  Proteins can locate their specific targets on DNA up to two orders of
magnitude faster than the Smoluchowski three-dimensional diffusion rate. This
happens due to non-specific adsorption of proteins to DNA and subsequent
one-dimensional sliding along DNA. We call such one-dimensional route towards
the target "antenna". We studied the role of the dispersion of nonspecific
binding energies within the antenna due to quasi random sequence of natural
DNA. Random energy profile for sliding proteins slows the searching rate for
the target. We show that this slowdown is different for the macroscopic and
mesoscopic antennas.
