1) > (2) > (3)]. Assuming that (1) represents a full agonist, (2) and (3) depict partial agonists with a gradually lower efficacy. Upper row middle: Antagonism: the ligand–target complex has no intrinsic power to generate a cell response. Once bound to the target, the antagonist can, however, compete with and displace an endogenous agonist ligand from the target site (in turn, leading to a lower response; bottom middle plot). Upper row right: Inverse agonism: even in the absence of a drug–target complex, there may be a constitutive activity/cell signal. This activity diminishes upon increased amounts of inverse agonist ligand forming a complex with the available target. Similar to the classic agonist case described (upper row left), the steepness of the slope correlates with the relative efficacy of the inverse agonist ligand–target complex to alter the cellular response [(1) > (2) > (3)]. However, in contrast to the previous antagonist case, the inverse agonist ligand–target complex will weaken the baseline constitutive cell activity. NB!: Even though a neutral antagonist will not change a baseline target constitutive activity, it is able to counter the actions of classic as well as inverse agonist ligands, bringing both back to their corresponding baseline level. B,. log (ligand concentration L) vs. response. Bottom row left: Agonism: Log (ligand concentration L) vs. response is a saturable function (Model C in (Gabrielsson and Peletier, 2018; Gabrielsson et al., 2018a). With a transduction parameter ρ > 0, the response will increase from the baseline with increasing ligand concentrations; (1) represents a full agonist, (2) and (3) depict partial agonists with gradually lower efficacy. Bottom row middle: Antagonism: the endogenous agonist ligand is displaced by increasing concentrations of an antagonist drug ligand, thereby gradually reducing the baseline response (endogenous tone). The antagonist displacement of endogenous agonist ligand binding to target not only decreases the pharmacological response but also the concentration of free receptors available. Bottom row right: Inverse agonism: the constitutive activity of the target drops with more and more drug ligand bound to the target, forming an RL complex. L vs. RL is a nonlinear/saturable function that gives a declining, sigmoidal, L-vs.-response curve. Here, the transduction parameter ρ is < 0 and results in a progressively decremental response from the baseline as the concentration of ligand increases; (1) represents a full inverse agonist, (2) and (3) depict partial inverse agonists with a gradually lower efficacy.

We assume that the baseline effect E₀ is proportional to either an endogenous ligand–target interaction (at target baseline R₀) or a putative constitutive activity level expressed by the target in the absence of a ligand. In the former case (i.e., endogenous ligand–target interaction), the endogenous species may be readily displaced by a more potent drug ligand L. The efficacy parameter E_max is the absolute difference between the maximum drug- (or ligand-)induced effect response and the baseline effect E₀.

The in vivo efficacy parameter E_max is mathematically expressed as the product of maximum ligand complex RL_max (k_syn/k_e(RL)) and the transduction factor ρ (eq. 5) and will be ligand- and tissue-specific. Here, ρ is presented as a linear scalar, but may, in some instances, be a nonlinear expression, provided independent experimental data support that. The use of a nonlinear ρ term multiplied by a nonlinear expression of L_ss is challenging from a numerical (overparameterization of embedded expressions), conceptual (which parameter contributes to what), and translational (how are products/ratios of parameters scaled across species) point of view.

ρ is an additional parameter taking stimulus into account, which corresponds to transduction of RL_ss complex concentration into a pharmacological response (the relative ability of a ligand–target complex to trigger downstream transduction events; i.e., a parameter defining stimulus strength of the ligand); a full agonist has a ρ > > 0, which is greater than that of a partial agonist ρ > 0 or an antagonist where ρ = 0 (i.e., E_max = 0). Analogously, when the ligand–target complex activity is less than the natural constitutive tone of the “naked” target in the absence of a ligand (in the case of inverse agonism), there is an attenuation of the constitutive signal eq. 6 (Fig. 7, A) thus becomes to describe a maximum drug-induced response lower than the baseline activity E₀ (Fig. 7, A). The ρ is a conglomerate of multiple individual transduction processes (e.g., target signaling cascades, cellular and tissue environments, physiological amplification, dampening processes, feedback, etc.) (Cooper, 2000) across different organs, which may well be species/strain-, sex-, and disease-dependent. For an inverse agonist ligand, ρ, comprising all target-associated elements affecting the neuronal signal studied and conversion from a chemical or electrical signal to a pharmacologically measurable response, will change to a negative term in eq. 6 (I_max), which is analogous to E_max in eq. 5. Inverse agonists are therefore said to have negative intrinsic efficacy (i.e., the ability to decrease the activity of a constitutively active receptor). Such agents may display different degrees of negative intrinsic efficacy, resulting in strong and weak (partial) inverse agonists, analogous to classical agonist stimulatory intrinsic efficacy for full (strong) and partial (weaker) agonists (Costa and Herz, 1989; Berg and Clarke, 2018).

Whereas in vitro assays may quite easily be set up to discriminate pure antagonists from inverse agonist properties of drugs at various targets, it is decidedly more difficult to differentiate in the in vivo situation (Berg and Clarke, 2018). Currently, we are aware of only one drug that purports to derive its therapeutic efficacy from inverse agonism. The US Food and Drug Administration has recently approved pimavanserin as a 5-HT2A receptor inverse agonist to treat psychosis associated with Parkinson’s disease (Cummings et al., 2014). Whether this is indeed the true molecular mechanism of pimavanserin remains to be further investigated, as according to a recent review, constitutive activity at 5-HT2A receptor sites may be rare in vivo (De Deurwaerdere et al., 2020).

5. Chronic Drug Treatments and Disease States vs. Turnover

Typically, the treatment of many physiologic perturbations and disease states requires repeat drug administration over shorter or longer time periods (Table 4). Although studies do not uncommonly report net changes in the target density following different periods of chronic dosing, there is relatively little data on the impact of repeated drug treatment—and withdrawal thereof—on the dynamics of target turnover rates k_syn and k_deg that underlie the changes in receptor numbers.

