  It is known since the early days of molecular biology that proteins locate
their specific targets on DNA up to two orders of magnitude faster than the
Smoluchowski 3D diffusion rate. It was the idea due to Delbruck that they are
non-specifically adsorbed on DNA, and sliding along DNA provides for the faster
1D search. Surprisingly, the role of DNA conformation was never considered in
this context. In this article, we explicitly address the relative role of 3D
diffusion and 1D sliding along coiled or globular DNA and the possibility of
correlated re-adsorbtion of desorbed proteins. We have identified a wealth of
new different scaling regimes. We also found the maximal possible acceleration
of the reaction due to sliding, we found that the maximum on the
rate-versus-ionic strength curve is asymmetric, and that sliding can lead not
only to acceleration, but in some regimes to dramatic deceleration of the
reaction.
