Convective washout reduces the antidiarrheal efficacy of enterocyte surface–targeted antisecretory drugs

Abstract

Secretory diarrheas such as cholera are a major cause of morbidity and mortality in developing countries. We previously introduced the concept of antisecretory therapy for diarrhea using chloride channel inhibitors targeting the cystic fibrosis transmembrane conductance regulator channel pore on the extracellular surface of enterocytes. However, a concern with this strategy is that rapid fluid secretion could cause convective drug washout that would limit the efficacy of extracellularly targeted inhibitors. Here, we developed a convection-diffusion model of washout in an anatomically accurate three-dimensional model of human intestine comprising cylindrical crypts and villi secreting fluid into a central lumen. Input parameters included initial lumen flow and inhibitor concentration, inhibitor dissociation constant (K(d)), crypt/villus secretion, and inhibitor diffusion. We modeled both membrane-impermeant and permeable inhibitors. The model predicted greatly reduced inhibitor efficacy for high crypt fluid secretion as occurs in cholera. We conclude that the antisecretory efficacy of an orally administered membrane-impermeant, surface-targeted inhibitor requires both (a) high inhibitor affinity (low nanomolar K(d)) to obtain sufficiently high luminal inhibitor concentration (>100-fold K(d)), and (b) sustained high luminal inhibitor concentration or slow inhibitor dissociation compared with oral administration frequency. Efficacy of a surface-targeted permeable inhibitor delivered from the blood requires high inhibitor permeability and blood concentration (relative to K(d)).

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J. Gen. Physiol. Vol. 141 No. 2 261–272
www.jgp.org/cgi/doi/10.1085/jgp.201210885 261
INTRODUCTION
Excessive intestinal uid secretion occurs in entero-
toxin-mediated secretory diarrheas caused by Vibrio cholera
and enterotoxigenic Escherichia coli (Field, 1979). The
rate-limiting step in uid secretion is chloride transport
from the enterocyte cytoplasm into the intestinal lumen,
which creates the electroosmotic force driving sodium and
water secretion (Murek et al., 2010; Venkatasubramanian
et al., 2010; Thiagarajah and Verkman, 2012). Cell cul-
ture and animal models (Chao et al., 1994; Gabriel et al.,
1994; Thiagarajah et al., 2004) indicate that elevation in
cyclic nucleotides caused by bacterial enterotoxins
activates the CFTR, a chloride channel expressed on
the luminal surface of enterocytes. CFTR inhibition
is thus predicted to be of clinical benet as antisecre-
tory therapy in diarrheas caused by bacterial entero-
toxins (Al-Awqati, 2002; Zhang et al., 2012).
We identied a class of small molecules, the glycine
hydrazides and the related malonic acid hydrazides
(MalH), as CFTR inhibitors that target the extracellu-
lar-facing pore of CFTR (Muanprasat et al., 2004). An
extracellular site-of-action was suggested by patch-clamp
measurements showing outwardly rectifying whole-cell
currents and rapid single-channel icker (Muanprasat
et al., 2004), and proven from CFTR inhibition by mem-
brane-impermeant MalH–polyethylene glycol conjugates
Correspondence to Alan S. Verkman: a l a n . v e r k m a n @ u c s f . e d u
Abbreviation used in this paper: MalH, malonic acid hydrazides.
(Sonawane et al., 2006). Subsequently, multivalent
membrane-impermeant conjugates of MalH with lec-
tins (Sonawane et al., 2007) and polyethylene glycols
(Sonawane et al., 2008) were synthesized with Kd <
100 nM for inhibition of CFTR chloride conductance.
These membrane-impermeant, nonabsorbable con-
jugates showed antisecretory efcacy in closed-loop
and sucking mouse models of cholera. Membrane-
permeable, absorbable glycine hydrazide analogues
were also synthesized for potential therapy of polycys-
tic kidney disease, in which cyst growth is CFTR de-
pendent (Yang et al., 2008).
Nonabsorbable CFTR inhibitors are potentially useful
for antisecretory therapy because of their minimal sys-
temic exposure. A glycine hydrazide analogue, iOWH032
(de Hostos et al., 2011), with modest CFTR inhibition
potency (Kd of 8 µM), is currently in early-stage clinical
trials for cholera therapy. A natural product, crofelemer,
which is thought to act by inhibition of CFTR and cal-
cium-activated chloride channels (Tradtrantip et al.,
2010), is also in clinical trials (Cottreau et al., 2012). Cro-
felemer consists of large proanthocyanidin oligomers
that are predicted to be membrane impermeable and
thus externally acting.
Convective washout reduces the antidiarrheal efficacy of enterocyte
surface–targeted antisecretory drugs
Byung-Ju Jin,1,2 Jay R. Thiagarajah,1,2,3 and A.S. Verkman1,2
1Department of Medicine and 2Department of Physiology, University of California, San Francisco, San Francisco, CA 94143
3Department of Pediatrics, Massachusetts General Hospital, Boston, MA 02114
Secretory diarrheas such as cholera are a major cause of morbidity and mortality in developing countries. We previ-
ously introduced the concept of antisecretory therapy for diarrhea using chloride channel inhibitors targeting the
cystic brosis transmembrane conductance regulator channel pore on the extracellular surface of enterocytes.