However, studies on D2R recovery following acute or more chronic depletion of endogenous DA, either by (6-hydroxydopamine–induced) denervation or repeated reserpine treatment, did find an acceleration of D2R reappearance (Leff et al., 1984; Neve et al., 1985), as might be expected for a compensatory process. Chronic monoamine depletion accompanying reserpine treatment likewise accelerated the return of cortical α2-adrenoceptors (Ribas et al., 2001). These reserpine-induced accelerations of turnover were reported to primarily reflect an increase in k_syn rather than a decrease in k_deg, and to result in an increased density of (high-affinity state) receptors. For comparison, chronic administration of the NA-selective reuptake-blocking antidepressant desipramine shortened the half-life of α2-adrenoceptors in rat brain tissue, mainly via increased k_deg, although alterations in k_syn were also noted (Barturen and Garcia-Sevilla, 1992). Similarly, repeat administration of the bipolar disorder medication lithium resulted in a significant reduction of α2-adrenoceptor half-life in the rat cortex (Carbonell et al., 2004), as did chronic MAO A inhibition by means of clorgyline (Ribas et al., 1993). Repeat electroconvulsive shock or citalopram treatment approximately doubled rat striatal D2R half-life, while limbic D2R turnover remained essentially unchanged (Nowak and Zak, 1991a). Repeat electroconvulsive shock treatment also enhanced striatal D1R turnover (Nowak and Zak, 1989) but did not modify the cortical α1-adrenoceptor half-life (Nowak and Zak, 1991b) in the rat. Estrogen is known to modulate central D2R, and chronic estradiol in female ovariectomized rats leads to a slowing of striatal D2R recovery (Levesque and Di Paolo, 1991). Interestingly, Kuhar and collaborators (Kuhar and Joyce, 200, 2003; Joyce et al., 2006; Kuhar, 2009) have also discussed in a series of papers the hypothesis that altered target turnover is an important contributor to the slow onset of the therapeutic as well as dependence-inducing actions of CNS-acting agents. Since the fractional turnover rate k_deg of a target is present in the in vivo potency EC₅₀ expression of both reversible and irreversible systems, it becomes evident from the compiled literature how chronic drug treatment and disease states changes k_deg also impacts in vivo EC₅₀.

6. Up- and Dowregulation of Target: Impact of k_syn, k_deg, and k_e(RL)

As previously discussed, repeat drug administration may result in pharmacological target up- or downregulation. However, although an up- or downregulation of target synthesis rate (turnover rate; k_syn) will impact the baseline level of the target (R₀) and therefore change the efficacy parameter E_max of ligand L at steady-state, it will not affect the potency, EC₅₀ (Table 5; eqs. 2 and 3). The explanation for this is that efficacy will be determined by the total concentration of receptors but also by the transduction parameter ρ (eq. 4), which refers to the ligand–target complex stimulus strength if different from endogenous agonists or baseline activity (R₀).

Different from closed system predictions (Stephenson, 1956; Black and Leff, 1983), the present deliberations demonstrate that in vivo potency is not affected by the target expression level (R₀) per se. Instead, it is contingent on a conglomerate of fractional turnover rates of target and complex; hence, potency (eq. 2) is a function of binding and degradation rates (k_deg, k_e(RL), k_off, and k_on). For comparison, efficacy is composed by ligand–target complex expression level (k_syn/k_e(RL)) and the transduction parameter (ρ). Thus, ligand–target binding properties (k_off and k_on) per se will not influence the efficacy parameter (E_max) in the open model. The relative impact of individual changes in the turnover parameters k_syn, k_deg, and k_e(RL), respectively, are shown in Table 5 and Fig. 8 (see eq. 2).

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Fig. 8

Schematic illustration of ligand concentration C-response relationships following changes in target turnover rate (k_syn), fractional target turnover rate (k_deg), or ligand–target complex (k_e(RL)). Note that only k_e(RL) impacts both in vivo potency and efficacy. Changes in k_syn shift intensity of the response and k_deg changes in vivo potency. If E_max is changed without any concomitant changes in baseline, it is most probably due to changes in either k_e(RL) or ρ. Baseline response E₀ is governed by target exposure k_syn/k_deg and target constitutive activity, whereas maximum ligand-induced response E_max by ρ k_syn/k_e(RL). Altered implies a new concentration–response relationship after a parameter change.

A corollary of these expressions and reasoning is that an increase in the fractional turnover rate of ligand–target complex (k_e(RL)) alone results in an increased ligand potency (i.e., the numerical EC₅₀ value decreases) and decreased efficacy (decrease in the efficacy parameter E_max). In other words, the compound is able to operate at lower concentrations but displays less efficacy, provided transduction (ρ) remains the same.

In addition to drug-induced processes, cancerous and miscellaneous inflammatory states have also been reported to change (mainly increase) the rate of protein turnover (for a review, see Biolo et al., 2003). Alterations in synthesis, as well as breakdown, have been described, the magnitude, distribution, and allocation of which also depend on the severity of the condition (Powell-Tuck et al., 1984; Fearon et al., 1988; Biolo et al., 2003). Myasthenia gravis, an autoimmune condition, appears associated primarily with an enhanced breakdown (k_deg↑) of the muscular ACh receptor protein (Appel et al., 1977; Sher and Clementi, 1984). For comparison, mice with the Ax¹ (ataxia) mutation display impaired GABAA receptor turnover, possibly associated with deficient protease activity [i.e., reduced degradation (k_deg↓)] of the receptors (Lappe-Siefke et al., 2009). Other examples of likely alterations in target k_syn and/or k_deg as a consequence of the disease and associated medications include Parkinson’s disease (i.e., increased levels of DA receptors, tolerance to levodopa treatment) (Antonini et al., 1997), delayed onset of antidepressant drug action in major depressive states (i.e., downregulation of 5-HT, NA autoreceptors) (Commons and Linnros, 2019), neuroleptic-induced motor and psychotic supersensitivity conditions (i.e., tardive dyskinesia, DA supersensitivity psychosis (Stahl, 2017; Thompson et al., 2020), and reversal of such alterations upon withdrawal from drug treatment.

