Fluid-phase Endocytosis in the Amoebae of the Cellular Slime MouldDictyostelium discoideum: Mathematical Modelling of Kinetics and pH Evolution

Fluid-phase endocytosis (pinocytosis) is a very active nutritive process in axenic strains ofDictyostelium discoideumamoebae. Fluorescein-labelled dextran was used as a dual fluid-phase and pH marker to characterize endocytosis pathway regarding the kinetics of fluid internalisation and vesicular pH. Continuous loading and pulse-chase experiments have been conducted. In the latter case, marker transit and efflux was monitored on cells loaded for short periods of time, washed then suspended in marker-free medium. To account simultaneously for fluid-phase endocytosis kinetics and pH evolution we have developed a mathematical model consisting of interconnected delay stages and compartments. A delay stage is defined as a directional path in which access to the following endocytic space occurs only after a characteristic transit time. In contrast to this behaviour, exit probability from a compartment is independent of the time spent in the compartment. The model describes correctly both the kinetics and pH changes inDictyosteliumamoeba endocytic pathway. Useful estimates were obtained for kinetic constants, pH and fractional apparent volume of endocytic spaces. This modelling work provides a theoretical basis on which to design further experimental studies. It is of general applicability and could be useful to examine the characteristics of fluid-phase endocytosis in other eukaryotes.