However, a concern with this strategy is that rapid uid secretion could cause convective drug washout that would
limit the efcacy of extracellularly targeted inhibitors. Here, we developed a convection–diffusion model of wash-
out in an anatomically accurate three-dimensional model of human intestine comprising cylindrical crypts and villi
secreting uid into a central lumen. Input parameters included initial lumen ow and inhibitor concentration,
inhibitor dissociation constant (Kd), crypt/villus secretion, and inhibitor diffusion. We modeled both membrane-
impermeant and permeable inhibitors. The model predicted greatly reduced inhibitor efcacy for high crypt uid
secretion as occurs in cholera. We conclude that the antisecretory efcacy of an orally administered membrane-
impermeant, surface-targeted inhibitor requires both (a) high inhibitor afnity (low nanomolar Kd) to obtain
sufciently high luminal inhibitor concentration (>100-fold Kd), and (b) sustained high luminal inhibitor concen-
tration or slow inhibitor dissociation compared with oral administration frequency. Efcacy of a surface-targeted
permeable inhibitor delivered from the blood requires high inhibitor permeability and blood concentration (rela-
tive to Kd).
© 2013 Jin et al. This article is distributed under the terms of an Attribution–Noncommer-
cial–Share Alike–No Mirror Sites license for the first six months after the publication date
(see http://www.rupress.org/terms). After six months it is available under a Creative Com-
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The Journal of General Physiology

262 Convection–diffusion model of intestine
from the intestinal wall, and the villi project in an inward radial
direction. The inhibitor target, CFTR, is heterogeneously dis-
tributed in the lumen-facing (apical) membrane of epithelial
cells along the crypt–villus axis, with its extracellular surface ex-
posed to the luminal uid. Based on published anatomical data
in human male adult mid-jejunum (Loehry and Creamer, 1969;
Marsh and Swift, 1969; Trbojević-Stanković et al., 2010), typical
crypt length is 150 µm and inner diameter (of the aqueous lu-
men) is 20–25 µm; typical villus length is 350 µm and inter-crypt
spacing is 100 µm. Volume ux across the epithelium at loca-
tion z along the crypt–villus, Jv(z), depends on CFTR density, the
magnitude of the secretory stimulus, and the concentration of
inhibitor contacting the villus–crypt wall. In cholera, typical
uid secretion rate in mid-jejunum is 4.5 ml/h per cm intes-
tine (Banwell et al., 1970; Van Loon et al., 1992; Bearcroft et al.,
1997), which, together with a crypt density of 12,500 cm2
(Trbojević-Stanković et al., 2010) and a jejunal diameter of 4–5
cm, corresponds to a single-crypt uid secretion rate of 4 ×
107 cm3/min (7 × 102 µL/cm2/s at the crypt surface). Fluid
viscosity in the crypt lumen is 10-fold greater than that of water,
as measured by photobleaching and dye polarization (Naftalin
et al., 1995). Material properties and baseline parameters are listed
in Table 1. For a single cylindrical crypt–villus unit, the com-
puted parameters include inhibitor concentration Ci (r,z) and
velocity Vi (r,z), in which cylindrical symmetry allows specica-
tion of location by radial dimension r and axial position z.
Fig. 1 B shows the generic three-dimensional geometry of the
intestine, with crypts and villi projecting radially from the cylin-
drical intestinal wall. The diameter of the intestinal lumen is
orders of magnitude greater than crypt length. Fluid entering
the intestinal lumen has a specied inhibitor concentration and
ow velocity, which may vary in time (because of intermittent
oral administration). Because the intestinal lumen is cylindri-
cally symmetric and large compared with crypt dimensions, dif-
fusion–convection for the geometry shown in Fig. 1 B can
be simplied to that of a truncated radial wedge of uid with
A potentially important though largely ignored con-
cern in the application of externally targeted inhibitors
is washout as a result of convection caused by rapid
uid secretion. Convection effects cannot be addressed
easily in animal models because of differences from
humans in crypt–villus geometry and uid secretion
rates, as well as the lack of suitable animal models of
secretory diarrhea. As diagrammed in Fig. 1 A, the intes-
tine contains a dense array of long, narrow cylindrical
crypts that secrete uid into a central lumen. Because
of uid convection, crypt uid secretion is predicted to
reduce inhibitor concentration at the enterocyte sur-
face and hence reduce inhibitor efcacy. Further, if
therapeutic inhibitor concentration is not sustained in
the intestinal lumen, its antisecretory effect would di-
minish rapidly unless inhibitor dissociation from its tar-
get at the enterocyte surface is slow compared with the
time between oral doses. Here, we model CFTR inhibi-
tor washout to predict the conditions (concentration/
target afnity, dissociation rate) under which an extra-
cellularly targeted antisecretory drug could be effective
in reducing intestinal uid secretion.
MATERIALS AND METHODS
Model formulation
Fig. 1 A diagrams a cross section of a generic intestinal villus–
crypt unit, as found in mid-jejunum, which consists of a long,
narrow aqueous compartment bounded by a cylindrical layer of
epithelial cells. The crypts project in an outward radial direction
Figure 1. Model of drug convection–
diffusion in intestinal crypt–villus units.
(A) Schematic of epithelial cell–lined crypt–
villus units (lengths, Lcrypt and Lvillus). Fluid
secretion into the lumen produces convec-
tive (upward) solute transport. (B) Three-
dimensional model of radially oriented
crypt–villus units projecting from a cylin-
drical lumen. (C) Section near the intes-
tinal wall showing crypt–villus units and a
wedge of luminal aqueous-phase volume.
Cylindrical symmetry reduces computation
complexity. An example of pseudocolored
inhibitor concentration prole is shown.

Jin et al. 263
∇ ⋅ =Vi0, (3)
where  is uid density, Pi is pressure, and  is dynamic viscosity.
For computations on single-crypt/villus units, as shown in Fig. 2 A,
constant inhibitor concentration was imposed at the outer boundary
and an insulation boundary condition (no ux through membrane)
was imposed at the crypt/villus surface. Volume ux at the crypt sur-
face in the steady state, Jv(z), depends on volume ux in the absence
of inhibitor, Jvo(z), and local inhibitor concentration, Ci(ro,z),
J z J z 1 C r z
v v
o
i o d
( ) ( )/[ , / ],= +
( )
K (4)
where Kd is the equilibrium dissociation constant for inhibitor-target
(CFTR) binding.