Based on these and several other examples (Biolo et al., 2003), it appears reasonable to speculate that not only disease states but also numerous other less grave situations would be associated with alterations in the turnover of the whole or specific parts of the proteome, such as conditions including, for example, hormonal and nutritional state, day–night cycle, and various forms of stress (surgical, trauma, environmental, etc.), to mention a few (Richardson and Rose, 1971; Adam and Oswald, 1983; Biolo et al., 2003).

1. Case 1

If k_e(RL) is greater than k_off, the system behaves irreversibly, and in vivo potency EC₅₀ may be approximated by k_deg/k_on alone (see Fig. 9). K_d is still k_off/k_on, and therefore the relative magnitude of the EC₅₀-to-K_d (in vivo-to-in vitro) ratio is governed by k_deg/k_off as where k_deg represents the turnover of the target and k_off the dissociation rate constant of ligand–target binding. This implies an essentially irreversible system in which the fractional turnover rate of the target becomes more important for the level of the in vivo EC₅₀ than does the ligand-to-target affinity parameters per se. Examples of this situation are discussed further later in the text with proton pump inhibitors.

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Fig. 9

Schematic depiction of response [arbitrary units (a.u.)] vs. test compound concentration (a.u.) for situations along an irreversible/reversible ligand–target interaction scale. Shown are simulations of changes in ligand–target complex elimination k_e(RL) and the corresponding impact on in vivo potency EC₅₀. (1) Blue curve, right: A reversible system where k_e(RL) is much less than k_off. Potency EC₅₀ is approximately k_deg/k_e(RL) ⋅ K_d; off-rate k_off from ligand–target complex binding will be an important covariate. (2) Red curve, middle: k_e(RL) = k_off ; EC₅₀ corresponds to eq. 2. (3) Black curve, left: Irreversible in the sense that there is only an infinitesimal contribution of ligand regenerated from the ligand–target complex pool since k_e(RL) is much greater than k_off. Potency EC₅₀ is approximately k_deg/k_on; target turnover will again be an important covariate as in eq. 2.

2. Case 2

When k_e(RL) is smaller than k_off, the system behaves reversibly, and in vivo EC₅₀ is approximated by (k_deg/k_e(RL)) × K_d (Fig. 9). Hence, the relative magnitude of the EC₅₀-to-K_d ratio is then governed by k_deg/k_e(RL) where k_deg represents turnover of target and k_e(RL) loss of the (non-dissociated) target–ligand complex. If k_deg is smaller than k_e(RL), the in vivo EC₅₀ will be numerically lower (potency higher) than anticipated from the in vitro binding K_d. Therefore, converse to case 1, complex loss k_e(RL) plays a relatively greater role in the magnitude of in vivo-to-in vitro potency ratio than k_off. Hence, it is evident that the magnitude of the target turnover k_deg influences the relation between in vitro and in vivo potency in both cases and should not be ignored.

While the previous discussion clearly applies to most single therapeutic drug entities, how do you deal with the situation when a drug has an active metabolite or metabolites? A potential approach is to predict the active moiety of the parent and metabolite(s) at steady-state. For example, the M₃-muscarinic receptor antagonist tolterodine and its 5-OH-methyl metabolite have similar in vitro binding affinity (K_i 2.7 and 2.9 nM, respectively) at muscarinic receptors (Brynne et al., 1997; Nilvebrant et al., 1997). Therefore, Brynne et al. (Brynne et al., 1999) used the sum of the unbound concentrations of drug and metabolite at steady-state as the active moiety. The corresponding efficacious unbound plasma concentration of active moiety-to-K_i ratio will then be <0.1. Again, this is yet another example consistent with the finding (Jansson-Lofmark et al., 2020) that a multiple of in vitro potency greater than unity is not a compulsory requirement for an acceptable clinical effect.

The in vivo-to-in vitro ratio is influenced by k_deg and will be less than unity if the turnover of target k_deg is slower than either complex kinetics k_e(RL) or dissociation rate of the complex into ligand and target k_off for reversible and irreversible systems, respectively. However, recall that irrespective of the efficacious concentration C_u where a drug operates, the turnover of the target will impact the ratio, as EC₅₀ is an element comprising both drug and target properties (see eq. 7). Uncritical use of a ratio approach for ranking of drug candidates should thus be avoided unless a reasonable scientific foundation is at hand.

1. Irreversible Ligand–Enzyme Target Systems

Important but less common are situations with irreversible loss of the substrate–enzyme complex and irreversible binding of substrate to the enzyme in question so that no enzyme is regenerated from the substrate–enzyme complex after binding. Therefore, this permanent obliteration of the enzyme ]affects the associated biologic response until sufficient quantities of the enzyme protein have been produced again to restore functionality. The use of acetylcholinesterase (AChE) inhibitors such as poisonous nerve gases and similar agents with intended harmful effects are illustrative, including, for example, the recent incident with the organophosphorus chemical Novichok with potentially life-threatening consequences like convulsions, asphyxiation, and cardiac arrest (Greathouse et al., 2021; Steindl et al., 2021).

