Mathematical modeling of marker influx and efflux in cells

The turner promoter, phorbol 12-myristate 13-acetate (PMA), affects the pro cessing 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 unt reated 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 pr ocessing can be attributed entirely to a change in the cell's limiting memb rane. To this end, a model for fluid uptake and processing was developed an d applied to experiments in which a marker for extracellular fluid was adde d 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. Comp artment II is a slowly filling and emptying compartment. Three routes of ve sicle traffic must be considered, one mediating influx from the ambient med ium into compartment I, a second, efflux from compartment I to the medium, and a third efflux from compartment I into compartment II. Using earlier mo dels for processing, workers found it difficult to estimate rates of moveme nt through either of the latter routes, as well as the volume of compartmen t I. The difficulty arises from the fact that only one kinetic constant can be estimated directly fr om data, namely the instantaneous uptake rate. Th e remaining data depend on measuring the total mass of marker in the eels. Since the concentration of marker in the cell changes continuously, it is a dvantageous to employ differential equations to simulate the tracer movemen t. 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 thoug ht that the model will enable us to determine whether apparent alterations in the time course of uptake arise solely fi om altered properties of the l imiting membrane. (C) 2001 Society for Mathematical Biology.