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

—— Even though signiﬁcant efforts have been spent in recent years to understand and deﬁne the determinants of in vivo potency and clearance, important pieces of information are still lacking. By introducing target turnover into the reasoning, we open up to further the understanding of central factors important to the optimization of translational dose–concentration–response predictions. We describe (i) new (open model) expressions of the in vivo potency and efﬁcacy parameters, which embody target turnover, binding, and complex kinetics, also capturing full, partial, and inverse agonism and antagonism; (ii) a detailed examination of open models to show what potency and efﬁcacy parameters have in common and how they differ; and (iii) a comprehensive literature review showing that target turnover rate varies with age, species, tissue/subregion, treatment, disease state, hormonal and nutritional state, and day–night cycle. The new open model expression, which integrates system and drug properties, shows the following. Fractional turnover rates rather than the absolute target or ligand–target complex expression determine necessary drug exposure via in vivo potency. Absolute ligand–target expression determines the need of a drug, based on the transduction q and in vivo efﬁcacy parameters. The free enzyme concentration determines clearance and maximum metabolic rate. The fractional turnover rate determines time to equilibrium between substrate, free enzyme, and complex.The properties of substrate, target, and the complex demonstrate non-saturable metabolic behavior at equilibrium. Nonlinear processes, previously referred to as capacity-and time-dependent kinetics, may occasionally have been disequilibria. Finally, the open model may pinpoint why some subjects differ in their demand of drug. Signiﬁcance statement—— Understanding the target turnover is a central tenet in many translational dose–concentration–response predictions. New open model expressions of in vivo potency, efﬁcacy parameter, and clearance are derived and anchored onto a comprehensive literature review showing that target turnover rate varies with age, species, tissue/subregion, treatment, disease, hormonal and nutritional state, day–night


I. Introduction
In vivo potency guides at which plasma exposure a drug is active, and clearance carries information about how efficiently the body removes the medicine.Combined, they define the clinically efficacious dose range.Variability in drug potency and clearance is thus of key importance to ascertain proper dosing and assessment of risk and needs to be meticulously tested and documented in drug application filings.In recent years, these topics have started to gain traction in basic research and drug discovery, yet the understanding of components essential to the definition of in vivo potency, efficacy parameter, and clearance still remains incomplete.

A. What Is the Problem?
Traditionally, in vivo potency estimates are projected from in vitro target affinity and clearance from enzymatic breakdown data.Drug disposition processes are likewise assayed in vitro and in preclinical species and viewed as more or less fixed uptake and/or elimination elements, in line with conventional basic mass action concepts.Importantly, however, these measures are derived and modeled from closed systems, typically at constant total protein expression levels, thus in sharp contrast to the inherent dynamics of a living system.
Proteins in the body are continuously produced and degraded, with turnover half-lives ranging from a few minutes to several days, months, or even longer in vivo ABBREVIATIONS: ACh, acetylcholine; AChE, acetylcholine esterase; ASA, acetylsalicylic acid; C, total plasma concentration; C u , unbound (free) plasma concentration; Cl (S) , clearance of substrate; CNS, central nervous system; COX-1, cyclooxygenase-1; D1R, D1 receptors; D2R, D2 receptors; E, free enzyme concentration; E 0 , free baseline enzyme concentration; E max /I max , efficacy parameter for in vivo maximum drug-induced effect (stimulatory effects/inhibitory effects) fitting the Hill equation including baseline; EC 50 , in vivo potency (stimulatory effects); EEDQ, ethoxycarbonyl-2ethoxy-12-dihydroquinoline; E ss , free enzyme concentration at equilibrium (steady state); ES ss , free enzyme-substrate complex concentration at equilibrium (steady state); E(t), free enzyme concentration as a function of time (disequilibrium); FFA, free fatty acid; GABAA, GABA type A; GPCR, G-protein coupled receptors; GSECR, gamma secretase; IC 50 , in vivo potency (inhibitory effects); ISF, interstitial fluid rate; k cat , fractional catabolic rate constant; k deg , fractional turnover rate (also known as k out ); K d , dissociation constant; k e(RL) , ligand-target complex elimination rate constant; k irr , second-order irreversible loss rate constant; K m , Michaelis-Menten constant; k off , dissociation rate constant of ligand-target complex; k on , association rate constant of ligand-target complex; k syn , turnover rate constant of target; L, ligand concentration; LFTR, ligand facilitated target removal; LPS, lipopolysaccharide; L ss , ligand concentration at steady-state; MABEL, minimal anticipated biological effect level; MAO-B, monoamine oxidase-B; MM, Michaelis-Menten; NiAc, nicotinic acid; NSAID, nonsteroidal anti-inflammatory drug; NT, nortriptyline; PD, pharmacodynamic; PK, pharmacokinetic; PPI, protonpump inhibitor; Q i , blood flow through the eliminating organ; R, target concentration; RL, ligand-target complex concentration; R ss , target concentration at steady-state; RL max , maximum ligand-target complex concentration; RL ss , ligandtarget complex concentration at steady-state; S ss , substrate concentration at steady state; TMDD, target-mediated drug disposition; V, volume of distribution; V max (t), maximum elimination (metabolic) rate during disequilibrium; V max (0), maximum elimination (metabolic) rate at baseline; q, transduction parameter for conversion of a ligand-receptor complex concentration to a pharmacological response, unique for each compound, target, and response.
Target Turnover Impacts Potency, Efficacy, and Clearance 417 at ASPET Journals on April 10, 2024 pharmrev.aspetjournals.orgDownloaded from (Boisvert et al., 2012).The turnover rates vary greatly among different organs and tissues, nutritional status, time of day, between sexes, across species, and also depending on age and lifespan (for a review, see Waterlow, 1984).Fig. 1 schematically shows how turnover is addressed in this review.
Furthermore, the synthesis and degradation of drug and metabolic targets (k syn and k deg of receptor or enzyme protein) differ depending on the overall energy (heat) turnover in a particular species.In general, the smaller the species, the faster the loss of heat, and therefore the higher energy turnover to maintain a 37 C homeostasis (Adolph, 1949;Waterlow, 1984).Even more crucial from the individual patient perspective is that the disease and/or treatment context may significantly influence protein/target degradation k deg (and synthesis k syn ) compared with normal healthy conditions.Examples include altered protein synthesis and degradation in fever or hyperinflammatory states (Waterlow, 1984;Fearon et al., 1988) or after chronic drug treatment (Pich et al., 1987).Factors like the aforementioned may give rise to systematic deviations when predicting drug in vivo potency and clearance from in vitro binding/ metabolism data (Jansson-Lofmark et al., 2020).The insufficient power of applied methods is also a challenge to interspecies in vivo extrapolations of pharmacological and metabolic data (Gabrielsson et al., 2018b).This is a contrast to reductionist approaches that define/assess mechanisms of drug action with ligands, cells, or tissues (in vitro or ex vivo, and perhaps purified targets versus in vivo studies in experimental animals or humans.

B. What Is Lacking?
A more complete and mechanistic description of the determinants of potency, the efficacy parameter, and clearance properties is required to optimize predictions of in vivo pharmacologic effectiveness toward clinical use.Not least, there is a crucial need for further insight into and quantification of the impact of turnover rates of corresponding target protein entities.Thus, taken together, a greater focus on target biology properties relative to drug features (such as binding affinity) is warranted.

C. How Can We Address the Problem?
The time-dependent and varying turnover rates of target proteins across species are typically not captured by most contemporary in vitro assay systems or in preclinical profiling.Recently, we have therefore introduced new mathematical expressions of in vivo potency and the efficacy parameter derived in part from target-mediated drug disposition (TMDD) reasoning (Gabrielsson and Peletier, 2017;Gabrielsson et al., 2018a) and have shown how variations in target synthesis and loss might impact pharmacodynamic (PD) variability (Gabrielsson et al., 2018a).The present account builds further on these ideas, expanding the open system concept and accompanying expressions to describe and consider the dynamics of in vivo potency-, efficacy-, and clearance-related parameters, with representative literature examples included to illustrate their impact.Among these, we discuss in particular drug target and metabolic enzyme turnover within the context of chronic treatment, aging, disease, and nutritional state influences.Fig. 2 illustrates schematically the background and key differences between closed and open drug target and metabolic systems along with their corresponding parameters.By open, we mean that all major determinants of the pharmacological response and/or of clearance have input (synthesis, dosing, binding) and loss (elimination, dissociation, transport, clearance) terms.