However, there are also multiple instances of irreversible enzyme inhibitors with important therapeutic uses. In addition to the COX-1 and PPI drug classes discussed previously (Singh et al., 2021) and associated text portions, penicillin is perhaps one of the most immediate examples that springs to mind. Penicillins act by covalently modifying the bacterial enzyme transpeptidase, thereby preventing the synthesis of bacterial cell walls and hence becomes bactericidal (Yocum et al., 1980). The dosing of such agents is, however, typically primarily based on in vitro estimates of minimum inhibitory concentrations for bacterial growth and a set ratio of (free) in vivo plasma exposures across time (e.g., area under the plasma concentration–time curve) versus the minimum inhibitory concentration level (Mouton et al., 2018). Regarding antibiotic therapies focus is still to use simple exposure metrices (area under the plasma concentration-time curve, C_max, etc.) as a replacement of a more meaningful PD metric related to the mechanism(s) of action. It would be interesting to know whether a dosing approach taking into account the turnover of the actual enzyme target (i.e., transpeptidase) would improve and refine the specificity and PK–PD modeling to the benefit of treatment protocols and downstream limiting antibiotic resistance development (Khan, 2016). A related example, this time with human cells, is cancer treatment where irreversible enzyme inhibitors (e.g., 5-fluorouracil) may block certain growth-critical enzymes in cancer cells and thus act oncolytic. While drug–tissue distribution and penetrance obviously are important factors for efficiency against different tumor varieties, perhaps studies of target turnover rates might also contribute to further optimize personalized PK–PD-based cytostatic medication regimens. Irreversible GABA transaminase inhibitors are used in the treatment of epilepsy (Ben-Menachem, 2011), and covalent unselective MAO inhibitors like phenelzine and tranylcypromine are still available as (licensed) options for affective disorder (Birkenhager et al., 2004). Similar to the aforementioned antimicrobial and antiviral cases, it remains an open question if taking target turnover into account in an extended PK–PD algorithm may help further optimize treatment schedules in these latter conditions.

In the global pharmacotherapeutic armamentarium, irreversible target ligands are relatively scarce but appear to have received renewed interest over the last decade—perhaps at least partly related to oncology indications (Bauer, 2015). The overarching issue with covalently bound agents has been the widespread view that they all carry increased safety and (on- and off-target) toxicity risks (Bauer, 2015). Nonetheless, several irreversibly acting ligands have provided therapeutically important advances in the treatment of a variety of human afflictions. Such agents include, for example, ASA, penicillin, rivastigmine, rasagiline, and a host of recent anticancer agent varieties. Furthermore, situations involving prolonged drug residence time (k_off) may be described as a pseudo-irreversible ligand–target interaction – thus, a variation of a strictly irreversible process where k_off and k_e(RL) operate in the same time domain.

As discussed by Bauer (Bauer, 2015), some of the pros with irreversible or pseudo-irreversible agents include less frequent dosing (convenience to the patient), the potential for lower doses (due to high and prolonged efficiency against competing endogenous ligands), and less off-target issues. Naturally, these advantages need to be balanced against the theoretical risk for idiosyncratic toxicity, as well as the toxicity inherent in the reactive ligand chemistry per se. However, the irreversible drug approach should not be a priori discarded without a thorough benefit/risk analysis, particularly if the drug ligand design may produce tissue/target-directed selectivity. However, Bauer unfortunately also concluded, based on closed system reasoning, that the k_inact/K_i metric for compound ranking is preferred over in vivo IC₅₀. As shown in eq. 8, a better metric would be k_deg/k_on for an irreversible system. Moreover, within the present context, it is worth noting that dependent on the desired clinical outcome versus indication, conditions involving targets with rapid turnover or requiring only short-lived or partial target response modification may be less accessible for irreversible ligand treatment (Bauer, 2015). That said, when both of these target aspects (rapid turnover, partial response) coexist, an irreversible ligand may still be an option to trigger a useful clinical response.

2. Reversible Ligand–Target Interactions

In the development of therapies to treat more or less severe excess gastric acid-induced afflictions (e.g., ulcus, reflux), the historical approach relied on drugs that interact with upstream targets influencing the acid secretion, such as, for example, antihistaminergic and anticholinergic agents. These medications may now be largely obsolete for the indications mentioned, as they have been replaced by compounds such as omeprazole, lansoprazole, and the like, the metabolites of which directly and irreversibly interact with the downstream H⁺/K⁺-ATPase-dependent pump in the gastric parietal cells, thereby inhibiting the final step of acid production (Wallmark et al., 1985).

In contrast with the irreversible proton pump inhibition resulting from omeprazole, as previously discussed, it may be illustrative to consider and compare with the fate of a reversible upstream treatment of the same indication. Thus, an example of reversible drug (cimetidine) interaction with an endogenous ligand (histamine) is the therapeutic effect of cimetidine mediated by the histamine H2 receptor modulating acid secretion in the stomach. Since the target protein is the same for both cimetidine and histamine, the differences in in vivo potency values are primarily due to ligand–target binding affinities of these two reversible agonists and not target turnover per se. For the open in vivo system (Peletier and Gabrielsson, 2018), the interaction model of two ligands acting on one target at equilibrium is given as where θ equals the ratio EC_{50,cimetidine}/EC_{50, Hist}. Therapeutic plasma concentrations (C_u = 0.8 µM at a steady-state corresponding to a daily dose of 1 g of cimetidine, taking human plasma protein binding into account (f_u = 0.2), correspond to its in vitro binding affinity (K_d = 0.79 µM). Therefore, substantially lower local concentrations of cimetidine (0.80 µM as compared to histamine 165 µM) will suffice for 50% acid reduction of the free target. Since the partial agonist cimetidine exhibits a very low efficacy parameter, it will behave like an antagonist in the presence of histamine. See also Lin (Lin, 1991) for review.

