Principles and Models of Biological Transport

Abstract

In this chapter, we consider the simplest of transport processes: the passive diffusion of a solute that occurs when its electrochemical potentials on the two sides of a per- meable barrier are different. Indeed, this process is so simple that it fails to represent many aspects of transport in living systems. Nonetheless, it does describe some as- pects of biological transport quite well, and it also provides a “base case” whose be- havior can be compared against that of more complex transport mechanisms. This chapter is divided into two sections; the first deals with free diffusion of nonelectrolytes, and the second with that of ionic species. The principal property vari- able determining the flux of a nonelectrolyte is its permeability, a quantity that can in principle be related to the diffusion coefficient of the solute. Electrolyte diffusion in free solution is most rigorously described by classical electrodiffusion theory. The flux equations provided by this theory are very complex, and they have not seen nearly as much use as have approximations to them. Accordingly, emphasis will be placed here on the principles of electrodiffusion, and on the approximate solutions and special cases that are most commonly used. The equations of free diffusion can describe a wide variety of transport phenom- ena, including steady and unsteady transport processes; processes that can be de- scribed in one, two or three dimensions and in a variety of geometries; and processes in which chemical reactions and fluid flow take place simultaneously with diffusion. In this chapter, we will discuss a small subset of these, focusing on the tools that are applied to living systems. Comprehensive discussions of diffusional processes can be found in other texts, such as Crank's (1975) classic text, published thirty years ago and still being reprinted! A more limited set of solutions, but with more consistent bio- logical applicability, can be found in Truskey et al. (2004).