Carrier-mediated transport can obey fractal kinetics

A model based on the fractal methodology is proposed for the kinetic study of carrier-mediated transport under heterogeneous conditions, i.e., when the drug-carrier interaction occurs at an interface with an effective dimensionality smaller than the embedding dimension of d = 2. A model equation is derived for the flux, based on a similar approach for an analogous equation for enzyme kinetics. It is shown that the total flux-solute concentration plots are curvilinear when the fractal dimension is smaller than unity while they become biexponential, with ascending and descending limbs, when the fractal dimension D is in the range 1 < D < 2. Nonlinear Lineweaver-Burk plots are obtained when this fractal kinetics approach is used. Good fittings are obtained when the fractal model is applied to literature data previously analysed with a combined transport mechanism, revealing experimental systems that display a D value in the range 1 < D < 2. It is suggested that transport studies should be carried out at a wider working solute concentration range and various agitation and incubation conditions in order to derive definite conclusions for the transport pathways.