Transepithelial glucose transport and Na+/K+ homeostasis in enterocytes: an integrative model

Abstract

The uptake of glucose and the nutrient coupled transcellular sodium traffic across epithelial cells in the small intestine has been an ongoing topic in physiological research for over half a century. Driving the uptake of nutrients like glucose, enterocytes must have regulatory mechanisms that respond to the considerable changes in the inflow of sodium during absorption. The Na-K-ATPase membrane protein plays a major role in this regulation. We propose the hypothesis that the amount of active Na-K-ATPase in enterocytes is directly regulated by the concentration of intracellular Na(+) and that this regulation together with a regulation of basolateral K permeability by intracellular ATP gives the enterocyte the ability to maintain ionic Na(+)/K(+) homeostasis. To explore these regulatory mechanisms, we present a mathematical model of the sodium coupled uptake of glucose in epithelial enterocytes. Our model integrates knowledge about individual transporter proteins including apical SGLT1, basolateral Na-K-ATPase, and GLUT2, together with diffusion and membrane potentials. The intracellular concentrations of glucose, sodium, potassium, and chloride are modeled by nonlinear differential equations, and molecular flows are calculated based on experimental kinetic data from the literature, including substrate saturation, product inhibition, and modulation by membrane potential. Simulation results of the model without the addition of regulatory mechanisms fit well with published short-term observations, including cell depolarization and increased concentration of intracellular glucose and sodium during increased concentration of luminal glucose/sodium. Adding regulatory mechanisms for regulation of Na-K-ATPase and K permeability to the model show that our hypothesis predicts observed long-term ionic homeostasis.

Keywords: enterocytes; epithelial transport; homeostasis; ionic regulation; mathematical modeling.

Copyright © 2014 the American Physiological Society.

Figures

Fig. 1.

Epithelial enterocytes in absorbing state. Subscripts m, c, and s mark mucosal, cell inside, and serosal concentrations. SGLT1 absorbs glucose from the intestinal lumen on the apical side of the enterocyte. GLUT2 transports glucose from the cell into the extracellular space on the basolateral side, where the glucose diffuses into capillaries. The absorption of glucose is driven by a sodium gradient maintained by basolateral Na-K-ATPase. Additional sodium enters together with chloride by a coupled flow. Ions also diffuse in and out of the enterocyte (dotted arrows) and directly from the mucosal to the serosal space through paracellular tight junctions between the enterocytes (paracellular flow is not shown in the figure). The arrows point in the normal direction of each flow, which may not be the same as the positive defined direction in our flow expressions. ψmc is the membrane potential between the mucosal side and the cell inside, ψsc is the membrane potential between the serosal side and the cell inside, and ψms is the transepithelial potential from the mucosal to the serosal side. The apical membrane consists of several microvilli, called the brush border, which greatly increases the effective membrane area where nutrient uptake can occur.

Fig. 2.

Six-state kinetic model for SGLT1 first introduced in Ref. . The empty carrier has a charge of −2; this means that steps to or from state 1 and 6 may be dependent on the membrane potential. α1 and α2 are phenomenological constants that describe the fraction of the electrical field sensed by the Na+ binding. δ is the fraction of the electrical field sensed by the empty ion binding sites on the carrier during membrane translocation. μ is the electrochemical potential Fψmc/RT. F, R, and T are the Faraday constant, the gas constant, and the temperature, respectively. We have used rate constants from Ref. but with no leakage, i.e., k25 and k52 are set to zero. The values of the rate constants are listed in Table A2.

Fig. 3.

Simulated model response to a short-term change in mucosal glucose using parameters in Table A2. A: at t = 1 min, the mucosal side glucose concentration ([Gm]) is increased from 100 μM to 20 mM (step). The mucosal side is then flushed with media without glucose (using a flush time of 20 s as in Ref. 69). This gives in an impulse shaped change in [Gm]. B: cell glucose concentration ([Gc]). C: concentration of cell sodium ([Nac]). D: concentration of cell potassium ([Kc]). E: concentration of cell chloride ([Clc]). F: mucosal to cell membrane potential (ψmc). G: serosal to cell membrane potential (ψsc). H: mucosal to serosal membrane potential (ψms).

