We have examined the kinetic parameters of linear diffusion of EcoRV on DNA. The data were analyzed by Monte Carlo simulations in which the efficiency of recognition of EcoRV sites during linear diffusion, the efficiency of linear diffusion, and the behavior of enzymes at the ends of linear DNA is explicitly treated. The analysis of the dependence of linear diffusion on the concentrations of NaCl and MgCl2 shows that linear diffusion is maximal at 50 mM NaCl under all concentrations of MgCl2 tested and increases with increasing concentrations of Mg2+ up to 10 mM, the highest concentration used in the test. Under these conditions, EcoRV scans 2 x 10(6) bp during one binding event with a velocity of about 1.7 x 10(6) bp s-1. The enzyme tends to overlook cleavage sites at 1 mM but not at 10 mM MgCl2. This result confirms the thermodynamic finding that EcoRV does not bind very specifically to DNA in the absence of Mg2+. It demonstrates that there is a Mg2+-dependent continuous transition between a nonspecific and a specific binding mode of EcoRV to DNA. By comparing cleavage rates of linear DNA whose ends are free or blocked, we have shown that EcoRV has a very low probability to fall off at the ends of linear DNA. The enzyme rather is "reflected" and continues linear diffusion. EcoRV does not cleave oligonucleotides containing two EcoRV sites processively. Consequently, dissociation of the enzyme from the cleavage products is not preceded by a transfer to nonspecific DNA, and linear diffusion is not involved in product dissociation in EcoRV.