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Closed-Loop Doluisio (Colon, Small Intestine) and Single-Pass Intestinal Perfusion (Colon, Jejunum) in Rat—Biophysical Model and Predictions Based on Caco-2

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ABSTRACT

Purpose

The effective rat intestinal permeability (P eff ) was deconvolved using a biophysical model based on parameterized paracellular, aqueous boundary layer, transcellular permeabilities, and the villus-fold surface area expansion factor.

Methods

Four types of rat intestinal perfusion data were considered: single-pass intestinal perfusion (SPIP) in the jejunum (n = 40), and colon (n = 15), closed-loop (Doluisio type) in the small intestine (n = 78), and colon (n = 74). Moreover, in vitro Caco-2 permeability values were used to predict rat in vivo values in the rat data studied.

Results

Comparable number of molecules permeate via paracellular water channels as by the lipoidal transcellular route in the SPIP method, although in the closed-loop method, the paracellular route appears dominant in the colon. The aqueous boundary layer thickness in the small intestine is comparable to that found in unstirred in vitro monolayer assays; it is thinner in the colon. The mucosal surface area in anaesthetized rats is 0.96–1.4 times the smooth cylinder calculated value in the colon, and it is 3.1–3.6 times in the small intestine. The paracellular permeability of the intestine appeared to be greater in rat than human, with the colon showing more leakiness (higher P para ) than the small intestine.

Conclusion

Based on log intrinsic permeability values, the correlations between the in vitro and in vivo models ranged from r2 0.82 to 0.92. The SPIP-Doluisio method comparison indicated identical log permeability selectivity trend with negligible bias.

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Abbreviations

ε/δ :

Porosity of paracellular junction pores divided by the rate-limiting paracellular pathlength (cm−1); size-restricted, cation-selective

(ε/δ) 2 :

Secondary porosity-pathlength ratio (cm−1); charge/size nonspecific “free diffusion” term

Δφ :

Electrical potential drop (mV) across the electric field created by negatively-charged residues lining the junctional pores

ABL:

Aqueous boundary layer—adjacent to the surface of a cell monolayer or luminal side of intestine

A SS :

“smooth surface” area in intestinal segment (= 2π R e ·L) of length L and effective radius R e (cm2)

A eff :

Effective surface area (= k VF ·A SS ) of luminal absorptive surface in the intestine (cm2)

Caco-2:

Human cancer of the colon epithelial cell line

D aq :

Aqueous diffusivity (cm·s−1)

DRW:

Dynamic range window: observable permeability, with P ABL as top limit and P para as bottom limit

E(Δφ):

Function due to electrical potential drop across the cell junction (dimensionless)

f(0), f(+), f(−) :

Concentration fraction in uncharged, positively-, and negatively-charged forms, respectively

F(r HYD /R):

Renkin molecular sieving function, dimensionless fraction in the range of 0 to 1

h ABL :

ABL thickness (μm)

k VF :

Villus-fold surface area expansion factor (dimensionless)

MDCK:

Madin-Darby Canine Kidney epithelial cell line

P ABL :

ABL permeability (cm·s−1)

P app :

In vitro apparent permeability of an epithelial cell monolayer, e.g., Caco-2 (cm·s−1); can be pH dependent

P C :

Lipoidal transcellular permeability (cm·s−1); can be pH dependent

P eff :

Effective intestinal permeability (cm·s−1) in rat single-pass intestinal perfusion (SPIP) or closed-loop Doluisio (CLD) method; can be pH dependent

P 0 :

Intrinsic permeability of uncharged permeant (cm·s−1); pH independent. P 0 may be calculated from the plot of log P app vs. pH, as suggested by Fig. 2. However, if only a single P app -pH point is available, the calculation of P 0 is more complicated, as described in “Material and Methods” section, and further detailed in Appendix.

P para :

Paracellular permeability (cm·s−1); can be slightly pH dependent

R :

Cell junction pore radius (Å)

R e :

Effective radius of the rat intestinal segment (cm)

r HYD :

Hydrodynamic molecular radius (Å)

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Authors and Affiliations

  1. Pharmacokinetics and Pharmaceutical Technology, Miguel Hernandez University, Alicante, Spain

    Isabel Lozoya-Agullo, Isabel Gonzalez-Alvarez, Marta Gonzalez-Alvarez & Marival Bermejo

  2. Pharmacokinetics and Pharmaceutical Technology, University of Valencia, Valencia, Spain

    Isabel Lozoya-Agullo, Teresa M. Garrigues & Matilde Merino-Sanjuán

  3. Department of Clinical Pharmacology, Faculty of Health Sciences, Ben-Gurion University of the Negev, Beer-Sheva, Israel

    Moran Zur, Noa Fine-Shamir, Yael Cohen, Milica Markovic & Arik Dahan

  4. in-ADME Research, 1732 First Avenue, No.102, New York, New York, 10128, USA

    Alex Avdeef

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  1. Isabel Lozoya-Agullo
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Correspondence to Marival Bermejo.

Additional information

Isabel Lozoya-Agullo and Isabel Gonzalez-Alvarez should be considered as joint first co-authors.