To model a membrane-permeable inhibitor in which inhibitor is
transported from the circulation into the crypt/villus lumen, the
transepithelial ux of inhibitor, Jb(z), is described by
J z P [C C (r z J z [1 C r z C
b inh b i b
o
i o b
( ) , )] ( ) ( , )/ ],= ⋅ − = ⋅ − (5)
where Pinh describes inhibitor permeability across the intestinal epi-
thelium, and Cb is inhibitor concentration in blood. A convective
ux boundary condition was imposed at the outer boundary and at
the crypt/villus surface.
In multi-crypt computations, the same ux boundary condition is
imposed at the crypt surface. The parabolic velocity prole at the
lumen inlet was calculated from mean lumen velocity as
U(x y z 2U [1 s s
mean o
, , ) ( / ) ],= ⋅ − 2 (6)
where so is the distance from the lumen center to the top of villi, and
s is the distance from the center of the lumen. Symmetric boundary
conditions are imposed at the two side walls and a slip boundary
condition at the top surface. Details on boundary conditions are pro-
vided in the Appendix (Figs. A1 and A2, and Table 2).
The computation time to obtain the steady-state solution was
10 min for single-crypt computations and 4–24 h for multi-crypt
computations, as performed on an HP Z600 workstation (Xeon
E5645 CPU and 32G RAM; Intel). The time step was automatically
computed in COMSOL Multiphysics from mesh size and property
value variation. Computation validation studies are provided in the
supplemental text.
Inhibition of net uid secretion was computed as the ratio
of total crypt–villus uid secretion in the presence versus absence
of inhibitor,
% ( / ). inhibition 1 1 J J
v v
o
= ⋅ − ∑ ∑
00 (7)
For modeling the kinetics of inhibitor washout, the fraction of
bound inhibitor, fb (0 to 1, fb = Ci/(Ci + Kd) in the steady state), is
described by the differential equation,
df z dt k [1 f z C k f z
b 1 b i 1 b
( )/ ( )] ( ),= ⋅ − ⋅ − ⋅
− (8)
where k1 is inhibitor dissociation rate constant, and k1 is inhibi-
tor bimolecular association rate constant, subject to the condi-
tion, Kd = k1/k1.
The percent inhibition of uid secretion along the length of
the intestine was deduced from the computational results done
for small segments, in which inhibitor concentration in each
segment is diluted progressively because of uid secretion. Con-
servation of inhibitor molecules (Eq. 9) and of fluid volume
(Eq. 10) requires
U C U C
out out in in
= (9)
attached crypt–villus units as diagrammed in Fig. 1 C, as described
in Results.
List of parameters
Parameters for single-crypt/villus computations:
D, diffusion coefcient in crypt/villus lumen (cm2/s)
Jv(z), volume ux across the epithelium at location z along the
crypt (µL/cm2/s)
Jvo(z), volume ux across the epithelium in the absence of inhibi-
tor (µL/cm2/s)
Jv, total volume ux from crypt (µL/s/crypt)
Ci(r,z), inhibitor concentration at location r,z (µM)
Vi(r,z), vectorial ow velocity at location r,z (cm/s)
Pi(r,z), pressure at location r,z (Pa)
P, pressure difference between Pi(r,z) and reference pressure in
the intestine (Pa)
Co, inhibitor concentration at outer boundary (µM)
Jb(z), transepithelial volume ux of (permeable) inhibitor
(mol/cm2/s)
Jbo(z), initial transepithelial volume ux of inhibitor (mol/cm2/s)
Pinh, transepithelial inhibitor permeability (cm/s)
Cb, inhibitor concentration in blood (µM)
Kd, inhibitor–CFTR binding dissociation constant (µM)
k-1, dissociation rate constant (min1)
k1, association rate constant (µM1 min1)
, uid density (kg/m3)
, uid dynamic viscosity (Pa · s)
t, computation time step (s)
L, crypt length (µm)
d, crypt diameter (µm)
fb(z), occupied fraction of inhibitor binding site
Additional parameters for multi-crypt/villus computations:
DL, diffusion coefcient in the intestinal lumen (cm2/s)
DM, diffusion coefcient in the mucosa (crypt/villus region)
(cm2/s)
L, uid dynamic viscosity in the lumen (Pa · s)
M, uid dynamic viscosity in the mucosa (Pa · s)
LV, villus length (µm)
LC, crypt length (µm)
dV, villus diameter (µm)
dC, crypt diameter (µm)
dL, intestinal lumen diameter (µm)
U(x,y,z), inhibitor velocity in the intestinal lumen (cm/s)
Umean, mean inhibitor velocity in the lumen (cm/s)
s, distance from the center of the lumen (cm)
so, distance from the center of the lumen to the top of the villus (cm)
Model computations
Models of convection–diffusion in single crypt–villus units (two-
dimensional) and the full intestine (three-dimensional) were im-
plemented using COMSOL Multiphysics (version 3.4; COMSOL).
The model is specied by a diffusion equation describing inhibitor
convection–diffusion coupled with the Navier–Stokes equation de-
scribing the uid ow eld. The convection–diffusion equation is
∂
∂= − ⋅ ∇ + ∇
C
tC D C
convection diffusion
ii i
2
i
V, (1)
which contains convection and diffusion terms. The velocity eld, Vi,
in the convection term was computed from the Navier–Stokes equa-
tion for an incompressible uid and the continuity equation,
ρ ρ η
∂
∂+ ⋅ ∇
( )
= − ∇ + ∇
VV V V
ii i i i
tP2 (2)

264 Convection–diffusion model of intestine
(12)
total inhibition =
1 1 U U A J d w
out
N
in
1
Lv
o
L
%
[ ( ) / { ( / )00 ⋅ − − ⋅
∑π ⋅⋅( / )}],L x
int ∆
where UoutN is mean ow velocity in the nal segment, and Uin1 is
mean inlet ow velocity at the rst segment, where UoutN is calcu-
lated iteratively applying conservation conditions (Eqs. 9 and 10).
