To imitate cells which have ceased to grow we have made models in which artificial sap is separated from the external solution by a non-aqueous layer (representing the protoplasm). A stream of CO2 is bubbled through the artificial sap to imitate its production by the living cell.
Potassium passes from the external solution through the non-aqueous layer into the artificial sap and there reacts with CO2 to form KHCO3: its rate of entrance depends on the supply of CO2. Hence the increase of volume depends on the supply of CO2 (as is probably true of the living cell).
By regulating the supply of CO2 and the osmotic pressure we are able to keep the volume and composition of the artificial sap approximately constant while maintaining a higher concentration of potassium than in the external solution. In these respects the model resembles certain mature cells which have ceased to grow.