antigens) in a solution. The binding of an antigen to an The diffusion-limited kinetics of binding of an analyte in soluantibody-coated surface (or vice versa) is sensed directly tion to a receptor immobilized on a biosensor surface is analyzed and rapidly. There is a need to characterize the reactions within a fractal framework. Antigen-antibody, analyte-receptor, occurring at the biosensor surface. and analyte-receptorless systems are analyzed. Most of the data The details of the association of antibodies (or antigens) presented are adequately described by a single-fractal analysis. with an antigen-coated (or antibody-coated) surface is of This was indicated by the regression analysis provided by Sigtremendous significance in the development and charactermaplot (Jandel Scientific, San Rafael, CA, 1993). It is of interest ization of immunodiagnostic devices as well as of biosensors
to note that the binding rate coefficient, k, and the fractal dimension, D f , both exhibit changes in the same direction for the anti-(2). Furthermore, external diffusional limitations play a role gen-antibody and analyte-receptor systems analyzed. The bindin the analysis of such assays (3-6). The influence of diffuing rate coefficient, k, expressed as a function of the fractal dimension in such systems has been analyzed to some extent (5, sion, D f , developed for the three types of binding systems indicates 7-13). The particle-enhanced sensitivity of the surface-plasthe sensitivity of k to D f . For example, for the antigen-antibody mon-resonance biosensor has been analyzed ( 14). These binding of mAb 447/D-II to rgp 120(MN) immobilized on a bioauthors indicate that the fractal dimension is a measure of sensor surface and for mAb 9205 to rgp (IIIB) (37), the order of the clustering of particles. For example, for colloidal gold dependence on D f was 10.221 and 9.668, respectively. The fracthere is clustering of particles that leads to significant signal tional order of dependence of k on D f further reinforces the fractal enhancement. nature of the system. For the single example of an analyte-recep- Kopelman (15) indicates that surface diffusion-controlled torless system (LDL protein adsorption) presented, a more organized biosensor surface (lower D f value) leads to an increased reactions that occur on clusters or islands are expected to value of k. Expressions of k as a function of the fractal dimension, exhibit anomalous and fractal-like kinetics. These fractal D f , are of particular value since they provide a means to better kinetics exhibit anomalous reaction orders and time-depencontrol biosensor performance by linking it to the heterogeneity dent rate (for example, binding) coefficients. Fractals are on the surface and further emphasize in a quantitative sense the disordered systems and the disorder is described by noninteimportance of the nature of the surface in biosensor performance. gral dimensions (16). These authors further indicate that as