Online supplemental material
The online supplemental material includes additional informa-
tion on the mathematical modeling, including the validations of
computation time and the number of mesh elements, and details
of the secretion ratio (Jvo) calculation. It is available at http://
www.jgp.org/cgi/content/full/jgp.201210885/DC1.
RESULTS
Single crypt–villus computations for a membrane-
impermeant, surface-targeted inhibitor
We rst analyzed convection–diffusion for a single crypt–
villus unit to explore the main features of the model.
U A U A J d w
out L in L vL
⋅ = ⋅ + ⋅
∑( / ),π (10)
where Cin and Cout are inhibitor concentration at the inlet and
the outlet in each segment, Uin and Uout are mean lumen veloc-
ity, AL is luminal cross-sectional area, dL is lumen diameter, w is
segment length, and ∑Jv (equal to ∑Jvo [1  0.01 · % inhibition])
is total single-segment secretion rate. Percent inhibition at each
segment was specied by an empirical t of computed results at
the segment.
Total percent inhibition (over the length of the intestine) is
the ratio of integrated secreted uid without versus with inhibi-
tor. Total secreted uid in the absence of inhibitor was computed
by summation of ux from each segment,
(11)
Secreted fluid (no inhibitor) J d w L x
v
o
L int
= ⋅ ⋅
∑( / ) ( / ),π ∆
where ∑Jv o is initial single-segment secretion rate, dL is lumen
diameter, w is segment length, Lint intestinal length, and x is
segment length. Total secreted uid in the presence of inhibi-
tor was computed from the difference in luminal ow in the
nal segment without versus with inhibitor, so that percent in-
hibition becomes
Figure 2. Convective inhibitor washout in
single crypts. Inhibitor convection–diffu-
sion was solved for a cylindrical crypt–villus
unit exposed at its outer boundary (intesti-
nal lumen) to a constant concentration of
membrane-impermeant inhibitor, Co/Kd.
(A) Cross section of a cylindrical crypt–
villus unit showing relative Jvo at indicated
regions (left). Two-dimensional compu-
tation volume showing mesh elements
(middle). Equivalent three-dimensional
crypt–villus unit showing downward in-
hibitor diffusion and upward convection.
(B) Steady-state proles of drug concen-
tration (left), uid ow velocity (middle),
and pressure (right) for single-crypt diffu-
sion–convection for indicated Co/Kd, with
Jvo = 4 × 102 µL/cm2/s. (C) Steady-state
proles for indicated Jvo, with Co/Kd = 1.

Jin et al. 265
shows similar computations for the colon, which con-
sists of long, narrow crypts (length 430 µm, diameter
16 µm) without villi. A similar dependence of percent
inhibition of uid secretion on Co/Kd and Jvo was seen,
in which 50% inhibition of uid secretion required
Co/Kd of 40 for Jvo = 7 × 103 µL/cm2/s, typical of
cholera in colon.
Single crypt/villus computations for a membrane-
permeable, surface-targeted inhibitor
Computations were also done for a membrane-permeable,
surface-targeted CFTR inhibitor in which the inhibitor en-
ters the crypt–villus lumen from the blood compartment
rather than the intestinal lumen. We assume constant in-
hibitor concentration in blood, with entry into the crypt–
villus lumen determined by the (blood-to-lumen) inhib itor
concentration gradient and enterocyte permeability.
Fig. 2 A (left) shows a cross section of the crypt–villus
structure in mid-jejunum (where the majority of uid
secretion occurs in cholera), which consists of a 350-µm-
long villus shown aligned with a 150-µm-long crypt.
Based on reported data on CFTR distribution (Jakab
et al., 2011), relative ∑Jv(ro,z) in the absence of inhibitor
was taken as 1.0 (lower 50% of crypt), 0.6 (upper 50%
of crypt), 0.28 (lower 50% of villus), and 0.15 (upper
50% of villus). Fig. 2 A (middle) shows mesh element in
the two-dimensional computation region, which, by sym-
metry, solves the equivalent three-dimensional crypt–
villus problem (Fig. 2 A, right).
For the two-dimensional computations, the intervil-
lous region was modeled as a simple cylinder approxi-
mating the actual three-dimensional geometry, which is
modeled below. We note that the further simplication
of our model to one dimension is not possible because
of the need to impose unrealistic boundary conditions,
which necessitated the inclusion of a “buffer zone” at
the crypt–villus outlet in the single-crypt computations.
As uid leaves the crypt–villus unit it takes with it solute
and so produces a complex two-dimensional prole ex-
tending from the outlet that can be quite large for high
ow velocities as found in diarrhea.
Fig. 2 B shows steady-state proles of drug concentra-
tion (left) and uid ow velocity (middle) for different
(dimensionless) Co/Kd, in which Co/Kd is xed at the
outer computational region. The increase in pressure is
negligible, as shown in the right panel of Fig. 2 B for
Co/Kd = 100. Convective effects are observed in the pro-
les, with marked axial concentration and velocity gra-
dients. At xed uid secretion rate (in the absence of
inhibitor) of Jvo = 4 × 102 µL/cm2/s, increasing Co/Kd
to 100 allowed inhibitor access deep in crypts (Fig. 2 B,
left). Increased inhibitor concentration reduced uid
velocity. Fig. 2 C shows the steady-state drug concentra-
tion and uid ow velocity proles at xed Co/Kd of 1
for different Jvo, and the pressure prole for Jvo = 101
µL/cm2/s. Increasing Jvo reduced inhibitor concentra-
tion in crypt-villus units because of convection, with a
very small pressure increase of <2 Pa (compared with
atmospheric pressure of 105 Pa).
