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)).

Figure 1.

Model of drug convection–diffusion in intestinal crypt–villus units. (A) Schematic of epithelial cell–lined crypt–villus units (lengths, L_crypt and L_villus). Fluid secretion into the lumen produces convective (upward) solute transport. (B) Three-dimensional model of radially oriented crypt–villus units projecting from a cylindrical lumen. (C) Section near the intestinal wall showing crypt–villus units and a wedge of luminal aqueous-phase volume. Cylindrical symmetry reduces computation complexity. An example of pseudocolored inhibitor concentration profile is shown.

Figure 2.

Convective inhibitor washout in single crypts. Inhibitor convection–diffusion was solved for a cylindrical crypt–villus unit exposed at its outer boundary (intestinal lumen) to a constant concentration of membrane-impermeant inhibitor, C_o/K_d. (A) Cross section of a cylindrical crypt–villus unit showing relative J_v^o at indicated regions (left). Two-dimensional computation volume showing mesh elements (middle). Equivalent three-dimensional crypt–villus unit showing downward inhibitor diffusion and upward convection. (B) Steady-state profiles of drug concentration (left), fluid flow velocity (middle), and pressure (right) for single-crypt diffusion–convection for indicated C_o/K_d, with J_v^o = 4 × 10⁻² µL/cm²/s. (C) Steady-state profiles for indicated J_v^o, with C_o/K_d = 1.

Figure 3.

Convective inhibitor washout requires a very high concentration of a membrane-impermeant inhibitor in the intestinal lumen for antisecretory efficacy. (A) Computations done for human mid-jejunal anatomy as in Fig. 2. Percent inhibition of net secreted fluid as a function of C_o/K_d for indicated J_v^o. J_v^o 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 fluid as a function of C_o/K_d for indicated J_v^o. J_v^o of ∼7 × 10⁻³ µL/cm²/s in colon is typical in cholera.

Figure 4.

Model of antidiarrheal efficacy of a membrane-permeant inhibitor. Computations done for human mid-jejunal crypt–villus anatomy. (A) Schematic showing inhibitor permeation across enterocytes from blood into the crypt–villus lumen, which depends on inhibitor transepithelial permeability coefficient, P_inh, and blood concentration C_b. (B) Steady-state inhibitor concentration profiles for indicated P_inh for J_v^o = 2 × 10⁻² µL/cm²/s (left), and for indicated J_v^o for P_inh = 10⁻⁵ cm/s (right), both for C_b = 10 µM and K_d = 10 µM. (C) Percent inhibition of net secreted fluid as a function of P_inh for indicated J_v^o at C_b = 10 µM and K_d = 10 µM. (D) Same as in C, with C_b = 1 µM and K_d = 0.1 µM.

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 J_v^o for C_o/K_d = 10. (C) Percent inhibition of net secreted fluid as a function of C_o/K_d for indicated J_v^o. J_v^o of ∼7 × 10⁻² µL/cm²/s is typical in cholera. (D) Percent inhibition along the intestine for indicated lumen axial mean velocity, U_mean. Segmental percent inhibition in C was described by an empirical regression to the equation: % inhibition = α · exp[β · log₁₀(C_in/K_d)], with α = 3.523 and β = 1.112 for J_v^o = 7 × 10⁻² µL/cm²/s, typical of cholera. (E) Percent inhibition for 5-m-long intestinal segment as a function of C_o/K_d for indicated U_mean. Results for a short (1-mm) intestinal segment are shown for comparison.

Figure 6.

Rapid washout of a luminally delivered membrane-impermeant inhibitor. After steady-state inhibition, inhibitor concentration in the intestinal lumen was reduced from C_o/K_d to 0. (A) Drug concentrations profiles for kinetic (presteady-state) solution of single-crypt diffusion–convection for C_o/K_d = 10, J_v^o = 10⁻³ µL/cm²/s, and k₋₁ = 10⁻¹ min⁻¹. (B) Kinetics of inhibition of fluid secretion after inhibitor washout. Percent inhibition of net fluid secretion as a function of time after washout for C_o/K_d = 10, J_v^o = 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.

Figure A1.

Schematic of boundary conditions for the three-dimensional multi-crypt computation. (A) Boundary conditions for the Navier–Stokes equation. (B) Boundary conditions for the diffusion–convection equation.

Figure A2.

Schematic of inlet boundary condition, where s is distance from the center of the lumen, s_o is distance from the center of the lumen to the top of the villus, and U_mean is the mean inhibitor velocity in the lumen.