II. Pharmacologic Systems and Ligand-Target Interactions
While in vitro ligand-target binding and functional preparations remain useful for the purpose of identifying fundamental drug properties, the impact of the target on drug responses in an integrated living organism can only be addressed by an open in vivo system approach.Ranking of test compounds based on their in vitro binding affinities (K d or in vitro potencies) and preclinical in vivo profiles is standard practice in the drug discovery context.However, in the in vivo situation, several factors (see the Introduction) pertaining to the synthesis and degradation rates (turnover) of corresponding target proteins may significantly influence the pharmacodynamic outcome of a drug.
To this end, turnover models and target turnover have been introduced to rejuvenate modeling and pharmacodynamic analysis, thereby expanding the Fig. 1.Schematic outline of various topics related to turnover concepts in this review.The strategy is to cover turnover from both a pharmacological and a metabolic (clearance) point of view.The review also covers how turnover is controlled and what potential covariates (age, sex, species, disease) are related to the topic.The review covers how turnover may differ across different tissues and proposes means for interspecies scaling.Finally, a set of points to consider related to experimental design, interpretation of data, and translational issues are listed.quantitative assessment of response-time courses (Nagashima et al., 1969;Dayneka et al., 1993;Gabrielsson and Peletier, 2017).In the current account, we further extend and develop this analysis with a comprehensive review of examples from the literature.Within this context, we exemplify and discuss the importance of integrating drug and target properties in reversible and irreversible pharmacodynamic systems.This provides a background to the origin of the corresponding expressions and an illustration of how changes in target turnover may affect the in vivo drug-induced response outcome.It should be noted that specific target turnover (or half-life) may be different from the pharmacodynamic half-life (or in vivo biologic half-life, biologic half-life) as assessed from biomarker information (although related to target turnover) due to distributional or transductional delays or feedback being the ratelimiting step in vivo.
A. In Vivo Open Systems; Reversible vs. Irreversible Ligand-Target Interactions A reversible system can exhibit both bidirectional ligand-target binding interactions and removal of the ligand-target complex.In a living organism (i.e., an in vivo open system) situation, these three key (row 1) Closed pharmacodynamic (left) and metabolic (right) systems.The closed system presented in most pharmacology text books assumes a constant pool of total target (left plot, free target R (blue box representing, for example, the concentration of free binding sites) and ligand-target complex bound RL) or a constant pool of total enzyme (right plot, free enzyme E and substrate-enzyme complex bound ES).The free enzyme is regenerated after the catalytic formation of product P from ES. R, k on , k off , and RL represent free target, second-order complex formation rate constant, first-order complex disintegration rate constant, and complex concentration, respectively.The k cat parameter denotes the first-order rate constant of the catalytic process.(Row 2) The open system has an ongoing zero-order production k syn and first-order loss k deg of target protein (blue box representing, for example, the concentration of free binding sites at the receptor on the left and free enzyme concentration on the right).In, L, and Cl(s) denote the input rate of ligand, ligand concentration, and ligand clearance, respectively.The k syn , k deg , and k e(RL) parameters are target synthesis and target degradation rate and the ligand-target complex elimination constants.(row 3).The open systems that are used for capturing irreversible mechanisms (row 4).The open system for LFTR, where the target is degraded and the ligand is returned to its free pool.Right-hand column: (metabolic systems) schematic comparisons of the closed (row 1) and open (rows 2-4) enzymatic systems.In and S denote the input rate of substrate and substrate concentration, respectively.k syn , E, and k deg are enzyme protein synthesis rate, free enzyme concentration, and enzyme degradation rate constant, respectively.k on , k off , ES, and k cat represent second-order substrate-enzyme complex formation rate constant, first-order complex disintegration rate constant, substrateenzyme complex, and the catabolic rate constant, respectively.
Target Turnover Impacts Potency, Efficacy, and Clearance 419 at ASPET Journals on April 10, 2024 pharmrev.aspetjournals.orgDownloaded from components (free ligand L, free target receptor R, and target receptor-ligand complex RL) fluctuate over time.This is described by eq. 1, where the dynamics of the free concentrations of L (drug) and of R (i.e., free binding sites) depend on drug input In and firstorder nonspecific clearance of L and on the zero-order turnover rate k syn and first-order fractional turnover rate k deg of free target R (Fig. 2, second row, left), respectively.The changes in RL are governed by k on and k off for the L in question (the second-order association and first-order dissociation rate constant, respectively) and k e(RL) , which is the first-order rate constant for irreversible loss via all relevant routes of complex removal (such as degradation, internalization, interstitial fluid turnover, etc.).
Thus, as evident from the previous discussion, the overall pharmacodynamic outcome in the in vivo context will depend not only on drug (ligand; i.e., L) levels versus input and elimination thereof (Cl) as well as affinity (i.e., k off /k on ) for its target R but also on the actual levels, production (k syn ), and removal (k deg ) of R and of the targetligand complex RL.From an in vivo biomarker or clinical response perspective, three key stages in the formation of a pharmacological effect may be discerned: (i) the input and loss of the drug, which is only captured by the open model (Fig. 2, row 2); (ii) the ligand-target binding process (k off /k on ), captured by both the closed in vitro and open in vivo models; target turnover k deg ; and complex kinetics k e(RL) , captured exclusively by the open in vivo model (Fig. 2, rows 1 and 2); and (iii) transduction/conversion triggered by the target-ligand complex RL to a measurable in vivo (biomarker or clinical) response via a series of physiologic and mechanistic events (e.g., amplification, feedback, synergy, buffering, parallel intertwined neuronal circuit processes), described by the q parameter [clinical efficacy is the maximum desired target-elicited effect in the presence of a composite of integrated buffering, amplifying, and compensatory processes.Importantly, clinical efficacy is also limited to what is possible to attain regarding a specific functional response without jeopardizing patient health (safety, tox)].(see II. Pharmacologic Systems and Ligand-Target Interactions) At equilibrium (steady state), the relationships of free target R ss (eq.2, top line) and target-ligand complex RL ss (second line) as functions of drug L ss , and the in vivo potency expressions EC 50 (third line) are described in eq. 2 ( Gabrielsson and Peletier, 2017, for a detailed derivation of the equilibrium relationships from the differential equation system in eq. 1).Note that the open in vivo model derived from eq. 1 will predict the same concentration EC 50 for a half-maximal drug-induced response of both free ligand L ss and the ligand-target complex RL ss at steady state (eq.2).RL ss is indirectly predicted from free ligand L ss via the nonlinear term in eq. 2 (second line).However, an important observation is that the pharmacological response at steady state can be driven by a nonlinear function of free ligand concentration L ss , and the model parameters E 0 , E max , and EC 50 (eq.5, bottom line), which is numerically robust, conceptually pragmatic, and transparent from a translational point of view.
As seen from eq. 2, the open system expressions now contain both free target turnover (k deg ) and complex kinetics (k e(RL) ) in addition to drug-target binding properties (k on , k off ).Target turnover and complex kinetics are in vivo properties, therefore making eq. 2 (third row) more versatile for translation across different species, particularly when species-specific terms for these parameters have been defined.The generic form of the open in vivo potency expression EC 50 in eq. 2 allows predictions of efficacious concentrations of agonists, antagonists, inverse agonists, and enzyme inhibition provided k on , k off , k deg , and k e(RL) are known.The bottom row in eq. 2 shows the expression of the ligand-target dissociation constant K d .A graphical presentation of the in vivo potency EC 50 expression in eq. 2 is shown in Fig. 3, A-D).
As shown in the contour plots of in vivo potency EC 50 (Fig. 3), changes in k deg and k off (keeping k e(RL) set to 0.1 for comparisons around which k off is varying) impact in vivo potency EC 50 .Note the apparent plateau (ceiling effect) when k off < k e(RL) (Fig. 3, A).In this situation, EC 50 may be approximated by k deg /k on (irreversible system) and is still sensitive to changes in k deg .For comparison, Fig. 3, B shows the influence of changes in k deg and k e(RL) (with k off set to 0.1) on in vivo potency EC 50 .In contrast, when k off > k e(RL) , EC 50 may be approximated with (k deg /k e(RL) ) Â (k off /k on ) (reversible system) and is still sensitive to changes in k deg .Fig. 3, C and D, show the same simulations of eq. 2 but with EC 50 presented on a log scale.
The exponential increase in in vivo potency EC 50 stemming from concurrent higher values of k deg and smaller values of k e(RL) (reversible system) is because of the multiplicative effect of changes in k deg and k e(RL) .The graphical presentation of in vivo potency EC 50 in eq. 2 thus (i) distinguish between irreversible and reversible systems; (ii) demonstrates individual contributions of k off , k e(RL , and k deg ; (iii) illustrates determinants of necessary exposure; (iv) gives the complex-to-free target ratio in k deg -to-k e(RL) ; and (v) demonstrates that target turnover k deg is always an important factor of EC 50 and, hence, duration of pharmacological response.A typical example of the latter is proton-pump inhibitors, where the duration of action (suppression of acid secretion) is governed by the de novo synthesis (t 1/2kdeg ) of proton pumps rather than by the (irreversible) drug-target interaction per se.Other examples include COX-1-and MAO-B inhibitors.Eq. 2 is therefore applicable to both small (Smith et al., 2018) and large (Gabrielsson et al., 2018a) molecule pharmacology.
As demonstrated in the previous discussion, in vivo potency thus contains information about the route of target elimination, either via direct catabolism k deg or internalization k e(RL) as a ligand-target complex.Increasing ligand concentrations pushes equilibrium further toward the complex formation.The higher the ligand concentration, the more target is eliminated via the ligand-complex route (k e(RL) ).Hence, the higher the potency (i.e., the lower its numerical value), the lower the necessary ligand (drug) concentration needed to drive target elimination via the complex route.At a ligand concentration equal to EC 50 , when the ligand impacts the free target and complex equally (50%), the steady-state concentrations of free target R ss and complex RL ss are expressed as in eq. 3.
As evident from eq. 3 (bottom row), the steady-state concentration ratio of RL ss -to-R ss is governed by the k deg /k e(RL) ratio.Therefore, this makes said parameters interesting also from a potency point of view (eq.2).The intimate interdependence of pharmacology-and clearance-associated target dynamics factors is illustrated in Fig. 2 and by the accompanying eqs. 1 to 3.
In certain situations, the ligand binds to the target, serves as a facilitator of target removal (Chaparro-Riggers et al., 2012) and then returns to the free ligand pool.It is based on the catch and release mechanism in which the ligand is caught by the target and subsequently released when the ligand-target complex is cleared, resulting in the loss of the target (Sarkar et al., 2002).The conceptual model for this process is referred to as ligand-facilitated target removal (LFTR), which may be viewed as a form of ligand recycling (Peletier et al., 2021).A similar process is involved in the mechanism of tocilizumab (Igawa et al., 2010), where a fraction of the ligand is returned to the free ligand pool, and the remaining fraction is cleared via irreversible loss of complex.Other illustrative examples of LFTR include the selective estrogen receptor degrader group of agents (e.g., giredestrant) (Liang et al., 2021) and PCSK9 inhibitors (Hess et al., 2018), as well as an emerging number of drug classes aimed, for example, at cancer indications (Mullard, 2021).