Results from computations as in Fig. 2 are summa-
rized in Fig. 3. Fig. 3 A shows the percent inhibition of
secreted uid for the crypt–villus geometry of the mid-
jejunum, as deduced from volume ux exiting the crypt
without inhibitor versus with inhibitor. The percent in-
hibition of uid secretion increased from 0 to 100%
with increasing Co/Kd, as expected, although the appar-
ent IC50 for inhibition was substantially increased with
increasing Jvo. For low, near static ow (Jvo = 103 µL/
cm2/s), Co/Kd of 1 produced 50% inhibition of uid
secretion, as expected. For Jvo of 7 × 102 µL/cm2/s,
which is typical of cholera, inhibition of net uid secre-
tion by 50% required Co/Kd of 200, and clinically rel-
evant inhibition by 90% required Co/Kd of 750. Fig. 3 B
Figure 3. Convective inhibitor washout requires a very high con-
centration of a membrane-impermeant inhibitor in the intesti-
nal lumen for antisecretory efcacy. (A) Computations done for
human mid-jejunal anatomy as in Fig. 2. Percent inhibition of net
secreted uid as a function of Co/Kd for indicated Jvo. Jvo of 7 ×
102 µL/cm2/s is typical in cholera. (B) Computations done for
human colonic anatomy with long, narrow crypts without villi.
Percent inhibition of net secreted uid as a function of Co/Kd
for indicated Jvo. Jvo of 7 × 103 µL/cm2/s in colon is typical
in cholera.

266 Convection–diffusion model of intestine
Multi-crypt computations with three-dimensional
intestinal geometry
Computations were also done for the three-dimensional
intestine as diagrammed in Fig. 1 B. Our approach was
to rst analyze percent inhibition versus Co/Kd (as done
in Fig. 3 A for single crypt–villus units) for a short seg-
ment of intestine (mid-jejunum), and then extend the
computation to model many meters of intestine. Fig. 5
A shows an en face view of the crypt–villus geometry in
this model, as deduced from electron microscopy data
(Loehry and Creamer, 1969; Marsh and Swift, 1969). Fin-
ger-shaped villi of 100–250-µm diameter extend out of the
plane, with inter-crypt distance of 100 µm and a crypt to
villus ratio of 3. We modeled crypts and villi as cylinders
with semispherical outer surfaces. Villus length was taken
as 350 µm, with an outer diameter of 120 µm and inter-
villus spacing of 150 µm. Crypt length was taken as 150 µm,
with an inner diameter of 20 µm and inter-crypt distance
of 100 µm. The villi to crypt ratio was 3, giving a crypt
density of 13,333 cm2, similar to the measured value of
12,500 cm2 (Trbojević-Stanković et al., 2010). Fig. 6 A
(middle) shows a small segment of 1-mm length and
150-µm width used as the computational volume (chosen
to allow a crypt to villus ratio of 3). The computational
volume is composed of two layers, mucosa and lumen, of
different viscosities. Fig. 5 A (right) shows 80,000–150,000
mesh elements in the computation volume.
Fig. 5 B shows the steady-state proles of drug con-
centration. Similar to the proles in Fig. 2 B, increasing
The hypothesis is that high blood inhibitor concentra-
tion and enterocyte permeability are required for anti-
secretory efcacy of a membrane-permeant, externally
targeted inhibitor. Our reasoning, as diagrammed in
Fig. 4 A, is that inhibitor molecules crossing the entero-
cyte barrier are convected away from the luminal sur-
face, impairing their ability to inhibit CFTR.
Fig. 4 B shows drug concentration proles for differ-
ent drug permeability coefcients for transepithelial
transport from blood into the crypt–villus lumen, Pinh
(left), and for different uid secretion rates, Jvo. Con-
vective washout of luminal inhibitor is seen as reduced
Ci/Cb with increasing Jvo. Fig. 4 C summarizes the per-
cent inhibition of net secreted uid as a function of Pinh
for different Jvo at xed Cb = 10 µM and Kd = 10 µM. At
a low Jvo of 103 µL/cm2/s, half-maximal inhibition re-
quired Pinh of 107 cm/s, whereas at high Jvo of 7 ×
102 µL/cm2/s, typical of cholera, 50% of maximal in-
hibition required an 100-fold increased Pinh of 105
cm/s. Maximal inhibition was 50% for Cb = Kd, as ex-
pected. Similar computations are shown in Fig. 4 D for
Cb = 1 µM and Kd = 0.1 µM, where maximal inhibition is
100%. At low Jvo of 103 µL/cm2/s, half-maximal inhi-
bition required Pinh of 109 cm/s, whereas at higher
Jvo of 7 × 102 µL/cm2/s, half-maximal inhibition re-
quired Pinh of 5 × 106 cm/s. These computations
show that convective washout effects can occur for a
membrane-permeable, surface-targeted inhibitor.
Figure 4. Model of antidiarrheal
efcacy of a membrane-permeant
inhibitor. Computations done for
human mid-jejunal crypt–villus
anatomy. (A) Schematic show-
ing inhibitor permeation across
enterocytes from blood into the
crypt–villus lumen, which de-
pends on inhibitor transepithe-
lial permeability coefcient, Pinh,
and blood concentration Cb.
(B) Steady-state inhibitor concen-
tration proles for indicated Pinh
for Jvo = 2 × 102 µL/cm2/s (left),
and for indicated Jvo for Pinh =
105 cm/s (right), both for Cb =
10 µM and Kd = 10 µM. (C) Per-
cent inhibition of net secreted
uid as a function of Pinh for in-
dicated Jvo at Cb = 10 µM and Kd =
10 µM. (D) Same as in C, with Cb =
1 µM and Kd = 0.1 µM.

