  Complex DNA topological structures, including polymer loops, are frequently
observed in biological processes when protein molecules simultaneously bind to
several distant sites on DNA. However, the molecular mechanisms of formation of
these systems remain not well understood. Existing theoretical studies focus
only on specific interactions between protein and DNA molecules at target
sequences. However, the electrostatic origin of primary protein-DNA
interactions suggests that interactions of proteins with all DNA segments
should be considered. Here we theoretically investigate the role of
non-specific interactions between protein and DNA molecules on the dynamics of
loop formation. Our approach is based on analyzing a discrete-state stochastic
model via a method of first-passage probabilities supplemented by Monte Carlo
computer simulations. It is found that depending on a protein sliding length
during the non-specific binding event three different dynamic regimes of the
DNA loop formation might be observed. In addition, the loop formation time
might be optimized by varying the protein sliding length, the size of the DNA
molecule, and the position of the specific target sequences on DNA. Our results
demonstrate the importance of non-specific protein-DNA interactions in the
dynamics of DNA loop formations. Several quantitative predictions that can be
experimentally tested are also presented.
