Mathematical modeling of marker influx and efflux in cells.

The tumor promoter, phorbol 12-myristate 13-acetate (PMA), affects the processing of fluid that enters a cell from the ambient medium. Previous work showed that marker accumulates to a higher level in PMA-treated than in untreated cells. Since PMA also affects the physical activity of the membrane and stimulates the normal process of taking up extracellular fluid, called endocytosis, it is important to learn whether the perturbations in fluid processing can be attributed entirely to a change in the cell's limiting membrane. To this end, a model for fluid uptake and processing was developed and applied to experiments in which a marker for extracellular fluid was added to cells. From previous work on marker accumulation, it was deduced that there were at least two functional compartments involved in fluid movement. Compartment I is a rapidly filling and rapidly recycling compartment. Compartment II is a slowly filling and emptying compartment. Three routes of vesicle traffic must be considered, one mediating influx from the ambient medium into compartment I, a second, efflux from compartment I to the medium, and a third efflux from compartment I into compartment II. Using earlier models for processing, workers found it difficult to estimate rates of movement through either of the latter routes, as well as the volume of compartment I. The difficulty arises from the fact that only one kinetic constant can be estimated directly from data, namely the instantaneous uptake rate. The remaining data depend on measuring the total mass of marker in the cells. Since the concentration of marker in the cell changes continuously, it is advantageous to employ differential equations to simulate the tracer movement. By applying the model to experimental values, we found estimates for all three rates of fluid movement and the volume of compartment I. It is thought that the model will enable us to determine whether apparent alterations in the time course of uptake arise solely from altered properties of the limiting membrane.

Persistent effects of phorbol 12-myristate 13-acetate: possible implication of vesicle traffic.

Relative to their normal counterparts, transformed epithelial cells have a distinctive and quantifiable three-dimensional shape. Biophysical and mathematical methods are used to distinguish these extremes in cells from two lines, cultured from rat liver and tracheal epithelium, respectively. Cells adopted a more transformed-looking configuration transiently when exposed to phorbol 12-myristate 13-acetate (PMA) (Plummer and Heckman, [1990] Exp. Cell Res., 188:66-74). The purpose of the present work was to dissect the physiological processes involved in the shape change. Ruffling activity, known to be PMA-stimulated in other cells, was investigated. Although the ruffles appeared less robust than normal, PMA stimulated ruffling activity over a 5 h period. The number of sites where ruffling was initiated declined by 5 h, however, and suppression was seen by 10 h. Cells from both lines adopted the transformed shape configuration when exposed for 2 h to monensin. When the subset of shape features changed by this treatment was compared with those originally changed during transformation, it was found that monensin-treated cells mimicked the features of transformed cells. Its effect on ruffling was, however, unlike PMA's. Thus, the phenotype was unlikely to arise from ruffling itself but might be a process driven by ruffling. Chloroquine also stimulated cells to assume characteristics of transformed cells. Since both it and monensin could interfere with endosomes and with the processing of endocytosed contents, this was a likely site of action. Experiments were done to determine whether PMA also affected the processing of extracellular fluids. When the accumulation of horseradish peroxidase (HRP) was measured, the rate was found to be higher in PMA-treated cells from 5 min, the earliest time assayed, onward. The results suggest that the transformed type of cell in these cell lines showed a constitutive dilation and/or reorganization of some portion of the endosomal pathway.