B. Assessment of Target Turnover Under Different Conditions
It is clear from the reasoning in the previous sections that states with alterations of the target turnover will affect the observed in vivo potency of a drug.In the current account, we have chosen to focus on G protein-coupled receptor (GPCR) and enzyme targets, as these classes together dominate human targets for drugs in clinical use (Rask-Andersen et al., 2011).
While over time, a number of novel methodological approaches to assess target turnover have emerged (e.g., pulse-chase, proteomic analyses, protein synthesis inhibitors), it appears that these have mostly been applied in a closed system context and have different pros and cons (Morey et al., 2021).Regardless of the assessment method, it is also evident that the lifetimes of proteins vary widely between types and entities, depending on, for example, cellular environment and composition, subcellular fraction, function (e.g., scaffolding, structural, synaptic), and abundance in different pathways, organelles, tissues, organs, or cells (Price et al., 2010;D€ orrbaum et al., 2018;Fornasiero et al., 2018).More recent methodological paths include developments in the organs-on-a-chip area (Sosa-Hernandez et al., 2018), which may potentially further extend information gathering relevant to assess drug targets and pharmacokinetic (PK) features, but still within a closed system frame.
Notwithstanding the previous discussion, with few exceptions, we find very little information derived from such methodologies pertaining to GPCRs-targets to a therapeutically dominant class of drugs (Hauser et al., 2017;Sriram and Insel, 2018).For comparison, there is a relative abundance of target half-life data for the latter type of agents using irreversible drug inactivation methods followed by monitoring of the time course of receptor recovery in vivo.Therefore, this ample literature source represents a useful alternative approach to assess rates of target synthesis and degradation within the open system setting (the target recovery half-lives presented in Tables 1, 2, and 3 are used as an in vivo proxy that may also encompass processes other than de novo target synthesis and degradation).Agents used for the purpose include, for example, N-ethoxycarbonyl-2-ethoxy-1,2-dihydroquinoline (EEDQ) (Belleau et al., 1968;Hamblin and Creese, 1983), phenoxybenzamine (Nickerson and Goodman, 1947), benextramine (Bodenstein et al., 2005), bromoacetyl-alprenolol menthane (Pitha et al., 1982), and clocinnamox (Burke et al., 1994), as well as a number of different irreversible enzyme and transporter inhibitors (e.g., clorgyline, deprenyl, RTI-76).
The formation of permanent target complexes means that the normal recycling/trafficking process cannot impact k off , as drug dissociation from the target does not occur under these conditions (Norman et al., 1987).Indeed, the protein synthesis inhibitor cycloheximide prevented the recovery of dopamine D2 receptors (D2R) after EEDQ treatment (Leff et al., 1984), in line with the view that the contribution from recycled target receptors was negligible.Therefore, the irreversible target inactivation approach gives direct and useful information on the actual rate of recovery derived from newly formed GPCR molecules, a view supported by reports on corresponding increases at the mRNA transcription level (Raghupathi et al., 1996a,b).In addition, most literature studies use antagonist agents to label and monitor receptor sites to follow the rate of recovery.This avoids the potential confounding of shifts between lowand high-affinity states of one and the same target protein, as antagonists are considered to label the entire population indiscriminately.Indeed, there are data to suggest that recovery rates followed by means of agonistversus antagonist-labeled binding may not necessarily result in exactly the same figures (Nelson et al., 1986;Ribas et al., 1998).
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;Th€ urmann, 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 andLakoski, 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 aand b-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 , 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 EC 50 (in vivo EC 50 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.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 EC 50 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  1; joint (D1/D2) line correlation and corresponding coefficient (R 2 ; inset) also shown.
Baseline E 0 E 0 / ksyn kdeg or constitutive activity R max and RL max are the maximum observed response in vivo, and maximum level of the ligand-target complex, respectively.E 0 is defined as above of an empirical function of time to capture baseline variability e.g., oscillations.
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 EC 50 expression of both reversible and irreversible systems, it becomes evident how changes with size (body weight) in k deg also impact in vivo EC 50 .
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).
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 a1-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 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 (R 2 ) 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/)].
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 EC 50 expression of both reversible and irreversible systems, it becomes evident from the compiled literature how species differences in k deg also impact in vivo EC 50 .
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 Kenakin, 2017).To account for this element, the linear transduction factor q [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 q (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 q from E max /RL max ).
Practically, E max is the parameter obtained by fitting the Hill function (eq.5, bottom line) to concentrationresponse 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 4suggests 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 q 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 targetligand complex concentration to a measurable pharmacological response in vivo) factor q 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 a2-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 R 0 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 (EC 50 by means of modeling) for a series of antilipolytic compounds (Fig. 6).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 (EC 50 ) of benzodiazepines (Visser et al., 2003).These three examples illustrate good correlations between in vitro binding properties and in vivo potency EC 50 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 EC 50 is a constant term across compounds.
Predictions of exposure levels for repeated dosing in animals in vivo are typically based on target in vitro IC 50 /EC 50 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 halflife of the drug with irreversible action (e.g., protonpump 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 nonnative 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 ligandtarget 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 E 0 and the nonlinear E max function, where the efficacy parameter E max and potency EC 50 are model parameters (eq.5).
We assume that the baseline effect E 0 is proportional to either an endogenous ligand-target interaction (at target baseline R 0 ) 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 E 0 .
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 q (eq.5) and will be ligand-and tissue-specific.Here, q 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 q 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.(eq. 4).Upper row left: Agonism: the steepness of the slope (q) 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 q > 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 q 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.
q 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 q > > 0, which is greater than that of a partial agonist q > 0 or an antagonist where q 5 0 (i.e., E max 5 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 E 0 (Fig. 7, A).The q 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, q, 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 a2-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 a2-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 a2-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 a1-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 EC 50 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 EC 50 .
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 Target Turnover Impacts Potency, Efficacy, and Clearance 435 at ASPET Journals on April 10, 2024 pharmrev.aspetjournals.orgdownregulation of target synthesis rate (turnover rate; k syn ) will impact the baseline level of the target (R 0 ) and therefore change the efficacy parameter E max of ligand L at steady-state, it will not affect the potency, EC 50 (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 q (eq.4), which refers to the ligand-target complex stimulus strength if different from endogenous agonists or baseline activity (R 0 ).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 (R 0 ) 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 (q).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).
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 EC 50 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 (q) 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 Ax 1 (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), neurolepticinduced 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).

C. Summary of Target Turnover-Modifying Influences
Taken together, it is evident that the rate of target turnover is subject to modification by several factors and conditions.Distinct variations are found across organs and tissues, as well as between species and stages of the life cycle.Therefore, it is evident that any of these may impact the translation of in vitro to Thus, to recapitulate, some key elements that may significantly influence target half-life are age, species (and strain/ethnicity), organ/tissue and region (subregion), and chronic treatment/withdrawal and disease states.
Hence, in vivo potency and efficacy should not be expected to be constant across species, ages, tissues, or chronic drug treatment.Further, it appears reasonable to hypothesize that sex differences in target turnover may also play a role in observed male versus female-related disparities in pharmacodynamic drug response, although so far such data remain scarce.In fact, barring studies addressing medications intended for female-specific conditions, most of the preclinical as well as clinical literature, in general, is still dominated by investigations carried out in the male sex.The topic of target turnover is no exception in this regard; this is indeed a limitation and one that certainly deserves more attention.Apart from scattered reports (of conceivable clinical implications (Abou Sawan et al., 2021;Farrell et al., 2021), sex differences in target turnover remain to be further documented and defined.Additionally, recent developments suggest that factors such as target genetic variants/SNPs, RNA stability, epigenetic effects, transcriptional and post-transcriptional regulation, targets existing in protein complexes, and/or in cellular subcompartments may also influence target expression, turnover, and resultant net output (Esteller, 2008;Pereira et al., 2010;Corradin et al., 2016).While not specifically addressed in the present review, it is clear that response differences may also result from diverse subcellular (microor nano-domains) locations of the targets and involve various post-translational modifications, possible dimeric/ heteromeric coexistence, partner proteins/lipids, etc.
Needless to say, the more defined and detailed knowledge about target turnover in a particular disease condition, the more precise prediction from in vitro and in vivo animal models to in vivo clinical target response.The relative importance and implications of the aforementioned factors thus need to be considered not only within the context of the actual intended therapeutic target but also taking into account characteristics of state and trait within the intended clinical treatment population.
Obviously, observed changes in target turnover may relate to alterations in target synthesis (k syn ) and/or breakdown (k deg ) as well as in the elimination of the target-ligand complex (k e(RL) ).In the following section, these aspects will be further gauged and scrutinized, including associated examples of possible clinical relevance and impact.A common misconception in drug discovery contexts is that unbound therapeutic concentrations (C u ) have to be a fixed multiple greater than in vitro potency (K d or in vitro IC 50 ) to demonstrate a satisfactory pharmacological response in vivo (Jansson-Lofmark et al., 2020).Jansson-Lofmark et al. (2020) reported that over 70% of 167 drugs across various chemical and pharmacological classes have an efficacious C u -to-in vitro potency ratio (eq.7) of less than unity.In fact, 30% and 50% of the compounds studied were found to have an in vivo-to-in vitro ratio of less than 0.1 and 0.3, respectively.
Occasionally, the in vivo potency of a drug exceeds the prediction from in vitro binding K d (i.e., displaying an in vivo EC 50 value numerically lower than its K d ), and vice versa.As shown in eq. 7, this depends primarily on the absolute size of k off and k e(RL) .
1. Case 1.If k e(RL) is greater than k off , the system behaves irreversibly, and in vivo potency EC 50 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 EC 50 -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 EC 50 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.
2. Case 2. When k e(RL) is smaller than k off , the system behaves reversibly, and in vivo EC 50 is approximated by (k deg /k e(RL) ) Â K d (Fig. 9).Hence, the relative magnitude of the EC 50 -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 EC 50 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 M 3 -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 EC 50 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.

