9 - Fractal Analysis of Proteins Involved in Drug Design on Biosensor Surfaces

Abstract

This chapter presents a fractal analysis to re-analyze the binding and dissociation kinetics of kalata B1 and kalata B6 in solution to DMPE (dimyristoyl-L-α-phosphatidylethanolamine) liposome immobilized on the L1 sensor chip. The values of the binding and dissociation rate coefficients and affinity values, and the fractal dimension values in the binding and in the dissociation phase are also provided. The fractal analysis is used with the aim to relate the binding and dissociation rate coefficients with the degree of heterogeneity or fractal dimension present on the DMPE liposome immobilized on the L1 sensor chip surface. The fractal analysis provides a quantitative indication of the state of disorder (fractal dimension) and the binding (and dissociation) rate coefficients on the sensor chip surface. On the basis of the prefactor analysis for fractal aggregates, quantitative (predictive) expressions are developed for the binding rate coefficients, k1and k2, as a function of the natural cyclotide, kalata B1 concentration in solution; the fractal dimension Dfin the binding phase and the fractal dimension in the dissociation phase Dfd as a function of the cyclotide, kalata B1 concentration; the binding rate coefficients, k1 and k2, as a function of the fractal dimensions, Df1and Df2, for the 10–50 μM kalata B1 concentration in solution; the affinity, K1 (=k1 /kd1), as a function of the ratio of fractal dimensions, Df/Dfd1; and the ratio of the binding rate coefficients, k2/k1, as a function of the fractal dimensions, Df2/Df1. Similar predictive relations are also developed and presented for the cyclotide analogue, kalata B6. The expressions obtained for the binding and the dissociation rate coefficients for a single- and a dual-fractal analysis as a function of the fractal dimension indicate a high sensitivity of these rate coefficients on the their respective fractal dimensions on the SPR sensor chip surface.