A theoretical model for non linear osmosis in biological membranes

Since the first studies on the osmotic properties of the cell membrane it is known that the water osmotic flow is often characterized by a non linear dependence upon its driving force. To date such a behaviour has been observed in a number of biological membranes, i.e. leucocytes, the alga Chara, erythrocytes, intestine, urinary bladder, the alga Nitella and gall bladder. Three main hypothesis have been proposed to explain such a non linearity. First the existence of unstirred layers between the membrane and the bulk solution may lower the effective osmotic gradient. This hypothesis accounts for part of the non linearity observed in Chara. Subsequently it has been shown that, assuming the validity of local linear phenomenological equations, a non linear flow – force relationship can be obtained by integration along the membrane thickness. Such a treatment, devised for obtaining the force – flow relationship for an asymmetrical series array of membranes, contains the former hypothesis as a particular case. In effect un unstirred layer may be considered as a series membrane with zero selectivity but with a definite permeability. Finally various Authors suggested that the water flow itself, or some concentration dependent solute – membrane interaction modify the membrane structure and thus the resistance to water flow. At present it seems likely that all these phenomena contribute to the observed non linearity in complex membranes. In effect it has been proved that the outer and inner unstirred layers influence the measured permeability and that the volume of the intercellular spaces is related to the functional state of various epithelia. The very fact that the unstirred layers contribute to the non linearity suggests that indeed an asymmetrical series array of membranes, as in epithelia, may be in part responsible of the observed non linear behaviour, but it seems experimentally difficult to obtain a direct measurement of this contribution to the overall non linearity. For these reasons we conducted a further study of the two membrane model introduced by Curran following the method proposed by Patlak, Goldstein and Hoffman, with the aim of individuating a) the relationships between the parameters characterizing the single membranes and the overall properties of the array, b) the parameters who influence more effectively the non linear behaviour and c) the flow dependence of the inner compartment characteristics which may contribute to the observed structural changes.