E. Examples of Irreversible and Reversible Ligand-Target Interactions
Most therapeutically used drugs interact with their corresponding target(s) in a reversible, noncovalent manner, but the pharmaceutical arsenal also contains several irreversibly acting agents of significant clinical importance.Next, we discuss examples of reversible as well as irreversible ligand-target interactions in relation to target turnover parameter impact and consequences thereof.
We define an irreversible system as one where removal of the ligand-target complex as such (k e(RL) ) dominates over first-order dissociation of ligand-target complex (k off ).Irreversible ligand-target interactions are indeed used pharmacologically, for example, among acetylcholine-esterase-, COX-1, H 1 /K 1 -ATPase-, and MAO-B inhibitors (Wallmark et al., 1985;Arnett et al., 1987;Gedda et al., 1995;Vane and Botting, 2003;Freedman et al., 2005;Mbonye et al., 2006;Kang et al., 2007;Colovic et al., 2013).In these cases, the ligand off-rate (k off ) from the complex is negligible compared to the elimination of the ligand-target complex such as k e(RL) .The duration of the pharmacological effect will therefore depend on target de novo synthesis and its halflife.An example of this is the duration of the effect of gastric proton pump inhibition following a single dose of omeprazole.The pharmacokinetic half-life of omeprazole is about 1 hour in humans, whereas the half-life of the proton pump falls in the range of 15 to 20 hours, thus making once-a-day dosing a practical approach (Wallmark et al., 1985).When the half-life of the target protein is shorter, the plasma half-life and presence of the drug become more important for the dosing interval and duration of response.
Using the derived generic expression of in vivo potency (EC 50 ) valid under a wide range of circumstances, the following illustrates the performance of an irreversible system.Here the removal of ligandtarget complex k e(RL) dominates over regeneration k off of free ligand L and target R from the complex pool RL (see eq. 8) (Fig. 8).The route of elimination of the ligand-target complex RL will therefore indirectly be important to the elimination of both ligand and target per se.
Recall that for the irreversible system shown in Figs. 2 and 9, the expression of in vivo potency from eq. 2 can be simplified to the ratio of k deg -to-k on as The notion of drug-target residence time, defined as 1/k off (Copeland, 2016;Copeland et al., 2006), deserves some comment in this context.Within this frame and a closed system setting, target off-rate may be an important factor in determining drug potency K d and in vivo effect duration (Lu and Tonge, 2010;Dahl and Akerud, 2013;Copeland, 2016;Hothersall et al., 2016;Bosma et al., 2017), this but has also been questioned (Folmer, 2018).The concept of ligand-receptor "rebinding," still based on a closed system in vitro approach, has also been introduced as a potential contributory mechanism with implications for the duration of drug action in vivo (Vauquelin, 2010;Vauquelin and Charlton, 2010) and it has further been argued that target saturation is an important component to the extended duration of a pharmacological effect (de Witte et al., 2018).However, in an open system, the loss of (non-dissociated) drug-target complex is an additional route of removal, and the drug-target residence time expression becomes 1/(k off 1 k e(RL) ).Therefore, despite a very small k off -suggestive of a long drug-target residence time and an extended duration of response according to the closed system nomenclature-rapid replenishment of target (k deg fast) or removal of the ligand-target complex (approximately 1/k e(RL) ) can appreciably shorten the apparent residence time and hence the duration of the drug-target effect (Corzo, 2006).On the other hand, even when the size of k off and k e(RL) confers a short residence time, the response duration may still be substantial due to a slow regeneration of free target levels in an open in vivo system [e.g., proton pump inhibitors (PPI)].In the latter case, it is the target half-life that governs the duration of response rather than the degree of saturation of the target system, as suggested by de Witte et al. (de Witte et al., 2018) using closed model arguments.
An instructive example is a comparison of the new PPI IY-81149 and omeprazole (Kwon et al., 2001).The in vitro IC 50 of H 1 K 1 -ATPase activity of IY-81149 and omeprazole were 6 mM and 100 mM, respectively, demonstrating a substantial difference in the in vitro binding affinities to the target.Based only on relative in vitro binding, IY-81149 would have been expected to be about 15 times more potent than omeprazole in vivo.However, the potency difference was more or less abolished when the effects were studied in a dog model in vivo (e.g., histamine-stimulated gastric secretion in the Heidenhain pouch (Kwon et al., 2001).No clinical differences were seen between compounds (Wang et al., 2019).This outcome is consistent with eqs. 2 and 8 and an irreversible system, where k e(RL) > > k off is required for irreversibility and hence in vivo potency is governed by target turnover k deg ; thus, basically independent of further changes in k off .It is evident that the notion about drug-target residence time according to closed system nomenclature does not hold since k deg , rather than k off , will be the major determinant of pharmacological in vivo potency of an irreversible system (eq.8) (Fig. 9).
If the target half-life is longer than the drug plasma half-life, the duration of response will be governed by de novo synthesis of the target and the target protein half-life.This reasoning is applicable to irreversible target interactions (e.g., H 1 /K 1 -ATPase, COX-1, MAO-B) (Table 6).Conversely, if the reverse is true (i.e., target half-life shorter than drug plasma half-life), the drug has to be present at adequate inhibitory concentrations throughout the desired duration of the pharmacological effect since target loss (through k e(RL) ) is quickly replenished by newly synthesized target molecules.
An interesting example is the COX-1 enzyme (prostaglandin-endoperoxide synthase) involved in the generation of prostaglandins throughout body organs and tissues.Drugs that are inhibitors of this enzyme (nonsteroidal anti-inflammatory drugs) may be acting either reversibly (ibuprofen, naproxen) or irreversibly [acetylsalicylic acid (ASA).In the case of the archetypal nonsteroidal anti-inflammatory drug, ASA, the COX-1 enzyme interaction is irreversible, and the duration of the biologic effect is thus entirely dependent on the turnover of the enzyme per se and/or the turnover of the COX-1-containing tissue.Despite a short plasma half-life of ASA (15-20 minutes), the return of platelet function to baseline thus occurs only after 72 to 96 hours as a result of irreversible COX-1 interaction (Hong et al., 2008) and the slow regeneration rate of blood platelets.For comparison, ibuprofen and naproxen are both reversible and, therefore, much more short-acting COX-1 inhibitors (Table 6).The pharmacodynamic action of these agents is thus less  (Wallmark et al., 1985).b Estimated target half-life (Hong et al., 2008).c Estimated target half-life (Fowler et al., 1994).d Estimated target half-life (Moss et al., 2017).e Estimated target half-life (Gabrielsson and Weiner, 2016).
dependent on fractional target turnover and more on ligand-target dissociation or ligand clearance per se.A slow off-rate (k off ) has been suggested to play a key role in the in vivo profiles of, for example, LABA and LAMA (e.g., tiotropium) (Disse et al., 1999) drugs for COPD treatment.However, although likely contributory, receptor kinetics may not be the full explanation for the clinical action duration and profiles of such agents (Sykes and Charlton, 2012;Sykes et al., 2012).
As discussed, previously, efforts to optimize compound affinity (in vitro binding potency) will be essentially futile if target and/or tissue turnover k deg is faster than the dissociation rate k off .In such a case, the duration of the response will be determined by the k deg process.The open model system allows estimation of the potency of both reversible and irreversible ligand-target interactions.The open model additionally has the potential to explain the pharmacodynamic drug-interaction potential between two or more compounds.
For example, Hong et al. (Hong et al., 2008) studied the inhibition of platelet aggregation in a singleblinded, randomized, three-way crossover study.Single doses of aspirin (ASA 325 mg) and ibuprofen (400 mg) versus concomitant administration of ASA and ibuprofen were studied in patients with musculoskeletal disorders and high cardiovascular risk, with a 2-week washout between the study occasions.A substantial inhibition (77%) of platelet aggregation was seen within 2 hours and returned to baseline values within 72 to 96 hours after ASA dosing.In contrast, treatment with ibuprofen alone or together with ASA resulted in only a transient inhibition of platelet aggregation and a return of responding to baseline levels within 6 to 8 hours.The mechanism-based model of Hong et al. (2008) contains a common single parameter comprising the fractional turnover rate of the target as well as complex, denoted k out .The model includes irreversible loss of free enzyme by ASA and reversible binding by ibuprofen.The estimated half-life of enzyme activity was 33 hours, which markedly differs from the first-order dissociation rate half-life of ibuprofen from the target complex (5.6 hours).
Superficially, it may seem paradoxical that there is an attenuated response (suppression of platelet aggregation) when ASA and ibuprofen were administered simultaneously as compared with when ASA is given alone.However, this may be attributed to the available target enzyme being occupied by ibuprofen binding (temporal protection as a reversible drug-target complex with slow irreversible loss of the ibuprofentarget complex per se) thereby shielding against (irreversible) simultaneous ASA interaction.This illustrates a pharmacodynamic drug-drug interaction that requires a strict dosing order of ASA (first) and ibuprofen or naproxen (later), taking into account both target recovery time (dependent on k deg ) and pharmacokinetic properties (plasma half-life) of ligand.
The combined interaction at equilibrium between ibuprofen and ASA is given as (Peletier and Gabrielsson, 2018) and the second-order irreversible loss k irr of ASA (denoted K in Hong et al., 2008).
What will be the outcome then if naproxen instead of ibuprofen is used together with ASA in the previously described patient category?Naproxen displays more extensive irreversibility (k out > k off ) than ibuprofen and also a much longer half-life in plasma (12-17 hours), in addition to its higher potency (0.3 mM) compared with ibuprofen (12 mM) (Gierse et al., 1999).
Using eq. 9 for the interaction between ASA and ibuprofen using data from Hong (k irr 5 0.152 where EC 50,ibu equals 12 mM (Gierse et al., 1999).The interaction model of ASA and naproxen is given as where EC 50,nap is 0.3 mM (Gierse et al., 1999), and all other parameters are the same as for ASA in the ibuprofen model.It is evident from eqs. 10 and 11 that ASA has the greatest inhibitory impact upon platelet aggregation per mole of the drug (40.4),followed by naproxen (3.3) and ibuprofen (0.083).The equilibrium model predicts that at fixed free plasma concentrations, the irreversible effect of ASA will be 486 (5 40.4/0.083)and 12.2 (5 40.4/3.3)times more effective than the reversible effects of ibuprofen and naproxen, respectively.
A similar model of second-order target removal, with the same rate of removal for the target and ligand-target complex (k deg 5 k e(RL) ), was used for assessment of H 1 /K 1 -ATPase turnover (half-life 15-20 hours) in the dog after drug intervention of the proton pump inhibitor omeprazole ( € Abel€ o et al., 2000).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 Target Turnover Impacts Potency, Efficacy, and Clearance 441 at ASPET Journals on April 10, 2024 pharmrev.aspetjournals.org

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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 interactionthus, 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 IC 50 .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 1 /K 1 -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 h equals the ratio EC 50,cimetidine /EC 50, Hist .Therapeutic plasma concentrations (C u 5 0.8 mM at a steadystate corresponding to a daily dose of 1 g of cimetidine, taking human plasma protein binding into account (f u 5 0.2), correspond to its in vitro binding affinity (K d 5 0.79 mM).Therefore, substantially lower local concentrations of cimetidine (0.80 mM as compared to histamine 165 mM) 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 halflife 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.