Fig. 4.

Simulated model flows during a short-term change in mucosal glucose, using model parameters from Table A2. A: glucose inflow through SGLT1 (solid) and outflow through GLUT2 (dashed). B: coupled NaCl inflow. C: outflow of Na+ through Na-K-ATPase. D: diffusive inflow of Na+ (top), K+ (middle), and Cl− (bottom) over the apical membrane. E: diffusive inflow of Na+ (top), K+ (middle), and Cl− (bottom) over the basolateral membrane. F: diffusive inflow to the serosal side of Na+ (top), K+ (middle), and Cl− (bottom) through the paracellular junctions (negative inflow is the same as outflow).

Fig. 5.

Simulated net inflows (positive into serosal area) over the epithelial layer; this is the net sum of transcellular and paracellular flows. A: inflow of Na+ (JNaEpi = 3JNaK − JNaDbl + JNaDp). B: inflow of K+ (JKEpi = −2JNaK − JKDbl + JKDp). C: inflow of Cl− (JClEpi = −JClDbl + JClDp).

Fig. 6.

Simulated model response to a short-term change in mucosal sodium using model parameters in Table A2. At t = 1 min, the mucosal side Na+ concentration ([Nam]) is decreased from 140 to 100 mM (step), and at t = 6 min, the Na+ concentration is changed back to 140 mM. A: cell sodium concentration ([Nac]). B: concentration of cell potassium ([Kc]). C: concentration of cell chloride ([Clc]). D: mucosal to cell membrane potential (ψmc). E: serosal to cell membrane potential (ψsc). F: mucosal to serosal membrane potential (ψms).

Fig. 7.

Controller motif proposed for the regulation of intracellular Na+ by production of Na-K-ATPase.

Fig. 8.

Controller motif proposed for the regulation of intracellular K+. The degradation of ATP is coupled to the pump rate of the Na-K-ATPase. ATP affects the basolateral permeability to K+ by inhibiting the K channels, working as an outflow controller of [Kc]. ATP also inhibits its own synthesis.

Fig. 9.

Simulated model response to long-term change in mucosal glucose (solid lines) using model parameters in Table A2. The motif parameters are fitted to achieve a setpoint for intracellular sodium at ∼49 mM, a setpoint for intracellular potassium at ∼130 mM, and a reasonable dynamic response (10). For reference, we have also included the results from simulating the model without the 2 regulatory mechanisms (dashed lines). A: at time t = 4 min mucosal glucose concentration ([Gm]) is stepped from 0.1 to 10 mM. B: cell glucose ([Gc]). C: cell sodium ([Nac]) D: cell potassium ([Kc]). E: cell chloride ([Clc]). F: mucosal to cell membrane potential (ψmc). G: serosal to cell membrane potential (ψsc). H: mucosal to serosal membrane potential (ψms).

Fig. 10.

Simulated model response to long-term change in mucosal glucose using model parameters from Table A2. A: amount of Na-K-ATPase (nNaK). B: concentration of ATP ([ATP]).

Fig. 11.

Simulated model response in membrane potential (solid) and replotted experimental values (dashed). [Reprinted from Rose and Schultz (69) with permission.] At t = 1 min the mucosal side glucose concentration ([Gm]) is increased from 10 μM to 20 mM (step). The mucosal side is then flushed so that it falls back to 10 μM (using a flush time of 20 s). A: mucosal to cell potential ψmc. B: mucosal to serosal potential ψms.

Fig. A1.

The spatial dimensions of an enterocyte in absorbing state. The apical part of the cell has a cylindrical shape, and the lower part has is shaped like a truncated cone. See text for typical values of rm, rs, hu, and hc.

Fig. A2.

Turnover rate for one single Na-K-ATPase protein as a function of serosal membrane potential, VNaK(ψsc). The function is a 4th order polynomial fitted to the original data from the work of Gadsby and Nakao (19; reprinted with permisssion) (circles). The polynomial is VNaK(ψsc) = 5.46·10−8ψsc4 − 2.43·10−7ψsc3 − 2.00·10−3ψsc2 + 0.16ψsc + 51 (found by the Matlab function polyfit).