Modeling membrane transport.

Abstract

Many substrates cross cell membranes by processes other than passive diffusion. When the transport is carrier-mediated, e.g., facilitated diffusion, active transport, and exchange diffusion, the carrier modifies the conductance of the membrane and may either increase or decrease the flux of the substrate across the membrane. A common characteristic of all carrier-mediated transport is its saturability, as only a finite amount of carrier is available to bind with the substrate; even the simplest one-site carrier model exhibits saturation. Inclusion of carrier-mediated transport adds additional model parameters that describe the transporter. In addition, the model must account for both labeled (tracer) and unlabeled (mother) substrate, but this introduces no new parameters. There are many possible models for a membrane carrier. The applicability of these models must be examined for the specific substrate of interest. Many experiments aimed at measuring carrier parameters are carried out on isolated cells or cell fragments. Experiments in intact organs (either in vivo and in vitro) are also possible. Of particular note is the "bolus sweep" method described by Rickaby et al. (1981) and Malcorps et al. (1984). The increasing sophistication of experimental procedures, data collection techniques, and computers available to investigators continues to extend the depth to which we can probe biological systems. With this increased sophistication comes increased costs in time and equipment. It behooves us then to extract the maximum amount of information from each experimental procedure. Mathematical models assist in doing so, and sophistication in model analysis should parallel that in other phases of the experiment. Increased realism brings several advantages. Simplification of a model to increase its ease of usage and speed in routine data analysis is a desirable goal, and comparing a simplified model against a more realistic model under the conditions specific to a given experiment is one way to test the simplifying assumptions. Additionally, increased model realism can bring new insight into unknown aspects of the system. All models, no matter how realistic, are always "wrong" in that they are less complex than the real system. Failure of the model to explain observed results forces us to further refine the model and teaches us something more about the system.