F. Key Insights and Translational Potential of New In Vivo Potency Expression
If the major component in a pharmacological response was only derived from ligand-target binding, this alone would still not explain why two different subjects may require different doses at a steady-state, provided their bioavailability and clearance are the same.However, differences in the target turnover may help to explain differences in the actual requirement of the drug.New expressions of in vivo potency (eq.2) and efficacy parameters (eq.5) show that these are inextricably linked via target turnover.
The data of Betts et al. (Betts et al., 2010) demonstrates the translational power of the open model explanatory potential in in vivo pharmacology.Table 7 shows the in vitro dissociation constant K d for humanized prototype anti-Dickkopf-1 IgG2 antibody against osteoporosis and the corresponding in vivo potency EC 50 values predicted from these data by means of eq. 2.
These data illustrate the discrepancy across different species with respect to target-binding affinity (> 30-fold) and in vivo potency (10-fold).Clearly, using the target affinity data of rat or monkey as guidance of human doses, in this case, will gravely misdirect predictions of dose.Even though the EC 50 -to-K d ratios of the rat and monkey are similar (5 64 and 66), the markedly slower target k off in man is accompanied by a 10-fold higher in vivo potency and an EC 50 -to-K d ratio of 188.These observations unequivocally stress the important role of including target turnover in defining efficacious concentrations and, thereby, the required dose.In vitro binding affinities clearly underestimate necessary drug exposure and human dose predictions and may therefore result in (costly) late-phase project failure.In this regard, while in vitro target binding affinity (defined by the physicochemical parameters k off and k on ) may be similar across species, they may also differ significantly, as shown in Table 7 (e.g., k off varies 100-fold but k on only sixfold), and thus give rise to major downstream effects on translational efforts during drug development.
TMDD captures the capacity-limited binding and/or loss of the drug via its target (receptor, enzyme, transporter, etc.), such that this interaction impacts the disposition of the drug.This phenomenon is commonly observed for antibody kinetics with high ligand specificity, where ligand and target often appear at equimolar concentrations.So far, it has received rather little attention for small molecules but might become important also in clinical studies of such entities (An, 2017(An, , 2020;;Smith et al., 2018;van Waterschoot et al., 2018).All in all, understanding the biology of the target, including expression level and target turnover properties, is, therefore, necessary in drug discovery programs for enhanced benefit/risk precision prior to delivering drug candidates to humans.

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Chronic diseases imply repeated dosing and steadystate, and several therapeutic biologics agents have been developed aiming at selective and efficient treatments for, for example, inflammatory states.In a commendable aim to address unresolved issues in drug efficiency against different autoimmune diseases, a minimized physiologically based pharmacokinetic model was recently used to assess the role of tissue fluid turnover rate on the magnitude and duration of soluble target suppression by therapeutic antibodies (Li et al., 2018).In Li et al. (2018), simulations were used incorporating the fractional turnover rate of interstitial fluid (ISF) to explain and classify the therapeutic outcome in Crohn's disease versus arthritis-associated joint synovium across a series of antibody compounds.It was concluded that ISF turnover rates strongly influenced the speed of drugtarget complex removal, particularly in situations with slow ligand-target binding kinetics (k off ).Although Lie et al. did not discuss target turnover per se, we were curious as to whether the application of our derivations of the ligand-target and ligand-complex equilibrium relationships coupled with the mechanistic expression of in vivo potency (eq.2) could further enhance the transparency of the findings.This notwithstanding, the duration of a pharmacological response may still be rate-limited by the target half-life.
As discussed previously, in vivo potency of eq. 2 (also see Fig. 3) summarizes the interrelations of target-and drug-associated properties, covering the entire spectrum from reversible (governed by k off and binding) to irreversible interactions (governed by k e(RL) representing all routes of first-order ligand-target complex loss) and demonstrates the importance of target turnover (k deg ) in both situations.Thus, eq. 2 demonstrates that for irreversible systems in vivo potency will be governed by k deg /k on (primarily determined by target turnover and association rate; fast k on is favored), whereas the (k deg /k e(RL) ) Â (k off /k on ) relation governs reversible interactions (i.e., primarily determined by target turnover, complex loss, and binding properties; high-affinity binding will be favored).Applying eq. 2 to the data by Li et al., (2018), but with k e(RL) replacing the ISF turnover-based expression, we find that this may be an alternative and a transparent option to help prioritize compounds in the development of therapeutic antibodies for various diseases (see Fig. 10).Note that target loss k deg is still an important factor to consider in both cases.
The use of the minimal anticipated biologic effect level (MABEL) approach is recommended for highrisk medicinal products for first-time-in-human dose predictions (EMEA, 2018).The MABEL is the anticipated dose level leading to a minimal biologic effect level in humans.The calculation of the MABEL dose should consider target binding and receptor occupancy studies in vitro in target cells from human and the relevant animal species and exposures at pharmacological doses in the relevant animal species.However, the MABEL approach of human dose predictions of bispecific antibodies may not be directly applicable using binding affinity K d (Saber et al., 2019).A tumor cell (target as such) typically has a slower turnover k deg (longer half-life) than the bispecific ligand-target complex k e(RL) .Tumor shrinkage will therefore increase via the complex since k e(RL) is faster than k deg of the tumor cell per se.Since the k deg -to-k e(RL) ratio in eq. 2 is less than unity, the in vivo potency EC 50 will be higher (numerically less) than predicted from K d (MABEL approach).Therefore, the conclusions by Saber et al. (Saber et al., 2019) indirectly support the application of the open model expression of in vivo potency (eq.2) for first-time-in-human dose predictions of bispecifics, rather than commonly used receptor occupancy K d .
Recently, van Waterschoot et al. (van Waterschoot et al., 2018) highlighted the poor knowledge of the actual target concentration commonly encountered in smallmolecule discovery projects.The consequences of this lack of target information can range from unreliable compound potency to highly variable pharmacokinetics.Smith et al. (Smith et al., 2018) conclude that TMDD phenomena are more common for small molecules than currently appreciated and should be factored into discovery projects.Eq. 2 shows that the target properties are equally important to ligand binding characteristics (Gabrielsson and Peletier, 2017;Gabrielsson et al., 2018a,b;Gabrielsson and Hjorth, 2018).A high correlation between where k e(RL) << k off .In vivo potency (eq.2) may then be approximated according to the bottom row expression where ligand-target binding components as well as target turnover and ligand-target complex removal will impact in vivo potency.Right: Schematic illustration of irreversible loss of ligand-target complex where k e(RL) >> k off .In vivo potency (eq.2) may then be approximated according to the bottom row expression where target turnover k deg and ligand-target association rate k on will impact in vivo potency.The k e(RL) parameter is the first-order loss of ligand-target complex (Gabrielsson and Peletier, 2017) corresponding to L T /V T Â (1 -r v ) in the work by Li et al. (2018).L T , V T , and r v represent lymph flow through the target tissue, interstitial flow of target tissue, and vascular reflection coefficient of the target tissue, respectively.in vivo potency EC 50 and in vitro K d relationship is not to be expected unless k deg /k e(RL) in eq. 2 is a constant term across compounds (also see Fig. 6).It is not surprising that this correlation fails for irreversible systems since in vivo potency EC 50 is proportional to k deg /k on and therefore less affected by ligand-target binding changes (Table 3).
G. Interspecies Scaling of In Vitro and In Vivo PD Properties 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) E 0 (Danhof et al., 2007;Mager et al., 2009;Gabrielsson and Weiner, 2016;Choe and Lee, 2017).The baseline E 0 may be a single parameter (constant) or function (e.g., time or an endogenous ligand concentration).E 0 may be due to biologic variation such as diurnal oscillation, endogenous ligands, stress, disease, or potentially constitutive activity.E 0 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 EC 50 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 q 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.
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-totarget 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 : 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.

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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.

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 a turnover after a lipopolysaccharide (LPS) challenge, listing half-lives of the inflammatory marker TNF a in mice, rats, and humans without reference to a specific target behavior (Larsson et al., 2021).The approach was a metaanalysis 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 (r 2 5 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 b-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 EC 50 correlation (r 2 5 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 EC 50 values correlated better with receptor binding K i values than with EC 50 values obtained from in vitro [35S] GTPcS experiments.It should be noted that K i measures affinity only, whereas in vitro C ´[35S] GTPcS EC 50 (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 Gprotein-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 ( € Abel€ o 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 q, 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 q.
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 feedingperiods, 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  (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 hu- mans (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.

III. Drug Metabolism and the Open
Michaelis-Menten System

Background to Equations and Models
In vivo potency guides at which plasma exposure a drug is active, and clearance carries information about how efficiently the body removes the medicine.For linear (first-order) systems, clearance is assumed to be constant independently of a change in the substrate (drug) concentration over time.A robust method to estimate systemic clearance is through intravenous injection of substrate followed by dividing the intravenous dose by the observed total area under the plasma concentration-time profile.At higher substrate (drug) exposure saturation of the eliminating pathways may occur, and clearance is then often expressed by means of the classic closed Michaelis-Menten (MM) model.Since its introduction in 1913, the MM equation has become a central tenet in biomedical sciences in general and as a function of saturable processes in particular (Michaelis and Menten, 1913;Michaelis et al., 2011).The closed MM model has been applied to in vitro and in vivo systems of acute and chronic data.The limitations of the closed MM system are, however, its lack of enzyme protein synthesis and loss in parallel to its metabolic processes (Fig. 2, metabolic systems, right-hand column).This means that the total pool E tot of free E and substrate-bound ES enzyme complex is constant and equal to the free baseline pool E 0 at any time.It is often assumed for closed systems that the initial substrate concentration S is initially constant and much greater than the total enzyme concentration E 0 .During oral dosing, for example, both the rate and extent of substrate exposure are highly variable and do not exceed the responsible enzyme concentrations at therapeutic drug concentrations (for a review on CYP450., see Zanger and Schwab, 2013).Daily 400 mg oral doses of the anti-inflammatory drug acetaminophen (Mw 5 151.16 g/mol) corresponds to a plasma peak concentration of about 10 mg/L (66 mM) (Raffa et al., 2018).The most abundant hepatic responsible enzyme, CYP3A4, for the metabolism of acetaminophen has a total amount of 60 to 150 nmol/g hepatic tissue (60-150 mmol/kg liver or 90-225 mmol/ liver) (Zanger and Schwab, 2013), which exceeds drug exposure to acetaminophen at any time.
The underlying assumptions of the open MM model are that the synthesis of free enzyme protein stays constant, but the rate of elimination of free enzyme decreases as the free enzyme concentration diminishes when temporarily occupied by substrate molecules (Gabrielsson and Peletier, 2018;Peletier and Gabrielsson, 2022).Total enzyme concentration (free and complex bound) is allowed to vary under chronic drug use, which means that it can exceed the initial enzyme level E 0 .Clearance of free substrate will vary until equilibrium is established.The closed MM approach assumes that the catalytic reaction, rather than the substrate-enzyme binding process, is the rate-limiting step.This assumption is not necessary in the open model.The open model does not exclude that drug-drug metabolic interactions may affect both rate and extent of binding.By including the substrate and target turnover (i.e., opening the system) to mimic the in vivo situation, new kinetic properties of enzyme and substrate enzyme evolve.A consequence of this will be that the open MM equation of clearance [originally denoted as the specificity constant fractional catabolic rate constant (k cat )/K m times the enzyme baseline concentration E 0 ] and rate of metabolism will take another functional form.
Studying drug metabolism outside the in vivo context is most often done in vitro.With purified enzymes, neither synthesis nor degradation of the enzyme is expected.In cell systems, the turnover of enzymes may still be an ongoing process.However, the timeframe within which this is done is important.Even though the cell system (in vitro) may have synthesis and catabolism of enzymes, studies of drug metabolism under chronic in vitro conditions are rarely performed.Synthesis and catabolism of enzyme proteins are seldom studied in parallel to drug substrate metabolism.Whereas drug metabolism is typically studied within a timeframe of a few hours or a maximum of a day, enzyme half-lives are most often much longer than that.A closed system approximation may therefore be valid for acute but not chronic situations assuming a stable enzyme level (Fig. 2) (von Bahr et al., 1998;Rostami-Hodjegan et al., 1999;Magnusson et al., 2008;Ramsden et al., 2015).
In this section, we first explore and compare the open model with the traditional closed system MM model derived by Gabrielsson and Peletier (Gabrielsson and Peletier, 2018) and recently further explored (Peletier and Gabrielsson, 2022).We derive steady-state equations of the substrate (S, drug), enzyme (E), and complex (ES) and then dissect the new relationship of in vivo V max , K m , and clearance Cl.Simulations are done with the open system showing its intrinsic behavior governed by experimental data.From this, conclusions about the drug-drug interaction potential are then drawn.
Let us start with the rate equations of the open system metabolic model of the free substrate (S), free enzyme e, and substrate-enzyme complex (ES), including zero-order input (Input) and nonspecific clearance (Cl (S) ) of the substrate, and zero-order turnover rate (k syn ) and first-order fractional turnover rate (k deg ) of enzyme shown in the following equation (Fig. 2, metabolic systems, right-hand column).The rate of formation of product (metabolite) via the substrate-enzyme complex activity (k cat ) is shown in eq.19 (bottom line): We assume that free substrate S is only eliminated via enzymatic degradation and therefore set nonspecific clearance of Cl (S) to zero.

