1. A multiphasic modelling approach [Heirwegh, Meuwissen, Vermeir & De Smedt (1988) Biochem. J. 254, 101-1081 is applied to systems containing poorly water-soluble amphipathic reactants, membrane material, soluble binding protein and acceptor protein (enzyme or membrane-bound carrier protein). 2. The field of application is constrained by the assumptions (i) that the amount of acceptor-bound substrate is small compared with the total amount and (ii) that all preceding chemical reactions and steps of mass transport are rapid compared with the chemical change monitored. 3. Initial-rate formulae for systems in which an acceptor interacts with unbound or protein-bound ligand are given. The saturation curves are near-hyperbolic or sigmoidal, depending both (i) on the form of ligand (unbound or protein-bound) acted upon by the acceptor and (ii) on whether the assays are performed at constant concentration of soluble binding protein C(p) or at constant substrate/binding-site molar ratio R(s). 4. Several diagnostic features permit unequivocal distinction between acceptor action on unbound or protein-bound substrate. In the former case, saturation curves, run at the same constant concentration of one of several binding proteins of increasing binding affinity, will show progressively increasing inhibition, the shape changing from near-hyperbolic at K(m)' < K1' to sigmoidal at K(m)' > K1'.K(m)' is the effective Michaelis constant of the acceptor and K1' the effective dissociation constant of the binding sites of the soluble protein (for the sites with the higher binding affinity, if several classes of binding site are present on the protein). Alternatively, the maximum velocity obtained at constant R(s) less-than-or-equal-to 1 should increase hyperbolically with R(s)/(1-R(s)) for a binding protein with a single class of binding site. The formula that applies when the binding protein contains two classes of independent binding site is also available. When the acceptor acts on protein-bound ligand, the maximum velocity obtained at constant binding-protein concentration, C(p), increases hyperbolically with C(p). 5. Application of these and additional criteria to initial-rate data on the uptake of oleate into isolated cells supports a mechanism of carrier-mediated uptake of the unbound ligand and allows one to clarify some observations that hitherto had been poorly explained. 6. The influence of soluble binding protein on the reaction and substrate specificities of ligand/acceptor interaction is also discussed. 7. In its present state, data treatment for 'double binding-protein systems' generally requires separate determination of the binding parameters of the soluble binding protein. Possible designs for direct application of data-fitting procedures are briefly discussed. 8. Details about the units used and about the derivation of ligand distribution functions, kinetic formulae and their properties, and formulae for interconversion of parameter values to various concentration scales have been deposited as Supplementary Publication SUP 50169 (16 pages) at the British Library Document Supply Centre, Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms indicated in Biochem. J. (1992) 281, 5.
