  We study a model for a protein searching for a target, using facilitated
diffusion, on a DNA molecule confined in a finite volume. The model includes
three distinct pathways for facilitated diffusion: (a) sliding - in which the
protein diffuses along the contour of the DNA (b) jumping - where the protein
travels between two sites along the DNA by three-dimensional diffusion, and
finally (c) intersegmental transfer - which allows the protein to move from one
site to another by transiently binding both at the same time. The typical
search time is calculated using scaling arguments which are verified
numerically. Our results suggest that the inclusion of intersegmental transfer
(i) decreases the search time considerably (ii) makes the search time much more
robust to variations in the parameters of the model and (iii) that the optimal
search time occurs in a regime very different than that found for models which
ignore intersegmental transfers. The behavior we find is rich and shows
surprising dependencies, for example, on the DNA length.