Equilibrium States and Clearance Expression of (Reversible) Metabolic Systems
Mechanistic expressions of the substrate, free enzyme, and substrate-enzyme complex concentrations are derived by incorporating target/enzyme turnover (Table 8).In particular, we show that whereas in closed systems, there is a built-in saturation beyond which the substrate TABLE 8 Generic expressions of the open and closed system properties of enzymes E 0 of the closed system is fixed over time unless changes occur due to changes in synthesis (induction/inhibition) or catabolism.The closed system demonstrates saturation of free enzyme, complex, clearance and rate of elimination at equilibrium in contrast to the open system which behaves nonlinearly until equilibrium is reached.
Metabolic system Open system Closed system Target Turnover Impacts Potency, Efficacy, and Clearance concentration keeps rising, in open systems involving enzyme turnover, this is no longer the case.However, after an initial period of disequilibrium, the expression of intrinsic clearance reduces to a linear expression.Here, clearance is assumed to be proportional to the free enzyme concentration E(t) over time and therefore varies in a similar pattern to E(t).At equilibrium, clearance returns to be proportional to the free baseline enzyme concentration E 0 .
A revision of the closed MM system to also include enzyme turnover was recently undertaken to attain a closer resemblance to the in vivo situation (Gabrielsson and Peletier, 2018).The revised expressions of intrinsic clearance and rate of elimination at equilibrium are given in as where E(t) denotes the time course of the free enzyme.Since the free enzyme level (E) changes over time and will initially decline during extended drug exposure, both V max (t) and clearance Cl will decrease and appear time-dependent until equilibrium [steadystate, Cl ss and V max (0)] is reached (Figs. 12 and 13).
The equilibrium relationships of target substrate (S ss ) free enzyme (E ss ) and substrate-enzyme complex (ES ss ) are shown as follows: The substrate concentration S ss increases proportionally with the Input rate at steady-state since clearance is a nonsaturable term at equilibrium (steady-state) in the open model of drug metabolism, which contrasts the closed system model (Table 8).
Surprisingly, the free enzyme level at steady-state E ss returns to the enzyme baseline value E 0 since it is only determined by k syn and k deg (Table 8; Fig. 12).The equilibrium level of the substrate-enzyme complex ES ss is the ratio of substrate Input to the catalytic clearance (elimination rate constant k cat times distribution volume) at equilibrium.Substrate clearance Cl is determined by the biologic properties of the responsible enzyme, synthesis k' syn , and degradation k deg , as well as the binding and catalytic properties k off , k on , and k cat .Cl can be simplified to (k' syn /k deg ) Á k on when k cat is much greater than k off , which means that Cl is a function of free enzyme baseline expression E 0 and the second-order rate constant k on at equilibrium.Table 8 summarizes the different properties of the open and closed systems.The time courses of substrate, enzyme, complex, clearance, and elimination rates display saturable behavior akin to the closed system.All of these variables and parameters follow dose-proportional (first-order) kinetics at equilibrium of the open model.The duality of the open system is that substrate, free enzyme, and the substrate-enzyme complex also display nonlinear behavior during the time to equilibrium.Table 8 contrasts Cl derived from the closed system, which decreases with increasing substrate exposure S, and Cl of the open system, which is independent of the substrate exposure at equilibrium.This stems from the fact that while in the closed system, the total amount of enzyme E tot is fixed to what it is initially, E 0 and the amount of the substrate-enzyme complex can never exceed the total amount of enzyme in closed systems.In the open system, the free enzyme is continuously synthesized and turned over via irreversible loss and complex formation.
The degree of target-ligand (substrate-enzyme) complex formation is a significant element affecting substrate metabolism rate in the open situation.Thus, as more substrate (drug)-enzyme complex is formed, the availability of free enzyme protein declines and, in turn, also the rate of elimination of free enzyme, while the rate of synthesis (replenishment) of free enzyme molecules is sustained.That is, the total concentration of enzyme (free 1 substrate complex-bound) will increase during the period of disequilibrium until a balance between the three entities (free and bound enzyme and Fig. 12. Observed (solid symbols) and regressed (eq.9, solid line) concentration-time data of compound X after 10 repeated intravenous injections.The first 120 mg intravenous injection was followed by nine 40 mg intravenous injections given every eighth hour.Concentration-time data and doses are taken from case study PK22 in Gabrielsson and Weiner (2016).This data set was included to demonstrate the flexibility of the open MM model.substrate) has been established.Typically, enzyme proteins have relatively long half-lives (von Bahr et al., 1998;Rostami-Hodjegan et al., 1999;Magnusson et al., 2008;Ramsden et al., 2015), often exceeding that of substrate per se.It follows that the time to equilibrium between free enzyme, substrate, and substrate-enzyme complex may therefore be much longer than the usual three to five substrate half-lives.The classic closed system MM model recognizes the referred disequilibrium as a nonlinear clearance [Cl 5 V max /(K m 1 C)] with clearance decreasing as substrate concentrations increase.However, by introducing turnover properties of the enzyme as such, this nonlinear (saturable) clearance term disappears for the equilibrium state, and clearance returns to its equilibrium state V max /K m , since free enzyme concentration (E) is determined only by the ratio of k syn -to-k deg at equilibrium (steady-state).
To illustrate the previous discussion, eq.20 was fitted to rapid repeated intravenous dose data in Fig. 12. Simulations were then done with a constant intravenous infusion over 100 hours to show how the time courses of substrate S, free enzyme E, substrate-enzyme complex ES, and clearance of substrate Cl of this open system varied over time (Fig. 13).
Synthesis k syn and clearance of free enzyme stays constant, but the rate of elimination of free enzyme decreases as the free enzyme concentration falls when the substrate-enzyme complex is formed.Total enzyme concentrations (free E and complex bound ES) are allowed to vary, which means that they can both exceed and become less than the initial enzyme level E 0 .The time course of clearance may be easier to understand and apply than that of free enzyme and relates to actual observable values.The k cat , k deg , k off , k on , and k syn were estimated at 0.151 hour À1 , 0.986 hour À1 , 0.109 hour À1 , 0.0082 hour À1 •(mg • L À1 ) À1 and 24.9 mg • L À1 • h À1 , respectively, with a resulting K m of 32 mg • L À1 and clearance Cl of about 17 L • h À1 .The reasons behind the data of Figs. 12 and 13 are thus as follows: (i) an initial decrease in free enzyme concentrations as a consequence of complex formation, resulting in (ii) a decrease in the rate of elimination of free enzyme since free concentrations decrease, (iii) since free enzyme concentrations decrease the substrate clearance will decrease (change) in parallel [Cl(S) 5 E(t) • k cat • V] (Table 8), and (iv) simultaneously, there is a buildup of substrate-enzyme complex (Fig. 13).Therefore, the total concentration of free and complex bound enzyme increases beyond the baseline concentration E 0 .
A constant substrate clearance model would not have captured the nonlinear concentration-time data in Fig. 12.For comparison, a time-dependent change Fig. 14.Schematic presentation of free enzyme and substrate levels pre-, during, and post-dosing.The free enzyme level (dashed blue line) decreases from its baseline value [predose (1)] to a trough value [after the start of infusion (2)] during the initial rise in plasma substrate concentration (dotted red line) since substrate will allocate portions of the free enzyme during a constant rate infusion.Steady-state is reached [yellow shaded area (3)] and lasts until the stop of infusion.Only synthesis k syn and loss k deg of free enzyme governs the steady-state free enzyme concentration.There is a rapid rise in free enzyme concentrations upon stop of substrate infusion [washout (4)]; this is due to the discharge of free enzyme from the disintegrating substrate-enzyme complex pool and no further free drug infusion to form a substrate-enzyme complex.The free enzyme concentration returns to the equilibrium concentration terminally [post-dose ( 5)]. .The free enzyme level deceases transiently from its baseline value (1) to a trough (2) during the initial rise in plasma concentration of substrate since substrate will bind to free enzyme.An apparent steady state is reached between 40 to 60 hours (3) and lasts until the end of infusion.Only synthesis k syn and loss k deg of free enzyme governs the steady-state free enzyme concentration.There is a rapid rise in free enzyme concentrations upon stop of infusion due to stop of complex formation (no further consumption of free enzyme for complex formation) and release of the free enzyme from the substrate-enzyme complex pool (4) as the rate of substrate input stops.The free enzyme concentration returns to the equilibrium concentration terminally ( 5). ( 1)-( 5) correspond to the different stages schematically shown in Fig. 14.
in maximum metabolic capacity [closed system V max (t)] (case study PK22 in Gabrielsson and Weiner, 2016) captured experimental data in Fig. 12.
The free enzyme-dependent clearance of compound A (substrate) in Fig. 14 (right) demonstrates a transient drop from baseline (1) to a trough of 20% (2) during the infusion, aiming at a substrate S concentration of about 180 mg/L.Substrate clearance then returns to its original value (E 0 ) at about 40 to 60 hours when the equilibrium of the whole system is reestablished (3).Substrate clearance has reached its predose value at equilibrium (3).When the infusion is stopped at 100 hours, substrate clearance rebounds (4) due to a transient rise in the free enzyme concentration.This is due to the sudden release of free enzyme from the substrate-enzyme complex as product is being formed and the lack of consumption of free enzyme due to complex formation.Substrate clearance (and free enzyme concentrations) reaches the predose equilibrium terminally (5) as all substrate is washed out.The time to equilibrium is substantially prolonged with a rise in substrate infusion rate, and vice versa.This is also shown schematically in Fig. 13.
The second example shows simulations of three different intravenous bolus doses of compound X.The substrate concentration-time courses in plasma are shown in Fig. 15, A, together with the corresponding time courses of clearance (Fig. 15, B) and substrate half-life (Fig. 15, C).
Note the dose-dependent change of substrate clearance with increasing concentrations after a bolus dose (Fig. 15, B), which exhibits the characteristics of a target-mediated drug disposition system.The transient dip in clearance over 6 to 36 hours results in a prolonged half-life (1).The dose-dependent rebound of clearance when concentrations fall below 100 mg•L À1 (clearance greater than its baseline value) is due to the replenishment of free enzyme from the substrate-enzyme complex, and less enzyme is used when substrate concentrations start to fall off.During the lowering of clearance below its baseline value, less free enzyme is available and can be cleared via natural catabolism k deg , (rate of enzyme elimination decreases, but the rate of synthesis stays constant, which means that the total amount (free 1 complex) increases.The free enzyme pool is then increased by released free enzyme from the complex pool, and there is a rebound in the free enzyme concentration is seen, which then causes clearance to rebound.The temporarily increased clearance results in a decrease in half-life (2), which then increases when clearance returns to its baseline value (3) terminally.The manifestation of nonlinear plasma concentration-time courses is the archetypal signature of an open MM system at disequilibrium.The dynamics of the intertwined differential equations of free substrate, free enzyme, and the substrateenzyme complex inherently captures the disequilibrium as a nonlinearity.This is the core difference between the closed system (assuming a constant total enzyme pool) and the recently derived open system models (Figs. 2 and 14) (Gabrielsson and Peletier, 2018), which puts clearance into a new light.Until simultaneous measurement of the total enzyme concentration implicated is carried out, the possibility cannot be completely dis- carded that, in some cases, results previously described as dose-or time-dependent kinetics may actually rather reflect a state of disequilibrium.

