By A. Sadana
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Extra info for Engineering Biosensors - Kinetics and Design Applns
Example text
The reaction scheme in Fig. 11a) where Ab is the antibody molecule and Ag is the antigen molecule. We now want to relate kf and kr to the elementary steps involved in the reaction scheme given in Fig. 5. Consider kl k2;Ag Ab + Ag~ Ab'Ag ~ Ag'Ab'Ag. 11b) 35 Influence of Diffusional Limitations and Reaction Order on Antigen From Eq. 12) - k2[Ab'Ag][Ag]- k-1 [Ab'Ag] = 0, from the steady-state assumption. Here [Ag] is the concentration of the antigen close to the surface, c~ and [Ag] may be used interchangeably.
2 . 3 . ANTIBODY IN S O L U T I O N / A N T I G E N ON THE SURFACE We did not present this case in Chapter 2, so we analyze all the steps in detail here, starting with second-order kinetics. Then we analyze the influence of lateral interactions on second-order kinetics. Second-Order Reaction Kinetics Consider dual-step binding. 7 shows the steps involved in the binding of the antibody in solution to the antigen covalently attached to the surface. The rate of binding of a single arm of the antibody to an antigen attached to the surface is given by d1,1 d--7 = 2k~c~(ro - r l - 2r2) - k2C~(Co - r~ - 2r2) + 2k_21,2 - k_IF1.
8 schematically depicts such an antibody targeted to a family of PACs. The concept of multivalency for antibodies requires certain conditions. In general, antibodies are larger than antigens. Therefore, certain size and steric conditions must be fulfilled to allow more than one antibody to be attached to an antigen. 8 Schematic diagram of antibodies having paratopes targeted to the antigen series of polycyclic aromatic compounds. Sadana, A. , Biotechnology Progress, 9, 259-266 (1993). Reprinted with permission from Academic Press.