The Implications of Target Saturation for the Use of Drug–Target Residence

Home , Dissociation rate, Residence time

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with simulations of hypothetical compounds that have the same K values as aclidinium and The implications of target d PF-3635659, but the koff value of ipratropium. These hypothetical compounds only showed saturation for the use of drug–target a rightward shift of the occupancy–time curve and had considerably shorter duration of tar- residence time get occupancy compared with aclidinium and PF-3635659, respectively. Another example of a decrease in k that Wilhelmus E. A. de Witte, Meindert Danhof, Piet H. van der Graaf and off leads only to an affinity-driven prolongation Elizabeth C. M. de Lange of target occupancy is given in the initial opin- ion article of Copeland and colleagues1, in The interaction between a drug and its bio- Importance of target saturation which the increasing duration of target occu- logical target is a key step in the causal chain When different compounds for which a reduc- pancy was (incorrectly) used to demonstrate between drug dosing and drug effect in the tion in koff is accompanied by an increased the influence of drug–target residence time. human body. The strength of this interaction affinity are compared, increased in vivo In these simulations, the koff values are all may be represented by the drug–target dis- duration of target occupancy is expected much higher than the elimination rate con- sociation constant (Kd), which describes the based on the increased affinity alone, if the stant and the decrease in koff only results in a drug concentration that results in 50% target tested concentrations are similar and lead to rightward shift of the occupancy–time curve, occupancy (that is, the percentage of target an initial target occupancy close to 100%. As as in FIG. 1b. molecules that are bound to a drug molecule) a consequence, the increased duration of drug The fact that a higher drug concentration at equilibrium. However, the value of Kd does action that is observed in such a comparison or increased affinity leads to an increased not provide information on the rate at which cannot be attributed to the koff but is purely duration of drug effects has been described target binding equilibrium is reached after a dependent on the Kd, the pharmacokinetics in quantitative terms since the early days of change in the drug concentration. The kinet- and the administered dose. An example of pharmacokinetic/pharmacodynamic (PK/PD) ics of target binding are most simply described such a comparison is given in FIG. 1b, where modelling7. More recently, the relationship by two rate constants: the second-order asso- we took the koff, kon and elimination half-life between target saturation and the duration ciation rate constant kon and the first-order values of the HIV protease inhibitors ampre- of target occupancy has also been discussed (FIG. 1a) REF.5 dissociation rate constant koff . navir, lopinavir and atazanavir from and more quantitatively with respect to drug– Drug–target residence time, defined as simulated their target occupancy. The com- target binding kinetics; for example, see REFS4,8 4 1/koff, has received increasing attention in drug pounds with the lowest koff values, lopinavir . In a previous publication , we inves- discovery following the publication of an arti- and atazanavir, also had increased affinities tigated with mathematical approximations cle by Copeland and colleagues in 2006 that and showed an increased duration of target when drug–target dissociation (that is, koff) discussed the beneficial effect of a long dis- occupancy. As can be clearly seen in FIG. 1b, becomes the rate-limiting step for the dura- sociative half-life of a drug–target complex the increased duration of target occupancy is tion of drug action compared with pharma-

(defined as ln[2]/koff) on (selective) prolon- only the consequence of a rightward shift in cokinetics, target saturation and rebinding gation of target occupancy and thus of phar- the occupancy–time curve and thus only the (that is, the influence of target binding on 1 macological effects . Since the publication of consequence of the Kd. To demonstrate this, the drug concentration around the target). this paper, we and others have highlighted we overlaid the simulations of lopinavir and Although the influence of target saturation some limitations of the simple drug–target atazanavir with simulations of hypothetical on the duration of target occupancy is math- residence time model and the interpretation compounds that have the same Kd values as ematically well defined, the relevance of target REFS2–5 of its results; for examples, see . The lopinavir and atazanavir, but the koff value of saturation for the influence of koff on the dura- aim of this article, which is based on previ- amprenavir. tion of target occupancy has not been a focus 4 ous research from our group , is to illustrate An example where a decrease in koff does of previous articles and has been ignored in the impact of the role of target saturation lead to an additional increase in the dura- several papers focusing on the influence of koff (that is, target occupancy close to 100%) on tion of target occupancy compared with the on target occupancy. the prolongation of target occupancy and to affinity-driven increase in target occupancy To find the koff value that gives a signifi- show that lack of consideration of this role is given in FIG. 1c. In this simulation, we took cant prolongation of target occupancy, we may contribute to inaccurate conclusions the koff, kon and elimination half-life values identified previously for what values of target about the influence of drug–target binding of ipratropium, aclidinium and PF-3635659 occupancy the elimination rate constant (kel) kinetics on the duration of target occupancy. from REF.5 and REF.6 and simulated their target of the drug from plasma would have less influ-

