TABLE 3.

Parameter estimates from exhaustive fitting

Drug	“Vmax” k21T(0) (M/s)*	Active P-gp density T(0) (per μm2)†	Association to P-gp k11 (M−1s−1)‡	Binding constant KB (M−1)§ “KD,Aq”	Efflux to apical chamber k21 (s−1)¶	Dissociation to bilayer kr1 (s−1)‖
AMP (n = 8)	9 × 10−3	32–320	2 × 109–2 × 1010	(1.3 ± 0.6) × 103 “3 μM”	20–200	>1 × 10+6
QND (n = 6)	8 × 10−4 (No fit for 1 μM)	8–80	2 × 108–1010	(6 ± 3) × 103 “0.2 μM”	8–80	>2 × 10+4
LPM (n = 6)	2 × 10−4 [LPM] = 3–20 μM (No fit for 0.3 μM)	8–80	108–1010	100–200 [LPM] ≥ 10 μM “2 μM”	2–20 [LPM] ≥ 10 μM	>5 × 10+5
				1000–3000 [LPM ]≤ 1 μM “0.2 μM”		>3 × 10+4

^*For amprenavir, the average value for 60–100 μM was k₂₁T(0) = 9 × 10⁻³ M/s, as shown in Fig.7. For quinidine, the asymptote for 0.3–20 μM was k₂₁T(0) ∼ 8 × 10⁻⁴ M/s. At 1 μM quinidine, no stable value for k₂₁T(0) was found. At 30 μM quinidine, the value was much smaller, due to the very small contribution of P-gp to overall transport because of saturation binding. For loperamide, the asymptote for 3–20 μM was roughly k₂₁T(0) ∼ 2 × 10⁻⁴ M/s. A value as large as k₂₁T(0) = 3 × 10⁻⁴ M/s was possible, but subsequent fits were not significantly sensitive to this choice. At 0.3 μM, there was no convergence to a single k₂₁T(0) value. At 30 μM, the value was smaller, likely due to the very small contribution of P-gp to overall transport, as was the case for quinidine. The k₂₁T(0) values shown were fixed by at least the first 250 best fits, which all have the same CV, i.e., these are robust fits at each concentration.

^†Efflux-active concentration of P-gp in the inner apical monolayer was bounded by T(0) = (4–40) × 10⁻⁵M for amprenavir, Fig. 9. For quinidine and loperamide, slightly lower ranges were found, (1–10) × 10⁻⁵M (data not shown), but there is substantial overlap. These units have been converted to a more typical form, assuming a 2 nm lipid monolayer thickness for the acyl chain region. T(0) (Pgp/μm²) = 0.8 × T(0) (μM, inner apical monolayer). The ratio of apical membrane to the insert cross-section area is irrelevant, since it cancels out in this calculation.

^‡Range for k₁₁ found in the final forward fit. As shown for amprenavir in Fig. 8, the range was k₁₁ = (1–10) × 10⁹ M⁻¹s⁻¹. For quinidine and loperamide, the range was broader, k₁₁ = (0.2–10) × 10⁹ M⁻¹s⁻¹ (data not shown).

^§Binding constant between P-gp and the inner apical monolayer shown is the average of the best fits (>160 for each drug concentration) as shown in Fig. 10 for amprenavir. For quinidine, the value for 30 μM was omitted due to active transport saturation, as noted above for k₂₁T(0). For loperamide, there were two ranges of binding constants. At 10 and 20 μM, the binding constant to P-gp was in the range of 100–200 M⁻¹. The fit at 30 μM was not used due to active transport saturation. At 0.3 and 1 μM, the binding constant was in the range of 1000–3000 M⁻¹. For 3 μM loperamide, the binding constant was an intermediate value of ∼600 M⁻¹. Since all A > B flux was fitted to a single binding constant, a better deconvolution of this parameter is not yet possible. Below each binding constant, we show in parentheses the appropriate dissociation constant for each drug relative to the aqueous phase, calculated as K_D,Aq = 1/(K_B × drug partition coefficient{PS/PE/chol}), the liposome mimic for the inner apical monolayer. These aqueous dissociation constants are given only to a single significant digit, and no error bars were calculated. These are intrinsic dissociation constants and are not the same as those derived from a steady-state Michaelis-Menten analyses.

^¶Estimate for the efflux rate constant k₂₁, from P-gp into the apical chamber, given by the ratio of the fitted k₂₁T(0) for each drug and the center-of-the-box value of T(0) = 5 × 10⁻⁵ M. See text and second footnote (^†) above.

^‖Estimate for the dissociation rate constant k_r1, given by the ratio of the center-of-the-box value of k₁₁ = 3 × 10⁹ M⁻¹s⁻¹ and the fitted K_B = k₁₁/k_r1 for each drug. See text and third footnote (^‡) above.