Reduced Dynamic Models in Epithelial Transport

Julio A Hernández

doi:10.1155/2013/654543

Abstract

Most models developed to represent transport across epithelia assume that the cell interior constitutes a homogeneous compartment, characterized by a single concentration value of the transported species. This conception differs significantly from the current view, in which the cellular compartment is regarded as a highly crowded media of marked structural heterogeneity. Can the finding of relatively simple dynamic properties of transport processes in epithelia be compatible with this complex structural conception of the cell interior? The purpose of this work is to contribute with one simple theoretical approach to answer this question. For this, the techniques of model reduction are utilized to obtain a two-state reduced model from more complex linear models of transcellular transport with a larger number of intermediate states. In these complex models, each state corresponds to the solute concentration in an intermediate intracellular compartment. In addition, the numerical studies reveal that it is possible to approximate a general two-state model under conditions where strict reduction of the complex models cannot be performed. These results contribute with arguments to reconcile the current conception of the cell interior as a highly complex medium with the finding of relatively simple dynamic properties of transport across epithelial cells.

Highlights

The transport of water and solutes across epithelia is a relevant physiological property of higher organisms
Can the finding of relatively simple dynamic properties of transport processes in epithelia be compatible with the complex structural conception of the cell interior? The general objective of this work is to contribute with the basic aspects of one formal theoretical approach to answer this question
The results of this theoretical study permit to suggest that complex models of transepithelial transport of solutes may exhibit dynamic properties undistinguishable from those of simple models

Summary

Introduction

The transport of water and solutes across epithelia is a relevant physiological property of higher organisms. The majority of the models classically developed to represent solute transport across epithelia have considered that the interior of the epithelial cells constitutes a well-stirred, homogeneous compartment, characterized by a single value of concentration of the transported species [3,4,5] This view implicitly assumes that the intracellular diffusion coefficient of the species remains constant and that diffusion occurs freely and rapidly, so that the intracellular solute concentrations attain a single equilibrium value at a faster time scale than the overall process. This conception differs markedly from the current view about the structural and functional characteristics of the cell interior. Realistic approaches to describe diffusion in cellular media require computational simulations that employ, for instance, Brownian dynamics [10, 11], finite-element methods [12, 13], or The Virtual Cell framework [14, 15]

Objectives

Results

Conclusion