In particular, a value of koff that is lower than occupancy at the muscarinic M3 receptor. The ence on the duration of target occupancy than 4 the pharmacokinetic elimination rate con- compounds with the lowest koff values, acli- koff (that is, for what values the koff is the main stant (kel) may not be the key determinant of dinium and PF-3635659, also had increased determinant of the duration of target occu- the duration of target occupancy as the target affinities and showed an increased duration pancy). We performed this approximation by becomes closer to being saturated. We also of target occupancy. However, the increased assuming that the slowest step on the path of discuss examples that help illustrate how to duration of target occupancy in FIG. 1c is not target dissociation and free drug elimination take into account the role of target saturation only the consequence of a rightward shift in determines the decline rate of target occu- in decisions about whether or not to select the occupancy–time curve and is therefore not pancy. To do this analysis correctly, target drug candidates with low koff values (that is, only the consequence of the increased Kd. To saturation needs to be taken into account. long drug–target residence times). demonstrate this, we overlaid the simulations The influence of target saturation becomes

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a most significant for target occupancies >50%, k a where a 1% increase in drug concentration k on leads to <0.5% increase in occupancy, while

koﬀ at target occupancies approaching 0%, a 1% increase in drug concentration leads to a 1% kel increase in target occupancy. The horizontal b 100 lines in FIG. 1c illustrate that slow drug–target dissociation is the main determinant of the 150 duration of target occupancy if both the dis- 75 sociation rate constant and the target occu-

pancy have values such that: BF < 1 − koff /kel 100 (in which BF is the target fraction bound). It 50 should be noted that this equation is rewritten from an approximation of the simple drug– target binding model and only holds for this 50 25 Concentration (nM) Concentration Target occupancy (%) Target model if the target concentration is lower than 4 the ratio kel/kon, as described previously . Of

0 0 note, the target occupancy–time curves in 0 25 50 75 100 0 25 50 75 100 FIG. 1b,c are independent of this approxima-

Time (h) –1 Time (h) tion, as they are simulated with the original koﬀ (h ) 2.3 18 2.5 18 18 equations, not with the approximations. Only the horizontal lines in FIG. 1c are based on the c 100 approximation. From this equation, it follows that when the clinical situation requires a high target 100 75 occupancy (as can be expected especially for antagonists for chronic diseases with daily or

less frequent dosing), then koff will need to 50 be much smaller than kel for it to become the 50 main determinant of the duration of target occupancy. 25 Concentration (nM) Concentration

Target occupancy (%) Target These findings can be applied directly to the selection of drug candidates. An example

0 0 in which our insights could have been applied 9 0 10 20 30 40 50 0 10 20 30 40 50 is the study of Lindström and colleagues , Time (h) Time (h) which compared the in vivo drug effects of k (h–1) oﬀ three neurokinin 1 (NK ) receptor antago- 0.029 0.072 4.0 4.0 4.0 1 nists with their pharmacokinetics. Aprepitant demonstrated a much longer duration of drug Figure 1 | Simulation of the implications of high target occupancyNature for Reviews drug–target | Drug Discovery residence effect, which can clearly be attributed to tar- time. a | Model used in the simulations. Here, ka and kel represent the first-order absorption constant −1 (3.0 h ) and elimination rate constant, respectively, while kon and koff represent the second-order asso- get saturation, considering that the effect is ciation rate constant and the first-order dissociation rate constant, respectively. b | Simulations of close to 100% for a long time in the experi- plasma drug concentrations (left panel) and the resulting target occupancy profiles (right panel) for ment, followed by a steep decline. In contrast, different compounds. The solid lines represent the HIV protease inhibitors amprenavir (red), ataza- the authors conclude that the duration of the navir (yellow) and lopinavir (green), with k values of 1.1, 6.2 and 23nM−1 h−1, respectively. The dotted on effect of aprepitant cannot be explained by lines represent hypothetical compounds with the same K values as atazanavir and lopinavir but the d its pharmacokinetics. The other two com- same k value as amprenavir, leading to k values of 44 (blue) and 176 (orange) nM−1 h−1, respectively. off on pounds in this study did not show this target The target concentration was set at 1 pM. The elimination rate constant was 0.082 h−1. The dose in the saturation and the authors conclude that this absorption compartment corresponds to an initial plasma concentration of 200 nM, if absorption would be immediate. All plasma concentration profiles overlap. For the associated differential equa- is probably explained by their faster binding tions, see Supplementary information S1, and for the R simulation script, see Supplementary informa- kinetics. However, our findings above indicate tion S2. Similar simulations can be performed online (see Related links).c | Simulations of plasma drug that the increased duration of the aprepitant concentrations (left panel) and the resulting target occupancy profiles (right panel) for different effect is mainly due to its high brain concen- compounds. The solid lines represent the muscarinic receptor antagonists ipratropium (red), acli- trations compared with its affinity, which −1 −1 dinium (yellow) and PF-3635659 (green), with kon values of 15, 4.0 and 1.4 nM h , respectively. The causes target saturation. dotted lines represent hypothetical compounds with the same K values as aclidinium and d Our quantitative approximations can also PF-3635659 but the same k value as ipratropium, leading to k values of 198 (blue) and 218 (orange) off on be applied to the decision as to whether to nM−1 h−1, respectively. All plasma concentration profiles overlap. The concentration of the target (the consider drug–target residence time in hit muscarinic M receptor was set at 1 pM. The elimination rate constant was 0.69 h−1. The dose in the 3 and/or lead selection. For C-C chemokine absorption compartment corresponds to an initial plasma concentration of 200 nM, if absorption is immediate. The dashed horizontal lines denote the situation in which the target fraction bound receptor type 2 (CCR2) antagonists, an occupancy of >90% is considered to be required equals 1 − koff/kel (see text). Below that line, the condition is met for which koff is the main determinant of the decline rate of target occupancy. for a sufficient drug effect. Based on the