Jin et al. 267
Fig. 5 E shows deduced percent inhibition versus Co/Kd
plots for different Umean for Jvo of 7 × 102 µL/cm2/s, typi-
cal of cholera. Because of inhibitor dilution effects, the
percent inhibition versus Co/Kd proles is right-shifted,
indicating the requirement of high Co/Kd (>1,000) for
efcient reduction in intestinal uid secretion. Even
greater Co/Kd would be predicted without the assump-
tion of a well-mixed intestinal lumen.
Inhibitor washout kinetics limits antidiarrheal efficacy
The computations described above for an orally admin-
istered (membrane-impermeable) inhibitor were done
for the steady state, with constant inhibitor concentra-
tion entering the intestinal lumen (at the boundary of
the computation region). However, because of intermit-
tent oral administration, inhibitor concentration varies
over time, with little inhibitor present in the intestinal
lumen much of the time. To model inhibitor washout,
inhibitor concentration in the lumen was reduced at
time 0 from Co/Kd to 0 (step-function). Fig. 6 A shows
the kinetics of inhibitor washout for a single crypt–villus
unit for dissociation rate constant, k1 = 101 min1.
Jvo produced greater convection, reducing inhibitor
access deep in crypts. Fig. 5 C shows percent net uid
inhibition versus Co/Kd for different Jvo, analogous to
the single crypt–villus analysis in Fig. 3 C. Co/Kd was 1
for low Jvo, as expected, increasing substantially for
higher Jvo. These computations for three-dimensional
crypt–villus geometry support the robustness of the con-
clusion that greatly increased Co/Kd is needed for effec-
tive inhibition at high uid secretion rates.
The short segment of intestinal surface with anatomi-
cally accurate three-dimensional geometry was extended
to model the human mid-jejunum with 5-mm length and
5-cm diameter (Fig. 5 D, top). Assuming a well-mixed in-
testinal lumen beyond the level of villus tips, the steady-
state prole of uid inhibition along the intestine was
computed as described under Model computations in
Materials and methods. Fig. 5 D (bottom) shows percent
inhibition along the intestine for different initial lumen
axial ow velocities, Umean, representing different axial
starting points along the length of the intestine. The per-
cent inhibition decreases along the length of intestine as
inhibitor is diluted by secreted uid from crypts and villi.
Figure 5. Inhibitor washout in a
three-dimensional multi-crypt model
of the intestine. (A) Crypt–villus
geometry in the three-dimensional
model showing a matrix of spatially
distinct narrow crypts and relatively
wide villi. (B) Drug concentration
profiles for steady-state solution
of multi-crypt diffusion–convection
for indicated Jvo for Co/Kd = 10.
(C) Percent inhibition of net se-
creted uid as a function of Co/Kd
for indicated Jvo. Jvo of 7 × 102
µL/cm2/s is typical in cholera.
(D) Percent inhibition along the
intestine for indicated lumen axial
mean velocity, Umean. Segmental per-
cent inhibition in C was described by
an empirical regression to the equa-
tion: % inhibition =  · exp[ · log10
(Cin/Kd)], with  = 3.523 and  =
1.112 for Jvo = 7 × 102 µL/cm2/s,
typical of cholera. (E) Percent in-
hibition for 5-m-long intestinal seg-
ment as a function of Co/Kd for
indicated Umean. Results for a short
(1-mm) intestinal segment are shown
for comparison.

268 Convection–diffusion model of intestine
Qualitatively, the effects of convection and diffusion
on washout can be derived from a simple dimensional
analysis of the convection and diffusion terms in Eq. 1,
giving a single dimensionless parameter, the Peclet
number (Pe),
washout effect(Pe)
convection term
diffusion term
V C
D
i i
2
=
≈⋅ ∇
∇CC
VC
L
DC
L
V L
D
L J
dD
i
ii
i
2
i
2
v
o
≈ = ≈ 4 ,
where Vi is ow velocity, L is length of crypt or villus, D
is diffusion coefcient, Jvo is initial volume ux, and d
is crypt/villus diameter. The washout effect is pro-
portional to crypt or villus length and volume ux, and
Washout occurs over time as CFTR inhibitor dissocia-
tion releases inhibitor molecules that are convected out
of the crypt. In addition to crypt–villus geometry, the
determinants of washout kinetics include k1, uid se-
cretion rate, and Co/Kd. Fig. 6 B shows the kinetics of
loss of inhibition of uid secretion for mid-jejunum,
with parameters chosen to give 90% inhibition of
uid secretion before washout. For a k1 of 101 min1
(well below that expected for small-molecule inhibitors
with micromolar Kd) and a high Co/Kd of 10, washout
occurs in tens of minutes. Very low k1 is required to
greatly slow inhibitor washout. For the three-dimen-
sional crypt–villus geometry, predicted washout is even
more rapid, occurring over a few minutes for a k1 of
101 min1 (Fig. 6 C).
