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 Smolu-
chowski three-dimensional (3D) diffusion rate. An accepted explanation of this
fact is that proteins are nonspecifically adsorbed on DNA, and sliding along DNA
provides for the faster one-dimensional (1D) search. We explicitly addressed the
role of DNA conformation and the dispersion of nonspecific adsorption energies.
We identified a wealth of new different scaling regimes and found that the maxi-
mum on the rate-versus-ionic strength curve is asymmetric.
We also studied the other facilitating mechanism termed intersegment trans-
ferwhere proteins which have two DNA binding sites can transfer from one DNA
segment to another without dissociation to water. We proposed a scaling the-
ory which combines the effects of protein 3D diffusion, 1D sliding, intersegment
transfer and DNA motion.
A direct application of our work on target search problem is the kinetics of
viral self-assembly. We show that due to the 1D sliding of capsid proteins on the
unassembled chain of single-stranded RNA, the self-assembly is more than ten
times faster than the case involving only three-dimensional diffusion.
We further extended our theory to the macroscopic diffusion coefficient of proteins in a semi-dilute solution of DNA pieces and the effective conductivity of a
composite made of well conducting nanowires suspended in some poor conducting