Key Insights and Translational Potential
An important advantage of using the open system approach is that an apparent temporal nonlinearity in clearance or rate of elimination does not have to be approximated using a saturable expression such as the one shown in Table 8.In open systems, the nonlinearity observed for higher intravenous bolus doses in which clearance temporarily decreases and half-life increases is an intrinsic property of the system, which results from the apparent disequilibrium between substrate S, free enzyme E, and the substrate-enzyme complex ES.Clearance behaves linearly at steady-state (Table 8, bottom row, left, V max /K m ).
However, in vitro studies in general and metabolic drug-drug interaction studies in particular operate within a short timeframe, often less than 24 hours and sometimes as short as 15 to 45 minutes (Fowler and Zhang, 2008), hence totally ignoring the impact of enzyme protein turnover.Also, clearance defined by closed systems is commonly applied even in a physiologic context for translation of in vitro to in vivo metabolic data (Rostami-Hodjegan, 2010).In these cases, the nonequilibrium between the substrate (drug), free enzyme, and the complex is approximated by a nonlinear saturable function.Clearly, a better understanding is required of the biologic elements involved, including the origin of the clearance model (open or closed).Accurate in vitro-to-in vivo predictions are possible only when in vitro data are robust and the biologic structure of the clearance model is integrated.Accordingly, we therefore suggest, based on the expanded quantitative insights of the MM system presented here, that in silico MM, pharmacological, and transporter models should be built on open systems.
The tools are available to more correctly scale in vivo data from preclinical species to humans, with a reasonable mechanistic structure of the determinants of clearance.Thus, it should be appreciated that V max is expressed as E(t) • k cat (or k syn • k cat /k deg at equilibrium), and K m equals (k off 1 k cat )/k on .The k syn and k deg parameters represent biology and are scalable across different species.The physicochemical parameters k on , k off , and k cat may also be species-dependent since the target properties varies across species.
The apparent clearance is determined by the free enzyme expression E and the turnover parameters k syn and k deg rather than its fixed baseline concentration E 0 , which is contrasted by the closed system model where clearance via its V max term is fixed by baseline concentration E 0 .This means that two subjects with the same free enzyme expression (same E 0 ) will have the same clearance (provided everything else is the same).
However, the subject with the higher enzyme synthesis k syn and degradation k deg rates will reach enzymatic equilibrium faster.Therefore, subjects or species will, despite similar free enzyme concentrations, display different substrate time courses due to different enzyme protein turnover rates.

Induction or Inhibition of Enzymatic and Catalytic Processes
Since clearance of most small drug substances depends upon CYP enzymes, CYP inhibition may lead to overexposure and toxicity and CYP induction to too low exposure and deficient therapeutic effect.Understanding the cause of inhibition or induction is, therefore crucial.A practical example of the time course of heterologous drug induction is the impact of pentobarbital treatment on the disposition of nortriptyline (NT) (von Bahr et al., 1998).Pentobarbital-induced induction of NT clearance (NT clearance increases due to increased exposure to the enzyme responsible for NT The reverse happens on cessation of pentobarbital treatment.The induced NT clearance decreased and half-life increased, resulting in an extended time of postinduction return of NT concentration to its pre-induced state.Analogous to, for example, ligand-receptor target interaction, as previously discussed, the administration of agents aiming at enzyme proteins may impact the number of target molecules or their activity.An increase in the synthesis rate (turnover rate) of enzyme k syn will impact the baseline value of enzyme E 0 and therefore cause an increase in clearance Cl of substrate S at steadystate.An increase in the fractional turnover rate of enzyme k deg will decrease the baseline value of enzyme E 0 and, hence, decrease in clearance Cl of substrate S at steady-state (Table 9).
This section has demonstrated how enzymatic turnover properties will affect clearance, time to equilibrium, and steady-state solutions of substrate, enzyme, and the complex and, consequently, drug dose.The new expression of in vivo MM systems will be useful for quantitative analysis of clearance properties and in translational science contexts.

IV. Discussion
A. What Is the Challenge, and Why Is It a Problem?
The introductory section identified two main questions: namely, what is the challenge with today's closed system models, and why is it a challenge in pharmacology, metabolism, and even for transporter systems?These closed system models, often in vitro based, lack robust information about the target protein biology and, hence, are approximations of the in vivo situations.Closed systems models further lack the capability beyond binding to describe drugdrug interactions, time-variant induction, inhibition, or displacement (up-or downregulation of the target) of competing drug molecules or pharmacodynamic drug interactions, as previously described.Moreover, closed systems are limited to binding interactions and hence cannot explain when the duration of the drug is limited by the turnover of the target (see previous PPIs and COX-1 examples).Finally, closed systems assume a constant clearance despite the fact that the availability of free enzymes will vary for the drug (substrate), particularly during repeated dosing conditions.Mitigating these limitations is necessary for adequate assessment of in vivo potency, efficacy, and clearance.
We have shown that target turnover (k syn , k deg ) is an important covariate to in vivo potency and effi-cacy.Thus, the rates (k off , k deg , k e(RL) , and k on ) or their half-lives determine potency, whereas the expression level of complex (RL max ) and transduction (stimulus force, q) determine efficacy, as in the following equation.In vivo potency and efficacy have ligand-target complex loss k e(RL) in common.A change in that property is therefore assumed to impact both potency and efficacy but in opposite directions.When k e(RL) increases, potency increases (numerical value decreases) whereas efficacy decreases, and vice versa, making the removal rate of ligand-target complex an important player.Here, target biology is an important covariate of in vivo potency and may capture between species or interindividual differences.Equation 23 partly explains why in some cases target concentrations in the micromolar range only require nanomolar drug exposure, and vice versa.Still, the open model, similarly to the closed, does not take into account post-target events such as synergy, potentiation, feedback, etc.However, incorporating target properties, assessment of activities adjacent to the target will be more apparent.
Blood clearance may be expressed by means of the well-stirred physiologic model with blood flow Q i as The determinants of free enzyme E(t) concentrations are k syn and k deg .Again, target protein turnover plays an important role and may explain interindividual differences in the disposition of substrate S.In situations where only plasma data are available of the drug, such as in therapeutic drug monitoring TDM, V max /(K m 1 C) gives the apparent plasma clearance rather than intrinsic clearance of eq.23.
V max and K m are typical parameters in TDM of phenytoin and salicylic acid and are based on the closed system expression of clearance (Table 8) (for a review of the clearance concept, see Benet, 2010).

B. Unifying and Separating Properties of Open Systems
The open models of pharmacological and metabolic systems have several properties (binding, target turnover and complex loss) in common that unify these systems.While not explicitly discussed in this article, it appears highly probable that similar reasoning may be applied to ligand interactions with transport proteins as well.The open in vivo models incorporate all necessary ligand and target protein interactions, such as target binding, target protein turnover, and irreversible loss of either complex or the associated drug.By virtue of their more physiologic properties, such approaches reach beyond binding and incorporate the actual target (receptor, enzyme, or transporter protein turnover) properties, thereby encompassing physiologic means to explain within-and between-subject differences.

