Fractal binding and dissociation kinetics of prion proteins on biosensor surfaces
This chapter presents a fractal analysis for the binding and dissociation of C1q in solution to the PrP protein immobilized on a sensor chip surface. The analysis provides physical insights into the interactions of C1q and the PrP protein occurring on the sensor chip surface. The values of the binding and dissociation rate coefficient k and k d respectively, and the state of disorder or degree of heterogeneity (fractal dimension) on the sensor chip surface are provided for both the binding phase D f and the dissociation phase D fd . On the basis of the pre-factor analysis for fractal aggregates, quantitative (predictive) expressions are developed for the binding rate coefficient k as a function of the C1q concentration in solution; the fractal dimension D fd as a function of the C1q concentration in solution; the dissociation rate coefficient k d as a function of the fractal dimension D fd ; the affinity K=k/k d as a function of the ratio of fractal dimensions D f / D fd and also as a function of the C1q concentration in solution; the binding rate coefficient k 2 as a function of the fractal dimension D f2 ; and the affinity K 2 (=k 2 / k d ) as a function of the ratio of fractal dimensions D f2 / D fd . The expressions obtained for the binding rate coefficient for a single- and a dual-fractal analysis as a function of the fractal dimension indicate the high sensitivity of the binding and dissociation rate coefficient on the fractal dimension on the SPR biosensor surface. The fractal analysis provides unique physical insights into the interactions between C1q and the PrP protein, and the quantitative expressions developed for the C1q–PrP interactions should assist in the better control of the SPR biosensor performance parameters such as stability, sensitivity, and response time.