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equation above, this means that the dissocia- kinetics for each specific project, depending 6 Keserü, G. M. & Swinney, D. C. Thermodynamics and Kinetics of Drug Binding (Wiley-VCH Verlag GmbH & tion half-life needs to be 10 times larger than on the required level of target occupancy and Co. KGaA, Heidelberg, Germany, 2015). the plasma half-life in order for it to be the the (predicted) pharmacokinetics. 7. Levy, G. Kinetics of pharmacologic effects. Clin. Pharmacol. Ther. 7, 362–372 (1966). main determinant of target occupancy. As the 8. Vauquelin, G. & Van Liefde, I. Slow antagonist plasma half-life of the CCR2 antagonist iden- Wilhelmus E. A. de Witte1*, Meindert Danhof1, Piet H. dissociation and long-lasting in vivo receptor 1,2 1 10 van der Graaf and Elizabeth C. M. de Lange protection. Trends Pharmacol. Sci. 27, 356–359 tified by Bot and colleagues was 11 hours , (2006). this means that the dissociation half-life 1Division of Pharmacology, Leiden Academic Centre 9. Lindström, E. et al. Neurokinin 1 receptor antagonists: correlation between in vitro receptor interaction would need to be 110 hours or longer before for Drug Research, Leiden University, Leiden, The Netherlands. and in vivo efficacy. J. Pharmacol. Exp. Ther. 322, it became the main determinant of the dura- 1286–93 (2007). 2 10. Bot, I. et al. A novel CCR2 antagonist inhibits tion of drug effect. In combination with the Certara Quantitative Systems Pharmacology, Canterbury Innovation Centre, Canterbury, UK. atherogenesis in apoE deficient mice by achieving high knowledge that such long dissociation half- receptor occupancy. Sci. Rep. 7, 52 (2017). 4 *e-mail: [email protected] lives are rarely observed , this suggests that Acknowledgements seeking to prolong the dissociation half-life doi:10.1038/nrd.2018.234 The authors are part of the K4DD consortium, which is sup- Published online 28 Dec 2018 ported by the Innovative Medicines Initiative Joint Under should not be prioritized when searching for taking (IMI JU) under grant agreement no 115366. The IMI CCR2 antagonists with a prolonged duration JU is a project supported by the EU’s Seventh Framework 1. Copeland, R. A., Pompliano, D. L. & Meek, T. D. Programme (FP7/2007–2013) and the European Federation of effect, or for other drug targets for which Drug–target residence time and its implications for of Pharmaceutical Industries and Associations (EFPIA). high occupancies are considered essential to lead optimization. Nat. Rev. Drug Discov. 5,730–739 (2006). Competing interests achieve the desired pharmacological effect. 2 Tonge, P. J. Drug–target kinetics in drug discovery. The authors declare no competing interests. ACS Chem. Neurosci. 9, 29–39 (2018). 3. Folmer, R. H. A. Drug target residence time: a Supplementary information Conclusion misleading concept. Drug Discov. Today 23 ,12–16 Supplementary information is available at https://doi.org/ (2018). 10.1038/nrd.2018.234 Target saturation is an important factor that 4 de Witte, W. E. A., Danhof, M., van der Graaf, P. H. & should be included in the analysis of the influ- de Lange, E. C. M. In vivo target residence time and kinetic selectivity: the association rate constant as ence of drug–target binding kinetics on tar- determinant. Trends Pharmacol. Sci. 37, 831–842 RELATED LINKS get occupancy. By doing so, drug discovery (2016). Absorption, binding and elimination model: https:// scientists would be better equipped to decide 5. Dahl, G. & Akerud, T. Pharmacokinetics and the drug wilbertdewitte.shinyapps.io/absorption_binding_elimination –target residence time concept. Drug Discov. Today ALL LINKS ARE ACTIVE IN THE ONLINE PDF on the relevance of drug–target binding 18, 697–707 (2013).