The Theory of Diffusion in Cell Models by Lewis

Osterhout and Stanley t have recently described some interesting experiments on diffusion between two aqueous phases separated by a non-aqueous phase. These experiments were modeled after living cells and duplicated the power of some cells to concentrate preferentially certain chemical substances. Furthermore, the volume increase shown by one of the aqueous phases in the model is somewhat analogous to the growth of living cells. In a model in which water and a salt are the only substances whose diffusion need be considered Osterhout* has shown that the results are in qualitative accord with the kinetics which characterize two consecutive monomolecular reactions. I t seems to the author, however, that the mechanism more nearly corresponds to that of two simultaneous and mutually dependent processes. Consequently it is the purpose of this paper to formulate and solve the simultaneous differential equations which probably describe the model. These equations will be derived starting with the simple but fundamental laws which describe diffusion processes in general. Jacobs 3 has recently formulated the simultaneous differential equations which describe the relation between cell volume and penetration of a solute. These equations, though similar to the ones which are derived in this paper, are somewhat more difficult to solve and the desired time curves are not obtained by direct integration.