Fractal binding and dissociation kinetics of prion proteins on biosensor surfaces

A fractal analysis is presented for the binding and the dissociation of prion proteins to biosensor surfaces. Both single- and dual-fractal analysis may be used to model the binding and the dissociation kinetics. The fractal dimension provides a quantitative measure of the degree of heterogeneity on the biosensor surface. The binding and dissociation of human C1q in solution to PrP immobilized on a sensor chip surface is analyzed [F. Blanquet-Grossard, N.M. Thielens, C. Vendrely, M. Jamin, G.J. Arlaud, Complement protein C1q recognizes conformationally modified form of prion protein, Biochemistry 44 (2005) 4349–4356]. Quantitative relations are presented for (a) the binding rate coefficient, k as a function of the C1q in solution, (b) the dissociation rate coefficient, kd as a function of the C1q in solution, (c) the affinity, K (=k/kd) as a function of the ratio of the fractal dimensions present in the binding and in the dissociation phase Df/Dfd, and (d) the affinity K as a function of the C1q concentration in solution. These relationships developed provide fresh physical insights into the interactions of prion proteins on biosensor surfaces and into these types of reactions in general.