Kinetics of adsorption of extended ligands on DNA at small fillings

In the present work, the adsorption kinetics of extended ligands on DNA duplexes at small fillings when molecules of DNA duplexes are on the underlayer within diffusion layer has been investigated. Both diffusion of ligands in solution (diffusion stage) and adsorption of ligands (kinetic stage) are taken into consideration at adsorption of ligands on DNA duplexes. Nonlinear system of differential equations describing adsorption of ligands where not only diffusion stage but also kinetic stage is taken into account, is obtained, moreover the equations allow localizing duplexes in arbitrary place within diffusion layer. Numeric solution of the equations makes possible to investigate the filling kinetics of DNA duplexes by ligands depending on parameters controlling adsorption process. It has been shown that depending on relation between adsorption parameters different kinetic regimes of adsorption - kinetic, complex, and diffusion regimes may be realized.