Chemical compounds studied in this article: Acetaminophen (PubChem CID:1983); Antipyrine (PubChem CID:2206); Atenolol (PubChem CID:2249); Caffeine (PubChem CID:2519); Carbamazepine (PubChem CID:2554); Cimetidine (PubChem CID:2756); Codeine (PubChem CID: 5284371); Colchicine (PubChem CID:6167); Digoxin (PubChem CID: 2724385); Furosemide (PubChem CID:3440); Hydrocortisone (PubChem CID:5754); Ibuprofen (PubChem CID:3672); Metformin (PubChem CID:4091); Metoprolol (PubChem CID: 4171); Pravastatin (PubChem CID: 54687).

Appendix. Computational Method—Permeability Model

Appendix. Computational Method—Permeability Model

Computational Method—Multi-Peff Group Values Used to Determine Rat DRW Parameters

The model used here begins with the deconvolution of rat intestinal P eff , measured at a particular physiological pH (ideally near the microclimate value), into its three effective components: P eff ABL, P eff trans, and P eff para (ABL, transcellular, and paracellular permeability, respectively). All the P eff values for a particular data type (segment: colon/small intestine; method: SPIP/CLD,) are pooled into a single group nonlinear regression analysis to determine a series of parameters (see below) that define the ABL and paracellular limits (cf. Fig. 2) of the dynamic range window (DRW) for the particular data type.

Since each P eff is a composite of ABL/paracellular, and transcellular contributions, it is necessary to remove the latter (transcellular) part, so as to focus just on the ABL and paracellular components which define the DRW limits. This can be accomplished by employing the apparent octanol-water partition coefficient, D OCT , and making the approximation P eff trans = a + b log D OCT , with the constants a and b determined by regression analysis, along with all the other parameters defining the DRW limits (44). Alternatively, in place of D OCT , one could use the P C derived from Caco-2 P app values measured as a function of pH (with P C determined by the pK a FLUX method, as described by Avdeef et al.(35). This second approach was used in the analysis of the DRW limits of the human jejunum permeability (27). It was decided also to use the Caco-2 approximation in the present study.

The equation to deconvolve the three components of effective permeability may be stated as

$$ \frac{1}{P_{eff}}\kern0.5em =\left(\frac{1}{P_{eff}^{ABL}}\kern0.5em +\kern0.5em \frac{1}{P_{eff}^{trans}+{P}_{eff}^{para}}\right)\kern0.5em =\kern1em \frac{1}{k_{VF}}\kern0.5em \cdot \left(\frac{h_{ABL}}{D_{aq}}\kern0.5em +\kern0.5em \frac{1}{P_C+{P}_{para}}\right) $$
(4)

It is assumed that P eff trans in the rat intestine can be approximated using the P C values derived from Caco-2 measurements: P eff trans ≈ k VF ·P C Caco-2. It is assumed that P eff ABL = k VF ·D aq / h ABL , where D aq is the aqueous diffusivity of the molecule and h ABL is the ABL thickness (with reference to the actual surface area, i.e., smooth cylinder value multiplied by k VF ) in the perfusion experiment. Values of D aq (cm2·s−1) at 37°C were empirically estimated from the molecular weight, MW, as

$$ {D}_{aq}=0.991\times {10}^{-4}{\mathrm{MW}}^{-0.453} $$
(5)

which was derived from the analysis of mostly drug-like molecules (44). The thickness of the physical boundary layer, h ABL , depends on the effective agitation level in the perfusion experiment, which is expected to depend on flow rate used and animal handling. For in vitro (microtitre plate) methods, typical values are about 1500–2500 μm in unstirred solutions, and about 150 μm in solutions stirred at 450 RPM (rev·min−1).

P C represents the transcellular permeability contribution, associated with cell membranes (apical, basolateral and cytosol organelle) and any contributions from CM processes. For a molecule with a single ionizable group (ionization constant, pK a ), P C is defined by a sigmoidal function, as shown in Fig. 2 by the solid curve:

$$ {P}_C=\frac{P_0}{10^{\pm \left( pH-{pK}_a\right)}+1}+\frac{P_i}{10^{\pm \left({pK}_a- pH\right)}+1}+\cdots $$
(6)

where the ‘±’ is ‘+’ for acids and ‘-’ is for bases. The maximum possible value of P C is the permeability of the neutral species, P 0 ; the minimum possible P C value is the permeability of the ionized species, P i (most likely effected by CM transport). Figure 2 summarizes the relationship between these components of permeability.

