We show that the site-specific interaction of a probe DNA with the template DNA can be well modeled as an unbiased random jump process, where the probe molecule first nonspecifically binds to the template DNA and then searches for the specific site via unbiased random jump motion on the template DNA. By investigating the effects of increasing the jump size, and the fluctuations in the position of the specific site and the fluctuations in the specific site interval on the affinity-specificity negative correlation, we show that (1) increasing the jump size will in turn increase the affinity of the probe toward its target site on the template DNA, however, with a limiting value-the maximum affinity condition; (2) the degree of supercoiling or condensation of the template DNA as well as the electrostatic interactions between the probe and the template in turn control the jump size associated with the dynamics of the probe on the template DNA; (3) under a maximum specificity condition (therefore with minimum affinity), by introducing an external fluctuation in the relative position of the target site on the template DNA with respect to the probe, one can still improve the affinity rate; (4) on the other hand, one can improve the specificity of the probe toward the target site on the template DNA by introducing external fluctuations in the target-site interval. Finally, we propose the design strategies and optimum experimental conditions to simultaneously enhance the affinity as well as the specificity of probe toward its target site on the template DNA. © 2006 The American Physical Society.