A reversible process removes the free target (R) temporarily by pushing the ligand–target complex equilibrium toward complex formation (Fig. 2). This process is typically saturable and therefore requires substantial exposures beyond the potency to be efficient. Accordingly, the response duration will depend on target turnover and the ligand half-life. To achieve less frequent dosing, a long half-life (12 hours for naproxen compared to 2 hours for ibuprofen) is thus favorable. The longer half-life of naproxen also allows time for more of the complex to be (irreversibly) removed as such. When free drug (ligand) levels then decline, equilibrium starts shifting back from complex toward free target and ligand. Thereby, as a consequence of diminished complex concentration, the response begins to decline. High exposures (multiples of the potency) of ligand are therefore typically needed to fully execute suppression of that free target and a buildup of complex to maintain a reversible drug action over longer periods of time. For example, the reversible inhibitory action by cimetidine upon gastric acid-secretion modulating H1 receptors requires high daily doses (approximately 1 g).

The reversible GSECR inhibitor (Table 6) has a plasma half-life of 2 hours in mice. Due to the shorter target half-life (20 minutes) of GSECR in mouse brain tissue, the experimental compound needs to be constantly present at substantial exposure for adequate inhibitory effect. Assuming a similar relation between drug and target half-life also in human results in a relatively large projected human daily dose (Gabrielsson and Weiner, 2016). Similar to the GSECR inhibitor, exposure is the rate-limiting factor also for the AChE inhibitor donepezil, but in this case, only low clinical doses (5–10 mg/day) are required (Doody et al., 2008). This may seem paradoxical but is explained by (i) the high bioavailability and low clearance of the latter (Lee et al., 2015) compared with the experimental GSECR inhibitor compound, which has a very short half-life, and (ii) the long target half-life of AChE versus the very short of GSECR (Table 6). That is, even if the GSECR inhibitor compound's half-life is approximately six times longer compared with its target (Table 6), a drug half-life of 2 hours is simply not sufficient to provide for low and convenient dosing within a reversible mode of target interaction where, instead, a continuous exposure would be required. In fact, even if the GSECR drug had been acting irreversibly with the same half-life, it would have been challenging to produce a very prolonged action given the rapid regeneration of its target. An interesting parallel is the pseudo-irreversible (slow k_off) AChE inhibitor rivastigmine, which, due to its mode of target interaction coupled with the slow target turnover, can be dosed in very low dosage (1.5–6 mg, twice daily) for clinical effect, despite a modest bioavailability (approximately 40%) and very short drug half-life (approximately 1 hour) (Jann, 2000). The previous examples again demonstrate the importance of integrating target- and drug-related (PK and PD) properties for optimization toward attaining clinically effective dosing regimens.

An irreversible process removes free target R permanently, and the newly synthesized target has to replenish the loss. This means that the duration of response will depend upon—and potentially benefit from—a long target half-life, which determines the time of return of target levels toward baseline. Therefore, a short ligand half-life does not exclude a long duration of response. An irreversible process, such as for PPIs, may also show a faster onset of action as the removal of the target is immediate. The irreversible PPI omeprazole requires low daily doses of 20 to 40 mg for effective and rapid reduction in acid secretion.

A special case of reversible or irreversible action is when the pharmacological response discloses synergistic mechanisms. Synergism may be seen with combinations of drugs or during monotherapy with agents carrying multiple mechanisms of action. An illustrative example of synergistic action in the same drug molecule on lipid metabolism is shown for the antilipolytic compound tesaglitazar (Oakes et al., 2005). The simultaneous reversible inhibition of fatty acid production (50% reduction of k_syn) and stimulation of plasma fatty acid loss (5.8-fold increase in k_deg) resulted in a dramatic synergistic (multiplicative) effect in Zucker rats after three weeks of treatment at a single-dose level. The authors concluded that thiazolidinediones ameliorate hypertriglyceridemia by lowering hepatic triglyceride production and augmenting triglyceride clearance. This highlights how a mechanism-based pharmacodynamic (open) model demonstrates its superiority over closed systems in analyzing and communicating complex pharmacodynamic processes. Similar results have also been obtained for other thiazolidinedione derivatives (Oakes et al., 2001). The assessment of drug interactions relevant to pharmacodynamic turnover models has been provided elsewhere (Gabrielsson and Weiner, 2000; Earp et al., 2004; Peletier and Gabrielsson, 2012).

To summarize, the drug efficacy parameter primarily impacts the onset and intensity, whereas potency impacts the onset and effect duration, particularly for irreversible reactions.

The examples discussed previously further emphasize the advantages of open versus closed system approaches. As shown by these cases, the inclusion of target (e.g., tissue) dynamics together with knowledge of ligand–target interaction characteristics and ligand pharmacokinetics further increases the precision in predictions of in vivo concentrations to elicit defined drug responses. Therefore, it is worth highlighting the need to assess each and every new drug candidate on a uniquely case-by-case basis, taking into account the turnover of its intended target, the type and characteristics of ligand–target interaction, and the clearance of the ligand itself. Only by doing so, improvements in the precision of projections to clinical properties and usage may be achieved.

1. Background and Pruning of Data

Interspecies scaling of pharmacodynamic PD properties aims at the quantitative prediction of parameters responsible for the onset, intensity, and duration of a pharmacological response in different species. Following mechanism-based modeling of biomarker data, results need to be verified by extended approaches to assess factors influencing target function. To our knowledge, few studies specifically anchor their kinetic–dynamic modeling efforts to encompass properties derived from target behavior per se (e.g., turnover). This makes modeling results less reliable, particularly for interspecies scaling of pharmacodynamic PD properties. Hence, not only the origin and quality of in vitro and/or in vivo data but also the methods for PD scaling have to be scrutinized.