DISCUSSION
CFTR offers a unique target for antisecretory therapy of
enterotoxin-mediated diarrheas because it is expressed
on the luminal membrane of enterocytes and is hence
exposed to the aqueous-phase contents of the intestinal
lumen. The luminal exposure of CFTR allows the pos-
sibility of developing inhibitors that are targeted to its
external surface that could act after oral administration
and without systemic absorption. High throughput
screening of chemically diverse small-molecule libraries
identied glycine hydrazides and related analogues that
blocked the external CFTR pore directly (Muanprasat
et al., 2004). The glycine hydrazides were engineered
into nonabsorbable macromolecular conjugates with
high afnity binding to CFTR and slow dissociation
(Sonawane et al., 2007, 2008). However, because of the
high volume of uid that can be secreted in diarrhea,
inhibitor washout from the surface of the intestine is a
concern. Convection–diffusion, as uid is secreted out
of the long, narrow intestinal crypts, is predicted to
reduce inhibitor concentration at the luminal sur-
face of the crypt epithelial cells. Washout effects can
also be important for systemically absorbed inhibitors
that target an extracellular site on crypt epithelial
cells, as inhibitor dissociation from the surface and
subsequent convection out of crypts can reduce surface
inhibitor concentration. Although orally administered
nonabsorbable drugs are in use (Charmot, 2012), such
as cholesterol-binding resins and antimicrobials, drug
targeting to the external site of a luminal receptor on
the intestinal epithelium is a new concept in drug deliv-
ery. Because there was no precedent for existing drugs
using this targeting strategy, or data to evaluate the
magnitude or kinetics of washout effects, we modeled
the CFTR–inhibitor system in the intestine using data
applicable to secretory diarrhea, although our model
would apply in general to drugs that target luminal re-
ceptors on enterocytes.
Figure 6. Rapid washout of a luminally delivered membrane-
impermeant inhibitor. After steady-state inhibition, inhibitor
concentration in the intestinal lumen was reduced from Co/Kd to 0.
(A) Drug concentrations proles for kinetic (presteady-state)
solution of single-crypt diffusion–convection for Co/Kd = 10, Jvo =
103 µL/cm2/s, and k1 = 101 min1. (B) Kinetics of inhibition
of uid secretion after inhibitor washout. Percent inhibition of
net uid secretion as a function of time after washout for Co/Kd =
10, Jvo = 103 µL/cm2/s, and indicated k1. (C) Washout kinetics
for the three-dimensional multi-crypt model for same parameters
as in A.

Jin et al. 269
potentially helpful, are unlikely to produce sustained
therapeutic inhibitor concentrations when the uid se-
cretion rate is high as in cholera and traveler’s diarrhea.
Of the available externally targeted CFTR inhibitors,
GlyH-101 (Sonawane et al., 2006) and small-molecule
analogues such as MalH (Sonawane et al., 2007) and
iOWH032 (de Hostos et al., 2011) have IC50 in the
range of 2–8 µM and dissociate from CFTR within sec-
onds. We conclude from the modeling here that such
compounds would not fulll criteria (a) or (b). MalH-
lectin conjugates have higher afnity (Kd of 50 nM)
and slow washout over several hours or longer (Sonawane
et al., 2007), as the lectin moiety is bound tightly and
trapped in the dense glycocalyx lining the intestinal sur-
face. However, although MalH-lectin conjugates can thus
fulll criteria (a) and (b), lectin conjugates may not be
practical for antisecretory therapy in developing coun-
tries because the lectin moiety signicantly increases
the drug cost and reduces its stability during storage.
The antidiarrheal efcacy of a surface-targeted, mem-
brane-permeable inhibitor that is systemically absorbed
and enters the intestinal lumen from the blood side was
also considered. Fluid convection can cause washout of
inhibitor molecules that enter the crypt lumen from the
blood. Typical intestinal transepithelial permeability
coefcients for absorbable drugs, based on Caco-2 data,
are in the range of 106 to 105 cm/s, with values up to
7 × 105 cm/s for the most highly permeable drugs
(Usansky and Sinko, 2005). The computations in Fig. 4
indicate that antidiarrheal efcacy is limited by inhibi-
tor convective washout at high drug Kd  Cb for typical
drug permeability (106  105 cm/s). A more potent
drug (Kd of 0.1 Cb) predicted good antidiarrheal ef-
cacy. Therefore, provided that therapeutic drug con-
centration in the blood can be maintained, and that
drug Kd is sufciently low and drug permeability suf-
ciently high, a surface-targeted, membrane-permeable
inhibitor can be efcacious in secretory diarrhea.
Although our model was formulated to closely reca-
pitulate the in vivo three-dimensional geometry of a
high density of radially oriented crypt–villus units lining
inversely proportional to crypt or villus radius and
diffusion coefcient. Substantial washout effect occurs
for small crypt/villi radius and long crypt/villi length.
The geometric term (L2/d) for villi (L = 350 µm, d =
120 µm from effective diameter) is similar to that for
crypts (L = 150 µm, d = 20 µm), which gives a Pe of 14
and 16, respectively, for the severe diarrhea case (Jvo = 7
× 102 µL/cm2/s). Therefore, both crypts and villi are
important determinants of washout, although the wash-
out effect in crypts is greater because of higher uid
secretion rate. In any case, quantitative analysis required
full computational analysis because of nonlinear effects
and the complex geometry of crypt–villus units.
The main conclusion of the modeling is that the anti-
secretory efcacy of a surface-targeted channel inhib-
itor requires both (a) very high luminal inhibitor
concentration compared with its Kd, and (b) sustained
very high luminal inhibitor concentration or slow in-
hibitor dissociation compared with the interval between
oral dosing. For a crypt secretion rate of 7 × 102 µL/
cm2/s, typical of cholera, the luminal concentration of
a membrane-impermeant inhibitor should be >200 × Kd
to reduce net uid secretion by 50% and 800 × Kd to
reduce uid secretion by 90% (Figs. 3 A and 5 C). Even
higher inhibitor concentration is needed if the inhibi-
tor diffusion coefcient is lower than that used in the
model here, which may be the case because of mucus
and other viscous substances in the aqueous-phase
uid. Further, even if adequate inhibitor concentration
in the intestinal lumen is achieved for antisecretory ef-
cacy, a high concentration must be sustained, as deliv-
ery of inhibitor-free uid at the luminal surface results
in rapid loss of inhibitor efcacy unless inhibitor disso-
ciation from its luminal target is very slow. For a typical
small molecule with low micromolar Kd, dissociation oc-
curs over a few seconds or less, producing signicant
loss of antisecretory efcacy over minutes (Fig. 6). For
oral administration of an inhibitor every few hours, the
lumen is exposed to cyclical changes in inhibitor con-
centration, with little inhibitor present most of the
time. Sustained release or other formulations, although
TABLE 1
Material properties and baseline parameters
Material property Baseline parameter
Fluid density = 103 (kg/m3)
DLDiffusion coefcient in the intestinal lumen = 2 × 109 (m2/s)
DMDiffusion coefcient in the mucosa (crypt/villus region) = 2 × 1010 (m2/s)
LFluid dynamic viscosity in the lumen = 103 (Pa · s)
MFluid dynamic viscosity in the mucosa = 102 (Pa · s)
LVVillus length = 350 (µm)
LCCrypt length = 150 (µm)
dVVillus diameter = 120 (µm)
dCCrypt diameter = 20 (µm)
dLIntestinal lumen diameter = 5 (cm)

270 Convection–diffusion model of intestine
equation for the uid eld. Fig. A1 and Table 2 provide
details on boundary conditions.