C. General Conclusions and Perspectives
This review endeavors to illustrate and exemplify the importance of target protein turnover as a central player in pharmacology and drug metabolism.We hope these thoughts will inspire further development of concepts of in vivo pharmacology and drug metabolism to the benefit of basic scientists as well as for drug discovery and development ventures.The introduction of protein turnover unveils the bearing of target dynamics upon pharmacologic as well as metabolic readouts-key components in determining drug responses in vivo.Specifically, we describe and provide • The presentation of new (open model) expres- sions of in vivo potency, efficacy, and clearance, which notably embody target turnover, binding, and complex kinetics, as well as capturing drugresponse descriptors (i.e., full, partial, and inverse agonism and antagonism) Using this new open model expression which integrates system (k syn and k deg ) and drug (k on , k off , k e(RL) , and k cat ) properties, we further show that * The fractional turnover rates (k deg and k e(RL) ), rather than the absolute target expression (R or RL), determine necessary drug exposure via in vivo potency EC 50 .* The absolute ligand-target expression (RL) determines the need for the drug based on in vivo efficacy parameter (E max ) and the transduction parameter q. * The free enzyme concentration E determines clearance and the fractional turnover rate (k deg ), the time to equilibrium between the substrate, free enzyme, and the substrate-enzyme complex.
* Clearance is not a constant term but is driven by the free enzyme concentration.* The properties of substrate, target, and complex demonstrate nonsaturable metabolic behavior at equilibrium within reasonable substrate/ligand concentration ranges.* Nonlinear processes previously referred to as capacity-and time-dependent kinetics may have been disequilibria, which the open model handles as an intrinsic property.* The open model may pinpoint why some subjects differ in their demand for the drug, thus defining what makes the outlier an outlier, an issue important to scrutinize from a clinical but also a regulatory point of view.
All of these results need to be considered within the framework of projecting potency, efficacy, and clearance from in vitro, via in vivo animal model work, to clinically efficacious exposures in man.
To understand and approach the dynamics of target biology in an open system, we present new avenues to vastly different areas beyond pharmacology, drug metabolism, or cellular (transport) systems.Open systems capture in vivo disequilibria previously categorized as capacity-and time-dependent kinetics.Open systems increase the capability to capture these processes correctly and underpin the interpretation of data, translate functionality across species, and explain clinical and preclinical variability.
Only by continued integration of the multiple levels of biologic and pharmacological insight will the precision be further improved of translational predictions across the drug development process.It is our hope that the current account may be of value to that end, as it emphasizes the importance of in vivo veritas principles in such endeavors.

Fig
Fig.2.(row 1) Closed pharmacodynamic (left) and metabolic (right) systems.The closed system presented in most pharmacology text books assumes a constant pool of total target (left plot, free target R (blue box representing, for example, the concentration of free binding sites) and ligand-target complex bound RL) or a constant pool of total enzyme (right plot, free enzyme E and substrate-enzyme complex bound ES).The free enzyme is regenerated after the catalytic formation of product P from ES. R, k on , k off , and RL represent free target, second-order complex formation rate constant, first-order complex disintegration rate constant, and complex concentration, respectively.The k cat parameter denotes the first-order rate constant of the catalytic process.(Row 2) The open system has an ongoing zero-order production k syn and first-order loss k deg of target protein (blue box representing, for example, the concentration of free binding sites at the receptor on the left and free enzyme concentration on the right).In, L, and Cl(s) denote the input rate of ligand, ligand concentration, and ligand clearance, respectively.The k syn , k deg , and k e(RL) parameters are target synthesis and target degradation rate and the ligand-target complex elimination constants.(row 3).The open systems that are used for capturing irreversible mechanisms (row 4).The open system for LFTR, where the target is degraded and the ligand is returned to its free pool.Right-hand column: (metabolic systems) schematic comparisons of the closed (row 1) and open (rows 2-4) enzymatic systems.In and S denote the input rate of substrate and substrate concentration, respectively.k syn , E, and k deg are enzyme protein synthesis rate, free enzyme concentration, and enzyme degradation rate constant, respectively.k on , k off , ES, and k cat represent second-order substrate-enzyme complex formation rate constant, first-order complex disintegration rate constant, substrateenzyme complex, and the catabolic rate constant, respectively.

Fig. 3 .
Fig.3.Impact of changes in the parameters of in vivo potency in eq.2.(A)  In vivo potency vs. target degradation rate k deg and complex dissociation rate k off constants.The complex elimination rate constant k e(RL) is set to 0.1 time À1 .In vivo EC 50 moves toward infinity when k e(RL) approaches zero.The system approaches an irreversible behavior when k e(RL) is (much) greater than k off .(B) In vivo potency vs. target degradation rate k deg and complex elimination rat k e(RL) constants.The complex dissociation rate constant k off is set to 0.1 time À1 .In vivo EC 50 moves toward infinity when k e(RL) approaches zero.The system approaches an irreversible behavior when k e(RL) is (much) greater than k off .EC 50 is plotted on a linear scale in(A)  and (B) and on a logarithmic scale in (C) and (D).The multiplicative effect of changes in k deg and k e(RL) are shown in (B) and (D) and therefore requires a larger range of scale.

Fig. 6 .
Fig.6.In vitro lipolysis negative logarithm of unbound in vivo potency (pEC 50 ) vs. unbound in vivo potency (pEC 50 ) data redrawn fromAlmquist 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 pEC 50 5 -log 10 (EC 50 /1M).Note the pEC 50 scale, meaning that compounds become more potent toward the upper right corner.The endogenous ligand nicotinic acid NiAc is specifically identified in the graph.

Fig. 7 .
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 (q) 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 q > 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 q 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.

Fig. 8 .
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 q.Baseline response E 0 is governed by target exposure k syn /k deg and target constitutive activity, whereas maximum ligand-induced response E max by q k syn /k e(RL) .Altered implies a new concentration-response relationship after a parameter change.
D. In Vivo EC 50 Compared to In Vitro K d : Dependency on k deg , k off , and k e(RL)

Fig. 9 .
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 EC 50 .(1) Blue curve, right: A reversible system where k e(RL) is much less than k off .Potency EC 50 is approximately k deg /k e(RL) Á K d ; off-rate k off from ligand-target complex binding will be an important covariate.(2) Red curve, middle: k e(RL) 5 k off ; EC 50 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 EC 50 is approximately k deg /k on ; target turnover will again be an important covariate as in eq. 2.

Fig. 10 .
Fig.10.Left: Schematic illustration of reversible loss of ligand-target complex where k e(RL) << k off .In vivo potency (eq.2) may then be approximated according to the bottom row expression where ligand-target binding components as well as target turnover and ligand-target complex removal will impact in vivo potency.Right: Schematic illustration of irreversible loss of ligand-target complex where k e(RL) >> k off .In vivo potency (eq.2) may then be approximated according to the bottom row expression where target turnover k deg and ligand-target association rate k on will impact in vivo potency.The k e(RL) parameter is the first-order loss of ligand-target complex(Gabrielsson and Peletier, 2017) corresponding to L T /V T Â (1 -r v ) in the work byLi et al. (2018).L T , V T , and r v represent lymph flow through the target tissue, interstitial flow of target tissue, and vascular reflection coefficient of the target tissue, respectively.

Fig. 11 .
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.

Fig. 13 .
Fig. 13.Left: Model simulations of concentration-time courses of the substrate (S), free enzyme (E), and substrate-enzyme complex (ES) after a 100-hour constant-rate infusion aiming at about 200 mg•L À1 of test compound analyzed in Fig. 12. Therapeutic concentrations fall in the range of 100 to 500 mg•L À1 .Right: Model simulations of concentration-time courses of free enzyme (blue line) and clearance (red line).The free enzyme level deceases transiently from its baseline value (1) to a trough (2) during the initial rise in plasma concentration of substrate since substrate will bind to free enzyme.An apparent steady state is reached between 40 to 60 hours (3) and lasts until the end of infusion.Only synthesis k syn and loss k deg of free enzyme governs the steady-state free enzyme concentration.There is a rapid rise in free enzyme concentrations upon stop of infusion due to stop of complex formation (no further consumption of free enzyme for complex formation) and release of the free enzyme from the substrate-enzyme complex pool (4) as the rate of substrate input stops.The free enzyme concentration returns to the equilibrium concentration terminally (5).(1)-(5) correspond to the different stages schematically shown in Fig.14.

Fig. 15 .
Fig. 15.(A) A semilogarithmic plot of simulated concentration-time courses of compound X after three different bolus doses.The starting concentrations are 300, 1000, and 3000 mg•L À1 .Therapeutic concentrations fall in the range of 100 to 500 mg•L À1 .(B) Simulated time courses of clearance after three bolus time courses.(C) Simulated time courses of half-life after three bolus time courses.Numbers 1 to 5 correspond to the different stages schematically shown in Fig. 14.The numbers correspond to stages in Fig.13.Note that stage number 3 of Fig.15is not applicable to the bolus situation since there is no steady state during dosing, and is therefore omitted.

•
A detailed examination and analysis of open models to show what in vivo potency, efficacy, and clearance have in common and how they differ • A comprehensive literature review showing that target turnover rate varies with several factors: age, species, tissue/subregion, treatment, disease state, hormonal and nutritional state, day-night cycle, and more and therefore changes in vivo potency, efficacy, and clearance

TABLE 1
Target half-life vs. age in the rat or mouse (GABAA receptor/Bz site)

TABLE 2 Target
half-life vs. species and organ/tissue

TABLE 3
Generic expressions of open and closed pharmacological systems and their properties

TABLE 4
Treatment vs. target half-life in the rat or mouse a brain (continued) Target Turnover Impacts Potency, Efficacy, and Clearance 431 at ASPET Journals on April 10, 2024 pharmrev.aspetjournals.orgDownloaded from

TABLE 5
Impact of up-and downregulation on relevant pharmacological parameters for agonists

TABLE 6
Response duration dependence on drug and target half-lives in irreversible and reversible conditions a Estimated target half-life

TABLE 7
(Betts et al., 2010)tro K d with in vivo potency EC 50 propertiesThe EC 50 values are calculated by means of eq. 2 based on the original model parameters given in(Betts et al., 2010).

TABLE 9
Induction, inhibition or catalytic change in enzyme activity Induction is related to the metabolic activity (increase in free enzyme E or catalytic activity k cat ) which means an increase in synthesis k syn or decrease in loss k deg , or increase in k cat .Inhibition involves the opposite.If k cat decreases V max decreases.K m decreases if k cat % k off .Substrate clearance is unaffected if V max and K m changes the same.Target Turnover Impacts Potency, Efficacy, and Clearance 455 at ASPET Journals on April 10, 2024 pharmrev.aspetjournals.orgremoval) shortened the NT half-life and time to (induced) steady-state.The plasma concentration of NT decreased by 50% during pentobarbital treatment.