The pharmacological response is typically expressed by means of the Hill-function including a baseline parameter (Eq. 5, bottom) E₀ (Danhof et al., 2007; Mager et al., 2009; Gabrielsson and Weiner, 2016; Choe and Lee, 2017). The baseline E₀ may be a single parameter (constant) or function (e.g., time or an endogenous ligand concentration). E₀ may be due to biologic variation such as diurnal oscillation, endogenous ligands, stress, disease, or potentially constitutive activity. E₀ is often a conglomerate of processes that, in sum, are displayed as a baseline response. Typical biomarker responses are blood pressure, heart rate, depression scores, body weight, body temperature, etc., which all originate from a baseline time course prior to drug administration. Two additional parameters, the in vivo potency EC₅₀ and the efficacy parameter E_max are defined in eqs. 2 to 5. One regresses the Hill function simultaneously to (two or more) response-time profiles, letting the plasma ligand concentration-time course drive the response and then simulate (with the final parameter estimates) the steady-state ligand concentration–response relationship. The efficacy parameter E_max (Choe and Lee, 2017) is the absolute distance between the maximum response and the baseline in a concentration–response plot. If RL_max is measured, it can be input as a constant and ρ as a model parameter to be estimated. If some of the target and binding properties k_deg, k_off, and k_on are known for a particular species (or humans), the k_e(RL) parameter can be estimated in the in vivo potency expression.

Prior to use for comparisons across species, any confounding covariates such as plasma protein binding, active or interactive metabolites, or endogenous agonists to a PK or PD parameter must be accounted for. As a first step, data pruning should be performed to make sure that systemic exposure (a.k.a. unbound plasma concentration) is used across species (Rolan, 1994; Benet and Hoener, 2002; Smith et al., 2010). Chronic indications and treatment imply PD and PK equilibrium between plasma and the target tissue. Under these conditions, the steady-state unbound plasma-to-unbound tissue/biophase concentration ratio will form a constant ratio. This ratio may be less than, greater than, or equal to unity but remains constant nevertheless; therefore, the unbound plasma concentration serves as a relevant proxy reference for the assessment of in vivo potency. Time-variant influences [e.g., as a consequence of (patho-)physiologic drift factors) on the biophase may include perfusion rate fluctuations, energy and protein turnover (Pich et al., 1987; Fearon et al., 1988), capillary permeability, transporters (Peletier and Gabrielsson, 2018), drug metabolism (Zanger and Schwab, 2013), disease progression (Holford and Nutt, 2008)] have to be incorporated into the prediction as complementary steps. The interplay between unbound plasma and tissue concentration is schematically illustrated for simple diffusion, active transport, clearance, etc. in Fig. 11.

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Fig. 11

Schematic illustration of unbound plasma concentration C_u and unbound tissue (target) concentration C_uT at steady state. Case A: Only different concentration diffusion of drug molecules is responsible for drug distribution between plasma and the target tissue. Hence, unbound concentrations in plasma are equal at steady-state. In vivo potency based on plasma or target tissue will be the same. Case B: Efflux transporters, clearance, irreversible binding, ionization (pH differences between plasma and tissue), or bulk flow are responsible for decreasing unbound concentration in the target tissue. Unbound concentrations in plasma are higher than unbound concentrations in tissue at steady-state. In vivo potency based on plasma is lower (numerically higher) than estimated from the target tissue. Case C: Uptake transporters or ionization favor increased unbound concentrations at the target tissue. Unbound concentrations in plasma are lower than unbound concentrations in tissue at steady-state. In vivo potency based on plasma is higher (numerically lower) than estimated from the target tissue.

Because the unbound plasma concentration is less influenced by species-dependent plasma protein binding differences, conversion from total to unbound plasma concentrations should be performed for each species. As previously discussed, the unbound plasma concentration is a proxy for the thermodynamically active exposure at the target biophase and hence indirectly drives pharmacological response at equilibrium. Unbound plasma concentrations represent both practical experimental measures (easily measured in all mammalian species, including humans) and may be used for translational purposes. Together with unbound clearance, the free drug concentrations determine the oral dose necessary for therapeutic effect and will be of importance for the assessment of safety data as well (Miida et al., 2008). In conditions with adequate knowledge of (peripherally located) targets and corresponding dysfunctional tissue, including the ability to sample actual tissue levels of the ligand, assessment of potency has to consider plasma-to-target tissue concentration differences (Kalvass et al., 2007). This situation has recently been addressed conceptually (Peletier and Gabrielsson, 2018).

The use of the equilibrium unbound drug concentration C_u in plasma coupled to a robust and meaningful PD biomarker is a good strategy for cross-compound comparisons and for developing kinetic–dynamic relationships, irrespective of reversible or irreversible mechanisms of action. An excellent review of drug concentration asymmetry in tissues versus plasma addresses this topic for small molecule-related modalities (Zhang et al., 2019). Additional information on how endogenous ligands (Kroon et al., 2017), active or interactive metabolites (Obach, 2013), and target expression in animals and humans (Simon et al., 2013) are applied may be helpful in cross-species pruning of data (Levy, 1998).

2. Concepts of Allometry

Let us briefly review how interspecies scaling is done and then give a few recent examples related to a mechanistic interpretation of modeling output with related problems and pitfalls. We start by focusing on the most commonly used approach: allometry. Allometry, in its broadest sense, describes how the characteristics of, for example, mammals change with size. Adolph (Adolph, 1949), Boxenbaum (Boxenbaum, 1982), Kleiber (Kleiber, 1947), and Schmidt-Nielsen (Schmidt-Nielsen, 1984) provide seminal background reviews. Allometric relationships are given as power functions as where Y is the physiological (e.g., blood flow), pharmacokinetic (e.g., clearance), or pharmacodynamic (rate constants in the in vivo potency or efficacy expressions) variable; BW is the body weight of the particular animal (or human); and a and b are allometric parameters. When scaling properties from animals (e.g., primate) to human, the allometric relationship between the two species becomes where the scaling factor is the body weight ratio human-to-primate raised to the allometric exponent b. Y_primate has to be the absolute parameter based on the total body weight and not normalized per kg. In the open model (eqs. 1, 2, and 5), we have the three important properties (k_deg, k_off, k_e(RL)) expressing in vivo potency, which guide the operating concentration range in many situations. As first-order rate constants, a practical approach is to use simple allometry (eqs. 13 and 14) or use independent (literature) data for interspecies predictions (Gabrielsson and Weiner, 2016; Gosset et al., 2017). The fractional rate constant k_deg of the target can be scaled according to where BW and b (b power law with a typical range of 0.1–0.3 for first-order rate constants) (Gabrielsson and Weiner, 2016) denote body weight and the allometric exponent, respectively. Scaling the apparent synthesis rate k_syn,human [with units amount/(volume · time)] of target is done by multiplying the target expression level in humans R_0,human by the scaled fractional rate constant of target k_deg:

If clearance of target Cl_trg,human and target expression level R_0,human are known, the corrected synthesis rate k_syn,human (with units amount/time) of the target becomes

Since parameters that require energy, such as organ blood flows, clearances, and synthesis rates, often follow the 3/4 power law, the corrected synthesis rate k_syn,human will also scale in a similar way. Hence, the target synthesis rate (amount/time) k_syn may be scaled from animal data according to where the allometric exponent falls in the range of 0.6 to 0.9 (3/4 power law see) (Adolph, 1949; Schmidt-Nielsen, 1984) and is similar to how clearance is predicted. For practical case studies and inter-species scaling concepts, see the textbook by Gabrielsson and Weiner (Gabrielsson and Weiner, 2016).

Physiologic time (e.g., half-lives) may be scaled by means of where the allometric exponent falls in the range of 0.2 to 0.3.

3. Literature Case Examples

The following list of interspecies scaling case examples is not intended to be exhaustive but nevertheless demonstrates some problems and solutions commonly encountered in the literature. Frequently, studies lack accounting for plasma protein–binding differences across compounds and species, resolving the contribution of active or interactive metabolites, incorporation of endogenous ligands, considerations of the link between the biomarker applied and the target function, and consolidating modeling results with independent literature data.

A recent report studied TNF_α turnover after a lipopolysaccharide (LPS) challenge, listing half-lives of the inflammatory marker TNF_α in mice, rats, and humans without reference to a specific target behavior (Larsson et al., 2021). The approach was a meta-analysis of several preclinical studies in rats comparing the anti-inflammatory activity of new compounds with roflumilast. Proper assessment of unbound plasma concentrations and active metabolites and a clear link to target function was however lacking.

Gosset et al. (Gosset et al., 2017) presented interesting data on fractional turnover rates k_deg (denoted k_out) as a function of size (body weight) of the core body temperature in mice, rats, and dogs upon intervention with PF-05105679, a moderately potent TRPM8 ion-channel blocker evaluated for the treatment of cold pain sensitivity. In this case, however, results were not validated by independent turnover data of the intended TRPM8 target, and the model also failed to account for feedback, a central mechanism in body temperature control.

In a retrospective analysis, Ito et al. (Ito et al., 1997) found a high correlation (r² = 0.961 and slope 1.038) between the unbound plasma concentration C_u and dissociation constant K_d of 19 benzodiazepines BZ when aiming at 40% to 60% occupancy at the GABA-BZ site in vivo. Visser et al. (Visser et al., 2003) compiled similar data between the EEG effects of nine prototypical GABA_A receptor modulators (six benzodiazepines, one imidazopyridine, one cyclopyrrolone, and one β-carboline) and their in vivo closed model receptor affinity. Again, no quantitative information was given about the target receptor beyond drug-receptor affinities in spite of available quantitative literature data (Borden et al., 1984; Lyons et al., 2000) that might otherwise have been used for consolidating the validity of modeling results.

In a seminal paper by Kalvass et al. (Kalvass et al., 2007) results of seven opioids were presented, with a high in vitro K_i to in vivo EC₅₀ correlation (r² = 0.995) when data were corrected for plasma protein binding differences across compounds and species. This suggests that the unbound plasma concentration C_u is a better predictor of PD response than total plasma concentrations. The authors discussed why in vivo EC₅₀ values correlated better with receptor binding K_i values than with EC₅₀ values obtained from in vitro ^[35S]GTPγS experiments. It should be noted that K_i measures affinity only, whereas in vitro ^[35S]GTPγS EC₅₀ (i.e., functional) values may be contaminated by other factors in a nonsteady-state cell system.

Acute dosing estimates of the total in vivo potencies corrected for plasma protein binding of dual G-protein-coupled receptor 81/109A (GPR81/GPR109A) agonists were compared with their in vitro binding data (Almquist et al., 2018). The analysis made no efforts to dissect in vitro/in vivo differences beyond general covariates such as anesthetics. It is not clear whether experiments with compound intervention also measured and modeled active metabolites and the endogenous ligand nicotinic acid (NiAc). Simultaneous fitting of all experiments, particularly based on unbound test compound concentrations, and allowing individual efficacy parameters (I_max) would have allowed a more mechanistic approach.

A turnover model capturing inactive and active proton pump pools was applied to acid secretion data in cannulated Heidenhain pouch dogs (Äbelö et al., 2000). It allowed the estimation of the fractional turnover rate used for the prediction of gastric acid secretion inhibition upon repeated human dosing. Rate constants were scaled allometrically but not related to independent experiments of the target, nor was the binding dissociation rate of the complex compared with the fractional turnover rate. The application of such reasoning might have been of importance for optimizing the ligand synthesis program.