Lumen inlet boundary condition
The circular lumen inlet has parabolic velocity pro-
le with mean velocity, Umean. Because the intestinal
lumen (5-cm diameter) is much bigger than crypt
dimensions (20-µm diameter and 150-µm length),
the computation was simplified to greatly reduce
computation time. A small segment near the mucosa
(crypt and villus), with computation volume of 1,250
µm (crypt length of 150 µm, villus length of 350 µm),
was used (Fig. 1 C). The velocity prole at the lumen
inlet was taken as part of the parabolic prole as
shown in Fig. A2. The lumen inlet boundary condi-
tion (the magnitude of mean velocity) had negligible
effect on percent inhibition (not depicted) because
the viscosity in the mucosa is >10-fold greater than that
in the intestinal lumen, so that the ow eld produced
by secretion is dominant in the crypt/villus mucosa.
A constant inhibitor concentration boundary condi-
tion was used for the inhibitor concentration at the
lumen inlet.
Left and right surface boundary condition
As shown in Fig. 5 A, the small segment containing
crypts and villi unit is repeated symmetrically around
the lumen, producing laminar ow in the lumen (vis-
cous forces dominant over inertia), Re = UmeandL/() <
0.1, where dL is lumen diameter and  is kinematic vis-
cosity. Thus, symmetric boundary conditions were im-
posed at the left and the right surface boundaries.
Top surface boundary condition
A slip boundary condition was used for the Navier–Stokes
equation, and an insulation (no ux) boundary condi-
tion was used for the diffusion–convection equation.
Crypt and villus surface boundary condition
As described in Materials and methods, the rate of
uid secretion at the crypt and villus surface was deter-
mined by initial secretion rate and inhibitor concentra-
tion. For a membrane-impermeant inhibitor insulation
the intestinal lumen, several features of the intestine
were not included in the model. The model does not
consider differences in the detailed geometry and trans-
port properties of the different regions of the small and
large intestine, nor does it include uid absorption or
mechanical peristalsis. Although these additional com-
plexities were not modeled explicitly, the major con-
clusions of our model are robust and should not be
inuenced by these ne details. The majority of se-
creted uid comes from the jejunum, as was modeled
here, and uid secretion in secretory diarrheas such as
cholera greatly exceeds absorption. Peristaltic effects
would be predicted to have little time-averaged effect
on inhibitor diffusion in the unstirred crypt luminal
compartment.
Notwithstanding these potential limitations of our
model, we conclude that washout in secretory diarrhea
is a major factor for nonabsorbable drugs that target
surface receptors or transporters on enterocytes in in-
testinal crypts. Therapeutic efcacy requires sustained
high drug concentration in the intestinal lumen. For
the inhibitor–CFTR system, surface-targeted small
molecules with micromolar Kd are unlikely to be efca-
cious for therapy of secretory diarrhea, whereas mac-
romolecular conjugates with nanomolar Kd and very
slow dissociation might be effective. We conclude, there-
fore, that although surface-targeted glycine hydrazide
and MalH originally appeared to be attractive candi-
dates for antisecretory therapy, absorbable CFTR in-
hibitors, such as thiazolidinones (Thiagarajah et al.,
2004) and PPQ/BPO compounds (Tradtrantip et al.,
2009; Snyder et al., 2011), are better development can-
didates for CFTR inhibition therapy of enterotoxin-
mediated secretory diarrheas.
AppENDIx
Boundary conditions
As described in Materials and methods, the three-
dimensional multi-crypt computation involves solution of
the diffusion–convection equation for inhibitor con-
centration and the (incompressible uid) Navier–Stokes
TABLE 2
Boundary conditions for Navier–Stokes and diffusion–convection equations
Navier–Stokes equation Diffusion–convection equation
(1) Inlet BC U = 2Umean · [1(s/so)2] (1) Inlet BC C = Co
(lumen ow velocity) Vi = U∙n(constant Co)
(2) Symmetric BC n∙Vi = 0, t · [pI + µ(Vi + (Vi)T] = 0 (2) Symmetric BC n · n = 0, N = D ∙ C + CVi
(3) Slip BC n∙Vi = 0, t · [pI + µ(Vi + (Vi)T] = 0 (3) Insulation BC n · n = 0, N = D ∙ C + CVi
(4) Flux BC Vi = -Jv · n, Jv = Jvo(1  Ci/(Ci + Kd)) (4) Insulation BC n · n = 0, N = D ∙ C + CVi
(5) Outlet BC [µ(Vi + (Vi)T]n = 0, p = p0
(5) Outlet BC n·(DC) = 0
(no viscous stress) (convective ux)
BC, boundary condition; n, surface normal vector; I, unit vector; , gradient operator. Other variables are dened in the main text.

Jin et al. 271
Submitted: 23 August 2012
Accepted: 3 January 2013
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