Diffusion-reaction modelling of DNA hybridization kinetics on biochips

An analytical expression for the rate of DNA hybridization on the surface of DNA biochips is established for the case of a finite 1-D diffusion space. The expression allows to account for the diffusion-limited supply of unreacted probe DNA and was obtained by solving the continuous 1-D reaction-diffusion mass balance using a Finite Fourier Transform technique. The extrapolation of the presently considered 1-D case to the full 3-D case is outlined as well. By bringing the obtained result into concurrence with the results of a stochastic random walk study, the kinetic constant k of the continuous reaction-diffusion model could be expressed as a function of the basic physico-chemical parameters (persistence length and jump frequency of the Brownian motion, collision frequency, binding probability) of the individual molecules. With the availability of an analytical expression describing the full time course of the 1-D hybridization process, and by using the Damkohler number Da = kh/D-mol the different reaction- and diffusion-limited regimes occurring during the course of a hybridization process can now be described in general, dimensionless terms, allowing to establish some very simple rules for the design of DNA biochips and flow-through biosensors. (C) 2003 Elsevier Ltd. All rights reserved.