Abstract
Purpose
Unexpected and complex experimental observations related to efflux transport have been reported in the literature. This work was conducted to develop relationships for efflux activity (PSefflux) as a function of commonly studied kinetic parameters [permeability-surface area product (PS), efflux ratio (ER), degree of efflux inhibition (ϕi), 50% inhibitory concentration (IC50), and Michaelis–Menten constant (Km)].
Methods
A three-compartment model (apical, cellular, and basolateral) was used to derive flux equations relating the initial rate of flux and steady-state mass transfer in the presence or absence of active efflux. Various definitions of efflux ratio (ER) were examined in terms of permeability-surface area products. The efflux activity (PSefflux) was expressed in terms of ER and PS. The relationships between PSefflux and PS, ER, ϕi, IC50, and Km were solved mathematically. Simulations and examples from the literature were used to illustrate the resulting mathematical relationships.
Results
The relationships derived according to a three-compartment model differed fundamentally from commonly accepted approaches for determining PSefflux, ϕi, IC50 and Km. Based on the model assumptions and mathematical derivations, currently used mathematical relationships erroneously imply that efflux activity is proportional to change in PS (i.e., flux or Papp) and thus underestimate PSefflux and ϕi, and overestimate IC50 and Km.
Conclusions
An understanding of the relationship between efflux inhibition and kinetic parameters is critical for appropriate data interpretation, standardization in calculating and expressing the influence of efflux transport, and predicting the clinical significance of efflux inhibition.
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Abbreviations
- ϕi :
-
degree of efflux inhibition
- \({\text{\rm ER}}_{\alpha } \) :
-
asymmetry efflux ratio (PSB→A/PSA→B) or steady-state (CA/CB)
- ERA :
-
apical efflux ratio (PS0,B→A/PSB→A) or steady-state (CA,0/CA)
- ERB :
-
basolateral efflux ratio (PSI,A→B/PSA→B ) or steady-state (CB,I/CB)
- ERC :
-
cellular efflux ratio (PSI,A→C/PSA→C ) or steady-state (CC,I,/CC)
- [I]:
-
inhibitor concentration
- IC50 :
-
50% inhibitory concentration
- Ki :
-
inhibitor constant
- Km :
-
Michaelis–Menten constant
- PS:
-
observed permeability-surface area product
- PS0 :
-
permeability–surface area product in the absence of efflux inhibition
- PSI :
-
permeability–surface area product when efflux is completely inhibited or saturated; passive permeability-surface area product
- [S]:
-
substrate concentration
- A:
-
apical
- B:
-
basolateral
- C:
-
cellular
- app:
-
apparent
- max:
-
maximum
- 0:
-
absence of efflux inhibition
- I:
-
efflux is completely inhibited or saturated
- A→B:
-
apical to basolateral; apical compartment dosed
- B→A:
-
basolateral to apical; basolateral compartment dosed
- A→C:
-
apical to cellular; apical compartment dosed
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Acknowledgments
We gratefully thank Maciej Zamek-Gliszczynski, Rong Zhao, and Beverly Mowrey for critically reading the manuscript. This work was supported by NIH GM61191 and Pfizer Inc. J. Cory Kalvass was supported by a predoctoral fellowship in pharmacokinetics and drug disposition from the Eli Lilly and Company Foundation.
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Kalvass, J.C., Pollack, G.M. Kinetic Considerations for the Quantitative Assessment of Efflux Activity and Inhibition: Implications for Understanding and Predicting the Effects of Efflux Inhibition. Pharm Res 24, 265–276 (2007). https://doi.org/10.1007/s11095-006-9135-x
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DOI: https://doi.org/10.1007/s11095-006-9135-x