Liposomes as carriers of poorly water-soluble substrates: linear modelling of membrane systems with catalytic or binding sites of different facedness. Significance of experimental membrane partition coefficients and of kinetic and equilibrium parameters.
1. A multiphasic modelling approach to systems containing membrane-bound receptors or catalytic sites and a liposomal preparation as a substrate carrier is described. Kinetic expressions are derived for a single-substrate enzymic reaction operating at constant liposome concentration or at a fixed substrate/liposome concentration ratio. 2. The assumption that accumulation of exchangeable components into the phospholipid bilayers can be described by linear bulk-phase partition leads to simple relationships between the initial reaction rate and (a) two kinetic coefficients (V and K'm), (b) the partition coefficients of the solutes for the lipid compartments of the membrane (Pms) and liposomal preparations (P1s) and (c) the total concentrations of substrate, membrane lipid and liposomal lipid. K'm is called the effective Michaelis constant. 3. For correct estimation of the coefficients V, K', Pms and P1s extrapolation to zero lipid concentration is required. 4. The distinction is introduced between hydrophilic and hydrophobic aqueous-faced sites, lipid-faced sites and mixed sites, i.e. sites overlapping an aqueous and a lipid region. For hydrophilic aqueous-faced sites K'm is equal to the true Km and for the other types of site to Km/Ps. For lipid-faced and for mixed sites Ps corresponds to the membrane partition coefficient Pms. For binding of homologous compounds to a hydrophobic aqueous-faced binding pocket Ps is the incremental site partition coefficient Pbss, which takes into account the energetic contribution to the binding process due to the hydrophobic tail of the ligands. 5. K'm accounts for any effects due to the facedness and nature of the enzymic sites. The dependence of the systems on the size of the lipidic partition compartment(s) is expressed exclusively by a distribution function F.6. When enzyme assays are performed with a series of chemically different substrates containing the same catalytically sensitive group, independence of K'm from partition indicates a hydrophilic aqueous-faced binding site. For the low-molecular-mass members of the homologous series a linear increase in -log (K'm) with the logarithm of the partition coefficient will be observed with any of the other site types considered 7. Equilibrium relationships for binding of a ligand to a membrane-bound receptor are also derived. 8. The significance of experimental membrane partition coefficients is discussed.