Journal of Biological Physics 19:211-222, 1994. 211 (~) 1994 Kluwer Academic Publishers. Printed in the Netherlands. A Mathematical Model Relating Diffusion of Hydrophobic Ions to their Adsorption on Biological Membranes as Detected with a Microdialyzer PIERO FARISELLI, SALVATORE DI BERNARDO and RITA CASADIO Laboratory of Biophysics, Departmentof Biology, University of Bologna, Italy (Received: 28 October 1993) Abstract. We analyze the diffusion of hydrophobicmoleculesin a dialysis apparatus with respect to their adsorption on biological membranevesiclesconfinedto one dialysis chamber.The process is described with a kinetic model, which shows that, depending on the pattern of the adsorption isotherm, the kinetic parameter of the diffusionprocess through the dialysis membrane is up to two- fold increased by the presenceof the adsorbingvesiclesurface.The modelsuccessfully describesthe diffusion of tetraphenylborate and 9-aminoacridine in the presenceof chromatophoresfrom photo- syntheticmembrane,with whichthey interactwith hyperbolicand S-shapedisotherms,respectively. Key words: Microdialaysis, adsorption isotherms, biological membranes, tetraphenylboron, 9- aminoacridine,mathematical model. 1. Introduction The interaction of hydrophobic molecules with biological membranes is extensive- ly used as a tool to characterize chemical and physical properties of the membrane phase (for review, see [1-3]). The electrical properties of synthetic and biological membranes have been investigated and the thermodynamics of the interaction of hydrophobic ions, such as tetraphenylboron (TffB-) and tetraphenylphosphonium (T~P +) with model lipid membranes has been used to model the boundary region of the phospholipid bilayer in the absence of membrane proteins [4-5]. In some cases, hydrophobic ions have been also used to monitor transmembrane electrical potential (A~b) in vesicle systems, where direct measurements are generally precluded by the small dimensions of the inner osmotic volume (for review, see [6-7]). Another class of hydrophobic molecules, strongly interacting with biological membranes, includes fluorescent aromatic amines, such as 9-aminoacridine (9AA) and its derivatives. In the range of physiological pH's, due to the monocation- neutral molecule equilibrium of the probe (pKa = 9.99, for 9AA) the monocation is the predominant form [8]. These probes are widely used to detect transmembrane proton concentration difference in natural and model membrane systems, and the thermodynamics of membrane-probe interaction is a prerequisite to model the re-