P para can estimated from the differential flux equation describing size- and charge-restricted diffusion through a cylindrical channel containing charged groups, under sink boundary condition (42,77). Avdeef et al. (27) extended the model to include two populations of junctional pores: (i) high-capacity ε/δ, size-restricted and cation-selective pathways, and (ii) secondary (ε/δ) 2 low-capacity, “free diffusion” pathways independent on size and charge. The dual-pore population paracellular equation use in this study is

$$ {P}_{para}\kern0.5em =\frac{\varepsilon }{\delta}\cdot {D}_{aq}\cdot F\left(\frac{r_{HYD}}{R}\right)\cdot E\left(\Delta \phi \right)\kern0.5em +\kern0.5em {\left(\frac{\varepsilon }{\delta}\right)}_2\cdot {D}_{aq} $$
(7)

where most of the terms have been defined already (cf., Abbreviations). F(r HYD /R) is the Renkin hydrodynamic sieving function for cylindrical water channels, with values ranging from 0 to 1, defined as a function of molecular hydrodynamic radii (r HYD ) and pore radii (R), both usually expressed in Å units,

$$ F\left(\frac{r_{HYD}}{R}\right)={\left[1-\left(\frac{r_{HYD}}{R}\right)\right]}^2\cdot \left[1-2.104\left(\frac{r_{HYD}}{R}\right)+2.09{\left(\frac{r_{HYD}}{R}\right)}^3-0.95{\left(\frac{r_{HYD}}{R}\right)}^5\right] $$
(8)

Values of r HYD (Å) were estimated from the Sutherland-Stokes-Einstein spherical-particle empirical Eq. (44)

$$ {r}_{HYD}=\left(0.92+\frac{21.8}{MW}\right)\cdot \frac{10^8{k}_BT}{6\pi\;\eta\;{D}_{aq}} $$
(9)

where kB = Boltzmann constant, T = absolute temperature, and η = solvent kinematic viscosity (0.00696 cm2·s−1, 37°C).

The E(Δφ) term in Eq. 7 is a function of the potential drop, Δφ, across the electric field created by negatively-charged residues lining the junctional pores (42,77),

$$ E\left(\Delta \phi \right)={f}_{(0)}+{f}_{\left(+\right)}\cdot \frac{\kappa \cdot \left|\Delta \phi \right|}{1-{e}^{-\kappa \cdot \left|\Delta \phi \right|}}+{f}_{\left(-\right)}\cdot \frac{\kappa \cdot \left|\Delta \phi \right|}{e^{+\kappa \cdot \left|\Delta \phi \right|}-1} $$
(10)

where f (0) , f (+) , and f (−) are the concentration fractions of the molecule in the uncharged, cationic, and anionic forms, respectively. The constant, κ = (Ғ /NAkBT) = 0.037414 mV−1 at 37°C, where Ғ is the Faraday constant, and other symbols have their usual meaning. The average Δφ of −43 mV, from many Caco-2 studies. For very large channels (r < < R) or for channels not lined with a high charge density, E(Δφ) ~ 1.

In the case of very leaky cell junctions (R > 20 Å), it may not be possible to determine all of the parameters in Eq. (7). A simplified “free diffusion” form may be used.

$$ {P}_{para}\approx {\left(\frac{\varepsilon }{\delta}\right)}_2\cdot {D}_{aq} $$
(11)

Refinement of the Permeability Parameters which Define the Dynamic Range Window

The pCEL-X program (v4.03, in-ADME Research) can be used to determine the k VF , h ABL , ε/δ, (ε/δ)2, R, and Δφ parameters by a weighted nonlinear regression analysis based on the logarithmic form of Eq. 4, expanded with Eqs. 5–10:

$$ G\left({k}_{VF},{h}_{ABL},\frac{\varepsilon }{\delta },{\frac{\varepsilon }{\delta}}_2,R,\Delta \phi \right)=\log {k}_{VF}-\log \left[\frac{h_{ABL}}{D_{aq}}+\frac{1}{P_c^{6.5}\kern0.5em +\kern0.5em \frac{\varepsilon }{\delta}\cdot {D}_{aq}\cdot F\left(\frac{r_{HYD}}{R}\right)\kern0.5em \cdot \kern0.5em E\left(\Delta \phi \right)+\kern0.5em {\frac{\varepsilon }{\delta}}_2\cdot {D}_{aq}}\kern0.5em \right] $$
(12)

The partial derivatives of G with respect to ε/δ, (ε/δ)2, R, Δφ, h ABL , and k VF are calculated explicitly in the pCEL-X program, based on standard mathematical techniques. The weighted residuals function minimized was

$$ {R}_w\kern0.5em =\kern0.5em \sum \limits_i^n{\left(\frac{\log {P}_{eff,i}^{obs}-{G}_i^{calc}}{\sigma_i\left(\log\;{P}_{eff}\right)}\right)}^2 $$
(13)

where n is the number of P eff values used in the model refinement, and σ i (log P eff ) is the reported standard deviation of the logarithm of the ith measured rat intestinal permeability. The effectiveness of the refinement is characterized by the “goodness-of-fit”, GOF = [Rw/(n-nV)]1/2, where nV refers to the number of varied parameters. The expected value of GOF is 1 if the model is suitable for the data and the measured standard deviations accurately reflect the precision of the data.

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Lozoya-Agullo, I., Gonzalez-Alvarez, I., Zur, M. et al. Closed-Loop Doluisio (Colon, Small Intestine) and Single-Pass Intestinal Perfusion (Colon, Jejunum) in Rat—Biophysical Model and Predictions Based on Caco-2. Pharm Res 35, 2 (2018). https://doi.org/10.1007/s11095-017-2331-z

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