In two seminal reviews, including interspecies scaling of pharmacodynamic data, the authors referred to binding properties based upon the closed system approach, keeping the total amount of target fixed to the baseline level (Danhof et al., 2007; Mager et al., 2009). Both reviews concluded that pharmacodynamic parameters such as potency and efficacy tend to be species independent. However, it is more likely that in vivo potency will demonstrate the opposite if system properties such as target turnover k_deg vary across different species (Betts et al., 2010; Gosset et al., 2017). Surprisingly, Danhof et al. (Danhof et al., 2007) state: “For drugs acting at extracellular targets, . . . binding to plasma proteins and other blood constituents can restrict distribution to the biophase,” which is contrary to the well-known fact that plasma protein binding does not restrict a compound from distributing to a target site. Unbound exposure of small molecules after oral dosing is governed by dosing rate and unbound clearance (Benet and Hoener, 2002).

Interspecies scaling of the efficacy parameter E_max is still a challenge since transduction, denoted by ρ, may vary depending on age, sex, tissue, species, etc. Transduction contains not only the conversion of a chemical or electrical signal in the cell to physiologic action but also the cascade of events leading to downstream gene-modified amplification and/or feedback control. For example, gene expression patterns in the ischemic penumbra differed strikingly between mice and rats at both 2 and 6 hours after permanent middle cerebral artery occlusion (Wu et al., 2022). The faster cessation of penumbral oxidative stress in preclinical animal models (Nilsson et al., 1990) as compared with humans (Benveniste et al., 1984; Bullock et al., 1995a; Bullock et al., 1995b) may be an important factor that differentiates clearcut therapeutic effects in small animals but lack thereof in humans. Adjustments for differences in physiologic time (species longevity differences) (Mestas and Hughes, 2004; Dutta and Sengupta, 2016) may be a starting point when designing future human stroke studies. Positive outcomes of 3 to 5 days dosing duration in, for example, the gerbil stroke model middle cerebral artery occlusion (100 g body weight), may correspond to 3 to 4 weeks (21 days using eq. 19) treatment in humans. To our knowledge, no stroke trials have specifically addressed physiologic time differences between animals and humans. A physiologic time difference of oxidative stress was unfortunately neglected also in clinical stroke trials of the radical scavenger NXY-059, which had demonstrated good neuroprotection in several animal models (Marshall et al., 2003). Obviously, multifaceted biomarkers (such as the size of the penumbra in this case) are consequences of a host of target interactions and distributional phenomena, thus not specifically mirroring a single target turnover but rather a cascade of events. Therefore, beyond scaling determinants of ligand–target complex expression (RL), such as target synthesis rate k_syn and complex removal k_e(RL), few attempts have been made to scale the transduction parameter ρ.

Kroon et al. (Kroon et al., 2017) formulated a dosing strategy based on PD findings of the highly intricate NiAc and plasma FFA interaction:

An intermittent but not continuous NiAc dosing strategy, succeeded in retaining NiAc’s ability to lower plasma FFA and improve insulin sensitivity. Furthermore, a well-defined NiAc exposure, timed to feeding-periods, but not fasting-periods, profoundly improves the metabolic phenotype of this animal model.

This was concluded by refining the design of in vivo experiments (Kroon et al., 2017) and mechanistic PKPD modeling (Andersson et al., 2019), which allowed the best timing of dosing and shaping of NiAc exposure to improve therapeutic value. The authors’ approach better captures what is necessary for understanding the onset, intensity, and duration of a therapeutic effect.

It appears unlikely that certain therapeutic areas, such as behavioral (CNS) effects can be reliably predicted from in vitro data per se. The symphony of interactions that impact turnover of the target systems involved (DA, 5-HT, Glu, etc.) may have entirely different time courses in vivo versus what may be predicted from on/off binding processes in vitro alone. It is also particularly challenging to generate in vitro disease models with sufficient validity for the purpose (e.g., cognitive behavioral cotreatment involved in studies of antidepressant actions of psychedelics in humans). Speculatively, a battery of in vivo behavioral (disease-related) models accompanied by robust biomarkers might be partially helpful (e.g., phenotypic drug screening approaches) (Waters et al., 2017). Overall, the mechanisms underlying psychiatric readout responses likely reflect a cascade of events through multiple circuit and target involvement greatly exceeding the duration of the initial drug–target interaction process per se. A seminal paper discussing some of the challenges in translational pharmacology was published by Green et al. (Green et al., 2011).

Human predictions of biomarker responses and PD properties from preclinical in vivo are instrumental when designing first-time-in-human studies. The aforementioned examples highlight specifically in vivo biomarker applications representing a specific target turnover, data pruning, mechanism-based PD models, and/or how interspecies predictions of PD properties are typically done. In this context, we foresee that interspecies scaling will be particularly important in pediatrics, frail elderly, or rare diseases (de Aguiar Vallim et al., 2017), where deviating target expression levels and/or turnover rates are likely to occur. Needless to say, while the target behavior-related modeling refinements represent a clear advancement in these aims, there is still room for further mechanistic enhancements.

The following are some general points to consider with respect to the interspecies scaling of PD data:

• Target knowledge (pathophysiological conditions, rare diseases, pediatrics, frail elderly)?

• Drug mechanism(s) of action?

• Is biomarker/disease marker applicable in humans (species-specificity of targets)?

• Does biomarker/disease marker capture target behavior?

• Quality of in vitro and in vivo preclinical data available (e.g., unbound concentrations and unbound target tissue-to-plasma concentration differences)?

• Is quantitative target information available?

• Is allometry applicable to a specific parameter or expression?

• Differences in physiologic time (species longevity differences)?

• Information about robust safety marker(s)?

• Use of the model as a knowledge repository, as predictions are never better than background data used for generating predictions (uncertainty range, sensitivity analysis, etc.)?

This section has addressed how target turnover properties will affect in vivo potency and efficacy and thereby predictions of therapeutically meaningful drug dosage. The new expression of in vivo potency will be a valuable tool in experimental pharmacology and translational and regulatory sciences. In the next section, the incorporation of turnover in drug elimination enzymatic systems, new properties of clearance, time to equilibrium, and steady-state solutions of substrate, the enzyme and complex will be discussed.