CARRIER-MEDIATED TRANSPORT CAN OBEY FRACTAL KINETICS

A model based on the fractal methodology is proposed for the kinetic s tudy of carrier-mediated transport under heterogeneous conditions, i.e ., when the drug-carrier interaction occurs at an interface with an ef fective 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 to tal flux-solute concentration plots are curvilinear when the fractal d imension is smaller than unity while they become biexponential, with a scending and descending limbs, when the fractal dimension D is in the range 1 < D < 2. Nonlinear Lineweaver-Burk plots are obtained when thi s fractal kinetics approach is used. Good fittings are obtained when t he fractal model is applied to literature data previously analysed wit h a combined transport mechanism, revealing experimental systems that display a D value in the range 1 < D < 2. It is suggested that transpo rt studies should be carried out at a wider working solute concentrati on range and various agitation and incubation conditions in order to d erive definite conclusions for the transport pathways.